Financial index

Market Capitalization

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Market Capitalization

Nithisha CHALLA

In this article, Nithisha CHALLA (ESSEC Business School, Grande Ecole Program – Master in Management, 2021-2023) explains Market Capitalization and its specificities.

What is Market Capitalization?

Market capitalization is a key metric used to assess the size and value of publicly traded companies. It represents the company’s value for the owners of the company (the shareholders or stockholders). This metric allows companies to be classified as large-cap, mid-cap, or small-cap based on their respective market-capitalization sizes.

Large-cap companies are typically more established, with market capitalizations exceeding several billion dollars. They are more stable and frequently represent industry leaders. In the US stock market, Apple, Microsoft, and Amazon are examples of large-cap companies.

Mid-cap companies fall between large-cap and small-cap companies. They are typically businesses that have seen moderate growth and may still have room for expansion. Mid-cap companies are frequently regarded as having a good balance of growth potential and stability. For example, Etsy Inc., DocuSign Inc., Spotify Technology S.A. etc.

Small-cap companies have lower market capitalizations than large-cap and mid-cap firms. They are generally thought to have greater growth potential, but also greater risk due to their smaller size and possibly limited resources. NeoGenomics, Inc., Clean Energy Fuels Corp., Axon Enterprise Inc. etc.

Mathematical formula?

The general formula for calculating market capitalization:

Market Capitalization = Current Share Price x Number of Outstanding Shares

In this formula:
“Current Share Price” refers to the price of a single share of the company’s stock. It is the latest transaction price. As Market Capitalization is usually computed every day, the current share price corresponds to the closing price of the trading session.

“Number of Outstanding Shares” represents the total number of shares of the company’s stock that are publicly available and held by investors.

The Significance of Stock Price

When considering market capitalization, the stock price is an important factor to consider. It represents the current market price at which a company’s shares are bought and sold. Stock prices, which are influenced by factors such as supply and demand, market sentiment, and company-specific news, play a critical role in determining a company’s market capitalization.

On the short term, as the number of shares issued by the company is stable, the stock price is the main factor which influences market capitalization.

How is the Number of Shares Computed?

The total number of outstanding shares of a company’s stock is used to calculate market capitalization. The outstanding shares are those that the company has issued and are held by shareholders, which include individual investors, institutional investors, and insiders.

The number of outstanding shares can be found in the company’s financial statements, specifically the balance sheet and the notes to the financial statements.

Which Shares are Included?

The outstanding shares generally include common shares or ordinary shares, which are the most common types of shares issued by companies. Preferred shares or other types of securities that may have different rights or characteristics are typically excluded from the calculation of market capitalization.

When we compute market capitalization, we take into consideration all outstanding shares of stock, which include publicly traded shares plus restricted shares held by the top management team and the founders of the company. Note that market capitalization is different from the float which takes into consideration only the shares available for trading in the secondary market.

If a company has different classes of shares with different voting rights or other characteristics, each class of shares may have its own market capitalization calculation based on the respective share price and the number of outstanding shares for that class.

Market capitalization provides an estimate of the overall value of the publicly traded portion of a company and is commonly used as a measure to compare companies or track changes in a company’s value over time.

Why should I be interested in this post?

Understanding market capitalization allows management students to analyze the financial health and performance of companies. By considering market capitalization along with other financial indicators, students can assess the relative size and value of companies in the market. Management students need to evaluate investment opportunities and determine the attractiveness of different stocks or companies based on their market capitalization and growth potential. Large-cap companies often offer stability and lower risk, while small-cap companies tend to be riskier but may have higher growth potential. Management students need to understand the risk-return tradeoff associated with different market capitalization segments.

Related posts on the SimTrade blog

   ▶ Nithisha CHALLA Financial indexes

   ▶ Nithisha CHALLA Calculation of financial indexes

   ▶ Nithisha CHALLA Float

   ▶ Nithisha CHALLA Top 5 companies by market capitalization in India

   ▶ Nithisha CHALLA Top 5 companies by market capitalization in China

   ▶ Nithisha CHALLA Top 5 companies by market capitalization in the United States

   ▶ Nithisha CHALLA Top 5 companies by market capitalization in Europe

Useful resources

Fidelity Investments Market capitalization

Wikipedia Market capitalization

Motley Fool An Example of Market Capitalization

About the author

The article was written in June 2023 by Nithisha CHALLA (ESSEC Business School, Grande Ecole Program – Master in Management, 2021-2023).

The KOSPI 50 index

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The KOSPI 50 index

Nithisha CHALLA

In this article, Nithisha CHALLA (ESSEC Business School, Grande Ecole Program – Master in Management, 2021-2023) presents the KOSPI 50 index representing the South Korean equity market and details its characteristics.

The KOSPI 50 index

A well-known stock market index in South Korea, the KOSPI 50 index serves as a crucial benchmark for the South Korean equity market. It represents the performance of the 50 biggest and busiest companies traded on the main South Korean stock exchange, the Korea Exchange (KRX), listed on the market.

The KOSPI 50 index, which was created on April 1, 2002, is managed by the Korea Exchange and is widely regarded as an accurate indicator of the Korean economy and its key sectors. Market capitalization, trading volume, and liquidity are used in the index selection process to make sure that only the most significant and representative companies from the Korean market are included.

The KOSPI 50, a market capitalization-weighted index, takes into account the market value of each constituent stock to reflect the relative importance of each stock. The KOSPI 50 is prominently displayed on trading platforms and financial websites, similar to other significant stock market indices, making it simple for investors and analysts worldwide to access. It is a crucial indicator of the state and trends of the Korean economy and is important for making investment decisions.

The ticker symbol commonly used in the financial industry to represent the KOSPI 50 index is “KOSPI50”.

Table 1 below gives the Top 10 stocks in the KOSPI 50 index in terms of market capitalization as of January 31, 2023.

Table 1. Top 10 stocks in the KOSPI 50 index.
Top 10 stocks in the KOSPI 50 index
Source: computation by the author (data: Yahoo! Finance website).

Table 2 below gives the sector representation of the KOSPI 50 index in terms of number of stocks and market capitalization as of January 31, 2023.

Table 2. Sector representation in the KOSPI 50 index.
Sector representation in the KOSPI 50 index
Source: computation by the author (data: Yahoo! Finance website).

Calculation of the KOSPI 50 index value

The KOSPI 50 index is a float-adjusted market-capitalization-weighted index. It is adjusted for the proportion of shares that are available for trading in the market as well as the market value of each constituent stock. With the help of this weighting methodology, investors can get a complete picture of the Korean market by ensuring that larger companies have a greater influence on the index’s movements than smaller ones.

The formula to compute the KOSPI 50 index is given by

Float Adjusted Market Capitalization Index value

where I is the index value, k a given asset, K the number of assets in the index, Pk the market price of asset k, Nk the number of issued shares for asset k, Fk the float factor of asset k, and t the time of calculation of the index.

In a float-adjusted market-capitalization-weighted index, the weight of asset k is given by

Float Adjusted Market Capitalization Weighted Index Weight

Use of the KOSPI 50 index in asset management

The analysis of the companies that make up the KOSPI 50 index offers important new perspectives on the Korean economy, its key industries, and the elements that influence business success there. The index also acts as a crucial tool for investors, allowing them to assess the performance of their portfolios in comparison to the larger Korean market and make well-informed investment choices. It supports various asset management tasks, such as passive investments, evaluating corporate risk, asset allocation, and portfolio management, and offers investors insightful information.

Benchmark for equity funds

Investors can gain a thorough understanding of the South Korean market and make wise investment decisions by following the KOSPI 50 index. It is significant to remember that the KOSPI 50 index, which includes the 50 largest and most actively traded companies in South Korea, represents a particular market segment. While it offers an accurate indicator of the performance of these well-known businesses, it might not accurately reflect the performance of all markets and industry sectors nationwide. Investors should think about incorporating other indices, such as the KOSPI 200, which covers a wider range of companies listed on the Korea Exchange, or the MSCI Korea Index, which includes a more diverse set of companies, to obtain a more thorough evaluation of the South Korean market.

Financial products around the KOSPI 50 index

Different financial products linked to the KOSPI 50 index are available for investors looking to diversify their portfolios and increase their exposure to the South Korean stock market. These products offer chances to possibly profit from changes in the market and take part in the performance of the 50 biggest and most actively traded South Korean companies.

Here are some of the main financial products associated with the KOSPI 50 index:

  • Exchange-Traded Funds (ETFs): similar to stocks, investors can trade and invest in ETFs that track the KOSPI 50 index. These ETFs offer a practical way to get exposure to the KOSPI 50 companies’ performance. The KODEX KOSPI 200 ETF and the Samsung KODEX Leverage ETF are two examples of KOSPI 50 ETFs.
  • Options and Futures Contracts: Investors can use options and futures contracts based on the KOSPI 50 index to manage risk, make predictions about market trends, or put trading strategies into practice. Investors can purchase or sell the index through these derivative contracts at predetermined future prices and dates.
  • Mutual Funds and Index Funds: A number of mutual funds and index funds concentrate their investments in the businesses represented by the KOSPI 50 index. These funds seek to match the performance of the index or build portfolios that closely resemble the index’s components. Through these funds, investors can gain exposure to the KOSPI 50, allowing for investment diversification and expert management.

Historical data for the KOSPI 50 index

How to get the data?

The KOSPI 50 index is the most common index used in finance, and historical data for the KOSPI 50 index can be easily downloaded from the internet.

For example, you can download data for the KOSPI 50 index from December 11, 1996 on Yahoo! Finance (the Yahoo! code for KOSPI 50 index is ^KS11).

Yahoo! Finance
Source: Yahoo! Finance.

You can also download the same data from a Bloomberg terminal.

R program

The R program below written by Shengyu ZHENG allows you to download the data from Yahoo! Finance website and to compute summary statistics and risk measures about the KOSPI 50 index.

Download R file

Data file

The R program that you can download above allows you to download the data for the KOSPI 50 index from the Yahoo! Finance website. The database starts on December 11, 1996. It also computes the returns (logarithmic returns) from closing prices.

Table 3 below represents the top of the data file for the KOSPI 50 index downloaded from the Yahoo! Finance website with the R program.

Table 3. Top of the data file for the KOSPI 50 index.
Top of the file for the KOSPI 50 index data
Source: computation by the author (data: Yahoo! Finance website).

Evolution of the KOSPI 50 index

Figure 1 below gives the evolution of the KOSPI 50 index from December 11, 1996 to December 30, 2022 on a daily basis.

Figure 1. Evolution of the KOSPI 50 index.
Evolution of the KOSPI 50 index
Source: computation by the author (data: Yahoo! Finance website).

Figure 2 below gives the evolution of the KOSPI 50 index returns from December 11, 1996 to December 30, 2022 on a daily basis.

Figure 2. Evolution of the KOSPI 50 index returns.
Evolution of the KOSPI 50 index return
Source: computation by the author (data: Yahoo! Finance website).

Summary statistics for the KOSPI 50 index

The R program that you can download above also allows you to compute summary statistics about the returns of the KOSPI 50 index.

Table 4 below presents the following summary statistics estimated for the KOSPI 50 index:

  • The mean
  • The standard deviation (the squared root of the variance)
  • The skewness
  • The kurtosis.

The mean, the standard deviation / variance, the skewness, and the kurtosis refer to the first, second, third and fourth moments of statistical distribution of returns respectively.

Table 4. Summary statistics for the KOSPI 50 index.
Summary statistics for the KOSPI 50 index
Source: computation by the author (data: Yahoo! Finance website).

Statistical distribution of the KOSPI 50 index returns

Historical distribution

Figure 3 represents the historical distribution of the KOSPI 50 index daily returns for the period from December 11, 1996 to December 30, 2022.

Figure 3. Historical distribution of the KOSPI 50 index returns.
Historical distribution of the daily KOSPI 50 index returns
Source: computation by the author (data: Yahoo! Finance website).

Gaussian distribution

The Gaussian distribution (also called the normal distribution) is a parametric distribution with two parameters: the mean and the standard deviation of returns. We estimated these two parameters over the period from December 11, 1996 to December 30, 2022. The mean of daily returns is equal to 0.02% and the standard deviation of daily returns is equal to 1.37% (or equivalently 3.94% for the annual mean and 28.02% for the annual standard deviation as shown in Table 3 above).

Figure 4 below represents the Gaussian distribution of the KOSPI 50 index daily returns with parameters estimated over the period from December 11, 1996 to December 30, 2022.

Figure 4. Gaussian distribution of the KOSPI 50 index returns.
Gaussian distribution of the daily KOSPI 50 index returns
Source: computation by the author (data: Yahoo! Finance website).

Risk measures of the KOSPI 50 index returns

The R program that you can download above also allows you to compute risk measures about the returns of the KOSPI 50 index.

Table 5 below presents the following risk measures estimated for the KOSPI 50 index:

  • The long-term volatility (the unconditional standard deviation estimated over the entire period)
  • The short-term volatility (the standard deviation estimated over the last three months)
  • The Value at Risk (VaR) for the left tail (the 5% quantile of the historical distribution)
  • The Value at Risk (VaR) for the right tail (the 95% quantile of the historical distribution)
  • The Expected Shortfall (ES) for the left tail (the average loss over the 5% quantile of the historical distribution)
  • The Expected Shortfall (ES) for the right tail (the average loss over the 95% quantile of the historical distribution)
  • The Stress Value (SV) for the left tail (the 1% quantile of the tail distribution estimated with a Generalized Pareto distribution)
  • The Stress Value (SV) for the right tail (the 99% quantile of the tail distribution estimated with a Generalized Pareto distribution)

Table 5. Risk measures for the KOSPI 50 index.
Risk measures for the KOSPI 50 index
Source: computation by the author (data: Yahoo! Finance website).

The volatility is a global measure of risk as it considers all the returns. The Value at Risk (VaR), Expected Shortfall (ES) and Stress Value (SV) are local measures of risk as they focus on the tails of the distribution. The study of the left tail is relevant for an investor holding a long position in the KOSPI 50 index while the study of the right tail is relevant for an investor holding a short position in the KOSPI 50 index.

Why should I be interested in this post?

For a number of reasons, management students (as future managers and individual investors) should learn about the KOSPI 50 index. The index includes wide range of industries, including energy, finance, telecommunications, and consumer goods, and it covers the biggest and most liquid German companies. Understanding how the index is constructed, how it performs, and the companies that make up the index is important for anyone studying finance or business in Russia or interested in investing in German equities.

Individual investors can assess the performance of their own investments in the German equity market with the KOSPI 50 index. Last but not least, a lot of asset management firms base their mutual funds and exchange-traded funds (ETFs) on the KOSPI 50 index which can considered as interesting assets to diversify a portfolio. Learning about these products and their portfolio and risk management applications can be valuable for management students.

Related posts on the SimTrade blog

About financial indexes

   ▶ Nithisha CHALLA Financial indexes

   ▶ Nithisha CHALLA Calculation of financial indexes

   ▶ Nithisha CHALLA The business of financial indexes

   ▶ Nithisha CHALLA Float

Other financial indexes

   ▶ Nithisha CHALLA The S&P 500 index

   ▶ Nithisha CHALLA The FTSE 100 index

   ▶ Nithisha CHALLA The CSI 300 index

   ▶ Nithisha CHALLA The Nikkei 225 index

About portfolio management

   ▶ Youssef LOURAOUI Portfolio

   ▶ Jayati WALIA Returns

About statistics

   ▶ Shengyu ZHENG Moments de la distribution

   ▶ Shengyu ZHENG Mesures de risques

Useful resources

Academic research about risk

Longin F. (2000) From VaR to stress testing: the extreme value approach Journal of Banking and Finance, N°24, pp 1097-1130.

Longin F. (2016) Extreme events in finance: a handbook of extreme value theory and its applications Wiley Editions.

Business

Wikipedia What is the KOSPI 50 index

PWC A guide to listing on the Korean exchange

Data

Yahoo! Finance

Yahoo! Finance Historical data for the KOSPI 50 index

About the author

The article was written in June 2023 by Nithisha CHALLA (ESSEC Business School, Grande Ecole Program – Master in Management, 2021-2023).

The OMX Copenhagen 25 (OMXC 25) index

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The OMX Copenhagen 25 (OMXC 25) index

Nithisha CHALLA

In this article, Nithisha CHALLA (ESSEC Business School, Grande Ecole Program – Master in Management, 2021-2023) presents the OMX Copenhagen 25 (OMXC25 or OMXC 25) index representing the Danish equity market and details its characteristics.

The OMX Copenhagen 25 index

The 25 biggest and busiest companies listed on Nasdaq Copenhagen, the main stock exchange in Denmark, make up the OMX Copenhagen 25 (OMXC 25) index, which is a market-capitalization-weighted index. With 1,000 points as the base point, the index was introduced on December 4th, 1996.

Nasdaq Copenhagen chooses the stocks for the OMXC 25 index, taking into account elements like market capitalization, liquidity, and free float. To maintain its representation of the Danish stock market, the index is reviewed twice a year, in June and December, and rebalanced as necessary.

The OMXC 25 is a market-capitalization-weighted index, which means that the index’s weight is based on the market capitalization of each company. This increases the OMXC 25’s comparability to the Danish market as a whole.

Investors and analysts pay close attention to the performance of the OMXC 25 index, which is widely used as a benchmark for the Danish stock market. Through financial products like exchange-traded funds (ETFs) and index funds that follow the OMXC 25 index, investors can gain exposure to the Danish market. The ticker symbol “OMXC25” is frequently used in trading platforms and financial websites to denote the OMXC 25 index.

Table 1 below gives the Top 10 stocks in the OMXC 25 index in terms of market capitalization as of January 31, 2023.

Table 1. Top 10 stocks in the OMXC 25 index.
Top 10 stocks in the OMXC 25 index
Source: computation by the author (data: Yahoo! Finance website).

Table 2 below gives the sector representation of the OMXC 25 index in terms of number of stocks and market capitalization as of January 31, 2023.

Table 2. Sector representation in the OMXC 25 index.
Sector representation in the OMXC 25 index
Source: computation by the author (data: Yahoo! Finance website).

Calculation of the OMXC 25 index value

The performance of the 25 most actively traded and highly capitalized companies listed on the Danish Nasdaq Copenhagen stock exchange is reflected in the OMX Copenhagen 25 (OMXC 25) index, which is a float-adjusted market-capitalization-weighted index. The index is evaluated twice a year by Nasdaq Copenhagen and includes businesses from a variety of industries, including technology, healthcare, and finance. Each year, the index is rebalanced in June and December, and the companies that make up the index are chosen using criteria like market capitalization, trading volume, and free float.

The formula to compute the OMXC 25 index is given by

Float Adjusted Market Capitalization Index value

where I is the index value, k a given asset, K the number of assets in the index, Pk the market price of asset k, Nk the number of issued shares for asset k, Fk the float factor of asset k, and t the time of calculation of the index.

In a float-adjusted market-capitalization-weighted index, the weight of asset k is given by

Float Adjusted Market Capitalization Weighted Index Weight

Use of the OMXC 25 index in asset management

A common benchmark used by investors to evaluate the performance of their investment portfolios in relation to the Danish stock market is the OMXC 25 index. Investors and analysts can learn a lot about the state of the Danish economy overall and the performance of important industries like technology, healthcare, and industrials by closely following the changes in the OMXC 25 index. Through ticker symbols like “OMXC25” or “OMXC25.CO,” the index is frequently mentioned in financial news outlets and is readily available to investors and traders worldwide.

Benchmark for equity funds

The performance of the top 25 companies listed on the Copenhagen Stock Exchange (Nasdaq Copenhagen) is represented by the OMXC 25 index, but it does not fully represent the size of the Danish equity market. Because of this, investors seeking a more thorough representation of the Danish market may want to think about other, wider market indices, like the OMXC 25 or the OMXC All-Share.

The 25 most active and liquid companies listed on Nasdaq Copenhagen are included in the OMXC 25 index, which offers a more comprehensive view of the Danish market. The OMXC All-Share index, on the other hand, provides a more thorough overview of the Danish equity market as a whole and covers a wider range of companies, including both large and small caps. In order to accurately track their performance and align it with their investment goals in the Danish market, investors should carefully assess their investment objectives and strategies to determine the most appropriate benchmark index.

Financial products around the OMXC 25 index

With the help of the OMXC 25 index, these financial products give investors the chance to diversify their portfolios, get exposure to the Danish stock market, and perhaps even profit from market fluctuations.

Some of the main financial products associated with the OMXC 25 index are:

  • Exchange-Traded Funds (ETFs): ETFs, which are traded on stock exchanges like individual stocks, allow investors access to the OMXX 25 index. ETFs that track the performance of the OMXC 25 index, like the iShares OMXC 25 UCITS ETF and the Xact OMXC 25 ETF, give investors a broad view of the Danish market.
  • Options and Futures Contracts: Investors can purchase or sell the OMXC 25 index through options and futures contracts that are linked to the index at a specified price and future date. These derivative contracts can be used for hedging, speculation, and portfolio management, among other things.
  • Mutual Funds and Index Funds: A few mutual funds and index funds concentrate their investments in businesses that are part of the OMXX 25 index or seek to match its performance. With the help of these funds, investors now have an easy way to expose themselves to a diverse portfolio of Danish stocks.

Historical data for the OMXC 25 index

How to get the data?

The OMXC 25 index is the most common index used in finance, and historical data for the OMXC 25 index can be easily downloaded from the internet.

For example, you can download data for the OMXC 25 index from December 19, 2016 on Yahoo! Finance (the Yahoo! code for OMXC 25 index is ^OMXC25).

Yahoo! Finance
Source: Yahoo! Finance.

You can also download the same data from a Bloomberg terminal.

R program

The R program below written by Shengyu ZHENG allows you to download the data from Yahoo! Finance website and to compute summary statistics and risk measures about the OMXC 25 index.

Download R file

Data file

The R program that you can download above allows you to download the data for the OMXC 25 index from the Yahoo! Finance website. The database starts on December 19, 2016. It also computes the returns (logarithmic returns) from closing prices.

Table 3 below represents the top of the data file for the OMXC 25 index downloaded from the Yahoo! Finance website with the R program.

Table 3. Top of the data file for the OMXC 25 index.
Top of the file for the OMXC 25 index data
Source: computation by the author (data: Yahoo! Finance website).

Evolution of the OMXC 25 index

Figure 1 below gives the evolution of the OMXC 25 index from December 19, 2016 to December 30, 2022 on a daily basis.

Figure 1. Evolution of the OMXC 25 index.
Evolution of the OMXC 25 index
Source: computation by the author (data: Yahoo! Finance website).

Figure 2 below gives the evolution of the OMXC 25 index returns from December 19, 2016 to December 30, 2022 on a daily basis.

Figure 2. Evolution of the OMXC 25 index returns.
Evolution of the OMXC 25 index return
Source: computation by the author (data: Yahoo! Finance website).

Summary statistics for the OMXC 25 index

The R program that you can download above also allows you to compute summary statistics about the returns of the OMXC 25 index.

Table 4 below presents the following summary statistics estimated for the OMXC 25 index:

  • The mean
  • The standard deviation (the squared root of the variance)
  • The skewness
  • The kurtosis.

The mean, the standard deviation / variance, the skewness, and the kurtosis refer to the first, second, third and fourth moments of statistical distribution of returns respectively.

Table 4. Summary statistics for the OMXC 25 index.
Summary statistics for the OMXC 25 index
Source: computation by the author (data: Yahoo! Finance website).

Statistical distribution of the OMXC 25 index returns

Historical distribution

Figure 3 represents the historical distribution of the OMXC 25 index daily returns for the period from December 19, 2016 to December 30, 2022.

Figure 3. Historical distribution of the OMXC 25 index returns.
Historical distribution of the daily OMXC 25 index returns
Source: computation by the author (data: Yahoo! Finance website).

Gaussian distribution

The Gaussian distribution (also called the normal distribution) is a parametric distribution with two parameters: the mean and the standard deviation of returns. We estimated these two parameters over the period from December 19, 2016 to December 30, 2022. The mean of daily returns is equal to 0.02% and the standard deviation of daily returns is equal to 1.37% (or equivalently 3.94% for the annual mean and 28.02% for the annual standard deviation as shown in Table 3 above).

Figure 4 below represents the Gaussian distribution of the OMXC 25 index daily returns with parameters estimated over the period from December 19, 2016 to December 30, 2022.

Figure 4. Gaussian distribution of the OMXC 25 index returns.
Gaussian distribution of the daily OMXC 25 index returns
Source: computation by the author (data: Yahoo! Finance website).

Risk measures of the OMXC 25 index returns

The R program that you can download above also allows you to compute risk measures about the returns of the OMXC 25 index.

Table 5 below presents the following risk measures estimated for the OMXC 25 index:

  • The long-term volatility (the unconditional standard deviation estimated over the entire period)
  • The short-term volatility (the standard deviation estimated over the last three months)
  • The Value at Risk (VaR) for the left tail (the 5% quantile of the historical distribution)
  • The Value at Risk (VaR) for the right tail (the 95% quantile of the historical distribution)
  • The Expected Shortfall (ES) for the left tail (the average loss over the 5% quantile of the historical distribution)
  • The Expected Shortfall (ES) for the right tail (the average loss over the 95% quantile of the historical distribution)
  • The Stress Value (SV) for the left tail (the 1% quantile of the tail distribution estimated with a Generalized Pareto distribution)
  • The Stress Value (SV) for the right tail (the 99% quantile of the tail distribution estimated with a Generalized Pareto distribution)

Table 5. Risk measures for the OMXC 25 index.
Risk measures for the OMXC 25 index
Source: computation by the author (data: Yahoo! Finance website).

The volatility is a global measure of risk as it considers all the returns. The Value at Risk (VaR), Expected Shortfall (ES) and Stress Value (SV) are local measures of risk as they focus on the tails of the distribution. The study of the left tail is relevant for an investor holding a long position in the OMXC 25 index while the study of the right tail is relevant for an investor holding a short position in the OMXC 25 index.

Why should I be interested in this post?

Students can gain a thorough understanding of industry dynamics, market competition, and the interplay of various factors that affect business success in Denmark by studying the OMXC 25 index. Investors can compare the performance of their portfolios to that of the larger Danish stock market using the OMXC 25 index as a benchmark. In addition to reflecting investor sentiment toward Denmark’s biggest and most actively traded companies, it offers a snapshot of the market’s health.

Related posts on the SimTrade blog

About financial indexes

   ▶ Nithisha CHALLA Financial indexes

   ▶ Nithisha CHALLA Calculation of financial indexes

   ▶ Nithisha CHALLA The business of financial indexes

   ▶ Nithisha CHALLA Float

Other financial indexes

   ▶ Nithisha CHALLA The S&P 500 index

   ▶ Nithisha CHALLA The FTSE 100 index

   ▶ Nithisha CHALLA The DAX 30 index

   ▶ Nithisha CHALLA The CAC 40 index

About portfolio management

   ▶ Youssef LOURAOUI Portfolio

   ▶ Jayati WALIA Returns

About statistics

   ▶ Shengyu ZHENG Moments de la distribution

   ▶ Shengyu ZHENG Mesures de risques

Useful resources

Academic research about risk

Longin F. (2000) From VaR to stress testing: the extreme value approach Journal of Banking and Finance, N°24, pp 1097-1130.

Longin F. (2016) Extreme events in finance: a handbook of extreme value theory and its applications Wiley Editions.

About the OMXC 25 index

Nasdaq Index Description

Capital.com What is the OMXC20 index?

Data

Yahoo! Finance

Yahoo! Finance Data for the OMXC 25 index

About the author

The article was written in June 2023 by Nithisha CHALLA (ESSEC Business School, Grande Ecole Program – Master in Management, 2021-2023).

The BEL 20 index

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The BEL 20 index

Nithisha CHALLA

In this article, Nithisha CHALLA (ESSEC Business School, Grande Ecole Program – Master in Management, 2021-2023) presents the BEL 20 index representing the Belgian equity market and details its characteristics.

The BEL 20 index

The top 20 companies listed on Euronext Brussels, Belgium’s main stock exchange, make up the BEL 20 index, a stock market index that measures performance. The BEL 20 index was created in 1991, and Euronext oversees its operation. The market capitalization, liquidity, and sector representation of the companies chosen for the index are taken into consideration.

The market capitalization of each stock determines its weight in the BEL 20 index, which is a capitalization-weighted index. To guarantee that the index continues to be a trustworthy representation of the Belgian equity market, it is rebalanced four times per year.

With the widely used ticker symbol “BEL20” in the financial sector, investors and traders can access the BEL 20 index through various financial news sources and trading platforms. The BEL 20 index is a useful tool for investors and financial professionals because it can give important insights into the performance of the Belgian economy and its best-performing companies.

Table 1 below gives the Top 10 stocks in the BEL 20 index in terms of market capitalization as of January 31, 2023.

Table 1. Top 10 stocks in the BEL 20 index.
Top 10 stocks in the BEL 20 index
Source: computation by the author (data: Yahoo! Finance website).

Table 2 below gives the sector representation of the BEL 20 index in terms of number of stocks and market capitalization as of January 31, 2023.

Table 2. Sector representation in the BEL 20 index.
Sector representation in the BEL 20 index
Source: computation by the author (data: Yahoo! Finance website).

Calculation of the BEL 20 index value

The performance of the 20 largest and most actively traded companies listed on the Brussels Stock Exchange (Euronext Brussels) in Belgium is reflected in the BEL 20 index, which is a float-adjusted market-capitalization-weighted index. The Belgian Association of Financial Analysts (ABAF-BVFA), which chooses the companies to be included in the index based on their liquidity, market capitalization, and free float, reviews the index on a quarterly basis.

The BEL 20 is rebalanced quarterly, taking into account any changes in the market capitalization of the constituent companies, to make sure the index accurately reflects the performance of the Belgian stock market.

The formula to compute the BEL 20 index is given by

Float Adjusted Market Capitalization Index value

where I is the index value, k a given asset, K the number of assets in the index, Pk the market price of asset k, Nk the number of issued shares for asset k, Fk the float factor of asset k, and t the time of calculation of the index.

In a float-adjusted market-capitalization-weighted index, the weight of asset k is given by formula

Float Adjusted Market Capitalization Weighted Index Weight

Use of the BEL 20 index in asset management

Investors frequently use the BEL 20 index as a benchmark to assess the performance of their investment portfolios in relation to the larger Belgian stock market.

Investors and analysts can learn more about the performance of the Belgian economy and its major sectors—such as financial services, consumer goods, and energy—by examining the changes in the BEL 20 index. Investors and traders can access the index using ticker symbols like “BEL20” or “BEL20.BR” and it is frequently covered in financial news outlets. Investors should take into account other indexes and benchmarks for a more thorough evaluation of the Belgian market, however, as the BEL 20 index does not cover all industries and sectors in Belgium.

Benchmark for equity funds

For equity funds investing across the board in the Belgian market, the BEL 20 index may not always be the best benchmark. This is due to the fact that the BEL 20 index does not account for the entire Belgian equity market; rather, it only tracks the performance of the top 20 companies listed on Euronext Brussels. Investors may need to take into account other broader market indices, such as the BEL Mid, which includes the 60 next most significant listed companies after the BEL 20, or the BEL Small, which includes the smallest companies listed on Euronext Brussels, in order to obtain a more complete representation of the Belgian market. Investors should therefore assess their investment goals and plans before choosing the appropriate benchmark indices.

Financial products around the BEL 20 index

The performance of the businesses that make up the BEL 20 index is the main objective of these products. Several financial products follow the BEL 20 index, including:

  • Exchange-Traded Funds: ETFs that track the BEL 20 index include the Lyxor UCITS Bel 20 ETF and the iShares Bel 20 UCITS ETF
  • Index funds: The Candriam Equities Belgium Index and the BNP Paribas B Fund Belgium Index are examples of index funds that track the performance of the Bel 20 index

These financial products allow investors to follow the performance of the top 20 companies listed on the Euronext Brussels exchange as well as gain exposure to the Belgian equity market. These financial products could produce returns based on the performance of the Belgian equity market and assist investors in diversifying their portfolios.

Historical data for the BEL 20 index

How to get the data?

The BEL 20 index is the most common index used in finance, and historical data for the BEL 20 index can be easily downloaded from the internet.

For example, you can download data for the BEL 20 index from January 3, 1984 on Yahoo! Finance (the Yahoo! code for BEL 20 index is ^BFX).

Yahoo! Finance
Source: Yahoo! Finance.

You can also download the same data from a Bloomberg terminal.

R program

The R program below written by Shengyu ZHENG allows you to download the data from Yahoo! Finance website and to compute summary statistics and risk measures about the BEL 20 index.

Download R file

Data file

The R program that you can download above allows you to download the data for the BEL 20 index from the Yahoo! Finance website. The database starts on January 3, 1984. It also computes the returns (logarithmic returns) from closing prices.

Table 3 below represents the top of the data file for the BEL 20 index downloaded from the Yahoo! Finance website with the R program.

Table 3. Top of the data file for the BEL 20 index.
Top of the file for the BEL 20 index data
Source: computation by the author (data: Yahoo! Finance website).

Evolution of the BEL 20 index

Figure 1 below gives the evolution of the BEL 20 index from January 3, 1984 to December 30, 2022 on a daily basis.

Figure 1. Evolution of the BEL 20 index.
Evolution of the BEL 20 index
Source: computation by the author (data: Yahoo! Finance website).

Figure 2 below gives the evolution of the BEL 20 index returns from January 3, 1984 to December 30, 2022 on a daily basis.

Figure 2. Evolution of the BEL 20 index returns.
Evolution of the BEL 20 index return
Source: computation by the author (data: Yahoo! Finance website).

Summary statistics for the BEL 20 index

The R program that you can download above also allows you to compute summary statistics about the returns of the BEL 20 index.

Table 4 below presents the following summary statistics estimated for the BEL 20 index:

  • The mean
  • The standard deviation (the squared root of the variance)
  • The skewness
  • The kurtosis.

The mean, the standard deviation / variance, the skewness, and the kurtosis refer to the first, second, third and fourth moments of statistical distribution of returns respectively.

Table 4. Summary statistics for the BEL 20 index.
Summary statistics for the BEL 20 index
Source: computation by the author (data: Yahoo! Finance website).

Statistical distribution of the BEL 20 index returns

Historical distribution

Figure 3 represents the historical distribution of the BEL 20 index daily returns for the period from January 3, 1984 to December 30, 2022.

Figure 3. Historical distribution of the BEL 20 index returns.
Historical distribution of the daily BEL 20 index returns
Source: computation by the author (data: Yahoo! Finance website).

Gaussian distribution

The Gaussian distribution (also called the normal distribution) is a parametric distribution with two parameters: the mean and the standard deviation of returns. We estimated these two parameters over the period from January 3, 1984 to December 30, 2022. The mean of daily returns is equal to 0.02% and the standard deviation of daily returns is equal to 1.37% (or equivalently 3.94% for the annual mean and 28.02% for the annual standard deviation as shown in Table 3 above).

Figure 4 below represents the Gaussian distribution of the BEL 20 index daily returns with parameters estimated over the period from January 3, 1984 to December 30, 2022.

Figure 4. Gaussian distribution of the BEL 20 index returns.
Gaussian distribution of the daily BEL 20 index returns
Source: computation by the author (data: Yahoo! Finance website).

Risk measures of the BEL 20 index returns

The R program that you can download above also allows you to compute risk measures about the returns of the BEL 20 index.

Table 5 below presents the following risk measures estimated for the BEL 20 index:

  • The long-term volatility (the unconditional standard deviation estimated over the entire period)
  • The short-term volatility (the standard deviation estimated over the last three months)
  • The Value at Risk (VaR) for the left tail (the 5% quantile of the historical distribution)
  • The Value at Risk (VaR) for the right tail (the 95% quantile of the historical distribution)
  • The Expected Shortfall (ES) for the left tail (the average loss over the 5% quantile of the historical distribution)
  • The Expected Shortfall (ES) for the right tail (the average loss over the 95% quantile of the historical distribution)
  • The Stress Value (SV) for the left tail (the 1% quantile of the tail distribution estimated with a Generalized Pareto distribution)
  • The Stress Value (SV) for the right tail (the 99% quantile of the tail distribution estimated with a Generalized Pareto distribution)

Table 5. Risk measures for the BEL 20 index.
Risk measures for the BEL 20 index
Source: computation by the author (data: Yahoo! Finance website).

The volatility is a global measure of risk as it considers all the returns. The Value at Risk (VaR), Expected Shortfall (ES) and Stress Value (SV) are local measures of risk as they focus on the tails of the distribution. The study of the left tail is relevant for an investor holding a long position in the BEL 20 index while the study of the right tail is relevant for an investor holding a short position in the BEL 20 index.

Why should I be interested in this post?

By analyzing the companies in the BEL 20 index, students can gain an understanding of how these industries operate and the factors that influence their success. For example, students can explore how regulations affect the financial services industry, how innovation drives growth in the pharmaceutical sector, and how geopolitical events impact energy markets. This knowledge can be particularly useful for those pursuing careers in finance, economics, or business.

Related posts on the SimTrade blog

About financial indexes

   ▶ Nithisha CHALLA Financial indexes

   ▶ Nithisha CHALLA Calculation of financial indexes

   ▶ Nithisha CHALLA The business of financial indexes

   ▶ Nithisha CHALLA Float

Other financial indexes

   ▶ Nithisha CHALLA The S&P 500 index

   ▶ Nithisha CHALLA The FTSE 100 index

   ▶ Nithisha CHALLA The DAX 30 index

   ▶ Nithisha CHALLA The CAC 40 index

About portfolio management

   ▶ Youssef LOURAOUI Portfolio

   ▶ Jayati WALIA Returns

About statistics

   ▶ Shengyu ZHENG Moments de la distribution

   ▶ Shengyu ZHENG Mesures de risques

Useful resources

Academic research about risk

Longin F. (2000) From VaR to stress testing: the extreme value approach Journal of Banking and Finance, N°24, pp 1097-1130.

Longin F. (2016) Extreme events in finance: a handbook of extreme value theory and its applications Wiley Editions.

About the BEL 20 index

Wikipedia What is the BEL 20 index

Currency BEL 20 index explained

Trading economics About Belgium Stock Market Index BEL20

Data

Yahoo! Finance

Yahoo! Finance Data for the BEL 20 index

About the author

The article was written in June 2023 by Nithisha CHALLA (ESSEC Business School, Grande Ecole Program – Master in Management, 2021-2023).

The IBEX 35 index

by

The IBEX 35 index

Nithisha CHALLA

In this article, Nithisha CHALLA (ESSEC Business School, Grande Ecole Program – Master in Management, 2021-2023) presents the IBEX 35 index representing the Spanish equity market and details its characteristics.

The IBEX 35 index

The Bolsa de Madrid’s benchmark stock market index, the IBEX 35 index, is regarded as Spain’s primary stock exchange. The company that runs the Spanish stock exchanges, Bolsas y Mercados Espaoles (BME), which was founded on January 14, 1992, is in charge of managing it.

The 35 most liquid and well-capitalized companies traded on the Bolsa de Madrid make up the index. Based on trading volume, liquidity, and free-float market capitalization, the companies listed are chosen. The index includes businesses from a wide range of industries, including consumer goods, energy, finance, and telecommunications.

The IBEX 35 index is a free-float market capitalization-weighted index, which means that the index’s weights are based on market capitalization and are float-adjusted for each stock. This makes sure that the movements of the index are more influenced by larger companies than by smaller ones.

The IBEX 35 index is widely represented on trading platforms and financial websites, like other significant stock market indices. The performance of the Spanish economy and the overall health of the European Union are closely watched by investors and analysts around the world.

The ticker symbol used in the financial industry for the IBEX 35 index is “IBEX”.

Table 1 below gives the Top 10 stocks in the IBEX 35 index in terms of market capitalization as of January 31, 2023.

Table 1. Top 10 stocks in the IBEX 35 index.
Top 10 stocks in the IBEX 35 index
Source: computation by the author (data: Yahoo! Finance financial website).

Table 2 below gives the sector representation of the IBEX 35 index in terms of number of stocks and market capitalization as of January 31, 2023.

Table 2. Sector representation in the IBEX 35 index.
Sector representation in the IBEX 35 index
Source: computation by the author (data: Yahoo! Finance website).

Calculation of the IBEX 35 index value

As a free-float market-capitalization-weighted index that is float-adjusted, the IBEX 35 index is calculated by taking into account the market capitalization of each of the companies that make up the index. To ensure that the index accurately captures the performance of the Spanish stock market, Bolsas y Mercados Espaoles (BME), the Spanish stock exchange, reviews and rebalances the index twice a year. The stocks that will be included in the index are chosen by the Technical Advisory Committee of the BME, which takes into account elements like liquidity, market capitalization, and trading volume.

The formula to compute the IBEX 35 index is given by

Float Adjusted Market Capitalization Index value

where I is the index value, k a given asset, K the number of assets in the index, Pk the market price of asset k, Nk the number of issued shares for asset k, Fk the float factor of asset k, and t the time of calculation of the index.

In a float-adjusted market-capitalization-weighted index, the weight of asset k is given by

Float Adjusted Market Capitalization Weighted Index Weight

Use of the IBEX 35 index in asset management

The IBEX 35 index serves as a benchmark for assessing the performance of the Spanish stock market. Because it is a widely used indicator of the performance of the Spanish stock market, it can help investors with important asset management tasks like passive investments, evaluating corporate risk, asset allocation, portfolio management, and so forth. However, the performance of all markets or sectors is not accurately reflected by the IBEX 35 index, which only includes the 35 Spanish stocks with the highest level of liquidity. Therefore, when evaluating the performance of the Spanish equity market, investors should also consider other indices like the FTSE Spain Index and the MSCI Spain Index.

Benchmark for equity funds

Investors frequently use the IBEX 35 index as a benchmark. When using the IBEX 35 index as a benchmark for equity funds in Spain, it is important to remember that it only includes 35 of the largest and most popularly traded companies listed on the Spanish stock exchange. As a result, it might not accurately represent the whole Spanish market, as there are many small and mid-cap companies in Spain that are not represented by the index. The benchmark index to be used will ultimately depend on the specific investment objectives and strategies of the fund in question.

Financial products around the IBEX 35 index

Through the IBEX 35 index, these financial products give investors access to the Spanish stock market, portfolio diversification, and the potential to profit from market fluctuations.

Some of the main financial products related to the IBEX 35 index are:

  • Exchange-Traded Funds (ETFs): Through ETFs, which are traded like stocks, investors can gain access to the IBEX 35 index. ETFs that follow the Ibex 35 index include the iShares Ibex 35 UCITS ETF and the Amundi ETF Ibex 35.
  • Options and Futures Contracts: Investors can use options and futures contracts to buy or sell the IBEX 35 index at a predetermined price and date in the future. This is typically done to generate income through trading strategies, hedge against market volatility, or predict the index’s performance.
  • Mutual Funds and Index Funds: Some mutual funds and index funds concentrate on investing in businesses that are part of the IBEX 35 index or seek to replicate the performance of the index by acquiring the same stocks that comprise the index.

Historical data for the IBEX 35 index

How to get the data?

The IBEX 35 index is the most common index used in finance, and historical data for the IBEX 35 index can be easily downloaded from the internet.

For example, you can download data for the IBEX 35 index from July 12, 1993 on Yahoo! Finance (the Yahoo! code for IBEX 35 index is ^IBEX).

Yahoo! Finance
Source: Yahoo! Finance.

You can also download the same data from a Bloomberg terminal.

R program

The R program below written by Shengyu ZHENG allows you to download the data from Yahoo! Finance website and to compute summary statistics and risk measures about the IBEX 35 index.

Download R file

Data file

The R program that you can download above allows you to download the data for the IBEX 35 index from the Yahoo! Finance website. The database starts on July 12, 1993. It also computes the returns (logarithmic returns) from closing prices.

Table 3 below represents the top of the data file for the IBEX 35 index downloaded from the Yahoo! Finance website with the R program.

Table 3. Top of the data file for the IBEX 35 index.
Top of the file for the IBEX 35 index data
Source: computation by the author (data: Yahoo! Finance website).

Evolution of the IBEX 35 index

Figure 1 below gives the evolution of the IBEX 35 index from July 12, 1993 to December 30, 2022 on a daily basis.

Figure 1. Evolution of the IBEX 35 index.
Evolution of the IBEX 35 index
Source: computation by the author (data: Yahoo! Finance website).

Figure 2 below gives the evolution of the IBEX 35 index returns from July 12, 1993 to December 30, 2022 on a daily basis.

Figure 2. Evolution of the IBEX 35 index returns.
Evolution of the IBEX 35 index return
Source: computation by the author (data: Yahoo! Finance website).

Summary statistics for the IBEX 35 index

The R program that you can download above also allows you to compute summary statistics about the returns of the IBEX 35 index.

Table 4 below presents the following summary statistics estimated for the IBEX 35 index:

  • The mean
  • The standard deviation (the squared root of the variance)
  • The skewness
  • The kurtosis.

The mean, the standard deviation / variance, the skewness, and the kurtosis refer to the first, second, third and fourth moments of statistical distribution of returns respectively.

Table 4. Summary statistics for the IBEX 35 index.
Summary statistics for the IBEX 35 index
Source: computation by the author (data: Yahoo! Finance website).

Statistical distribution of the IBEX 35 index returns

Historical distribution

Figure 3 represents the historical distribution of the IBEX 35 index daily returns for the period from July 12, 1993 to December 30, 2022.

Figure 3. Historical distribution of the IBEX 35 index returns.
Historical distribution of the daily IBEX 35 index returns
Source: computation by the author (data: Yahoo! Finance website).

Gaussian distribution

The Gaussian distribution (also called the normal distribution) is a parametric distribution with two parameters: the mean and the standard deviation of returns. We estimated these two parameters over the period from July 12, 1993 to December 30, 2022. The mean of daily returns is equal to 0.02% and the standard deviation of daily returns is equal to 1.37% (or equivalently 3.94% for the annual mean and 28.02% for the annual standard deviation as shown in Table 3 above).

Figure 4 below represents the Gaussian distribution of the IBEX 35 index daily returns with parameters estimated over the period from July 12, 1993 to December 30, 2022.

Figure 4. Gaussian distribution of the IBEX 35 index returns.
Gaussian distribution of the daily IBEX 35 index returns
Source: computation by the author (data: Yahoo! Finance website).

Risk measures of the IBEX 35 index returns

The R program that you can download above also allows you to compute risk measures about the returns of the IBEX 35 index.

Table 5 below presents the following risk measures estimated for the IBEX 35 index:

  • The long-term volatility (the unconditional standard deviation estimated over the entire period)
  • The short-term volatility (the standard deviation estimated over the last three months)
  • The Value at Risk (VaR) for the left tail (the 5% quantile of the historical distribution)
  • The Value at Risk (VaR) for the right tail (the 95% quantile of the historical distribution)
  • The Expected Shortfall (ES) for the left tail (the average loss over the 5% quantile of the historical distribution)
  • The Expected Shortfall (ES) for the right tail (the average loss over the 95% quantile of the historical distribution)
  • The Stress Value (SV) for the left tail (the 1% quantile of the tail distribution estimated with a Generalized Pareto distribution)
  • The Stress Value (SV) for the right tail (the 99% quantile of the tail distribution estimated with a Generalized Pareto distribution)

Table 5. Risk measures for the IBEX 35 index.
Risk measures for the IBEX 35 index
Source: computation by the author (data: Yahoo! Finance website).

The volatility is a global measure of risk as it considers all the returns. The Value at Risk (VaR), Expected Shortfall (ES) and Stress Value (SV) are local measures of risk as they focus on the tails of the distribution. The study of the left tail is relevant for an investor holding a long position in the IBEX 35 index while the study of the right tail is relevant for an investor holding a short position in theIBEX 35 index.

Why should I be interested in this post?

Students can gain useful knowledge about the Spanish stock market and its major sectors by looking at the IBEX 35 index. These firms represent a wide range of industries, including consumer goods, energy, finance, and telecommunications, making the index a useful benchmark for the Spanish economy. Students can learn how industries function, how competition affects the market, and what elements contribute to business success in Spain by examining the performance of the companies included in the index.

Furthermore, investors can use financial products linked to the IBEX 35 index, such as exchange-traded funds (ETFs), futures, and options contracts, to access the Spanish market and potentially generate returns. By understanding the dynamics of the IBEX 35 index and the Spanish economy, students can develop valuable skills for careers in investment banking, portfolio management, and corporate finance.

Related posts on the SimTrade blog

About financial indexes

   ▶ Nithisha CHALLA Financial indexes

   ▶ Nithisha CHALLA Calculation of financial indexes

   ▶ Nithisha CHALLA The business of financial indexes

   ▶ Nithisha CHALLA Float

Other financial indexes

   ▶ Nithisha CHALLA The S&P 500 index

   ▶ Nithisha CHALLA The FTSE 100 index

   ▶ Nithisha CHALLA The DAX 30 index

   ▶ Nithisha CHALLA The CAC 40 index

About portfolio management

   ▶ Youssef LOURAOUI Portfolio

   ▶ Jayati WALIA Returns

About statistics

   ▶ Shengyu ZHENG Moments de la distribution

   ▶ Shengyu ZHENG Mesures de risques

Useful resources

About the IBEX 35 index

Wikipedia What is the IBEX 35 index

AVA trade An Overview of Spain’s Financial Engine – IBEX 35

DailyFX What is the IBEX 35 Index and what influences its price?

Academic research about risk

Longin F. (2000) From VaR to stress testing: the extreme value approach Journal of Banking and Finance, N°24, pp 1097-1130.

Longin F. (2016) Extreme events in finance: a handbook of extreme value theory and its applications Wiley Editions.

Data

Yahoo! Finance

Yahoo! Finance Data for the IBEX 35 index

About the author

The article was written in June 2023 by Nithisha CHALLA (ESSEC Business School, Grande Ecole Program – Master in Management, 2021-2023).

The DAX 30 index

by

The DAX 30 index

Nithisha CHALLA

In this article, Nithisha CHALLA (ESSEC Business School, Grande Ecole Program – Master in Management, 2021-2023) presents the DAX 30 index and details its characteristics.

The DAX 30 index

The largest and most liquid 30 publicly traded German companies are represented by the DAX 30 index. This index was established by the Frankfurt Stock Exchange on July 1, 1988. “Deutscher Aktienindex” or the German stock index in English, is abbreviated as DAX. Deutsche Boerse AG, which also runs the Frankfurt Stock Exchange, is in charge of managing the DAX 30.

The choice of the companies for the DAX index is based on a number of variables, such as trading volume, market capitalization, and liquidity. The Deutsche Boerse Index Commission regularly modifies and reviews the index’s composition, ensuring that DAX 30 accurately captures the overall performance of the German stock market.

The DAX 30 is a free float market capitalization-weighted index, which means that each company’s weight in the index is based on the calculation of its market capitalization. The performance of the German stock market is measured against the DAX 30, which is closely monitored by traders and investors worldwide. Investors and traders wishing to follow the performance of the German stock market can easily access the index as it is published and distributed in real-time by several financial news sources.

The ticker symbol “DAX” is used in trading platforms and financial websites to identify the DAX 30.

Table 1 below gives the Top 10 stocks in the DAX 30 index in terms of market capitalization as of January 31, 2023.

Table 1. Top 10 stocks in the DAX 30 index.
Top 10 stocks in the DAX 30 index
Source: computation by the author (data: Yahoo! Finance website).

Calculation of the DAX 30 index value

The performance of the 30 largest and busiest German companies listed on Frankfurt Stock Exchange is reflected in the DAX 30, a blue-chip stock market index. A free-float market-capitalization-weighted methodology is utilized to calculate the index, which means that each company’s weight in the index is determined by its market capitalization adjusted for the shares that are actually traded in the secondary market (float).

The formula to compute the DAX 30 index is given by

Float Adjusted Market Capitalization Index value

where I is the index value, k a given asset, K the number of assets in the index, Pk the market price of asset k, Nk the number of issued shares for asset k, Fk the float factor of asset k, and t the time of calculation of the index.

In a float-adjusted market-capitalization-weighted index, the weight of asset k is given by formula

Float Adjusted Market Capitalization Weighted Index Weight

Use of the DAX 30 index in asset management

Investors can examine the sector weightings and geographic exposure of the index to gain insights into performance of the German economy to identify potential opportunities and risks in particular industries or regions. Asset managers compare performance of their equity portfolios to the performance of the complete market using the DAX 30 as the benchmark. Multiple investment products, including exchange-traded funds (ETFs), options, and futures contracts, all have the index as the starting point.

Benchmark for equity funds

One of the highly significant indices in Europe, the DAX 30 serves as standard for the overall performance of German stock market. The businesses represent numerous industries, including those in the automotive, financial, healthcare, technology, and retail sectors. Asset managers and investors use the DAX 30 as the benchmark to compare performance of their portfolios to that of the market as a whole. It is used as gauge of investor sentiment toward the nation’s businesses and financial markets as well as a barometer for the health of the German economy.

Financial products around the DAX 30 index

There are various financial products available that allow investors to gain exposure to German equity market through the DAX 30 index.

  • ETFs are investment funds traded on stock exchanges which are designed to track the performance of an index. Some of the ETFs that track the DAX 30 index include the iShares DAX UCITS and the X Trackers DAX UCITS.
  • Index funds are designed to track the performance of the index. Examples of the index funds based on the DAX 30 index include the DWS Deutschland Index Fund and the Allianz DAX Index Fund.
  • Futures and options contracts based on the DAX 30 index provide investors with ability to speculate on the future performance of the index. Eurex offers futures and options contracts based on the DAX 30 index.
  • Certificates are investment products allowing investors to gain exposure to the DAX 30 index. Commerzbank offers a range of certificates linked to the DAX 30 index, such as the ComStage DAX UCITS ETF.

Overall, these financial products offer investors the ability to diversify their portfolios and gain exposure to German equity market, as well as potentially benefit from the performance of the DAX 30 index.

Historical data for the DAX 30 index

How to get the data?

The DAX 30 index is the most common index used in finance, and historical data for the DAX 30 index can be easily downloaded from the internet.

For example, you can download data for the DAX 30 index from December 30, 1987 on Yahoo! Finance (the Yahoo! code for DAX 30 index is ^GDAXI).

Yahoo! Finance
Source: Yahoo! Finance.

You can also download the same data from a Bloomberg terminal.

R program

The R program below written by Shengyu ZHENG allows you to download the data from Yahoo! Finance website and to compute summary statistics and risk measures about the DAX 30 index.

Download R file

Data file

The R program that you can download above allows you to download the data for the DAX 30 index from the Yahoo! Finance website. The database starts on December 30, 1987. It also computes the returns (logarithmic returns) from closing prices.

Table 3 below represents the top of the data file for the DAX 30 index downloaded from the Yahoo! Finance website with the R program.

Table 3. Top of the data file for the DAX 30 index.
Top of the file for the DAX 30 index data
Source: computation by the author (data: Yahoo! Finance website).

Evolution of the DAX 30 index

Figure 1 below gives the evolution of the DAX 30 index from December 30, 1987 to December 30, 2022 on a daily basis.

Figure 1. Evolution of the DAX 30 index.
Evolution of the DAX 30 index
Source: computation by the author (data: Yahoo! Finance website).

Figure 2 below gives the evolution of the DAX 30 index returns from December 30, 1987 to December 30, 2022 on a daily basis.

Figure 2. Evolution of the DAX 30 index returns.
Evolution of the DAX 30 index return
Source: computation by the author (data: Yahoo! Finance website).

Summary statistics for the DAX 30 index

The R program that you can download above also allows you to compute summary statistics about the returns of the DAX 30 index.

Table 4 below presents the following summary statistics estimated for the DAX 30 index:

  • The mean
  • The standard deviation (the squared root of the variance)
  • The skewness
  • The kurtosis.

The mean, the standard deviation / variance, the skewness, and the kurtosis refer to the first, second, third and fourth moments of statistical distribution of returns respectively.

Table 4. Summary statistics for the DAX 30 index.
Summary statistics for the DAX 30 index
Source: computation by the author (data: Yahoo! Finance website).

Statistical distribution of the DAX 30 index returns

Historical distribution

Figure 3 represents the historical distribution of the DAX 30 index daily returns for the period from December 30, 1987 to December 30, 2022.

Figure 3. Historical distribution of the DAX 30 index returns.
Historical distribution of the daily DAX 30 index returns
Source: computation by the author (data: Yahoo! Finance website).

Gaussian distribution

The Gaussian distribution (also called the normal distribution) is a parametric distribution with two parameters: the mean and the standard deviation of returns. We estimated these two parameters over the period from December 30, 1987 to December 30, 2022. The mean of daily returns is equal to 0.02% and the standard deviation of daily returns is equal to 1.37% (or equivalently 3.94% for the annual mean and 28.02% for the annual standard deviation as shown in Table 3 above).

Figure 4 below represents the Gaussian distribution of the DAX 30 index daily returns with parameters estimated over the period from v to December 30, 2022.

Figure 4. Gaussian distribution of the DAX 30 index returns.
Gaussian distribution of the daily DAX 30 index returns
Source: computation by the author (data: Yahoo! Finance website).

Risk measures of the DAX 30 index returns

The R program that you can download above also allows you to compute risk measures about the returns of the DAX 30 index.

Table 5 below presents the following risk measures estimated for the DAX 30 index:

  • The long-term volatility (the unconditional standard deviation estimated over the entire period)
  • The short-term volatility (the standard deviation estimated over the last three months)
  • The Value at Risk (VaR) for the left tail (the 5% quantile of the historical distribution)
  • The Value at Risk (VaR) for the right tail (the 95% quantile of the historical distribution)
  • The Expected Shortfall (ES) for the left tail (the average loss over the 5% quantile of the historical distribution)
  • The Expected Shortfall (ES) for the right tail (the average loss over the 95% quantile of the historical distribution)
  • The Stress Value (SV) for the left tail (the 1% quantile of the tail distribution estimated with a Generalized Pareto distribution)
  • The Stress Value (SV) for the right tail (the 99% quantile of the tail distribution estimated with a Generalized Pareto distribution)

Table 5. Risk measures for the DAX 30 index.
Risk measures for the DAX 30 index
Source: computation by the author (data: Yahoo! Finance website).

The volatility is a global measure of risk as it considers all the returns. The Value at Risk (VaR), Expected Shortfall (ES) and Stress Value (SV) are local measures of risk as they focus on the tails of the distribution. The study of the left tail is relevant for an investor holding a long position in the DAX 30 index while the study of the right tail is relevant for an investor holding a short position in the DAX 30 index.

Why should I be interested in this post?

For a number of reasons, management students (as future managers and individual investors) should learn about the DAX 30 index. The index includes wide range of industries, including energy, finance, telecommunications, and consumer goods, and it covers the biggest and most liquid German companies. Understanding how the index is constructed, how it performs, and the companies that make up the index is important for anyone studying finance or business in Russia or interested in investing in German equities.

Individual investors can assess the performance of their own investments in the German equity market with the DAX 30 index. Last but not least, a lot of asset management firms base their mutual funds and exchange-traded funds (ETFs) on the DAX 30 index which can considered as interesting assets to diversify a portfolio. Learning about these products and their portfolio and risk management applications can be valuable for management students.

Related posts on the SimTrade blog

About financial indexes

   ▶ Nithisha CHALLA Financial indexes

   ▶ Nithisha CHALLA Calculation of financial indexes

   ▶ Nithisha CHALLA The business of financial indexes

   ▶ Nithisha CHALLA Float

Other financial indexes

   ▶ Nithisha CHALLA The S&P 500 index

   ▶ Nithisha CHALLA The FTSE 100 index

   ▶ Nithisha CHALLA The CAC 40 index

   ▶ Nithisha CHALLA The CSI 300 index

   ▶ Nithisha CHALLA The Nikkei 225 index

About portfolio management

   ▶ Youssef LOURAOUI Portfolio

   ▶ Jayati WALIA Returns

About statistics

   ▶ Shengyu ZHENG Moments de la distribution

   ▶ Shengyu ZHENG Mesures de risques

Useful resources

Academic research about risk

Longin F. (2000) From VaR to stress testing: the extreme value approach Journal of Banking and Finance, N°24, pp 1097-1130.

Longin F. (2016) Extreme events in finance: a handbook of extreme value theory and its applications Wiley Editions.

Business

CFI DAX Stock Index Explained

Wikipedia An introduction to the DAX 30 index

Avatrade Trade the DAX index

Data

Yahoo! Finance

Yahoo! Finance Historical data for the DAX 30 index

About the author

The article was written in May 2023 by Nithisha CHALLA (ESSEC Business School, Grande Ecole Program – Master in Management, 2021-2023).

The MOEX Russia index

by

The MOEX Russia index

Nithisha CHALLA

In this article, Nithisha CHALLA (ESSEC Business School, Grande Ecole Program – Master in Management, 2021-2023) presents the MOEX Russia index and details its characteristics.

The MOEX Russia index

The Moscow Exchange Russia Index (MOEX Russia Index) is market-capitalization-weighted index of the 50 biggest and most liquid companies listed on the Moscow Exchange. It was first presented in 1997 and serves as the benchmark index for the Russian stock market.

A wide range of sectors are covered by the MOEX Russia Index, including consumer goods, energy, finance, and telecommunications. By market capitalization, Gazprom, Sberbank, Lukoil, Novatek, and Tatneft were the top five index members as of September 2021.

The MOEX Russia Index is a market-capitalization-weighted index, which means that rather than using share price to determine a company’s weight in the index, it utilizes market capitalization. This enables it to depict the overall performance of the Russian equity market with greater accuracy.

Investors and asset managers frequently use the MOEX Russia Index as a benchmark to monitor the performance of the Russian equity market. ETFs and index funds are examples of financial products that are made to track the MOEX Russia Index.

The MOEX Russia Index has the ticker “IMOEX” in the financial sector.

Table 1 below gives the Top 10 stocks in the MOEX Russia index in terms of market capitalization as of January 31, 2023.

Table 1. Top 10 stocks in the MOEX Russia index.
Top 10 stocks in the MOEX Russia index
Source: computation by the author (data: Yahoo! Finance website).

Calculation of the MOEX Russia index value

As per the free-float methodology, which is used to calculate the MOEX Russia Index, each company’s weight in the index is determined by the percentage of its shares that are available for public trading rather than by its overall market capitalization. The goal of this methodology is to present a more accurate picture of the market value of each company.

The formula to compute the MOEX Russia is given by

Float Adjusted Market Capitalization Index value

Where I is the index value, k a given asset, K the number of assets in the index, Pk the market price of asset k, Nk the number of issued shares for asset k, Fk the float factor of asset k, and t the time of calculation of the index.

In a float-adjusted market-capitalization-weighted index, the weight of asset k is given by formula can be rewritten as

Float Adjusted Market Capitalization Weighted Index Weight

Use of the MOEX Russia index in asset management

For asset managers who make investments in the Russian equity market, the MOEX Russia index serves as a crucial benchmark. It is used as an exchange-traded fund (ETF) and Russian equity fund performance benchmark. The index can be used by investors to assess the performance of their portfolios and compare it to the performance of the complete market.

Benchmark for equity funds

Equity funds that invest in Russian companies use the MOEX Russia Index as a benchmark. The MOEX Russia index can also serve as the foundation for the investment products that track indices, like index funds and ETFs. These goods are made to follow the index’s performance and give buyers access to Russian equity market. Investors can gain broad market exposure through the purchase of these products without picking individual stocks.

Financial products around the MOEX Russia index

There are several financial products tracking the performance of the MOEX Russia Index, allowing investors to gain exposure to the Russian stock market.

  • ETFs are investment funds traded on the stock exchanges, designed to track performance of an index. There are several ETFs that track the MOEX Russia Index, such as the Xtrackers Russia UCITS and the VanEck Vectors Russia
  • Index funds are designed to track performance of an index. Index funds based on the MOEX Russia Index include the Sberbank Asset Management MOEX Russia Index Fund and the Raiffeisen Russia Equity Fund.
  • Futures and options contracts based on the MOEX Russia Index provide investors with the ability to speculate on the future performance of the index. For example, the Moscow Exchange offers futures contracts based on the MOEX Russia Index.
  • Certificates are investment products that allow investors to get exposure to the MOEX Russia Index. Société Générale offers a range of certificates linked to the MOEX Russia Index, such as the MOEX Russia Index Tracker Certificate.

Historical data for the MOEX Russia index

How to get the data?

The MOEX Russia index is the most common index used in finance, and historical data for the MOEX Russia index can be easily downloaded from the internet.

For example, you can download data for the MOEX Russia index from January 3, 1984 on Yahoo! Finance (the Yahoo! code for MOEX Russia index is IMOEX.ME).

Yahoo! Finance
Source: Yahoo! Finance.

You can also download the same data from a Bloomberg terminal.

R program

The R program below written by Shengyu ZHENG allows you to download the data from Yahoo! Finance website and to compute summary statistics and risk measures about the MOEX Russia index.

Download R file

Data file

The R program that you can download above allows you to download the data for the MOEX Russia index from the Yahoo! Finance website. The database starts on January 3, 1984. It also computes the returns (logarithmic returns) from closing prices.

Table 3 below represents the top of the data file for the MOEX Russia index downloaded from the Yahoo! Finance website with the R program.

Table 3. Top of the data file for the MOEX Russia index.
Top of the file for the MOEX Russia index data
Source: computation by the author (data: Yahoo! Finance website).

Evolution of the MOEX Russia index

Figure 1 below gives the evolution of the MOEX Russia index from January 3, 1984 to December 30, 2022 on a daily basis.

Figure 1. Evolution of the MOEX Russia index.
Evolution of the MOEX Russia index
Source: computation by the author (data: Yahoo! Finance website).

Figure 2 below gives the evolution of the MOEX Russia index returns from January 3, 1984 to December 30, 2022 on a daily basis.

Figure 2. Evolution of the MOEX Russia index returns.
Evolution of the MOEX Russia index return
Source: computation by the author (data: Yahoo! Finance website).

Summary statistics for the MOEX Russia index

The R program that you can download above also allows you to compute summary statistics about the returns of the MOEX Russia index.

Table 4 below presents the following summary statistics estimated for the MOEX Russia index:

  • The mean
  • The standard deviation (the squared root of the variance)
  • The skewness
  • The kurtosis.

The mean, the standard deviation / variance, the skewness, and the kurtosis refer to the first, second, third and fourth moments of statistical distribution of returns respectively.

Table 4. Summary statistics for the MOEX Russia index.
Summary statistics for the MOEX Russia index
Source: computation by the author (data: Yahoo! Finance website).

Statistical distribution of the MOEX Russia index returns

Historical distribution

Figure 3 represents the historical distribution of the MOEX Russia index daily returns for the period from January 3, 1984 to December 30, 2022.

Figure 3. Historical distribution of the MOEX Russia index returns.
Historical distribution of the daily MOEX Russia index returns
Source: computation by the author (data: Yahoo! Finance website).

Gaussian distribution

The Gaussian distribution (also called the normal distribution) is a parametric distribution with two parameters: the mean and the standard deviation of returns. We estimated these two parameters over the period from January 3, 1984 to December 30, 2022. The mean of daily returns is equal to 0.02% and the standard deviation of daily returns is equal to 1.37% (or equivalently 3.94% for the annual mean and 28.02% for the annual standard deviation as shown in Table 3 above).

Figure 4 below represents the Gaussian distribution of the MOEX Russia index daily returns with parameters estimated over the period from January 3, 1984 to December 30, 2022.

Figure 4. Gaussian distribution of the MOEX Russia index returns.
Gaussian distribution of the daily MOEX Russia index returns
Source: computation by the author (data: Yahoo! Finance website).

Risk measures of the MOEX Russia index returns

The R program that you can download above also allows you to compute risk measures about the returns of the MOEX Russia index.

Table 5 below presents the following risk measures estimated for the MOEX Russia index:

  • The long-term volatility (the unconditional standard deviation estimated over the entire period)
  • The short-term volatility (the standard deviation estimated over the last three months)
  • The Value at Risk (VaR) for the left tail (the 5% quantile of the historical distribution)
  • The Value at Risk (VaR) for the right tail (the 95% quantile of the historical distribution)
  • The Expected Shortfall (ES) for the left tail (the average loss over the 5% quantile of the historical distribution)
  • The Expected Shortfall (ES) for the right tail (the average loss over the 95% quantile of the historical distribution)
  • The Stress Value (SV) for the left tail (the 1% quantile of the tail distribution estimated with a Generalized Pareto distribution)
  • The Stress Value (SV) for the right tail (the 99% quantile of the tail distribution estimated with a Generalized Pareto distribution)

Table 5. Risk measures for the MOEX Russia index.
Risk measures for the MOEX Russia index
Source: computation by the author (data: Yahoo! Finance website).

The volatility is a global measure of risk as it considers all the returns. The Value at Risk (VaR), Expected Shortfall (ES) and Stress Value (SV) are local measures of risk as they focus on the tails of the distribution. The study of the left tail is relevant for an investor holding a long position in the MOEX Russia index while the study of the right tail is relevant for an investor holding a short position in the MOEX Russia index.

Why should I be interested in this post?

For a number of reasons, management students (as future managers and individual investors) should learn about the MOEX Russia index. The index includes wide range of industries, including energy, finance, telecommunications, and consumer goods, and it covers the biggest and most liquid companies listed on the Moscow Exchange. Understanding how the index is constructed, how it performs, and the companies that make up the index is important for anyone studying finance or business in Russia or interested in investing in Russian equities.

Individual investors can assess the performance of their own investments in the Russian equity market with the MOEX Russia index. Last but not least, a lot of asset management firms base their mutual funds and exchange-traded funds (ETFs) on the MOEX Russia index which can considered as interesting assets to diversify a portfolio. Learning about these products and their portfolio and risk management applications can be valuable for management students.

Related posts on the SimTrade blog

About financial indexes

   ▶ Nithisha CHALLA Financial indexes

   ▶ Nithisha CHALLA Calculation of financial indexes

   ▶ Nithisha CHALLA The business of financial indexes

   ▶ Nithisha CHALLA Float

Other financial indexes

   ▶ Nithisha CHALLA The S&P 500 index

   ▶ Nithisha CHALLA The FTSE 100 index

   ▶ Nithisha CHALLA The Nikkei 225 index

   ▶ Nithisha CHALLA The CSI 300 index

About portfolio management

   ▶ Youssef LOURAOUI Portfolio

   ▶ Jayati WALIA Returns

About statistics

   ▶ Shengyu ZHENG Moments de la distribution

   ▶ Shengyu ZHENG Mesures de risques

Useful resources

Academic research about risk

Longin F. (2000) From VaR to stress testing: the extreme value approach Journal of Banking and Finance, N°24, pp 1097-1130.

Longin F. (2016) Extreme events in finance: a handbook of extreme value theory and its applications Wiley Editions.

Business

wikipedia What is the MOEX Russia index?

Moex Everything about MOEX

Data

Yahoo! Finance

Yahoo! Finance MOEX Russia index

About the author

The article was written in May 2023 by Nithisha CHALLA (ESSEC Business School, Grande Ecole Program – Master in Management, 2021-2023).

The BOVESPA index

by

The BOVESPA index

Nithisha CHALLA

In this article, Nithisha CHALLA (ESSEC Business School, Grande Ecole Program – Master in Management, 2021-2023) presents the BOVESPA index and details its characteristics.

The BOVESPA index

The BOVESPA Index, or IBOVESPA, is the benchmark stock market index of the São Paulo Stock Exchange (B3) in Brazil. The index was launched on January 2, 1968, and tracks the performance of the 80 most traded stocks on the exchange.

As of 2021, the top 10 constituents of the BOVESPA Index included companies from a range of sectors such as finance, energy, materials, and consumer goods. Some of the largest companies in the index include Petrobras, Vale, Itau Unibanco, and Banco Bradesco.

The BOVESPA Index is considered a crucial indicator of the Brazilian stock market’s overall health and serves as a benchmark for Brazilian equity mutual funds and exchange-traded funds (ETFs). The index is weighted by free float market capitalization, which means that the more valuable a company is, the more significant its impact on the index’s movements.

The BOVESPA Index has experienced significant fluctuations in the past due to factors such as political instability, economic crises, and shifts in global commodity prices. Trading platforms and financial websites represent the BOVESPA Index using the ticker symbol “IBOV”.

Table 1 below gives the Top 10 stocks in the BOVESPA index in terms of market capitalization as of January 31, 2023.

Table 1. Top 10 stocks in the BOVESPA index.
Top 10 stocks in the BOVESPA index
Source: computation by the author (data: Yahoo! Finance website).

Calculation of the BOVESPA index value

The index is a market-capitalization-weighted index, which means that the weight of each company in the index is determined by its market capitalization, calculated by multiplying the number of outstanding shares by the current market price per share. It tracks the performance of the largest and most actively traded companies listed on the Sao Paulo Stock Exchange (B3).

The formula to compute the BOVESPA index is given by

Market Capitalization Index value

Where I is the index value, k a given asset, K the number of assets in the index, Pk the market price of asset k, Nk the number of issued shares for asset k, and t the time of calculation of the index.

In a market capitalization-weighted index, the weight of asset k is given by formula can be rewritten as

Market Capitalization Weighted Index Weight

Which clearly shows that the weight of each asset in the index is its market capitalization of the asset divided by the sum of the market capitalizations of all assets.

Note that the divisor, whose calculation is based on the number of shares, is typically adjusted for events such as stock splits and dividends. The divisor is used to ensure that the value of the index remains consistent over time despite changes in the number of outstanding shares.

Use of the BOVESPA index in asset management

The BOVESPA Index is frequently used by investors, analysts, and financial institutions to track the overall trend of the Brazilian stock market and to make investment decisions. It is also used as a basis for the creation of financial products such as exchange-traded funds (ETFs) and index futures contracts.

Benchmark for equity funds

The BOVESPA index is widely considered as the benchmark index for the Brazilian stock market and is used as a measure of the performance of the Brazilian economy. It includes a diverse range of companies from various sectors such as finance, mining, energy, and consumer goods. Some of the largest companies listed on the BOVESPA Index include Petrobras, Vale, Itau Unibanco, and Banco Bradesco.

Financial products around the BOVESPA index

There are various financial instruments available to investors seeking to track the performance of the BOVESPA index.

  • ETFs are popular investment products that allow investors to gain exposure to the BOVESPA index. These include the iShares MSCI Brazil ETF and the BMO MSCI Brazil Index ETF.
  • Index funds are also designed to track the performance of an index. The BlackRock Brazil Equity Index Fund and the Bradesco FIA BOVESPA Index Fund are examples of index funds that track the BOVESPA index.
  • Futures and options contracts based on the BOVESPA index provide investors with the ability to speculate on the future performance of the index. BM&FBOVESPA, the Brazilian futures and options exchange, offers futures contracts based on the BOVESPA index.
  • Certificates are investment products that allow investors to gain exposure to the BOVESPA index. Credit Suisse and Itau Unibanco offer certificates linked to the BOVESPA index, such as the Brazil Index Tracker Certificate.

Historical data for the BOVESPA index

How to get the data?

The BOVESPA index is the most common index used in finance, and historical data for the BOVESPA index can be easily downloaded from the internet.

For example, you can download data for the BOVESPA index from January 3, 1984 on Yahoo! Finance (the Yahoo! code for BOVESPA index is ^NSEI).

Yahoo! Finance
Source: Yahoo! Finance.

You can also download the same data from a Bloomberg terminal.

R program

The R program below written by Shengyu ZHENG allows you to download the data from Yahoo! Finance website and to compute summary statistics and risk measures about the BOVESPA index.

Download R file

Data file

The R program that you can download above allows you to download the data for the BOVESPA index from the Yahoo! Finance website. The database starts on January 3, 1984. It also computes the returns (logarithmic returns) from closing prices.

Table 3 below represents the top of the data file for the BOVESPA index downloaded from the Yahoo! Finance website with the R program.

Table 3. Top of the data file for the BOVESPA index.
Top of the file for the BOVESPA index data
Source: computation by the author (data: Yahoo! Finance website).

Evolution of the BOVESPA index

Figure 1 below gives the evolution of the BOVESPA index from January 3, 1984 to December 30, 2022 on a daily basis.

Figure 1. Evolution of the BOVESPA index.
Evolution of the BOVESPA index
Source: computation by the author (data: Yahoo! Finance website).

Figure 2 below gives the evolution of the BOVESPA index returns from January 3, 1984 to December 30, 2022 on a daily basis.

Figure 2. Evolution of the BOVESPA index returns.
Evolution of the BOVESPA index return
Source: computation by the author (data: Yahoo! Finance website).

Summary statistics for the BOVESPA index

The R program that you can download above also allows you to compute summary statistics about the returns of the BOVESPA index.

Table 4 below presents the following summary statistics estimated for the BOVESPA index:

  • The mean
  • The standard deviation (the squared root of the variance)
  • The skewness
  • The kurtosis.

The mean, the standard deviation / variance, the skewness, and the kurtosis refer to the first, second, third and fourth moments of statistical distribution of returns respectively.

Table 4. Summary statistics for the BOVESPA index.
Summary statistics for the BOVESPA index
Source: computation by the author (data: Yahoo! Finance website).

Statistical distribution of the BOVESPA index returns

Historical distribution

Figure 3 represents the historical distribution of the BOVESPA index daily returns for the period from January 3, 1984 to December 30, 2022.

Figure 3. Historical distribution of the BOVESPA index returns.
Historical distribution of the daily BOVESPA index returns
Source: computation by the author (data: Yahoo! Finance website).

Gaussian distribution

The Gaussian distribution (also called the normal distribution) is a parametric distribution with two parameters: the mean and the standard deviation of returns. We estimated these two parameters over the period from January 3, 1984 to December 30, 2022. The mean of daily returns is equal to 0.02% and the standard deviation of daily returns is equal to 1.37% (or equivalently 3.94% for the annual mean and 28.02% for the annual standard deviation as shown in Table 3 above).

Figure 4 below represents the Gaussian distribution of the BOVESPA index daily returns with parameters estimated over the period from January 3, 1984 to December 30, 2022.

Figure 4. Gaussian distribution of the BOVESPA index returns.
Gaussian distribution of the daily BOVESPA index returns
Source: computation by the author (data: Yahoo! Finance website).

Risk measures of the BOVESPA index returns

The R program that you can download above also allows you to compute risk measures about the returns of the BOVESPA index.

Table 5 below presents the following risk measures estimated for the BOVESPA index:

  • The long-term volatility (the unconditional standard deviation estimated over the entire period)
  • The short-term volatility (the standard deviation estimated over the last three months)
  • The Value at Risk (VaR) for the left tail (the 5% quantile of the historical distribution)
  • The Value at Risk (VaR) for the right tail (the 95% quantile of the historical distribution)
  • The Expected Shortfall (ES) for the left tail (the average loss over the 5% quantile of the historical distribution)
  • The Expected Shortfall (ES) for the right tail (the average loss over the 95% quantile of the historical distribution)
  • The Stress Value (SV) for the left tail (the 1% quantile of the tail distribution estimated with a Generalized Pareto distribution)
  • The Stress Value (SV) for the right tail (the 99% quantile of the tail distribution estimated with a Generalized Pareto distribution)

Table 5. Risk measures for the BOVESPA index.
Risk measures for the BOVESPA index
Source: computation by the author (data: Yahoo! Finance website).

The volatility is a global measure of risk as it considers all the returns. The Value at Risk (VaR), Expected Shortfall (ES) and Stress Value (SV) are local measures of risk as they focus on the tails of the distribution. The study of the left tail is relevant for an investor holding a long position in the BOVESPA index while the study of the right tail is relevant for an investor holding a short position in the BOVESPA index.

Why should I be interested in this post?

For a number of reasons, management students (as future managers and individual investors) should learn about the BOVESPA index. The BOVESPA index is a key benchmark for the Indian equity market, which is a fast developing market. Understanding how the index is constructed, how it performs, and the companies that make up the index is important for anyone studying finance or business in India or interested in investing in Indian equities.

Individual investors can assess the performance of their own investments in the Japanese equity market with the BOVESPA index. Last but not least, a lot of asset management firms base their mutual funds and exchange-traded funds (ETFs) on the BOVESPA index which can considered as interesting assets to diversify a portfolio. Learning about these products and their portfolio and risk management applications can be valuable for management students.

Related posts on the SimTrade blog

About financial indexes

   ▶ Nithisha CHALLA Financial indexes

   ▶ Nithisha CHALLA Calculation of financial indexes

   ▶ Nithisha CHALLA The business of financial indexes

   ▶ Nithisha CHALLA Float

Other financial indexes

   ▶ Nithisha CHALLA The S&P 500 index

   ▶ Nithisha CHALLA The FTSE 100 index

   ▶ Nithisha CHALLA The CSI 300 index

   ▶ Nithisha CHALLA The Nikkei 225 index

About portfolio management

   ▶ Youssef LOURAOUI Portfolio

   ▶ Jayati WALIA Returns

About statistics

   ▶ Shengyu ZHENG Moments de la distribution

   ▶ Shengyu ZHENG Mesures de risques

Useful resources

Academic research about risk

Longin F. (2000) From VaR to stress testing: the extreme value approach Journal of Banking and Finance, N°24, pp 1097-1130.

Longin F. (2016) Extreme events in finance: a handbook of extreme value theory and its applications Wiley Editions.

Business

Capital What is the Bovespa index?

Wikipedia An introduction to the Bovespa

International Finance Corporation Everything about Bovespa

Data

Yahoo! Finance

Yahoo! Finance BOVESPA index

About the author

The article was written in May 2023 by Nithisha CHALLA (ESSEC Business School, Grande Ecole Program – Master in Management, 2021-2023).

The Nifty 50 index

by

The Nifty 50 index

Nithisha CHALLA

In this article, Nithisha CHALLA (ESSEC Business School, Grande Ecole Program – Master in Management, 2021-2023) presents the Nifty 50 index and details its characteristics.

The Nifty 50 index

One of the important stock market indices in India is the Nifty 50 index, also referred to as the NSE Nifty. The National Stock Exchange (NSE) of India first introduced this index in 1996, and it currently measures the performance of the top 50 companies listed on the exchange.

Market capitalization, liquidity, and trading volumes are just a few of the criteria that are used to choose the companies that will be included in the Nifty 50 index. The index’s companies come from a variety of industries, including, among others, banking, IT, healthcare, and energy.

The Nifty50 is a free float market capitalization-weighted index, which means that the market capitalization of each stock determines how much of that stock is included in the index. In comparison to a price-weighted index, the Nifty 50 is a better representation of the Indian stock market as a whole because of this.

Indian mutual funds, exchange-traded funds, and other financial products frequently use the Nifty 50 index as a benchmark. Since it offers insightful information about how the Indian economy and stock market are performing, it is also closely watched by investors and traders worldwide.

The ticker symbol used for the Nifty 50 index is “NIFTY”.

Table 1 below gives the Top 10 stocks in the Nifty 50 index in terms of market capitalization as of January 31, 2023.

Table 1. Top 10 stocks in the Nifty 50 index.
Top 10 stocks in the Nifty 50 index
Source: computation by the author (data: Yahoo Finance! financial website).

Calculation of the Nifty 50 index value

The top 50 companies listed on the National Stock Exchange (NSE) of India are tracked by the Nifty 50 stock market index in India. It is frequently used as the benchmark index for the Indian equity market and as a gauge of the state of the Indian economy as a whole. Companies from a variety of industries, including financial services, information technology, energy, and consumer goods, make up the Nifty50 index.

A free-float market-capitalization-weighted methodology is utilized to calculate the Nifty 50 index, which means that each company’s weight in the index is determined by its market capitalization adjusted for the shares that are actually traded in the secondary market (float).

The formula to compute the Nifty 50 index is given by

Float Adjusted Market Capitalization Index value

where I is the index value, k a given asset, K the number of assets in the index, Pk the market price of asset k, Nk the number of issued shares for asset k, Fk the float factor of asset k, and t the time of calculation of the index.

In a float-adjusted market-capitalization-weighted index, the weight of asset k is given by formula can be rewritten as

Float Adjusted Market Capitalization Weighted Index Weight

Use of the Nifty 50 index in asset management

The Nifty 50 serves as a benchmark for asset managers to assess the performance of their Indian equity portfolios. Asset managers can determine whether their investments are producing alpha, or outperforming the market, by comparing the returns of their portfolios to the performance of the index. If their portfolios underperform the index, they might need to adjust their stock selection or investment strategies to boost returns.

Benchmark for equity funds

In India, the Nifty 50 is frequently used as a benchmark for equity funds. By reflecting the performance of the top 50 companies listed on the National Stock Exchange of India, the index offers a snapshot of the performance of the Indian stock market. Investors can learn how well their investment is doing relative to the market by comparing the performance of a fund to the Nifty 50. If a fund consistently outperforms the index, the asset manager likely has a sound investment strategy and is adept at stock selection and market timing.

Financial products around the Nifty 50 index

There are several financial products that track the performance of the Nifty 50 index, allowing investors to gain exposure to the Indian stock market.

  • ETFs are investment funds traded on stock exchanges, designed to track the performance of an index. There are several ETFs that track the Nifty 50 index, such as the ICICI Prudential Nifty ETF and the Kotak Nifty ETF.
  • Index funds are also designed to track the performance of an index. Index funds based on the Nifty50 index include the HDFC Index Fund-Nifty 50 Plan and the UTI Nifty Index Fund.
  • Futures and options contracts based on the Nifty 50 index provide investors with the ability to speculate on the future performance of the index. For example, the National Stock Exchange of India (NSE) offers futures contracts based on the Nifty 50 index.
  • Certificates are investment products that allow investors to gain exposure to the Nifty50 index. Some banks in India offer certificates linked to the Nifty 50 index, such as the SBI Magnum Nifty Next 50 Index Fund.

With the help of these financial products, investors can invest in a diversified portfolio of 50 large-cap Indian companies from a range of industries and get exposure to the performance of the Nifty 50 index. Investors can gain a deeper understanding of industry trends, market competition, and the elements that contribute to business success by examining the performance of companies within these sectors. Asset managers can use these financial products as a benchmark to compare the performance of their equity portfolios to the performance of the entire market.

Historical data for the Nifty 50 index

How to get the data?

The Nifty 50 index is the most common index used in finance, and historical data for the Nifty 50 index can be easily downloaded from the internet.

For example, you can download data for the Nifty 50 index from January 3, 1984 on Yahoo! Finance (the Yahoo! code for Nifty 50 index is ^NSEI).

Yahoo! Finance
Source: Yahoo! Finance.

You can also download the same data from a Bloomberg terminal.

R program

The R program below written by Shengyu ZHENG allows you to download the data from Yahoo! Finance website and to compute summary statistics and risk measures about the Nifty 50 index.

Download R file

Data file

The R program that you can download above allows you to download the data for the Nifty 50 index from the Yahoo! Finance website. The database starts on January 3, 1984. It also computes the returns (logarithmic returns) from closing prices.

Table 3 below represents the top of the data file for the Nifty 50 index downloaded from the Yahoo! Finance website with the R program.

Table 3. Top of the data file for the Nifty 50 index.
Top of the file for the Nifty 50 index data
Source: computation by the author (data: Yahoo! Finance website).

Evolution of the Nifty 50 index

Figure 1 below gives the evolution of the Nifty 50 index from January 3, 1984 to December 30, 2022 on a daily basis.

Figure 1. Evolution of the Nifty 50 index.
Evolution of the Nifty 50 index
Source: computation by the author (data: Yahoo! Finance website).

Figure 2 below gives the evolution of the Nifty 50 index returns from January 3, 1984 to December 30, 2022 on a daily basis.

Figure 2. Evolution of the Nifty 50 index returns.
Evolution of the Nifty 50 index return
Source: computation by the author (data: Yahoo! Finance website).

Summary statistics for the Nifty 50 index

The R program that you can download above also allows you to compute summary statistics about the returns of the Nifty 50 index.

Table 4 below presents the following summary statistics estimated for the Nifty 50 index:

  • The mean
  • The standard deviation (the squared root of the variance)
  • The skewness
  • The kurtosis.

The mean, the standard deviation / variance, the skewness, and the kurtosis refer to the first, second, third and fourth moments of statistical distribution of returns respectively.

Table 4. Summary statistics for the Nifty 50 index.
Summary statistics for the Nifty 50 index
Source: computation by the author (data: Yahoo! Finance website).

Statistical distribution of the Nifty 50 index returns

Historical distribution

Figure 3 represents the historical distribution of the Nifty 50 index daily returns for the period from January 3, 1984 to December 30, 2022.

Figure 3. Historical distribution of the Nifty 50 index returns.
Historical distribution of the daily Nifty 50 index returns
Source: computation by the author (data: Yahoo! Finance website).

Gaussian distribution

The Gaussian distribution (also called the normal distribution) is a parametric distribution with two parameters: the mean and the standard deviation of returns. We estimated these two parameters over the period from January 3, 1984 to December 30, 2022. The mean of daily returns is equal to 0.02% and the standard deviation of daily returns is equal to 1.37% (or equivalently 3.94% for the annual mean and 28.02% for the annual standard deviation as shown in Table 3 above).

Figure 4 below represents the Gaussian distribution of the Nifty 50 index daily returns with parameters estimated over the period from January 3, 1984 to December 30, 2022.

Figure 4. Gaussian distribution of the Nifty 50 index returns.
Gaussian distribution of the daily Nifty 50 index returns
Source: computation by the author (data: Yahoo! Finance website).

Risk measures of the Nifty 50 index returns

The R program that you can download above also allows you to compute risk measures about the returns of the Nifty 50 index.

Table 5 below presents the following risk measures estimated for the Nifty 50 index:

  • The long-term volatility (the unconditional standard deviation estimated over the entire period)
  • The short-term volatility (the standard deviation estimated over the last three months)
  • The Value at Risk (VaR) for the left tail (the 5% quantile of the historical distribution)
  • The Value at Risk (VaR) for the right tail (the 95% quantile of the historical distribution)
  • The Expected Shortfall (ES) for the left tail (the average loss over the 5% quantile of the historical distribution)
  • The Expected Shortfall (ES) for the right tail (the average loss over the 95% quantile of the historical distribution)
  • The Stress Value (SV) for the left tail (the 1% quantile of the tail distribution estimated with a Generalized Pareto distribution)
  • The Stress Value (SV) for the right tail (the 99% quantile of the tail distribution estimated with a Generalized Pareto distribution)

Table 5. Risk measures for the Nifty 50 index.
Risk measures for the Nifty 50 index
Source: computation by the author (data: Yahoo! Finance website).

The volatility is a global measure of risk as it considers all the returns. The Value at Risk (VaR), Expected Shortfall (ES) and Stress Value (SV) are local measures of risk as they focus on the tails of the distribution. The study of the left tail is relevant for an investor holding a long position in the Nifty 50 index while the study of the right tail is relevant for an investor holding a short position in the Nifty 50 index.

Why should I be interested in this post?

For a number of reasons, management students (as future managers and individual investors) should learn about the Nifty 50 index. The Nifty 50 index is a key benchmark for the Indian equity market, which is a fast developing market. Understanding how the index is constructed, how it performs, and the companies that make up the index is important for anyone studying finance or business in India or interested in investing in Indian equities.

Individual investors can assess the performance of their own investments in the Japanese equity market with the Nifty 50 index. Last but not least, a lot of asset management firms base their mutual funds and exchange-traded funds (ETFs) on the Nifty 50 index which can considered as interesting assets to diversify a portfolio. Learning about these products and their portfolio and risk management applications can be valuable for management students.

Related posts on the SimTrade blog

About financial indexes

   ▶ Nithisha CHALLA Financial indexes

   ▶ Nithisha CHALLA Calculation of financial indexes

   ▶ Nithisha CHALLA The business of financial indexes

   ▶ Nithisha CHALLA Float

Other financial indexes

   ▶ Nithisha CHALLA The S&P 500 index

   ▶ Nithisha CHALLA The FTSE 100 index

   ▶ Nithisha CHALLA The CSI 300 index

   ▶ Nithisha CHALLA The Nikkei 225 index

About portfolio management

   ▶ Youssef LOURAOUI Portfolio

   ▶ Jayati WALIA Returns

About statistics

   ▶ Shengyu ZHENG Moments de la distribution

   ▶ Shengyu ZHENG Mesures de risques

Useful resources

Academic research about risk

Longin F. (2000) From VaR to stress testing: the extreme value approach Journal of Banking and Finance, N°24, pp 1097-1130.

Longin F. (2016) Extreme events in finance: a handbook of extreme value theory and its applications Wiley Editions.

Business

CFI What is the NIFTY 50 Index?

Wikipedia An introduction to the NIFTY 50

NSE India 25 years journey of NSE

Data

Yahoo! Finance

Yahoo! Finance Nifty 50 index

About the author

The article was written in May 2023 by Nithisha CHALLA (ESSEC Business School, Grande Ecole Program – Master in Management, 2021-2023).

The CSI 300 index

by

The CSI 300 index

Nithisha CHALLA

In this article, Nithisha CHALLA (ESSEC Business School, Grande Ecole Program – Master in Management, 2021-2023) presents the CSI 300 index and details its characteristics.

The CSI 300 index

The performance of 300 large-cap stocks traded on the Shanghai and Shenzhen stock exchanges in China is tracked by the capitalization-weighted stock market index known as the CSI 300 (China Securities Index 300). The China Securities Index Company, a joint venture between the Shanghai Stock Exchange and the Shenzhen Stock Exchange, introduced it in April 2005.

The CSI 300’s members are chosen based on their free float market capitalization, liquidity, as well as other aspects like profitability, potential for growth, and financial soundness. Companies from a wide range of industries, including finance, consumer goods, energy, and technology are included in the index.

The CSI 300 is frequently used by traders and investors as a benchmark for the Chinese stock market to gauge market trends and assess portfolio performance. As a measure of the health of China’s economy and of investor perception of the nation’s companies and financial markets, it is also closely watched by policymakers, economists, and analysts. The performance of the Chinese economy can be closely tracked by both domestic and foreign investors thanks to the CSI 300.

Through a range of financial products, including exchange-traded funds (ETFs), index funds, futures, and options contracts, investors can get exposure to the CSI 300 index.

The CSI 300 index has the ticker symbol “CSI300” in the financial sector.

Table 1 below gives the Top 10 stocks in the CSI 300 index in terms of market capitalization as of January 31, 2023.

Table 1. Top 10 stocks in the CSI 300 index.
Top 10 stocks in the CSI 300 index
Source: computation by the author (data: Yahoo Finance! financial website).

Table 2 below gives the sector representation of the CSI 300 index in terms of number of stocks and market capitalization as of January 31, 2023.

Table 2. Sector representation in the CSI 300 index.
Sector representation in the CSI 300 index
Source: computation by the author (data: Yahoo Finance! financial website).

Calculation of the CSI 300 index value

The China Securities Index Company, a joint venture between the Shanghai Stock Exchange and the Shenzhen Stock Exchange, is in charge of managing the index.

A free-float market-capitalization-weighted methodology is utilized to calculate the CSI 300 index, which means that each company’s weight in the index is determined by its market capitalization adjusted for the shares that are actually traded in the secondary market (float).

The formula to compute the CSI 300 index is given by

Float Adjusted Market Capitalization Index value

where I is the index value, k a given asset, K the number of assets in the index, Pk the market price of asset k, Nk the number of issued shares for asset k, Fk the float factor of asset k, and t the time of calculation of the index.

In a float-adjusted market-capitalization-weighted index, the weight of asset k is given by formula can be rewritten as

Float Adjusted Market Capitalization Weighted Index Weight

Use of the CSI 300 index in asset management

The performance of the biggest and most liquid stocks listed on the Shanghai and Shenzhen stock exchanges is frequently monitored by investors using the CSI 300 index, which serves as a benchmark for the Chinese equity market. Asset managers use the index to compare the returns on their portfolios to market returns and to decide which investments to make. The CSI 300 index, which is focused on China’s domestic A-share market, may not accurately reflect the entire Chinese market, it is important to note. To gain a deeper understanding of the Chinese equity market, investors should also take into account other indexes like the MSCI China index and the FTSE China index.

Benchmark for equity funds

We must take into account the index’s makeup in order to determine whether the CSI 300 index serves as a benchmark for equity funds in China. The top 300 companies listed on the Shanghai and Shenzhen stock exchanges, which together make up about 70% of the total market capitalization of the Chinese equity market, are represented by the CSI 300 index. The index provides a thorough representation of the Chinese economy by including businesses from a wide range of industries, including financial, industrial, consumer goods, and technology.

As a result, equity funds that invest in the Chinese equity market frequently use the CSI 300 index as a benchmark. Fund managers can assess their performance by comparing the returns on their investments to the returns produced by the index.

Financial products around the CSI 300 index

There are various financial products available to investors who wish to gain exposure to the Chinese stock market through the CSI 300 index.

  • ETFs are investment funds traded on stock exchanges that aim to track the performance of an index. There are several ETFs that track the CSI 300 index, such as the iShares CSI 300 Index ETF and the China AMC CSI 300 Index ETF.
  • Index funds are similar to ETFs in that they aim to track the performance of an index. Some examples of index funds that track the CSI 300 index include the E Fund CSI 300 Index Fund and the China Southern CSI 300 Index Fund.
  • Futures and options contracts based on the CSI 300 index allow investors to speculate on the future performance of the index. The China Financial Futures Exchange offers futures contracts based on the CSI 300 index.
  • Certificates linked to the CSI 300 index are investment products that offer exposure to the index. China Merchants Bank, for example, offers a range of certificates linked to the CSI 300 index.

Historical data for the CSI 300 index

How to get the data?

The CSI 300 index is the most common index used in finance, and historical data for the CSI 300 index can be easily downloaded from the internet.

For example, you can download data for the CSI 300 index from March 11, 2021 on Yahoo! Finance (the Yahoo! code for CSI 300 index is 000300.SS).

Yahoo! Finance
Source: Yahoo! Finance.

You can also download the same data from a Bloomberg terminal.

R program

The R program below written by Shengyu ZHENG allows you to download the data from Yahoo! Finance website and to compute summary statistics and risk measures about the CSI 300 index.

Download R file

Data file

The R program that you can download above allows you to download the data for the CSI 300 index from the Yahoo! Finance website. The database starts on March 11, 2021. It also computes the returns (logarithmic returns) from closing prices.

Table 3 below represents the top of the data file for the CSI 300 index downloaded from the Yahoo! Finance website with the R program.

Table 3. Top of the data file for the CSI 300 index.
Top of the file for the CSI 300 index data
Source: computation by the author (data: Yahoo! Finance website).

Evolution of the CSI 300 index

Figure 1 below gives the evolution of the CSI 300 index from March 11, 2021 to December 30, 2022 on a daily basis.

Figure 1. Evolution of the CSI 300 index.
Evolution of the CSI 300 index
Source: computation by the author (data: Yahoo! Finance website).

Figure 2 below gives the evolution of the CSI 300 index returns from March 11, 2021 to December 30, 2022 on a daily basis.

Figure 2. Evolution of the CSI 300 index returns.
Evolution of the CSI 300 index return
Source: computation by the author (data: Yahoo! Finance website).

Summary statistics for the CSI 300 index

The R program that you can download above also allows you to compute summary statistics about the returns of the CSI 300 index.

Table 4 below presents the following summary statistics estimated for the CSI 300 index:

  • The mean
  • The standard deviation (the squared root of the variance)
  • The skewness
  • The kurtosis.

The mean, the standard deviation / variance, the skewness, and the kurtosis refer to the first, second, third and fourth moments of statistical distribution of returns respectively.

Table 4. Summary statistics for the CSI 300 index.
Summary statistics for the CSI 300 index
Source: computation by the author (data: Yahoo! Finance website).

Statistical distribution of the CSI 300 index returns

Historical distribution

Figure 3 represents the historical distribution of the CSI 300 index daily returns for the period from March 11, 2021 to December 30, 2022.

Figure 3. Historical distribution of the CSI 300 index returns.
Historical distribution of the daily CSI 300 index returns
Source: computation by the author (data: Yahoo! Finance website).

Gaussian distribution

The Gaussian distribution (also called the normal distribution) is a parametric distribution with two parameters: the mean and the standard deviation of returns. We estimated these two parameters over the period from March 11, 2021 to December 30, 2022. The mean of daily returns is equal to 0.02% and the standard deviation of daily returns is equal to 1.37% (or equivalently 3.94% for the annual mean and 28.02% for the annual standard deviation as shown in Table 3 above).

Figure 4 below represents the Gaussian distribution of the CSI 300 index daily returns with parameters estimated over the period from March 11, 2021 to December 30, 2022.

Figure 4. Gaussian distribution of the CSI 300 index returns.
Gaussian distribution of the daily CSI 300 index returns
Source: computation by the author (data: Yahoo! Finance website).

Risk measures of the CSI 300 index returns

The R program that you can download above also allows you to compute risk measures about the returns of the CSI 300 index.

Table 5 below presents the following risk measures estimated for the CSI 300 index:

  • The long-term volatility (the unconditional standard deviation estimated over the entire period)
  • The short-term volatility (the standard deviation estimated over the last three months)
  • The Value at Risk (VaR) for the left tail (the 5% quantile of the historical distribution)
  • The Value at Risk (VaR) for the right tail (the 95% quantile of the historical distribution)
  • The Expected Shortfall (ES) for the left tail (the average loss over the 5% quantile of the historical distribution)
  • The Expected Shortfall (ES) for the right tail (the average loss over the 95% quantile of the historical distribution)
  • The Stress Value (SV) for the left tail (the 1% quantile of the tail distribution estimated with a Generalized Pareto distribution)
  • The Stress Value (SV) for the right tail (the 99% quantile of the tail distribution estimated with a Generalized Pareto distribution)

Table 5. Risk measures for the CSI 300 index.
Risk measures for the CSI 300 index
Source: computation by the author (data: Yahoo! Finance website).

The volatility is a global measure of risk as it considers all the returns. The Value at Risk (VaR), Expected Shortfall (ES) and Stress Value (SV) are local measures of risk as they focus on the tails of the distribution. The study of the left tail is relevant for an investor holding a long position in the CSI 300 index while the study of the right tail is relevant for an investor holding a short position in the CSI 300 index.

Why should I be interested in this post?

For a number of reasons, management students (as future managers and individual investors) should learn about the CSI 300 index. The CSI 300 index is a key benchmark for the Japanese equity market, which is one of the world’s largest market. Understanding how the index is constructed, how it performs, and the companies that make up the index is important for anyone studying finance or business in Japan or interested in investing in Japanese equities.

Individual investors can assess the performance of their own investments in the Japanese equity market with the CSI 300 index. Last but not least, a lot of asset management firms base their mutual funds and exchange-traded funds (ETFs) on the CSI 300 index which can considered as interesting assets to diversify a portfolio. Learning about these products and their portfolio and risk management applications can be valuable for management students.

Related posts on the SimTrade blog

About financial indexes

   ▶ Nithisha CHALLA Financial indexes

   ▶ Nithisha CHALLA Calculation of financial indexes

   ▶ Nithisha CHALLA The business of financial indexes

   ▶ Nithisha CHALLA Float

Other financial indexes

   ▶ Nithisha CHALLA The S&P 500 index

   ▶ Nithisha CHALLA The FTSE 100 index

   ▶ Nithisha CHALLA The KOSPI 50 index

   ▶ Nithisha CHALLA The Nikkei 225 index

About portfolio management

   ▶ Youssef LOURAOUI Portfolio

   ▶ Jayati WALIA Returns

About statistics

   ▶ Shengyu ZHENG Moments de la distribution

   ▶ Shengyu ZHENG Mesures de risques

Useful resources

Academic research about risk

Longin F. (2000) From VaR to stress testing: the extreme value approach Journal of Banking and Finance, N°24, pp 1097-1130.

Longin F. (2016) Extreme events in finance: a handbook of extreme value theory and its applications Wiley Editions.

Business

Wikipedia CSI 300 Index

Capital What is the CSI 300 Index?

CEI data China Index: CSI 300 Index: Financial

Data

Yahoo! Finance

Yahoo! Finance CSI 300 index

About the author

The article was written in May 2023 by Nithisha CHALLA (ESSEC Business School, Grande Ecole Program – Master in Management, 2021-2023).

The Euro Stoxx 50 index

by

The Euro Stoxx 50 index

Nithisha CHALLA

In this article, Nithisha CHALLA (ESSEC Business School, Grande Ecole Program – Master in Management, 2021-2023) presents the Euro Stoxx 50 index and details its characteristics.

The Euro Stoxx 50 index

The performance of 50 large-capital companies with headquarters in Eurozone nations is reflected in the Euro Stoxx 50 stock market index. On February 26, 1998, Stoxx Ltd., a partnership between Deutsche Börse AG, Dow Jones & Company, and SIX Group AG, launched it. Companies from a wide range of industries, including the financial, consumer goods, healthcare, and industrial sectors are all included in the index.

Stocks for the Euro Stoxx 50 index are chosen based on market capitalization, liquidity, and sector representation, among other things. Every year in September, the index’s composition is reviewed, and adjustments are made as needed to reflect the state of the market and the performance of the companies.

The free-float market-capitalization-weighted index known as the Euro Stoxx 50. This means that rather than stock price, the index weights each company according to its market capitalization. The index is made available to the investors and traders worldwide and is disseminated in real-time by several financial news outlets.

The Euro Stoxx 50 index’s ticker symbol in the financial sector is “STOXX50E.”

Table 1 below gives the Top 10 stocks in the Euro Stoxx 50 index in terms of market capitalization as of January 31, 2023.

Table 1. Top 10 stocks in the Euro Stoxx 50 index.
Top 10 stocks in the Euro Stoxx 50 index
Source: computation by the author (data: Yahoo! Finance website).

Table 2 below gives the sector representation of the Euro Stoxx 50 index in terms of number of stocks and market capitalization as of January 31, 2023.

Table 2. Sector representation in the Euro Stoxx 50 index.
Sector representation in the Euro Stoxx 50 index
Source: computation by the author (data: Yahoo! Finance website).

Calculation of the Euro Stoxx 50 index value

The performance of 50 sizable, blue-chip companies from 12 Eurozone nations, including France, Germany, Italy, and Spain, is tracked by the free-floating market-capitalization-weighted Euro Stoxx 50 index. The index, that includes a wide range of industries including financial services, energy, healthcare, consumer goods, and information technology, is intended to represent the performance of the most liquid and actively traded companies in Eurozone.

A free-float market-capitalization-weighted methodology is utilized to calculate the Euro Stoxx 50 index, which means that each company’s weight in the index is determined by its market capitalization adjusted for the shares that are actually traded in the secondary market (float).

The formula to compute the Euro Stoxx 50 index is given by

Float Adjusted Market Capitalization Index value

where I is index value, k a given asset, K the number of assets in the index, Pk the market price of asset k, Nk the number of issued shares for asset k, Fk the float factor of asset k, and t the time of calculation of the index.

In a float-adjusted market-capitalization-weighted index, the weight of asset k is given by formula can be rewritten as

Float Adjusted Market Capitalization Weighted Index Weight

Use of the Euro Stoxx 50 index in asset management

One of the significant indices in Europe, the Euro Stoxx 50 is quite famous and changes in it can have a big impact on market trends and investor sentiment. Investors and traders worldwide have access to index’s real-time values that are published and distributed by a number of financial news sources. The Euro Stoxx 50 is a crucial resource for investors putting efforts to understand the economic and political climate of the Eurozone and gain access to the equity market there. The index can be used by the asset managers as a benchmark to compare the performance of their portfolio to the overall market and to spot potential risk or opportunity areas.

Benchmark for equity funds

Investors and fund managers frequently use the Euro Stoxx 50 to track the health of the Eurozone economy and assess investment opportunities in the region. It is recognized as the top benchmark for the performance of the Eurozone equity market. It consists of businesses from a range of industries, including consumer goods, technology, and finance. The index is used by asset managers to monitor and assess performance of their portfolios in relation to the overall market.

Financial products around the Euro Stoxx 50 index

There are several financial products tracking performance of the Euro Stoxx 50 index. These products allow investors to get exposure to the European stock market.

  • ETFs are investment funds traded on stock exchanges that are designed to track the performance of an index. Several ETFs track the Euro Stoxx 50 index, such as the iShares EURO STOXX 50 UCITS and the Amundi ETF EURO STOXX 50 UCITS
  • Index funds based on the Euro Stoxx 50 index also allow investors to track performance of the index. Examples of index funds tracking Euro Stoxx 50 index include the DWS Invest Euro Stoxx 50 Fund and the BNP Paribas Easy Euro Stoxx 50 UCITS ETF.
  • Futures and options contracts based on Euro Stoxx 50 index provide investors with the ability to speculate on future performance of the index. For example, Eurex offers futures contracts based on the Euro Stoxx 50 index.
  • Certificates are investment products that allow investors to gain exposure to Euro Stoxx 50 index. Societe Generale offers range of certificates linked to the Euro Stoxx 50 index, such as the EURO STOXX 50 Tracker Certificate.

Investors and asset managers may use these financial products to gain exposure to the Euro Stoxx 50 index and manage their portfolios’ risk and return.

Historical data for the Euro Stoxx 50 index

How to get the data?

The Euro Stoxx 50 index is the most common index used in finance, and historical data for the Euro Stoxx 50 index can be easily downloaded from the internet.

For example, you can download data for the Euro Stoxx 50 index from January 3, 1984 on Yahoo! Finance (the Yahoo! code for Euro Stoxx 50 index is ^STOXX50E).

Yahoo! Finance
Source: Yahoo! Finance.

You can also download the same data from a Bloomberg terminal.

R program

The R program below written by Shengyu ZHENG allows you to download the data from Yahoo! Finance website and to compute summary statistics and risk measures about the Euro Stoxx 50 index.

Download R file

Data file

The R program that you can download above allows you to download the data for the Euro Stoxx 50 index from the Yahoo! Finance website. The database starts on January 3, 1984. It also computes the returns (logarithmic returns) from closing prices.

Table 3 below represents the top of the data file for the Euro Stoxx 50 index downloaded from the Yahoo! Finance website with the R program.

Table 3. Top of the data file for the Euro Stoxx 50 index.
Top of the file for the Euro Stoxx 50 index data
Source: computation by the author (data: Yahoo! Finance website).

Evolution of the Euro Stoxx 50 index

Figure 1 below gives the evolution of the Euro Stoxx 50 index from January 3, 1984 to December 30, 2022 on a daily basis.

Figure 1. Evolution of the Euro Stoxx 50 index.
Evolution of the Euro Stoxx 50 index
Source: computation by the author (data: Yahoo! Finance website).

Figure 2 below gives the evolution of the Euro Stoxx 50 index returns from January 3, 1984 to December 30, 2022 on a daily basis.

Figure 2. Evolution of the Euro Stoxx 50 index returns.
Evolution of the Euro Stoxx 50 index return
Source: computation by the author (data: Yahoo! Finance website).

Summary statistics for the Euro Stoxx 50 index

The R program that you can download above also allows you to compute summary statistics about the returns of the Euro Stoxx 50 index.

Table 4 below presents the following summary statistics estimated for the Euro Stoxx 50 index:

  • The mean
  • The standard deviation (the squared root of the variance)
  • The skewness
  • The kurtosis.

The mean, the standard deviation / variance, the skewness, and the kurtosis refer to the first, second, third and fourth moments of statistical distribution of returns respectively.

Table 4. Summary statistics for the Euro Stoxx 50 index.
Summary statistics for the Euro Stoxx 50 index
Source: computation by the author (data: Yahoo! Finance website).

Statistical distribution of the Euro Stoxx 50 index returns

Historical distribution

Figure 3 represents the historical distribution of the Euro Stoxx 50 index daily returns for the period from January 3, 1984 to December 30, 2022.

Figure 3. Historical distribution of the Euro Stoxx 50 index returns.
Historical distribution of the daily Euro Stoxx 50 index returns
Source: computation by the author (data: Yahoo! Finance website).

Gaussian distribution

The Gaussian distribution (also called the normal distribution) is a parametric distribution with two parameters: the mean and the standard deviation of returns. We estimated these two parameters over the period from January 3, 1984 to December 30, 2022. The mean of daily returns is equal to 0.02% and the standard deviation of daily returns is equal to 1.37% (or equivalently 3.94% for the annual mean and 28.02% for the annual standard deviation as shown in Table 3 above).

Figure 4 below represents the Gaussian distribution of the Euro Stoxx 50 index daily returns with parameters estimated over the period from January 3, 1984 to December 30, 2022.

Figure 4. Gaussian distribution of the Euro Stoxx 50 index returns.
Gaussian distribution of the daily Euro Stoxx 50 index returns
Source: computation by the author (data: Yahoo! Finance website).

Risk measures of the Euro Stoxx 50 index returns

The R program that you can download above also allows you to compute risk measures about the returns of the Euro Stoxx 50 index.

Table 5 below presents the following risk measures estimated for the Euro Stoxx 50 index:

  • The long-term volatility (the unconditional standard deviation estimated over the entire period)
  • The short-term volatility (the standard deviation estimated over the last three months)
  • The Value at Risk (VaR) for the left tail (the 5% quantile of the historical distribution)
  • The Value at Risk (VaR) for the right tail (the 95% quantile of the historical distribution)
  • The Expected Shortfall (ES) for the left tail (the average loss over the 5% quantile of the historical distribution)
  • The Expected Shortfall (ES) for the right tail (the average loss over the 95% quantile of the historical distribution)
  • The Stress Value (SV) for the left tail (the 1% quantile of the tail distribution estimated with a Generalized Pareto distribution)
  • The Stress Value (SV) for the right tail (the 99% quantile of the tail distribution estimated with a Generalized Pareto distribution)

Table 5. Risk measures for the Euro Stoxx 50 index.
Risk measures for the Euro Stoxx 50 index
Source: computation by the author (data: Yahoo! Finance website).

The volatility is a global measure of risk as it considers all the returns. The Value at Risk (VaR), Expected Shortfall (ES) and Stress Value (SV) are local measures of risk as they focus on the tails of the distribution. The study of the left tail is relevant for an investor holding a long position in the Euro Stoxx 50 index while the study of the right tail is relevant for an investor holding a short position in the Euro Stoxx 50 index.

Why should I be interested in this post?

For a number of reasons, management students (as future managers and individual investors) should learn about the Euro Stoxx 50 index. It is made up of businesses from 11 different Eurozone nations that operate in a variety of industries, including banking, technology, and healthcare. The Euro Stoxx 50 index is a key benchmark for the European equity market, which is one of the world’s largest market. Understanding how the index is constructed, how it performs, and the companies that make up the index is important for anyone studying finance or business in Europe or interested in investing in European equities. Students interested in careers in investment banking, asset management, or global business may find this information useful.

Individual investors can assess the performance of their own investments in the European equity market with the Euro Stoxx 50 index. Last but not least, a lot of asset management firms base their mutual funds and exchange-traded funds (ETFs) on the Euro Stoxx 50 index which can considered as interesting assets to diversify a portfolio. Learning about these products and their portfolio and risk management applications can be valuable for management students.

Related posts on the SimTrade blog

About financial indexes

   ▶ Nithisha CHALLA Financial indexes

   ▶ Nithisha CHALLA Calculation of financial indexes

   ▶ Nithisha CHALLA The business of financial indexes

   ▶ Nithisha CHALLA Float

Other financial indexes

   ▶ Nithisha CHALLA The S&P 500 index

   ▶ Nithisha CHALLA The FTSE 100 index

   ▶ Nithisha CHALLA The DAX 30 index

   ▶ Nithisha CHALLA The CAC 40 index

   ▶ Nithisha CHALLA The IBEX 35 index

About portfolio management

   ▶ Youssef LOURAOUI Portfolio

   ▶ Jayati WALIA Returns

About statistics

   ▶ Shengyu ZHENG Moments de la distribution

   ▶ Shengyu ZHENG Mesures de risques

Useful resources

Academic research about risk

Longin F. (2000) From VaR to stress testing: the extreme value approach Journal of Banking and Finance, N°24, pp 1097-1130.

Longin F. (2016) Extreme events in finance: a handbook of extreme value theory and its applications Wiley Editions.

Business

Wikipedia History of Euro Stoxx 50

Capital What is the Euro Stoxx Index Definition?

Deutsche Börse Xetra EURO STOXX 50® Index derivatives

Data

Yahoo! Finance

Yahoo Finance Euro Stoxx 50 index

About the author

The article was written in April 2023 by Nithisha CHALLA (ESSEC Business School, Grande Ecole Program – Master in Management, 2021-2023).

The FTSE 100 index

by

The FTSE 100 index

Nithisha CHALLA

In this article, Nithisha CHALLA (ESSEC Business School, Grande Ecole Program – Master in Management, 2021-2023) presents the FTSE 100 index and details its characteristics.

The FTSE 100 index

The Financial Times and the London Stock Exchange established the FTSE 100 index in 1984. It is now run by FTSE Group, a partnership between the Financial Times and the London Stock Exchange. The index, which is regarded as the standard index for the UK equity market, includes the 100 largest companies by market capitalization that are listed on the London Stock Exchange.

Larger companies have a greater influence on the index’s movements than smaller ones because the index is market capitalization-weighted. HSBC, Royal Dutch Shell, BP, and Unilever are a few of the biggest companies that make up the FTSE 100 as of 2021. The FTSE 100 is a key metric for gauging the state of the UK economy because it serves as a benchmark for funds and investment portfolios with UK roots. Recent occurrences like Brexit, the COVID-19 pandemic, and adjustments to the global economy have all had an effect on the index.

The sectoral composition of the FTSE 100 is one of its distinctive features. The financial and resource sectors account for a significant portion of the index’s total market capitalization, which heavily favors these industries.

How is the FTSE 100 index represented in trading platforms and financial websites? The ticker symbol used in the financial industry for the FTSE 100 index is “UKX”.

Table 1 below gives the Top 10 stocks in the FTSE 100 index in terms of market capitalization as of January 31, 2023.

Table 1. Top 10 stocks in the FTSE 100 index.
Top 10 stocks in the FTSE 100 index
Source: computation by the author (data: Yahoo! Finance financial website).

Table 2 below gives the sector representation of the FTSE 100 index in terms of number of stocks and market capitalization as of January 31, 2023.

Table 2. Sector representation in the FTSE 100 index.
Sector representation in the FTSE 100 index
Source: computation by the author (data: Yahoo! Finance financial website).

Calculation of the FTSE 100 index value

The FTSE 100 is a market capitalization-weighted index, which means that each company’s weight in the index is determined by its market capitalization, i.e., the total value of all its outstanding shares. The index, which is regarded as the standard index for the UK equity market, includes the 100 largest companies by market capitalization that are listed on the London Stock Exchange.

The formula to compute the FTSE 100 index is given by

Market Capitalization Index value

Where I is the index value, k a given asset, K the number of assets in the index, Pk the market price of asset k, Nk the number of issued shares for asset k, and t the time of calculation of the index.

In a market capitalization-weighted index, the weight of asset k is given by formula can be rewritten as

Market Capitalization Weighted Index Weight

Which clearly shows that the weight of each asset in the index is its market capitalization of the asset divided by the sum of the market capitalizations of all assets.

Note that the divisor, whose calculation is based on the number of shares, is typically adjusted for events such as stock splits and dividends. The divisor is used to ensure that the value of the index remains consistent over time despite changes in the number of outstanding shares.

Use of the FTSE 100 index in asset management

The performance of large-cap companies listed on the London Stock Exchange is frequently measured against the FTSE 100. Investors can gain insight into the overall health of the UK economy and spot potential opportunities or risks in particular industries or regions by examining the sector weightings and geographic exposure of the index. It serves as a benchmark for asset managers to compare the performance of their equity portfolios to the overall market performance.

Benchmark for equity funds

One of the most popular metrics for assessing the performance of the UK stock market is the FTSE 100. It includes businesses from a wide range of sectors, including consumer goods, healthcare, energy, and finance. As a result, it is frequently used by investors and fund managers to monitor the UK economy’s performance and evaluate the country’s investment opportunities.

Financial products around the FTSE 100 index

There are several financial products that track the performance of the FTSE 100 index, allowing investors to gain exposure to the Japanese stock market.

  • ETFs are investment funds traded on stock exchanges, designed to track the performance of an index. There are several ETFs that track the FTSE 100 index, such as the iShares Core FTSE 100 ETF and the Vanguard FTSE 100 UCITS ETF.
  • index funds are also designed to track the performance of an index. index funds based on the FTSE 100 index include the HSBC FTSE 100 Index Fund and the Legal & General UK 100 Index Fund.
  • Futures and options contracts based on the FTSE 100 index provide investors with the ability to speculate on the future performance of the index. For example, the London International Financial Futures and Options Exchange (LIFFE) offers futures contracts based on the FTSE 100 index.
  • Certificates are investment products that allow investors to gain exposure to the FTSE 100 index. Société Générale offers a range of certificates linked to the FTSE 100 index, such as the FTSE 100 Tracker Certificate.

Historical data for the FTSE 100 index

How to get the data?

The FTSE 100 index is the most common index used in finance, and historical data for the FTSE 100 index can be easily downloaded from the internet.

For example, you can download data for the FTSE 100 index from January 3, 1984 on Yahoo! Finance (the Yahoo! code for FTSE 100 index is ^FTSE).

Yahoo! Finance
Source: Yahoo! Finance.

You can also download the same data from a Bloomberg terminal.

R program

The R program below written by Shengyu ZHENG allows you to download the data from Yahoo! Finance website and to compute summary statistics and risk measures about the FTSE 100 index.

Download R file

Data file

The R program that you can download above allows you to download the data for the FTSE 100 index from the Yahoo! Finance website. The database starts on January 3, 1984. It also computes the returns (logarithmic returns) from closing prices.

Table 3 below represents the top of the data file for the FTSE 100 index downloaded from the Yahoo! Finance website with the R program.

Table 3. Top of the data file for the FTSE 100 index.
Top of the file for the FTSE 100 index data
Source: computation by the author (data: Yahoo! Finance website).

Evolution of the FTSE 100 index

Figure 1 below gives the evolution of the FTSE 100 index from January 3, 1984 to December 30, 2022 on a daily basis.

Figure 1. Evolution of the FTSE 100 index.
Evolution of the FTSE 100 index
Source: computation by the author (data: Yahoo! Finance website).

Figure 2 below gives the evolution of the FTSE 100 index returns from January 3, 1984 to December 30, 2022 on a daily basis.

Figure 2. Evolution of the FTSE 100 index returns.
Evolution of the FTSE 100 index return
Source: computation by the author (data: Yahoo! Finance website).

Summary statistics for the FTSE 100 index

The R program that you can download above also allows you to compute summary statistics about the returns of the FTSE 100 index.

Table 4 below presents the following summary statistics estimated for the FTSE 100 index:

  • The mean
  • The standard deviation (the squared root of the variance)
  • The skewness
  • The kurtosis.

The mean, the standard deviation / variance, the skewness, and the kurtosis refer to the first, second, third and fourth moments of statistical distribution of returns respectively.

Table 4. Summary statistics for the FTSE 100 index.
Summary statistics for the FTSE 100 index
Source: computation by the author (data: Yahoo! Finance website).

Statistical distribution of the FTSE 100 index returns

Historical distribution

Figure 3 represents the historical distribution of the FTSE 100 index daily returns for the period from January 3, 1984 to December 30, 2022.

Figure 3. Historical distribution of the FTSE 100 index returns.
Historical distribution of the daily FTSE 100 index returns
Source: computation by the author (data: Yahoo! Finance website).

Gaussian distribution

The Gaussian distribution (also called the normal distribution) is a parametric distribution with two parameters: the mean and the standard deviation of returns. We estimated these two parameters over the period from January 3, 1984 to December 30, 2022. The mean of daily returns is equal to 0.02% and the standard deviation of daily returns is equal to 1.37% (or equivalently 3.94% for the annual mean and 28.02% for the annual standard deviation as shown in Table 3 above).

Figure 4 below represents the Gaussian distribution of the FTSE 100 index daily returns with parameters estimated over the period from January 3, 1984 to December 30, 2022.

Figure 4. Gaussian distribution of the FTSE 100 index returns.
Gaussian distribution of the daily FTSE 100 index returns
Source: computation by the author (data: Yahoo! Finance website).

Risk measures of the FTSE 100 index returns

The R program that you can download above also allows you to compute risk measures about the returns of the FTSE 100 index.

Table 5 below presents the following risk measures estimated for the FTSE 100 index:

  • The long-term volatility (the unconditional standard deviation estimated over the entire period)
  • The short-term volatility (the standard deviation estimated over the last three months)
  • The Value at Risk (VaR) for the left tail (the 5% quantile of the historical distribution)
  • The Value at Risk (VaR) for the right tail (the 95% quantile of the historical distribution)
  • The Expected Shortfall (ES) for the left tail (the average loss over the 5% quantile of the historical distribution)
  • The Expected Shortfall (ES) for the right tail (the average loss over the 95% quantile of the historical distribution)
  • The Stress Value (SV) for the left tail (the 1% quantile of the tail distribution estimated with a Generalized Pareto distribution)
  • The Stress Value (SV) for the right tail (the 99% quantile of the tail distribution estimated with a Generalized Pareto distribution)

Table 5. Risk measures for the FTSE 100 index.
Risk measures for the FTSE 100 index
Source: computation by the author (data: Yahoo! Finance website).

The volatility is a global measure of risk as it considers all the returns. The Value at Risk (VaR), Expected Shortfall (ES) and Stress Value (SV) are local measures of risk as they focus on the tails of the distribution. The study of the left tail is relevant for an investor holding a long position in the FTSE 100 index while the study of the right tail is relevant for an investor holding a short position in the FTSE 100 index.

Why should I be interested in this post?

For a number of reasons, management students (as future managers and individual investors) should learn about the FTSE 100 index. The FTSE 100 index is a key benchmark for the Japanese equity market, which is one of the world’s largest market. Understanding how the index is constructed, how it performs, and the companies that make up the index is important for anyone studying finance or business in Japan or interested in investing in Japanese equities.

Individual investors can assess the performance of their own investments in the Japanese equity market with the FTSE 100 index. Last but not least, a lot of asset management firms base their mutual funds and exchange-traded funds (ETFs) on the FTSE 100 index which can considered as interesting assets to diversify a portfolio. Learning about these products and their portfolio and risk management applications can be valuable for management students.

Related posts on the SimTrade blog

About financial indexes

   ▶ Nithisha CHALLA Financial indexes

   ▶ Nithisha CHALLA Calculation of financial indexes

   ▶ Nithisha CHALLA The business of financial indexes

   ▶ Nithisha CHALLA Float

Other financial indexes

   ▶ Nithisha CHALLA The S&P 500 index

   ▶ Nithisha CHALLA The CSI 300 index

   ▶ Nithisha CHALLA The Nikkei 225 index

   ▶ Nithisha CHALLA The DAX 30 index

About portfolio management

   ▶ Youssef LOURAOUI Portfolio

   ▶ Jayati WALIA Returns

About statistics

   ▶ Shengyu ZHENG Moments de la distribution

   ▶ Shengyu ZHENG Mesures de risques

Useful resources

Academic research about risk

Longin F. (2000) From VaR to stress testing: the extreme value approach Journal of Banking and Finance, N°24, pp 1097-1130.

Longin F. (2016) Extreme events in finance: a handbook of extreme value theory and its applications Wiley Editions.

Business

Axi What is the FTSE 100 index and how to trade it?

CMC markets An introduction to the FTSE 100

Nerd Wallet What is the FTSE 100?

Data

Yahoo! Finance

Yahoo Finance FTSE 100 index

About the author

The article was written in April 2023 by Nithisha CHALLA (ESSEC Business School, Grande Ecole Program – Master in Management, 2021-2023).

The Nikkei 225 index

by

The Nikkei 225 index

Nithisha CHALLA

In this article, Nithisha CHALLA (ESSEC Business School, Grande Ecole Program – Master in Management, 2021-2023) presents the Nikkei 225 index and details its characteristics.

The Nikkei 225 index

The Nikkei 225 index is considered as the primary benchmark index of the Tokyo Stock Exchange (TSE) and is the most widely quoted average of Japanese equities. One of Japan’s top newspapers, the Nihon Keizai Shimbun (Nikkei), first published the index in 1950. The index consists of 225 blue-chip companies listed on the TSE, which are considered to represent the overall health of the Japanese economy. These companies come from various industries such as finance, technology, automobile, and retail, among others.

The Financial Times, a preeminent global provider of financial news, was purchased by Nikkei Inc, the parent company of Nikkei, for $1.3 billion in 2015. This acquisition highlighted Nikkei’s growing global presence and ambition to diversify beyond the Japanese market. The Nikkei 225 index follows a price-weighted methodology. This means that the components of the index are weighted based on their stock price, with higher-priced stocks carrying a greater weight in the index.

In the past few years, the Nikkei 225 index has been affected by various economic and political events, such as the COVID-19 pandemic and the Tokyo Olympics. The pandemic caused the index to significantly decline in 2020, but it has since recovered and reached new highs in 2021.

How is the Nikkei 225 index represented in trading platforms and financial websites? The ticker symbol used in the financial industry for the Nikkei 225 index is “NI225”.

Table 1 below gives the Top 10 stocks in the Nikkei 225 index in terms of market capitalization as of January 31, 2023.

Table 1. Top 10 stocks in the Nikkei index.
Top 10 stocks in the Nikkei 225 index
Source: computation by the author (data: YahooFinance! financial website).

Table 2 below gives the sector representation of the Nikkei 225 index in terms of number of stocks and market capitalization as of January 31, 2023.

Table 2. Sector representation in the Nikkei 225 index.
Sector representation in the Nikkei 225 index
Source: computation by the author (data: YahooFinance! financial website).

Calculation of the Nikkei 225 index value

The Nikkei 225 index is calculated using a price-weighted methodology. This means that the price of each stock in the index is multiplied by the number of shares outstanding to determine the total market value of the company. The Nikkei 225 index is frequently used as a leading indicator of the state of the Japanese stock market, and economy, and as a gauge of trends in the world economy.

The formula to compute the Nikkei 225 is given by

A price-weighted index is calculated by summing the prices of all the assets in the index and dividing by a divisor equal to the number of assets.

The formula for a price-weighted index is given by

Price-weighted index value

where I is the index value, k a given asset, K the number of assets in the index, Pk the market price of asset k, and t the time of calculation of the index.

In a price-weighted index, the weight of asset k is given by formula can be rewritten as

Price-weighted index weight

which clearly shows that the weight of each asset in the index is its market price divided by the sum of the market prices of all assets.

Note that the divisor, which is equal to the number of shares, is typically adjusted for events such as stock splits and dividends. The divisor is used to ensure that the value of the index remains consistent over time despite changes in the number of outstanding shares. A more general formula may then be:

Index value

Where D is the divisor which is adjusted over time to account for events such as stock splits and dividends.

Use of the Nikkei 225 index in asset management

Asset managers have shifted their attention in recent years to including environmental, social, and governance (ESG) factors in their investment choices. A number of ESG-related initiatives, such as the development of an ESG index that tracks businesses with high ESG scores, have been introduced by the Nikkei 225 index. The Nikkei 225 index may also be used by asset managers as a component of a more comprehensive global asset allocation strategy. For example, they may use the index to gain exposure to the Asian equity markets while also investing in other regions such as Europe and the Americas. In addition, the Nikkei 225 index can also be used as a risk management tool. Asset managers can spot potential risks and take action to reduce them by comparing a portfolio’s performance to the index.

Benchmark for equity funds

Equity funds that invest in Japanese stocks frequently use the Nikkei 225 index as a benchmark. The index is used by investment managers and individual investors to assess and contrast the performance of their holdings of Japanese equities with the performance of the overall market. Japanese exchange-traded funds (ETFs) and other investment products that follow the Japanese equity market use the index as a benchmark as well. Additionally, derivatives like futures and options that enable investors to trade on the Japanese equity market are based on the Nikkei 225 index.

Financial products around the Nikkei 225 index

There are several financial products that track the performance of the Nikkei 225 index, allowing investors to gain exposure to the Japanese stock market.

  • Nikkei 225 ETFs are a popular way for investors to gain exposure to the Japanese equity market, as they offer a low-cost and convenient way to invest in a diversified basket of stocks. Some of the largest Nikkei 225 ETFs by assets under management include the iShares Nikkei 225 ETF (NKY), the Nomura Nikkei 225 ETF (1321), and the Daiwa ETF Nikkei 225 (1320).
  • There are also mutual funds and index funds that track the Nikkei 225 index. These funds typically have higher fees than ETFs but may offer different investment strategies or options for investors.
  • Certificates are structured products that allow investors to gain exposure to the Nikkei 225 index without actually owning the underlying assets.
  • Futures contracts based on the Nikkei 225 index are also available for investors who want to trade the index with leverage or for hedging purposes. These futures contracts trade on the Osaka Exchange, a subsidiary of the Japan Exchange Group.

Historical data for the Nikkei 225 index

How to get the data?

The Nikkei 225 index is the most common index used in finance, and historical data for the Nikkei 225 index can be easily downloaded from the internet.

For example, you can download data for the Nikkei 225 index from March 1, 1990 on Yahoo! Finance (the Yahoo! code for Nikkei 225 index is ^N225).

Yahoo! Finance
Source: Yahoo! Finance.

You can also download the same data from a Bloomberg terminal.

R program

The R program below written by Shengyu ZHENG allows you to download the data from Yahoo! Finance website and to compute summary statistics and risk measures about the Nikkei 225 index.

Download R file

Data file

The R program that you can download above allows you to download the data for the Nikkei 225 index from the Yahoo! Finance website. The database starts on March 1, 1990. It also computes the returns (logarithmic returns) from closing prices.

Table 3 below represents the top of the data file for the Nikkei 225 index downloaded from the Yahoo! Finance website with the R program.

Table 3. Top of the data file for the Nikkei 225 index.
Top of the file for the Nikkei 225 index data
Source: computation by the author (data: Yahoo! Finance website).

Evolution of the Nikkei 225 index

Figure 1 below gives the evolution of the Nikkei 225 index from March 1, 1990 to December 30, 2022 on a daily basis.

Figure 1. Evolution of the Nikkei 225 index.
Evolution of the Nikkei 225 index
Source: computation by the author (data: Yahoo! Finance website).

Figure 2 below gives the evolution of the Nikkei 225 index returns from March 1, 1990 to December 30, 2022 on a daily basis.

Figure 2. Evolution of the Nikkei 225 index returns.
Evolution of the Nikkei 225 index return
Source: computation by the author (data: Yahoo! Finance website).

Summary statistics for the Nikkei 225 index

The R program that you can download above also allows you to compute summary statistics about the returns of the Nikkei 225 index.

Table 4 below presents the following summary statistics estimated for the Nikkei 225 index:

  • The mean
  • The standard deviation (the squared root of the variance)
  • The skewness
  • The kurtosis.

The mean, the standard deviation / variance, the skewness, and the kurtosis refer to the first, second, third and fourth moments of statistical distribution of returns respectively.

Table 4. Summary statistics for the Nikkei 225 index.
Summary statistics for the Nikkei 225 index
Source: computation by the author (data: Yahoo! Finance website).

Statistical distribution of the Nikkei 225 index returns

Historical distribution

Figure 3 represents the historical distribution of the Nikkei 225 index daily returns for the period from March 1, 1990 to December 30, 2022.

Figure 3. Historical distribution of the Nikkei 225 index returns.
Historical distribution of the daily Nikkei 225 index returns
Source: computation by the author (data: Yahoo! Finance website).

Gaussian distribution

The Gaussian distribution (also called the normal distribution) is a parametric distribution with two parameters: the mean and the standard deviation of returns. We estimated these two parameters over the period from March 1, 1990 to December 30, 2022. The mean of daily returns is equal to 0.02% and the standard deviation of daily returns is equal to 1.37% (or equivalently 3.94% for the annual mean and 28.02% for the annual standard deviation as shown in Table 3 above).

Figure 4 below represents the Gaussian distribution of the Nikkei 225 index daily returns with parameters estimated over the period from March 1, 1990 to December 30, 2022.

Figure 4. Gaussian distribution of the Nikkei 225 index returns.
Gaussian distribution of the daily Nikkei 225 index returns
Source: computation by the author (data: Yahoo! Finance website).

Risk measures of the Nikkei 225 index returns

The R program that you can download above also allows you to compute risk measures about the returns of the Nikkei 225 index.

Table 5 below presents the following risk measures estimated for the Nikkei 225 index:

  • The long-term volatility (the unconditional standard deviation estimated over the entire period)
  • The short-term volatility (the standard deviation estimated over the last three months)
  • The Value at Risk (VaR) for the left tail (the 5% quantile of the historical distribution)
  • The Value at Risk (VaR) for the right tail (the 95% quantile of the historical distribution)
  • The Expected Shortfall (ES) for the left tail (the average loss over the 5% quantile of the historical distribution)
  • The Expected Shortfall (ES) for the right tail (the average loss over the 95% quantile of the historical distribution)
  • The Stress Value (SV) for the left tail (the 1% quantile of the tail distribution estimated with a Generalized Pareto distribution)
  • The Stress Value (SV) for the right tail (the 99% quantile of the tail distribution estimated with a Generalized Pareto distribution)

Table 5. Risk measures for the Nikkei 225 index.
Risk measures for the Nikkei 225 index
Source: computation by the author (data: Yahoo! Finance website).

The volatility is a global measure of risk as it considers all the returns. The Value at Risk (VaR), Expected Shortfall (ES) and Stress Value (SV) are local measures of risk as they focus on the tails of the distribution. The study of the left tail is relevant for an investor holding a long position in the Nikkei 225 index while the study of the right tail is relevant for an investor holding a short position in the Nikkei 225 index.

Financial maps

You can find financial world maps on the Extreme Events in Finance website. These maps represent the performance, risk and extreme risk in international equity markets.

Figure 5 below represents the world map for extreme risk estimated by the extreme value distribution (see Longin (2016 and 2000)).

Figure 5. Extreme risk map.
Extreme risk map
Source: Extreme Events in Finance.

Why should I be interested in this post?

For a number of reasons, management students (as future managers and individual investors) should learn about the Nikkei 225 index. The Nikkei 225 index is a key benchmark for the Japanese equity market, which is one of the world’s largest market. Understanding how the index is constructed, how it performs, and the companies that make up the index is important for anyone studying finance or business in Japan or interested in investing in Japanese equities.

Individual investors can assess the performance of their own investments in the Japanese equity market with the Nikkei 225 index. Last but not least, a lot of asset management firms base their mutual funds and exchange-traded funds (ETFs) on the Nikkei 225 index which can considered as interesting assets to diversify a portfolio. Learning about these products and their portfolio and risk management applications can be valuable for management students.

Related posts on the SimTrade blog

About financial indexes

   ▶ Nithisha CHALLA Financial indexes

   ▶ Nithisha CHALLA Calculation of financial indexes

   ▶ Nithisha CHALLA The business of financial indexes

   ▶ Nithisha CHALLA Float

Other financial indexes

   ▶ Nithisha CHALLA The S&P 500 index

   ▶ Nithisha CHALLA The FTSE 100 index

   ▶ Nithisha CHALLA The CSI 300 index

   ▶ Nithisha CHALLA The KOSPI 50 index

About portfolio management

   ▶ Youssef LOURAOUI Portfolio

   ▶ Jayati WALIA Returns

About statistics

   ▶ Shengyu ZHENG Moments de la distribution

   ▶ Shengyu ZHENG Mesures de risques

Useful resources

Academic research about risk

Longin F. (2000) From VaR to stress testing: the extreme value approach Journal of Banking and Finance, N°24, pp 1097-1130.

Longin F. (2016) Extreme events in finance: a handbook of extreme value theory and its applications Wiley Editions.

Data

Yahoo! Finance

Yahoo! Finance Nikkei 225 index

Other

Extreme Events in Finance

Extreme Events in Finance Risk maps

Wikipedia Nikkei 225

About the author

The article was written in April 2023 by Nithisha CHALLA (ESSEC Business School, Grande Ecole Program – Master in Management, 2021-2023).

The CAC 40 index

by

The CAC 40 index

Nithisha CHALLA

In this article, Nithisha CHALLA (ESSEC Business School, Grande Ecole Program – Master in Management, 2021-2023) presents the CAC 40 index and details its characteristics.

The CAC 40 index

The CAC 40 index is one of the main indices of the Paris Bourse. It was launched on December 31, 1987. CAC is the abbreviation for Cotation Assistée en Continu which translates to “Continuous Assisted Quotation”. CAC 40 is a benchmark stock market index that tracks the performance of the 40 largest and most actively traded companies on the Euronext Paris exchange.

The companies in the CAC 40 index represent a variety of industries, including financial services, energy, consumer goods, and technology. Some of the largest and most well-known companies in the index include Total, L’Oréal, and Sanofi. Due to its extremely diverse portfolio, it enables investors to view a variety of French industries.

The CAC 40 index uses a free-float market-capitalization weighting methodology, which means that only the shares that are available for trading are used to determine the index’s weighting.

Given that France is the second-largest economy in the European Union (EU), and the CAC 40 index plays an important role in the French economy, it is a good benchmark for investors. The companies included in the index account for a significant portion of the country’s GDP and provide employment for a large number of people.

While the CAC 40 is a French stock market index, many of the companies included in the index have a global reach and operate in multiple countries. As a result, the index can serve as a gauge for the wider European and global economies in addition to the French economy.

How is the CAC 40 index represented in trading platforms and financial websites? The ticker symbol used in the financial industry for the CAC 40 index is “PX1”.

Table 1 gives the Top 10 stocks in the CAC 40 index in terms of market capitalization as of January 31, 2023.

Table 1. Top 10 stocks in the CAC 40 index.
Top 10 stocks in the CAC 40 index
Source: computation by the author (data: YahooFinance! financial website).

Table 2 gives the sector representation of the CAC 40 index in terms of number of stocks and market capitalization as of January 31, 2023.

Table 2. Sector representation in the CAC 40 index.
Sector representation in the CAC 40 index
Source: computation by the author (data: YahooFinance! financial website).

Calculation of the CAC 40 index value

The value of the CAC 40 index is determined using a market-capitalization-weighted formula that is float-adjusted, which means that only the shares that are available for trading in the secondary market are used to determine the index weighting. This helps to ensure that the index is representative of the companies that are actively traded in the market.

The formula to compute the CAC 40 index is given by

Float Adjusted Market Capitalization Index value

where I is the index value, k a given asset, K the number of assets in the index, Pk the market price of asset k, Nk the number of issued shares for asset k, Fk the float factor of asset k, and t the time of calculation of the index.

In a float-adjusted market-capitalization-weighted index, the weight of asset k is given by formula can be rewritten as

Float Adjusted Market Capitalization Weighted Index Weight

The index is reviewed quarterly to ensure that it remains representative of the French stock market and to add or remove companies based on their size, liquidity, and sector classification.

Use of the CAC 40 index in asset management

The CAC 40 index is a useful tool for asset managers to manage risk because it is quite diverse and represents the French economy across a variety of industries. While the CAC 40 index is primarily composed of French companies, many of these companies also have significant international exposure. The CAC 40 index is one of Europe’s most liquid stock market indices, with a high level of trading volume and relatively low bid-ask spreads. This can be particularly important for investors who are looking to trade in and out of positions quickly, or for those who are managing large portfolios and need to execute trades efficiently. Some index funds and ETFs based on the CAC 40 index have particular ESG standards for the businesses they invest in. This may be appealing to investors who want to match their investments with their values.

Benchmark for equity funds

Equity funds are types of investment funds that invest primarily in stocks or shares of companies that are publicly traded. These funds give investors exposure to equity markets and offer the potential growth for capital appreciation in the long term. Given that it gives a good enough picture of the French market, there are multiple financial products around the index. Using these products can help investors diversify their holdings and control risk. The CAC 40 index can also be used to create multi-asset portfolios, acting as a representative of the portfolio’s equity component. By including the CAC 40 index in a multi-asset portfolio, investors can potentially achieve diversification and reduce risk through exposure to a broad range of companies in the French economy.

Financial products around the CAC 40 index

Financial products around the CAC 40 index offer investors a range of options to gain exposure to the French equity market, including products with sustainability and ESG considerations.

  • Investment funds traded like stocks are called exchange-traded funds, or ETFs. The Lyxor ETF CAC 40 is the largest ETF that tracks the CAC 40 index, and other ETFs that do so include the Amundi ETF CAC 40, the BNP Paribas Easy CAC 40, and the Xtrackers CAC 40
  • Some mutual funds and investment trusts that make CAC 40 index investments have an environmental, social, and governance (ESG) or sustainability focus. For instance, the CAC 40 index and European businesses with strong ESG performance are among the investments made by the Mirova Europe Sustainable Equity Fund
  • The main stock exchange in France, Euronext Paris, offers futures and options on the CAC 40 index. Institutional investors and traders use these highly liquid financial contracts
  • Structured products linked to the CAC 40 index can have various features, such as capital protection, leverage, and participation rate

Historical data for the CAC 40 index

How to get the data?

The CAC 40 index is the most common index used in finance, and historical data for the CAC 40 index can be easily downloaded from the internet.

For example, you can download data for the CAC 40 index from March 1, 1990 on Yahoo! Finance (the Yahoo! code for CAC 40 index is ^FCHI).

Yahoo! Finance
Source: Yahoo! Finance.

You can also download the same data from a Bloomberg terminal.

R program

The R program below written by Shengyu ZHENG allows you to download the data from Yahoo! Finance website and to compute summary statistics and risk measures about the CAC 40 index.

Download R file

Data file

The R program that you can download above allows you to download the data for the CAC 40 index from the Yahoo! Finance website. The database starts on March 1, 1990. It also computes the returns (logarithmic returns) from closing prices.

Table 3 below represents the top of the data file for the CAC 40 index downloaded from the Yahoo! Finance website with the R program.

Table 3. Top of the data file for the CAC 40 index.
Top of the file for the CAC 40 index data
Source: computation by the author (data: Yahoo! Finance website).

Evolution of the CAC 40 index

Figure 1 below gives the evolution of the CAC 40 index from March 1, 1990 to December 30, 2022 on a daily basis.

Figure 1. Evolution of the CAC 40 index.
Evolution of the CAC 40 index
Source: computation by the author (data: Yahoo! Finance website).

Figure 2 below gives the evolution of the CAC 40 index returns from March 1, 1990 to December 30, 2022 on a daily basis.

Figure 2. Evolution of the CAC 40 index returns.
Evolution of the CAC 40 index return
Source: computation by the author (data: Yahoo! Finance website).

Summary statistics for the CAC 40 index

The R program that you can download above also allows you to compute summary statistics about the returns of the CAC 40 index.

Table 4 below presents the following summary statistics estimated for the CAC 40 index:

  • The mean
  • The standard deviation (the squared root of the variance)
  • The skewness
  • The kurtosis.

The mean, the standard deviation / variance, the skewness, and the kurtosis refer to the first, second, third and fourth moments of statistical distribution of returns respectively.

Table 4. Summary statistics for the CAC 40 index.
Summary statistics for the CAC 40 index
Source: computation by the author (data: Yahoo! Finance website).

Statistical distribution of the CAC 40 index returns

Historical distribution

Figure 3 represents the historical distribution of the CAC 40 index daily returns for the period from March 1, 1990 to December 30, 2022.

Figure 3. Historical distribution of the CAC 40 index returns.
Historical distribution of the daily CAC 40 index returns
Source: computation by the author (data: Yahoo! Finance website).

Gaussian distribution

The Gaussian distribution (also called the normal distribution) is a parametric distribution with two parameters: the mean and the standard deviation of returns. We estimated these two parameters over the period from March 1, 1990 to December 30, 2022. The mean of daily returns is equal to 0.02% and the standard deviation of daily returns is equal to 1.37% (or equivalently 3.94% for the annual mean and 28.02% for the annual standard deviation as shown in Table 3 above).

Figure 4 below represents the Gaussian distribution of the CAC 40 index daily returns with parameters estimated over the period from March 1, 1990 to December 30, 2022.

Figure 4. Gaussian distribution of the CAC 40 index returns.
Gaussian distribution of the daily CAC 40 index returns
Source: computation by the author (data: Yahoo! Finance website).

Risk measures of the CAC 40 index returns

The R program that you can download above also allows you to compute risk measures about the returns of the CAC 40 index.

Table 5 below presents the following risk measures estimated for the CAC 40 index:

  • The long-term volatility (the unconditional standard deviation estimated over the entire period)
  • The short-term volatility (the standard deviation estimated over the last three months)
  • The Value at Risk (VaR) for the left tail (the 5% quantile of the historical distribution)
  • The Value at Risk (VaR) for the right tail (the 95% quantile of the historical distribution)
  • The Expected Shortfall (ES) for the left tail (the average loss over the 5% quantile of the historical distribution)
  • The Expected Shortfall (ES) for the right tail (the average loss over the 95% quantile of the historical distribution)
  • The Stress Value (SV) for the left tail (the 1% quantile of the tail distribution estimated with a Generalized Pareto distribution)
  • The Stress Value (SV) for the right tail (the 99% quantile of the tail distribution estimated with a Generalized Pareto distribution)

Table 5. Risk measures for the CAC 40 index.
Risk measures for the CAC 40 index
Source: computation by the author (data: Yahoo! Finance website).

The volatility is a global measure of risk as it considers all the returns. The Value at Risk (VaR), Expected Shortfall (ES) and Stress Value (SV) are local measures of risk as they focus on the tails of the distribution. The study of the left tail is relevant for an investor holding a long position in the CAC 40 index while the study of the right tail is relevant for an investor holding a short position in the CAC 40 index.

Why should I be interested in this post?

For a number of reasons, management students (as future managers and individual investors) should learn about the CAC 40 index. The performance of large-cap listed French companies is tracked by this stock market index, which is first and foremost well-known and respected. Gaining a deeper understanding of the French large-cap stock market and the businesses that fuel its expansion requires knowledge of the CAC 40 index.

Individual investors can assess the performance of their own investments and those of their organization by comprehending the CAC 40 index and its components. Last but not least, a lot of businesses base their mutual funds and exchange-traded funds (ETFs) on the CAC 40 index which can considered as interesting assets to diversify a portfolio.

Related posts on the SimTrade blog

About financial indexes

   ▶ Nithisha CHALLA Financial indexes

   ▶ Nithisha CHALLA Calculation of financial indexes

   ▶ Nithisha CHALLA The business of financial indexes

   ▶ Nithisha CHALLA Float

Other financial indexes

   ▶ Nithisha CHALLA The S&P 500 index

   ▶ Nithisha CHALLA The FTSE 100 index

   ▶ Nithisha CHALLA The CSI 300 index

   ▶ Nithisha CHALLA The Nikkei 225 index

   ▶ Nithisha CHALLA The DAX 30 index

About portfolio management

   ▶ Youssef LOURAOUI Portfolio

   ▶ Jayati WALIA Returns

About statistics

   ▶ Shengyu ZHENG Moments de la distribution

   ▶ Shengyu ZHENG Mesures de risques

Useful resources

Academic research about risk

Longin F. (2000) From VaR to stress testing: the extreme value approach Journal of Banking and Finance, N°24, pp 1097-1130.

Longin F. (2016) Extreme events in finance: a handbook of extreme value theory and its applications Wiley Editions.

Other

Wikipedia CAC 40

FXCM Everything you need to know about the CAC 40 index

EFMAE The introduction of CAC40 Master unit

Data

Yahoo! Finance

Yahoo Finance CAC 40 index

About the author

The article was written in April 2023 by Nithisha CHALLA (ESSEC Business School, Grande Ecole Program – Master in Management, 2021-2023).

The Wilshire 5000 index

by

The Wilshire 5000 index

Nithisha CHALLA

In this article, Nithisha CHALLA (ESSEC Business School, Grande Ecole Program – Master in Management, 2021-2023) presents the Wilshire 5000 index and details its characteristics.

The Wilshire 5000 index

The Wilshire 5000 index was launched in 1974 by Wilshire Associates, an investment management company based in California. It monitors the performance of almost all publicly traded stocks in the US. This index is still currently managed by Wilshire Associates. The index name came from the fact that it initially contained about 5,000 U.S. stocks; however, it has since grown to include over 3,500 more stocks, bringing the total to close to 8,500 stocks, which more or less comprehensively represents the majority of the US equity market.

The Wilshire 5000 index is a float-adjusted, market-capitalization weighted index. As a result, rather than using the total number of shares outstanding, the index weights of each stock are changed to reflect the number of shares that are currently trading on the market. This makes it possible for the index to accurately reflect each company’s market capitalization rather than just the theoretical value of all outstanding shares.

The Wilshire 5000 index is distinctive in that it includes small- and mid-cap stocks in addition to large-cap stocks. This distinguishes it from other well-known indices like the S&P 500 or the Dow Jones Industrial Average, which only include large-cap stocks, as a more complete indicator of the American stock market. With a few exceptions, such as penny stocks and stocks that trade on over-the-counter markets, the index was created to include almost all publicly traded stocks in the US equity market.

How is the Wilshire 5000 index represented in trading platforms and financial websites? The ticker symbol used in the financial industry for the Wilshire 5000 index is “W5000”.

Table 1 below gives the Top 10 stocks in the Wilshire 5000 index in terms of market capitalization as of January 31, 2023.

Table 1. Top 10 stocks in the Wilshire 5000 index.
Top 10 stocks in the Wilshire 5000 index
Source: computation by the author (data: Yahoo! Finance website).

Table 2 below gives the sector representation of the Wilshire 5000 index in terms of number of stocks and market capitalization as of January 31, 2023.

Table 2. Sector representation in the Wilshire 5000 index.
Sector representation in the Wilshire 5000 index
Source: computation by the author (data: Yahoo! Finance website).

Calculation of the Wilshire 5000 index value

The Wilshire 5000 index is determined using a market-capitalization-weighted formula that is float-adjusted, which means that only the shares that are available for trading in the secondary market are used to determine the index weighting. This helps to ensure that the index is representative of the companies that are actively traded in the market.

The formula to compute the Wilshire 5000 is given by

Float-adjusted market-capitalization-weighted index value

where I is the index value, k a given asset, K the number of assets in the index, Pk the market price of asset k, Nk the number of issued shares for asset k, Fk the float factor of asset k, and t the time of calculation of the index.

In a float-adjusted market-capitalization-weighted index, the weight of asset k is given by formula can be rewritten as

Float-adjusted market-capitalization-weighted index weight

To make sure the index remains a reliable representation of the US equity market, it is rebalanced every quarter. The stocks that are chosen for inclusion in the index are chosen by Wilshire Associates, the index’s creator. When deciding which stocks to include, the company takes into account a variety of variables, including market capitalization, liquidity, and additional fundamentals like earnings and revenue growth.

Use of the Wilshire 5000 index in asset management

By comparing the volatility of their portfolio to the market as a whole, asset managers can use the Wilshire 5000 index to manage portfolio risk. Asset managers can use the index to determine the best-performing industries and sectors before choosing specific stocks to build a portfolio that is well-balanced. They can determine whether their portfolio is more or less risky than the market by examining the correlation between their portfolio and the Wilshire 5000 index. This enables them to establish whether their superior performance is the result of their ability to select stocks or whether it is simply the result of taking on greater risk than the market.

The Wilshire 5000 index is also used in various types of investment strategies, such as sector rotation and tactical asset allocation. These strategies entail using the index to find investment opportunities in particular industries or to make tactical asset class switches based on market performance.

Benchmark for equity funds

The Wilshire 5000 index is commonly used as a benchmark for equity funds because it represents a broad measure of the US equity market. It is often used by investment managers as a tool for asset allocation and performance evaluation. The Wilshire 5000 index is further divided into a number of sub-indices according to market capitalization, style, and sector. With the help of these sub-indices, investors can monitor the performance of particular sectors of the US stock market and design investment plans that are unique to their needs.

Academic studies frequently use the Wilshire 5000 index to examine US equity market behavior and test theories regarding the effectiveness and predictability of stock prices. In financial and economic modeling, it is frequently used as a benchmark.

Financial products around the Wilshire 5000 index

A number of financial products, including mutual funds, exchange-traded funds (ETFs), and index funds, use the Wilshire 5000 index as a benchmark. These products use investments in a diverse portfolio of the underlying securities to track the performance of the index.

  • The Vanguard Total Stock Market Index Fund, which invests in all of the securities in the Wilshire 5000 index in the same proportion as the index and aims to replicate the performance of the index, is one of the mutual funds that tracks the Wilshire 5000 index.
  • The SPDR Wilshire 5000 ETF is one example of an ETF that tracks the Wilshire 5000 index. ETFs can be bought and sold at any time during the trading day, just like stocks.
  • Futures contracts based on the Wilshire 5000 index are available for trading on futures exchanges. Investors can use these contracts to hedge their existing positions or make predictions about the index’s future course.
  • Index funds that follow the Wilshire 5000 index are an alternative to mutual funds and ETFs. These funds are frequently used by passive investors who want exposure to the larger U.S. equity market because they aim to closely replicate the performance of the index.

Historical data for the Wilshire 5000 index

How to get the data?

The Wilshire 5000 index is the most common index used in finance, and historical data for the Wilshire 5000 index can be easily downloaded from the internet.

For example, you can download data for the Wilshire 5000 index from January 3, 1989 on Yahoo! Finance (the Yahoo! code for Wilshire 5000 index is ^W5000).

Yahoo! Finance
Source: Yahoo! Finance.

You can also download the same data from a Bloomberg terminal.

R program

The R program below written by Shengyu ZHENG allows you to download the data from Yahoo! Finance website and to compute summary statistics and risk measures about the Wilshire 5000 index.

Download R file

Data file

The R program that you can download above allows you to download the data for the Wilshire 5000 index from the Yahoo! Finance website. The database starts on January 3, 1989. It also computes the returns (logarithmic returns) from closing prices.

Table 3 below represents the top of the data file for the Wilshire 5000 index downloaded from the Yahoo! Finance website with the R program.

Table 3. Top of the data file for the Wilshire 5000 index.
Top of the file for the Wilshire 5000 index data
Source: computation by the author (data: Yahoo! Finance website).

Evolution of the Wilshire 5000 index

Figure 1 below gives the evolution of the Wilshire 5000 index from January 3, 1989 to December 30, 2022 on a daily basis.

Figure 1. Evolution of the Wilshire 5000 index.
Evolution of the Wilshire 5000 index
Source: computation by the author (data: Yahoo! Finance website).

Figure 2 below gives the evolution of the Wilshire 5000 index returns from January 3, 1989 to December 30, 2022 on a daily basis.

Figure 2. Evolution of the Wilshire 5000 index returns.
Evolution of the Wilshire 5000 index return
Source: computation by the author (data: Yahoo! Finance website).

Summary statistics for the Wilshire 5000 index

The R program that you can download above also allows you to compute summary statistics about the returns of the Wilshire 5000 index.

Table 4 below presents the following summary statistics estimated for the Wilshire 5000 index:

  • The mean
  • The standard deviation (the squared root of the variance)
  • The skewness
  • The kurtosis.

The mean, the standard deviation / variance, the skewness, and the kurtosis refer to the first, second, third and fourth moments of statistical distribution of returns respectively.

Table 4. Summary statistics for the Wilshire 5000 index.
Summary statistics for the Wilshire 5000 index
Source: computation by the author (data: Yahoo! Finance website).

Statistical distribution of the Wilshire 5000 index returns

Historical distribution

Figure 3 represents the historical distribution of the Wilshire 5000 index daily returns for the period from January 3, 1989 to December 30, 2022.

Figure 3. Historical distribution of the Wilshire 5000 index returns.
Historical distribution of the daily Wilshire 5000 index returns
Source: computation by the author (data: Yahoo! Finance website).

Gaussian distribution

The Gaussian distribution (also called the normal distribution) is a parametric distribution with two parameters: the mean and the standard deviation of returns. We estimated these two parameters over the period from January 3, 1989 to December 30, 2022. The mean of daily returns is equal to 0.02% and the standard deviation of daily returns is equal to 1.20% (or equivalently 5.88% for the annual mean and 19.38% for the annual standard deviation as shown in Table 3 above).

Figure 4 below represents the Gaussian distribution of the Wilshire 5000 index daily returns with parameters estimated over the period from January 3, 1989 to December 30, 2022.

Figure 4. Gaussian distribution of the Wilshire 5000 index returns.
Gaussian distribution of the daily Wilshire 5000 index returns
Source: computation by the author (data: Yahoo! Finance website).

Risk measures of the Wilshire 5000 index returns

The R program that you can download above also allows you to compute risk measures about the returns of the Wilshire 5000 index.

Table 5 below presents the following risk measures estimated for the Wilshire 5000 index:

  • The long-term volatility (the unconditional standard deviation estimated over the entire period)
  • The short-term volatility (the standard deviation estimated over the last three months)
  • The Value at Risk (VaR) for the left tail (the 5% quantile of the historical distribution)
  • The Value at Risk (VaR) for the right tail (the 95% quantile of the historical distribution)
  • The Expected Shortfall (ES) for the left tail (the average loss over the 5% quantile of the historical distribution)
  • The Expected Shortfall (ES) for the right tail (the average loss over the 95% quantile of the historical distribution)
  • The Stress Value (SV) for the left tail (the 1% quantile of the tail distribution estimated with a Generalized Pareto distribution)
  • The Stress Value (SV) for the right tail (the 99% quantile of the tail distribution estimated with a Generalized Pareto distribution)

Table 5. Risk measures for the Wilshire 5000 index.
Risk measures for the Wilshire 5000 index
Source: computation by the author (data: Yahoo! Finance website).

The volatility is a global measure of risk as it considers all the returns. The Value at Risk (VaR), Expected Shortfall (ES) and Stress Value (SV) are local measures of risk as they focus on the tails of the distribution. The study of the left tail is relevant for an investor holding a long position in the Wilshire 5000 index while the study of the right tail is relevant for an investor holding a short position in the Wilshire 5000 index.

Why should I be interested in this post?

For a number of reasons, management students (as future managers and individual investors) should learn about the Wilshire 5000 index. The performance of almost all listed American companies is tracked by this stock market index, which is first and foremost well-known and respected. Gaining a deeper understanding of the US small-cap stock market and the businesses that fuel its expansion requires knowledge of the Wilshire 5000 index. Individual investors can assess the performance of their own investments and those of their organization by comprehending the Wilshire 5000 index and its components. Last but not least, a lot of businesses base their mutual funds and exchange-traded funds (ETFs) on the Wilshire 5000 index which can considered as interesting assets to diversify a portfolio.

Related posts on the SimTrade blog

About financial indexes

   ▶ Nithisha CHALLA Financial indexes

   ▶ Nithisha CHALLA Calculation of financial indexes

Related posts on the SimTrade blog

About financial indexes

   ▶ Nithisha CHALLA Financial indexes

   ▶ Nithisha CHALLA Calculation of financial indexes

   ▶ Nithisha CHALLA The business of financial indexes

   ▶ Nithisha CHALLA Float

About other US financial indexes

   ▶ Nithisha CHALLA The DJIA index

   ▶ Nithisha CHALLA The S&P 500 index

   ▶ Nithisha CHALLA The NASDAQ index

   ▶ Nithisha CHALLA The Russell 2000 index

About portfolio management

   ▶ Youssef LOURAOUI Portfolio

   ▶ Jayati WALIA Returns

About statistics

   ▶ Shengyu ZHENG Moments de la distribution

   ▶ Shengyu ZHENG Mesures de risques

Useful resources

Yahoo! Finance Wilshire 5000 Total Market Index

Wikipedia Wilshire 5000

Forbes The Wilshire 5000: Invest In The Entire U.S. Stock Market

The Street What Is the Wilshire 5000 and Why Is It Important?

Academic research

Academic research about risk

Longin F. (2000) From VaR to stress testing: the extreme value approach Journal of Banking and Finance, N°24, pp 1097-1130.

Longin F. (2016) Extreme events in finance: a handbook of extreme value theory and its applications Wiley Editions.

Data

Yahoo! Finance

Yahoo! Finance Data for the Wilshire 5000 index

About the author

The article was written in April 2023 by Nithisha CHALLA (ESSEC Business School, Grande Ecole Program – Master in Management, 2021-2023).

The Russell 2000 index

by

The Russell 2000 index

Nithisha CHALLA

In this article, Nithisha CHALLA (ESSEC Business School, Grande Ecole Program – Master in Management, 2021-2023) presents the Russell 2000 index and details its characteristics.

The Russell 2000 index

As we can already notice in the name, Russell 2000 Index is a stock market index that tracks the performance of 2,000 small-cap companies in the United States. It was introduced by the Russell Investment Group in 1984 and is now created, managed, and distributed by FTSE Russell, a subsidiary of the London Stock Exchange Group. The Russell Index family has three indexes in it, Russell 1000, Russell 2000 and the Russell 3000.

The Russell 2000 has historically outperformed the larger-cap S&P 500 Index over the long term. According to data from FTSE Russell, the Russell 2000 has returned an average of 10.7% annually over the past 20 years, compared to an average return of 7.5% for the S&P 500 over the same period.

The Russell 2000 is widely used as a benchmark by active fund managers who specialize in small-cap stocks. As of March 2023, the largest sector in the Russell 2000 was healthcare, followed by technology and financials. The index is market-capitalization weighted, which means that larger companies have a greater impact on the index performance. The index is also used as the basis for exchange-traded funds (ETFs) and other financial products that allow investors to gain exposure to small-cap stocks.

FTSE Russell is known for its commitment to transparency and the accuracy of its index calculations. The company uses a rules-based methodology for selecting and weighting stocks in its indices, and it provides detailed documentation on its methodology and data sources to ensure that investors can make informed decisions about using its indices for benchmarking and investment purposes.

How is the Russell 2000 index represented in trading platforms and financial websites? The ticker symbol used in the financial industry for the Russell 2000 index is “RUT”.

Table 1 below gives the Top 10 stocks in the Russell 2000 index in terms of market capitalization as of January 31, 2023.

Table 1. Top 10 stocks in the Russell 2000 index.
Top 10 stocks in the Russell 2000 index
Source: computation by the author (data: YahooFinance! financial website).

Table 2 gives the sector representation of the Russell 2000 index in terms of number of stocks and market capitalization as of January 31, 2023.

Table 2. Sector representation in the Russell 2000 index.
Sector representation in the Russell 2000 index
Source: computation by the author (data: YahooFinance! financial website).

Calculation of the Russell 2000 index value

The value of the Russell 2000 Index is calculated using a formula that takes into account the market capitalization of the individual stocks that are included in the index. This means the larger companies have a greater impact on the index than the smaller companies.

The Russell 2000 is reconstituted annually, typically in June. During this process, the index is updated to include the most recent data on small-cap stocks, and companies are added or removed from the index based on their market capitalization.

The formula for a market capitalization-weighted index is given by

Market Capitalization Index value

where I is the index value, k a given asset, K the number of assets in the index, Pk the market price of asset k, Nk the number of issued shares for asset k, and t the time of calculation of the index.

In a market capitalization-weighted index, the weight of asset k is given by formula can be rewritten as

Market Capitalization Weighted Index Weight

which clearly shows that the weight of each asset in the index is its market capitalization of the asset divided by the sum of the market capitalizations of all assets.

Note that the divisor, whose calculation is based on the number of shares, is typically adjusted for events such as stock splits and dividends. The divisor is used to ensure that the value of the index remains consistent over time despite changes in the number of outstanding shares.

Use of the Russell 2000 index in asset management

The Russell 2000 index is widely used in asset management as a benchmark for small-cap stocks in the United States. Small-cap stock experts who run active funds frequently use the Russell 2000 as a benchmark for their performance. On the other hand, passive fund managers can create index funds or exchange-traded funds (ETFs) that follow the performance of the Russell 2000 using the Russell 2000 as a base. In addition to serving as a benchmark for active and passive fund managers, the Russell 2000 index is also used by individual investors who are interested in small-cap stocks. Overall, the Russell 2000 index is a valuable tool for asset managers, and it has a significant impact on the investment strategies and decisions made in this market segment.

Benchmark for equity funds

Equity funds are actively managed investment vehicles that pool capital from a number of investors to buy stocks from a variety of industries. The Russell 2000 index serves as a benchmark for fund managers when assessing the performance of their small-cap equity funds. Fund managers might use a variety of investment strategies, such as top-down sector allocation or bottom-up stock selection, to outperform the benchmark.

Investors can get a good idea of how well a small-cap equity fund is doing in relation to the overall market by comparing the fund’s performance to that of the Russell 2000 index. However, it’s crucial to keep in mind that there are additional elements, such as fees, expenses, and the expertise and experience of the fund manager, that can impact the performance of an equity fund.

Financial products around the Russell 2000 index

There are a number of financial products that either provide exposure to the index or use information from the index. Not just the index funds but there are numerous ETFs and other financial products such as mutual funds, futures and options etc.

  • Exchange-Traded Funds, Options Contracts, Futures Contracts, Index funds and Mutual funds.
  • ETFs are the investment funds that are traded like stocks. ETFs based on the Russell 2000 Index include the iShares Russell 2000 ETF and the Vanguard Russell 2000 ETF.
  • Index mutual funds that track the performance of the Russell 2000 Index typically have low expense ratios and are designed to provide returns that closely match the performance of the index.
  • Futures and options contracts based on the Russell 2000 Index are traded on several exchanges, including the Chicago Mercantile Exchange (CME) and the Intercontinental Exchange (ICE).

Historical data for the Russell 2000 index

How to get the data?

The Russell 2000 index is the most common index used in finance, and historical data for the Russell 2000 index can be easily downloaded from the internet.

For example, you can download data for the Russell 2000 index from September 10, 1987 on Yahoo! Finance (the Yahoo! code for Russell 2000 index is ^RUT).

Yahoo! Finance
Source: Yahoo! Finance.

You can also download the same data from a Bloomberg terminal.

R program

The R program below written by Shengyu ZHENG allows you to download the data from Yahoo! Finance website and to compute summary statistics and risk measures about the Russell 2000 index.

Download R file

Data file

The R program that you can download above allows you to download the data for the Russell 2000 index from the Yahoo! Finance website. The database starts on September 10, 1987. It also computes the returns (logarithmic returns) from closing prices.

Table 3 below represents the top of the data file for the Russell 2000 index downloaded from the Yahoo! Finance website with the R program.

Table 3. Top of the data file for the Russell 2000 index.
Top of the file for the Russell 2000 index data
Source: computation by the author (data: Yahoo! Finance website).

Evolution of the Russell 2000 index

Figure 1 below gives the evolution of the Russell 2000 index from September 10, 1987 to December 30, 2022 on a daily basis.

Figure 1. Evolution of the Russell 2000 index.
Evolution of the Russell 2000 index
Source: computation by the author (data: Yahoo! Finance website).

Figure 2 below gives the evolution of the Russell 2000 index returns from September 10, 1987 to December 30, 2022 on a daily basis.

Figure 2. Evolution of the Russell 2000 index returns.
Evolution of the Russell 2000 index return
Source: computation by the author (data: Yahoo! Finance website).

Summary statistics for the Russell 2000 index

The R program that you can download above also allows you to compute summary statistics about the returns of the Russell 2000 index.

Table 4 below presents the following summary statistics estimated for the Russell 2000 index:

  • The mean
  • The standard deviation (the squared root of the variance)
  • The skewness
  • The kurtosis.

The mean, the standard deviation / variance, the skewness, and the kurtosis refer to the first, second, third and fourth moments of statistical distribution of returns respectively.

Table 4. Summary statistics for the Russell 2000 index.
Summary statistics for the Russell 2000 index
Source: computation by the author (data: Yahoo! Finance website).

Statistical distribution of the Russell 2000 index returns

Historical distribution

Figure 3 represents the historical distribution of the Russell 2000 index daily returns for the period from September 10, 1987 to December 30, 2022.

Figure 3. Historical distribution of the Russell 2000 index returns.
Historical distribution of the daily Russell 2000 index returns
Source: computation by the author (data: Yahoo! Finance website).

Gaussian distribution

The Gaussian distribution (also called the normal distribution) is a parametric distribution with two parameters: the mean and the standard deviation of returns. We estimated these two parameters over the period from September 10, 1987 to December 30, 2022. The mean of daily returns is equal to 0.02% and the standard deviation of daily returns is equal to 1.20% (or equivalently 5.88% for the annual mean and 19.38% for the annual standard deviation as shown in Table 3 above).

Figure 4 below represents the Gaussian distribution of the Russell 2000 index daily returns with parameters estimated over the period from September 10, 1987 to December 30, 2022.

Figure 4. Gaussian distribution of the Russell 2000 index returns.
Gaussian distribution of the daily Russell 2000 index returns
Source: computation by the author (data: Yahoo! Finance website).

Risk measures of the Russell 2000 index returns

The R program that you can download above also allows you to compute risk measures about the returns of the Russell 2000 index.

Table 5 below presents the following risk measures estimated for the Russell 2000 index:

  • The long-term volatility (the unconditional standard deviation estimated over the entire period)
  • The short-term volatility (the standard deviation estimated over the last three months)
  • The Value at Risk (VaR) for the left tail (the 5% quantile of the historical distribution)
  • The Value at Risk (VaR) for the right tail (the 95% quantile of the historical distribution)
  • The Expected Shortfall (ES) for the left tail (the average loss over the 5% quantile of the historical distribution)
  • The Expected Shortfall (ES) for the right tail (the average loss over the 95% quantile of the historical distribution)
  • The Stress Value (SV) for the left tail (the 1% quantile of the tail distribution estimated with a Generalized Pareto distribution)
  • The Stress Value (SV) for the right tail (the 99% quantile of the tail distribution estimated with a Generalized Pareto distribution)

Table 5. Risk measures for the Russell 2000 index.
Risk measures for the Russell 2000 index
Source: computation by the author (data: Yahoo! Finance website).

The volatility is a global measure of risk as it considers all the returns. The Value at Risk (VaR), Expected Shortfall (ES) and Stress Value (SV) are local measures of risk as they focus on the tails of the distribution. The study of the left tail is relevant for an investor holding a long position in the Russell 2000index while the study of the right tail is relevant for an investor holding a short position in the Russell 2000 index.

Why should I be interested in this post?

For a number of reasons, management students (as future managers and individual investors) should learn about the Russell 2000 index. The performance of 2000 small-cap American companies is tracked by this stock market index, which is first and foremost well-known and respected. Gaining a deeper understanding of the US small-cap stock market and the businesses that fuel its expansion requires knowledge of the Russell 2000 index. Individual investors can assess the performance of their own investments and those of their organization by comprehending the Russell 2000 index and its components. Last but not least, a lot of businesses base their mutual funds and exchange-traded funds (ETFs) on the Russell 2000 index which can considered as interesting assets to diversify a portfolio.

Related posts on the SimTrade blog

About financial indexes

   ▶ Nithisha CHALLA Financial indexes

   ▶ Nithisha CHALLA Calculation of financial indexes

   ▶ Nithisha CHALLA The business of financial indexes

   ▶ Nithisha CHALLA Float

About other US financial indexes

   ▶ Nithisha CHALLA The DJIA index

   ▶ Nithisha CHALLA The S&P 500 index

   ▶ Nithisha CHALLA The NASDAQ index

   ▶ Nithisha CHALLA The Wilshire 5000 index

About portfolio management

   ▶ Youssef LOURAOUI Portfolio

   ▶ Jayati WALIA Returns

About statistics

   ▶ Shengyu ZHENG Moments de la distribution

   ▶ Shengyu ZHENG Mesures de risques

Useful resources

Wikipedia Russell indexes

Finance Strategists Defining Russell 2000 Index

FTSE Russell The Russell 2000 Index: Small cap index of choice

Motley Fool 10 of the largest Russell 2000 companies

Academic research about risk

Longin F. (2000) From VaR to stress testing: the extreme value approach Journal of Banking and Finance, N°24, pp 1097-1130.

Longin F. (2016) Extreme events in finance: a handbook of extreme value theory and its applications Wiley Editions.

Data

Yahoo! Finance

Yahoo! Finance Data for the Russell 2000 index

About the author

The article was written in April 2023 by Nithisha CHALLA (ESSEC Business School, Grande Ecole Program – Master in Management, 2021-2023).

The NASDAQ index

by

The NASDAQ index

Nithisha CHALLA

In this article, Nithisha CHALLA (ESSEC Business School, Grande Ecole Program – Master in Management, 2021-2023) presents the NASDAQ index and details its characteristics.

The NASDAQ index

NASDAQ was first founded in 1971 and it is an American stock exchange. By market capitalization of shares traded it is the second-largest stock exchange in the world after the New York Stock Exchange (NYSE). As many of the technology and growth companies are listed on the exchange it is a popular benchmark for them. It has around 3000 companies listed on it, including some of the world’s top technology companies like Microsoft, Amazon, Facebook and Google.

The NASDAQ index is a market capitalization-weighted index that tracks the performance of the stocks listed on the NASDAQ exchange. It is widely used by investors and financial analysts to gauge the performance of the technology sector and the broader US economy.

Interestingly, there is a sister index, the Nasdaq Financial 100 that consists only of financial stocks. Both indices debuted together in 1985. The Nasdaq Financial 100 index was given more attention in the early years. However, the Nasdaq-100 has gained popularity over time due to the expansion of tech companies.

How is the NASDAQ index represented in trading platforms and financial websites? The ticker symbol used in the financial industry for the NASDAQ index is “NDAQ”.

Table 1 gives the Top 10 stocks in the NASDAQ index in terms of market capitalization as of August 26, 2022.

Table 1. Top 10 stocks in the NASDAQ index.
Top 10 stocks in the NASDAQ index
Source: computation by the author (data: NASDAQ! financial website).

Table 2 gives the sector representation of the NASDAQ index in terms of number of stocks and market capitalization as of January 31, 2023.

Table 2. Sector representation in the NASDAQ index.
Sector representation in the NASDAQ index
Source: computation by the author (data: ETmoney!).

Calculation of the NASDAQ index value

The NASDAQ index is a value-weighted index (also called a market-capitalization- weighted index). This means the larger companies have a greater impact on the index than the smaller companies.

At the end of each trading day the value of the NASDAQ index is determined in real-time and can be used as a benchmark for the performance of the index’s constituent companies’ current market prices.

The formula for a market-capitalization-weighted index is given by

Market Capitalization Index value

Where I is the index value, k a given asset, K the number of assets in the index, Pk the market price of asset k, Nk the number of issued shares for asset k, and t the time of calculation of the index.

In a market capitalization-weighted index, the weight of asset k is given by formula can be rewritten as

Market Capitalization Weighted Index Weight

which clearly shows that the weight of each asset in the index is its market capitalization of the asset divided by the sum of the market capitalizations of all assets.

Note that the divisor, whose calculation is based on the number of shares, is typically adjusted for events such as stock splits and dividends. The divisor is used to ensure that the value of the index remains consistent over time despite changes in the number of outstanding shares.

Use of the NASDAQ index in asset management

Given that the index is used for performance measuring it is widely used for constructing and analyzing investment portfolios. This index’s primary use is to create investment strategies, mitigate risk, and assess portfolio performance. Investors and asset managers utilize this index as a useful index to measure the overall performance of the market. It is mainly used for benchmarking, passive investing, active management and risk management.

Benchmark for equity funds

There are several indices that are used as a benchmark for equity funds, but the NASDAQ index is notable for its emphasis on businesses that invest in the technology sector, growth stocks, or both. It is primarily used to compare their performance to the overall market or a particular industry. Additionally, it gives investors a way to contrast the performance of various equity funds with various investment strategies or objectives.

While there are many advantages to using indexes as benchmarks, there are also some disadvantages and restrictions. For instance, benchmarks may not always be indicative of the precise investment goals or risk profile of a fund. Furthermore, benchmarks may be distorted by elements like the size or makeup of the companies included in the index.

Financial products around the NASDAQ index

Investors of all levels can invest in the Nasdaq-100 in a variety of ways, including through ETFs, mutual funds, options, futures, and annuities. ETFs that track the Nasdaq-100 are the easiest way to invest in the index. The ETF gives you exposure to all the 100 largest non-financial companies through a single investment. One of the most well-known ETFs that tracks the Nasdaq-100 index is the Invesco QQQ ETF and the First Trust NASDAQ-100 Technology Sector ETF (QTEC). The Nasdaq-100 is regarded as the best way to invest in some of the top non-financial companies listed on the Nasdaq because of its track record of strong index performance.

The Nasdaq-100 includes foreign stocks as well, unlike the S&P 500. Again, unlike the S&P 500, the Nasdaq-100 only permits non-financial companies to list on it. As of April 2023, a few of the international stocks that are a part of the Nasdaq-100 are Baidu from China, Ryanair from Ireland, Garmin from Cayman Island, and Infosys from India.

Index funds that attempt to track the Nasdaq Composite include Fidelity Investments’ FNCMX mutual fund and ONEQ exchange-traded fund. For investors looking for broad exposure to the stock market with relatively low fees, index funds are a popular option.

Historical data for the NASDAQ index

How to get the data?

The NASDAQ index is the most common index used in finance, and historical data for the NASDAQ index can be easily downloaded from the internet.

For example, you can download data for the NASDAQ index from January 5, 1972 on Yahoo! Finance (the Yahoo! code for NASDAQ index is ^IXIC).

Yahoo! Finance
Source: Yahoo! Finance.

You can also download the same data from a Bloomberg terminal.

R program

The R program below written by Shengyu ZHENG allows you to download the data from Yahoo! Finance website and to compute summary statistics and risk measures about the Nasdaq index.

Download R file

Data file

The R program that you can download above allows you to download the data for the Nasdaq index from the Yahoo! Finance website. The database starts on January 2, 1992. It also computes the returns (logarithmic returns) from closing prices.

Table 3 below represents the top of the data file for the Nasdaq index downloaded from the Yahoo! Finance website with the R program.

Table 3. Top of the data file for the Nasdaq index.
Top of the file for the Nasdaq index data
Source: computation by the author (data: Yahoo! Finance website).

Summary statistics for the Nasdaq index

The R program that you can download above also allows you to compute summary statistics about the returns of the Nasdaq index.

Table 4 below presents the following summary statistics estimated for the Nasdaq index:

  • The mean
  • The standard deviation (the squared root of the variance)
  • The skewness
  • The kurtosis.

The mean, the standard deviation / variance, the skewness, and the kurtosis refer to the first, second, third and fourth moments of statistical distribution of returns respectively.

Table 4. Summary statistics for the Nasdaq index.
Summary statistics for the Nasdaq index
Source: computation by the author (data: Yahoo! Finance website).

Evolution of the Nasdaq index

Figure 1 below gives the evolution of the Nasdaq index from January 2, 1992 to December 30, 2022 on a daily basis.

Figure 1. Evolution of the Nasdaq index.
Evolution of the Nasdaq index
Source: computation by the author (data: Yahoo! Finance website).

Figure 2 below gives the evolution of the Nasdaq index returns from January 2, 1992 to December 30, 2022 on a daily basis.

Figure 2. Evolution of the Nasdaq index returns.
Evolution of the Nasdaq index return
Source: computation by the author (data: Yahoo! Finance website).

Statistical distribution of the Nasdaq index returns

Historical distribution

Figure 3 represents the historical distribution of the Nasdaq index daily returns for the period from January 2, 1992 to December 30, 2022.

Figure 3. Historical distribution of the Nasdaq index returns.
Historical distribution of the daily Nasdaq index returns
Source: computation by the author (data: Yahoo! Finance website).

Gaussian distribution

The Gaussian distribution (also called the normal distribution) is a parametric distribution with two parameters: the mean and the standard deviation of returns. We estimated these two parameters over the period from January 2, 1992 to December 30, 2022. The mean of daily returns is equal to 0.02% and the standard deviation of daily returns is equal to 1.20% (or equivalently 5.88% for the annual mean and 19.38% for the annual standard deviation as shown in Table 3 above).

Figure 4 below represents the Gaussian distribution of the Nasdaq index daily returns with parameters estimated over the period from January 2, 1992 to December 30, 2022.

Figure 4. Gaussian distribution of the Nasdaq index returns.
Gaussian distribution of the daily Nasdaq index returns
Source: computation by the author (data: Yahoo! Finance website).

Risk measures of the Nasdaq index returns

The R program that you can download above also allows you to compute risk measures based the returns of the Nasdaq index.

Table 5 below presents the following risk measures estimated for the Nasdaq index:

  • The long-term volatility (the unconditional standard deviation estimated over the entire period)
  • The short-term volatility (the standard deviation estimated over the last three months)
  • The Value at Risk (VaR) for the left tail (the 5% quantile of the historical distribution)
  • The Value at Risk (VaR) for the right tail (the 95% quantile of the historical distribution)
  • The Expected Shortfall (ES) for the left tail (the average loss over the 5% quantile of the historical distribution)
  • The Expected Shortfall (ES) for the right tail (the average loss over the 95% quantile of the historical distribution)
  • The Stress Value (SV) for the left tail (the 1% quantile of the tail distribution estimated with a Generalized Pareto distribution)
  • The Stress Value (SV) for the right tail (the 99% quantile of the tail distribution estimated with a Generalized Pareto distribution)

Table 5. Risk measures for the Nasdaq index.
Risk measures for the Nasdaq index
Source: computation by the author (data: Yahoo! Finance website).

The volatility is a global measure of risk as it considers all the returns. The Value at Risk (VaR), Expected Shortfall (ES) and Stress Value (SV) are local measures of risk as they focus on the tails of the distribution. The study of the left tail is relevant for an investor holding a long position in the Nasdaq index while the study of the right tail is relevant for an investor holding a short position in the Nasdaq index.

Why should I be interested in this post?

For a number of reasons, ESSEC students should learn about the Nasdaq index. The performance of tech-oriented companies is tracked by this stock market index, which is first and foremost well-known and respected. Gaining a deeper understanding of the US stock market and the businesses that fuel its expansion requires knowledge of the Nasdaq index. Management students can assess the performance of their own investments and those of their organization by comprehending the Nasdaq index and its components. Last but not least, a lot of businesses base their mutual funds and exchange-traded funds (ETFs) on the Nasdaq index.

Related posts on the SimTrade blog

About financial indexes

   ▶ Nithisha CHALLA Financial indexes

   ▶ Nithisha CHALLA Calculation of financial indexes

   ▶ Nithisha CHALLA The business of financial indexes

   ▶ Nithisha CHALLA Float

About other US financial indexes

   ▶ Nithisha CHALLA The DJIA index

   ▶ Nithisha CHALLA The S&P 500 index

   ▶ Nithisha CHALLA The Russell 2000 index

   ▶ Nithisha CHALLA The Wilshire 5000 index

About portfolio management

   ▶ Jayati WALIA Returns

   ▶ Youssef LOURAOUI Portfolio

About statistics

   ▶ Shengyu ZHENG Moments de la distribution

   ▶ Shengyu ZHENG Mesures de risques

Useful resources

Academic research about risk

Longin F. (2000) From VaR to stress testing: the extreme value approach Journal of Banking and Finance, N°24, pp 1097-1130.

Longin F. (2016) Extreme events in finance: a handbook of extreme value theory and its applications Wiley Editions.

Data: Yahoo! Finance

Yahoo! Finance

Yahoo! Finance Data for the Nasdaq index

Data: Bloomberg

Bloomberg

Bloomberg Data for the Nasdaq index

About the author

The article was written in April 2023 by Nithisha CHALLA (ESSEC Business School, Grande Ecole Program – Master in Management, 2021-2023).

The DJIA index

by

The DJIA index

Nithisha CHALLA

In this article, Nithisha CHALLA (ESSEC Business School, Grande Ecole Program – Master in Management, 2021-2023) presents the Dow Jones Industrial Average (DJIA) index and details its characteristics.

The DJIA index

The Dow Jones Industrial Average (DJIA) index was created on May 26, 1896, by Charles Dow and Edward Jones, the co-founders of Dow Jones & Company. It is publicly known as the Dow Jones index or the Dow in general. The DJIA is currently owned and managed by The Wall Street Journal.

It is a stock market index in the United States which represents the performance of 30 large-capitalization publicly traded companies. Today, it is no longer limited to just industrial companies like how it was initially and includes stocks from a variety of sectors, such as technology, healthcare, and finance.

Who decides about the selection of stocks in the index? The Wall Street Journal, which owns the index, selects the stocks based on a variety of factors, such as the company’s size and reputation, and the representation of the industries.

The DJIA is a price-weighted index, which means that each stock’s weight in the index is determined by its price per share rather than its market capitalization such as the S&P 500 index (see below for the technical details). The DJIA is published and disseminated in real-time by various financial news outlets and can be accessed by investors and traders around the world.

How is the DJIA index represented in trading platforms and financial websites? The ticker symbol used in the financial industry for the DJIA index is “DJI”.

Table 1 gives the Top 10 stocks in the DJIA index in terms of market capitalization as of January 19, 2023.

Table 1. Top 10 stocks in the DJIA index.
Top 10 stocks in the DJIA index
Source: computation by the author (data: Motley Fool financial website).

Table 2 gives the sector representation of the DJIA index in terms of number of stocks and market capitalization as of January 31, 2023.

Table 2. Sector representation in the DJIA index.
Sector representation in the DJIA index
Source: computation by the author (data: Wikipedia).

Calculation of the DJIA index value

As a price-weighted index, the DJIA has a greater impact on the index value when the stock prices of companies are higher. The DJIA index value is determined solely based on stock prices, disregarding any dividends that the companies that make up the index have paid.

The formula for a price-weighted index is given by

Price Weighted Index value

where I is the index value, k a given asset, K the number of assets in the index, Pk the market price of asset k, and t the time of calculation of the index.

In a price-weighted index, the weight of asset k is given by the following formula

Price Weighted Index Weight

which clearly shows that the weight of each asset in the index is its market price divided by the sum of the market prices of all assets.

Note that the divisor, which is equal to the number of shares, is typically adjusted for events such as stock splits and dividends. The divisor is used to ensure that the value of the index remains consistent over time despite changes in the number of outstanding shares. A more general formula may then be:

Index value

Where D is the divisor which is adjusted over time to account for events such as stock splits and dividends.

Use the DJIA index in asset management

As we all know, investors frequently use the DJIA index as a benchmark. The DJIA index is used by asset managers to compare the returns on their investments to market returns. Given that it is an index that gauges market performance, it supports investors in carrying out key asset management tasks like passive investments, the capacity to assess corporate risk, asset allocation, portfolio management, etc. But we should always be aware that the DJIA does not encompass all markets and industries in the US. As a result, whenever we evaluate the performance of the US market, we should always take other indexes such as the S&P 500 index and the Russell 2000 into account.

Benchmark for equity funds

Now how do we decide if DJIA is a benchmark for equity funds in the US market? Precisely by seeing if the index indicates all the sectors and industries in the market. Since the DJIA is a price-weighted index and only takes the top 30 companies into account, it is not typically used as a benchmark for the entire US market. We should also take into account other diverse indexes, such as the S&P 500 or the Russell 2000, which offer a more complete representation of the market, if we need a benchmark for the entire US market.

Financial products around the DJIA index

There are a number of financial products centered around the DJIA index that can offer investors some insight, as we are aware that it measures the performance of sizable publicly traded companies listed on the New York Stock Exchange (NYSE) and the Nasdaq. I listed the main financial products associated with the DJIA index through which investors can access the index as below:

  • Exchange-Traded Funds, Options Contracts, Futures Contracts, Index funds and Mutual funds.
  • ETFs are the investment funds that are traded like stocks. The SPDR Dow Jones Industrial Average ETF (DIA) and the ProShares Ultra Dow30 ETF are two examples of ETFs that track the DJIA index (DDM)
  • Futures and Options Contracts allow investors to buy or sell the DJIA index at a specific price and date in the future. Primarily to combat market volatility, to generate income through trading strategies, or to make predictions about the index’s future course
  • Mutual funds and index funds tend to focus more on investing in firms that are included in the DJIA index or attempt to replicate the performance of the index by purchasing the same stocks that make up the index

Historical data for the DJIA index

How to get the data?

The DJIA index is the most common index used in finance, and historical data for the DJIA index can be easily downloaded from the internet.

For example, you can download data for the DJIA index from January 2, 1992 on Yahoo! Finance (the Yahoo! code for DJIA index is ^DJI).

Yahoo! Finance
Source: Yahoo! Finance.

You can also download the same data from a Bloomberg terminal.

R program

The R program below written by Shengyu ZHENG allows you to download the data from Yahoo! Finance website and to compute summary statistics and risk measures about the DJIA index.

Download R file

Data file

The R program that you can download above allows you to download the data for the DJIA index from the Yahoo! Finance website. The database starts on January 2, 1992. It also computes the returns (logarithmic returns) from closing prices.

Table 3 below represents the top of the data file for the DJIA index downloaded from the Yahoo! Finance website with the R program.

Table 3. Top of the data file for the DJIA index.
Top of the file for the DJIA index data
Source: computation by the author (data: Yahoo! Finance website).

Summary statistics for the Dow Jones index

The R program that you can download above also allows you to compute summary statistics about the returns of the Dow Jones index.

Table 4 below presents the following summary statistics estimated for the Dow Jones index:

  • The mean
  • The standard deviation (the squared root of the variance)
  • The skewness
  • The kurtosis.

The mean, the standard deviation / variance, the skewness, and the kurtosis refer to the first, second, third and fourth moments of statistical distribution of returns respectively.

Table 4. Summary statistics for the Dow Jones index.
Summary statistics for the Dow Jones index
Source: computation by the author (data: Yahoo! Finance website).

Evolution of the Dow Jones index

Figure 1 below gives the evolution of the Dow Jones index from January 2, 1992 to December 30, 2022 on a daily basis.

Figure 1. Evolution of the Dow Jones index.
Evolution of the Dow Jones index
Source: computation by the author (data: Yahoo! Finance website).

Figure 2 below gives the evolution of the Dow Jones index returns from January 2, 1992 to December 30, 2022 on a daily basis.

Figure 2. Evolution of the Dow Jones index returns.
Evolution of the Dow Jones index return
Source: computation by the author (data: Yahoo! Finance website).

Statistical distribution of the Dow Jones index returns

Historical distribution

Figure 3 represents the historical distribution of the Dow Jones index daily returns for the period from January 2, 1992 to December 30, 2022.

Figure 3. Historical distribution of the Dow Jones index returns.
Historical distribution of the daily Dow Jones index returns
Source: computation by the author (data: Yahoo! Finance website).

Gaussian distribution

The Gaussian distribution (also called the normal distribution) is a parametric distribution with two parameters: the mean and the standard deviation of returns. We estimated these two parameters over the period from January 2, 1992 to December 30, 2022. The mean of daily returns is equal to 0.02% and the standard deviation of daily returns is equal to 1.20% (or equivalently 5.88% for the annual mean and 19.38% for the annual standard deviation as shown in Table 3 above).

Figure 4 below represents the Gaussian distribution of the DJIA index daily returns with parameters estimated over the period from January 2, 1992 to December 30, 2022.

Figure 4. Gaussian distribution of the Dow Jones index returns.
Gaussian distribution of the daily Dow Jones index returns
Source: computation by the author (data: Yahoo! Finance website).

Risk measures of the Dow Jones index returns

The R program that you can download above also allows you to compute risk measures about the returns of the Dow Jones index.

Table 5 below presents the following risk measures estimated for the Dow Jones index:

  • The long-term volatility (the unconditional standard deviation estimated over the entire period)
  • The short-term volatility (the standard deviation estimated over the last three months)
  • The Value at Risk (VaR) for the left tail (the 5% quantile of the historical distribution)
  • The Value at Risk (VaR) for the right tail (the 95% quantile of the historical distribution)
  • The Expected Shortfall (ES) for the left tail (the average loss over the 5% quantile of the historical distribution)
  • The Expected Shortfall (ES) for the right tail (the average loss over the 95% quantile of the historical distribution)
  • The Stress Value (SV) for the left tail (the 1% quantile of the tail distribution estimated with a Generalized Pareto distribution)
  • The Stress Value (SV) for the right tail (the 99% quantile of the tail distribution estimated with a Generalized Pareto distribution)

Table 5. Risk measures for the Dow Jones index.
Risk measures for the Dow Jones index
Source: computation by the author (data: Yahoo! Finance website).

The volatility is a global measure of risk as it considers all the returns. The Value at Risk (VaR), Expected Shortfall (ES) and Stress Value (SV) are local measures of risk as they focus on the tails of the distribution. The study of the left tail is relevant for an investor holding a long position in the S&P 500 index while the study of the right tail is relevant for an investor holding a short position in the S&P 500 index.

Why should I be interested in this post?

For a number of reasons, ESSEC students should learn about the Dow Jones index. The performance of 30 large-cap American companies is tracked by this stock market index, which is first and foremost well-known and respected. Gaining a deeper understanding of the US stock market and the businesses that fuel its expansion requires knowledge of the Dow Jones index. Management students can assess the performance of their own investments and those of their organization by comprehending the Dow Jones index and its components. Last but not least, a lot of businesses base their mutual funds and exchange-traded funds (ETFs) on the Dow Jones index.

Related posts on the SimTrade blog

About financial indexes

   ▶ Nithisha CHALLA Financial indexes

   ▶ Nithisha CHALLA Calculation of financial indexes

   ▶ Nithisha CHALLA The business of financial indexes

   ▶ Nithisha CHALLA Float

About other US financial indexes

   ▶ Nithisha CHALLA The S&P 500 index

   ▶ Nithisha CHALLA The NASDAQ index

   ▶ Nithisha CHALLA The Russell 2000 index

   ▶ Nithisha CHALLA The Wilshire 5000 index

About portfolio management

   ▶ Jayati WALIA Returns

   ▶ Youssef LOURAOUI Portfolio

About statistics

   ▶ Shengyu ZHENG Moments de la distribution

   ▶ Shengyu ZHENG Mesures de risques

Useful resources

Academic research about risk

Longin F. (2000) From VaR to stress testing: the extreme value approach Journal of Banking and Finance, N°24, pp 1097-1130.

Longin F. (2016) Extreme events in finance: a handbook of extreme value theory and its applications Wiley Editions.

Data: Yahoo! Finance

Yahoo! Finance

Yahoo! Finance Data for the DJIA index

Data: Bloomberg

Bloomberg

Bloomberg Data for the DJIA index

About the author

The article was written in April 2023 by Nithisha CHALLA (ESSEC Business School, Grande Ecole Program – Master in Management, 2021-2023).

Float

by

Float

Nithisha CHALLA

In this article, Nithisha CHALLA (ESSEC Business School, Grande Ecole Program – Master in Management, 2021-2023) explains float and its use in the construction financial indexes.

What is Float?

The term “float” (sometimes mentioned as “free float”) refers to the quantity of shares that are readily tradable in financial markets. The float is defined as

Float = Total outstanding shares – Closely held shares – Restricted shares

Outstanding shares are the total number of shares issued by the company.

Closely held shares are the shares of a company that are owned by a small number of shareholders and are not traded on a public stock exchange. These shareholders may include company founders, family members, or a small group of private investors.

Restricted shares are the shares that are not transferable until certain conditions are met and are typically held by corporate management, such as executives and directors. Restricted shares are a type of equity compensation that some employees receive.

The float is usually expressed as a percentage of the total number of shares issued by the company.

Float and IPO

When a company conducts an initial public offering (IPO) or a seasoned offering (SEO) to finance its operational activities and investments, it releases a certain number of shares onto the market that are available for purchase by anyone interested in acquiring a piece of the company. The number of shares issued by the company increases the float. Before the IPO, the float is equal to zero. After the IPO, the float increases but may be relatively small as the founder or top managers of the company may want or have to keep some of their shares.

Why is the float important?

The float is crucial for the calculation of market capitalization-weighted stock market indices. The weight of a company’s stock in the index and, consequently, its impact on the performance of the index as a whole, can change depending on whether shares are included in or excluded from the float. Because of this, a lot of indices base their values solely on the shares in the float, known as the float-adjusted market capitalization method.

Stock market liquidity increases as the float increases. As the number of shares that can be purchased and sold increases, it makes it simpler for an investor to enter and exit the market.

High-float stocks and low-float stocks

In the equity market, we often distinguish high-float stocks and low-float stocks according to the percentage of shares that are available for trading in the market. High-float stocks have more supply and more shares available for trading than low-float stocks.

High float stocks have greater liquidity and are less volatile. In a situation where there is extremely heavy demand, supply and demand will become imbalanced, which will lead to extreme price moves.

Example

The percentage of float shares in relation to all outstanding shares is known as the float percentage. Let us consider the case of Amazon. As of September 2021, Amazon had approximately 505 million shares outstanding. Of these shares, approximately 425 million were considered “float shares”. Float shares are the shares available for trading by the public and exclude shares held by insiders, institutional investors, and other long-term investors.

Therefore, Amazon’s float share percentage would be calculated as follows:
(425 million float shares / 505 million outstanding shares) x 100% = 84.16%

This indicates that the public had access to about 84.16% of Amazon’s outstanding shares for trading. Insiders, institutions, and other long-term investors held the remaining 15.84% of the stock.

Indexes using the float

Equity indices that track the performance of a particular group of companies, such as small-cap or mid-cap companies, are frequently created using float-based indexes. The market capitalization of each company, which is determined by multiplying the total number of outstanding shares by the current share market price, is considered in the calculation of these indices.

The Russell 2000 index, which tracks the performance of 2,000 small-cap companies in the US, and the MSCI World Small Cap index, which tracks the performance of small-cap companies in developed markets worldwide, are two of the many examples of indexes that make use of the float.

We present below the formula for a market-capitalization-weighted index and a float-adjusted market-capitalization-weighted index.

Market-capitalization-weighted index

A market capitalization-weighted index is calculated by multiplying the price of each asset in the index by its number of outstanding shares and summing the resulting values. The weighting of each asset in the index is determined by its market capitalization, so that the largest and most influential companies have the greatest impact on the overall performance of the index.

The formula for a market-capitalization-weighted index is given by

Market Capitalization Index value

Where I is the index value, k a given asset, K the number of assets in the index, Pk the market price of asset k, Nk the number of issued shares for asset k, and t the time of calculation of the index.

In a market capitalization-weighted index, the weight of asset k is given by formula can be rewritten as

Market Capitalization Weighted Index Weight

Which clearly shows that the weight of each asset in the index is its market capitalization of the asset divided by the sum of the market capitalizations of all assets.

Note that the divisor, whose calculation is based on the number of shares, is typically adjusted for events such as stock splits and dividends. The divisor is used to ensure that the value of the index remains consistent over time despite changes in the number of outstanding shares.

Float-adjusted market-capitalization-weighted index

In a float-adjusted market-capitalization-weighted index, the market-capitalization weight of each asset is adjusted for its market float. It is also called a free float. Instead of taking into account shares held by insiders, governments, or other entities that might not be available for trading, the weight is adjusted based on the percentage of shares that are actually traded on the open market.

This differs from the market capitalization weighted index as it accounts for the shares outstanding of a company. A float-adjusted market capitalization-weighted index only takes into account shares that are freely available for trading, whereas a market capitalization-weighted index takes into account all outstanding shares, providing a more accurate picture of the performance of the market.

The formula for a float-adjusted market-capitalization-weighted index is given by

Float Adjusted Market Capitalization Index value

Where I is the index value, k a given asset, K the number of assets in the index, Pk the market price of asset k, Nk the number of issued shares for asset k, Fk the float factor of asset k, and t the time of calculation of the index.

In a float-adjusted market-capitalization-weighted index, the weight of asset k is given by formula can be rewritten as

Float Adjusted Market Capitalization Weighted Index Weight

Why should I be interested in this post?

As a key idea in finance and investment, float should be covered by management students. Float has important effects on both managers and investors. Analyzing a company’s financial statements can also benefit from having a solid understanding of floats. When making a choice, a management student who is researching a company’s stock as a potential investment should keep this in mind.

Related posts on the SimTrade blog

   ▶ All posts about Financial techniques

   ▶ Nithisha CHALLA Financial indexes

   ▶ Nithisha CHALLA Calculation of financial indexes

   ▶ Nithisha CHALLA The DJIA index

Useful resources

Bankrate What is a stock float
Business Insider Floating stock: Why it’s important for investors to know a company’s float

CFI What is Floating Stock?

The Economic Times Float and IPO

Russel How are indexes weighted?

About the author

The article was written in April 2023 by Nithisha CHALLA (ESSEC Business School, Grande Ecole Program – Master in Management, 2021-2023).

The S&P 500 index

by

The S&P 500 index

Nithisha CHALLA

In this article, Nithisha CHALLA (ESSEC Business School, Grande Ecole Program – Master in Management, 2021-2023) presents the S&P 500 index and details its characteristics.

The S&P 500 index

The performance of 500 major capital companies listed on the US stock exchange is summarized by a financial index called the S&P 500 index. The stocks of the S&P 500 index are traded on the New York Stock Exchange and NASDAQ, which are the two major stock exchanges in the United States of America. This index serves as a benchmark for the American stock market and investors use it to monitor the performance of the market. The selection of 500 stocks only is deemed enough to represent the stock market (in terms of market capitalization).

The S&P 500 index was first established by Standard & Poor’s, a provider of financial services, on March 4, 1957. In order to provide a comprehensive assessment of the U.S. stock market, the index consists of a range of large-capital businesses from various industries and sectors. The S&P 500 index is currently managed by the index provider S&P Dow Jones Indices (a division of S&P Global).

Who makes the shortlist of the index and how the field is narrowed down? The S&P Dow Jones Indices oversees the selection procedure for index inclusion. The public float, financial viability, market capitalization, and a diverse representation of the US stock market—including technology, healthcare, financials, consumer goods, etc.—are some of the key criteria used to define the composition of the index.

How is the S&P 500 index represented in trading platforms and financial websites? The ticker symbol used in the financial industry for the S&P 500 index is “SPX”.

Table 1 gives the Top 10 stocks in the S&P 500 index in terms of market capitalization as of January 31, 2023.

Table 1. Top 10 stocks in the S&P 500 index.
Top 10 stocks in the S&P 500 index
Source: computation by the author (data: YahooFinance! financial website).

Table 2 gives the sector representation of the S&P 500 index in terms of number of stocks and market capitalization as of January 31, 2023.

Table 2. Sector representation in the S&P 500 index.
Sector representation in the S&P 500 index
Source: computation by the author (data: YahooFinance! financial website).

Calculation of the S&P 500 index value

The S&P 500 index is a value-weighted index (also called a market-capitalization- weighted index). This means the larger companies have a greater impact on the index than the smaller companies.

At the end of each trading day the value of the S&P 500 index is determined in real-time and can be used as a benchmark for the performance of the index’s constituent companies’ current market prices.

The formula to compute the S&P 500 index is given by

SP500 Index value

where I is the index value, k a given asset, K the number of assets in the index, Pk the market price of asset k, Nk the number of issued shares for asset k, and t the time of calculation of the index.

In a S&P 500 index, the weight of asset k is given by formula can be rewritten as

SP500 Index Weight

which clearly shows that the weight of each asset in the index is its market capitalization of the asset divided by the sum of the market capitalizations of all assets.

The divisor, whose calculation is based on the number of shares, is typically adjusted for events such as stock splits and dividends. The divisor is used to ensure that the value of the index remains consistent over time despite changes in the number of outstanding shares.

Note that there are two versions of the S&P 500 index: one which includes the performance of the company as well as the dividends the companies pay (so it is a dividend included index), and another one which only considers the performance of the company but does not consider the dividends.

Use of the S&P 500 index in asset management

Given that the index is used for performance measuring it is widely used for constructing and analyzing investment portfolios. This index’s primary use is to create investment strategies, mitigate risk, and assess portfolio performance. Investors and asset managers utilize this index as an useful index to measure the overall performance of the market.

Benchmark for equity funds

There are a number of indices used as a benchmark for equity funds but the S&P 500 index particularly focuses on the large capped companies in the US market. It is mainly differentiated by the asset class the index is focusing on and the investment strategies followed by the companies. For Example: DJIA uses price weighted stock strategy for the top 30 blue chip companies, whereas the NASDAQ Composite Index uses market capitalization-weighted index of more than 3,000 stocks in the NASDAQ Composite.

Financial products around the S&P 500 index

There are a number of financial products that either provide exposure to the index or use information from the index. Not just the index funds but there are numerous ETFs and specific sector related indices which provide exposure to the S&P 500 index. Other financial products would be mutual funds, futures and options etc.

Historical data for the S&P 500 index

How to get the data?

The S&P 500 index is the most common index used in finance, and historical data for the S&P 500 index can be easily downloaded from the internet.

For example, you can download historical data for the S&P 500 index from December 30, 1927 on Yahoo! Finance (the Yahoo! code for S&P 500 index is ^GSPC).

Yahoo! Finance
Source: Yahoo! Finance.

You can also download the same data from a Bloomberg terminal.

R program

The R program below written by Shengyu ZHENG allows you to download the data from Yahoo! Finance website and to compute summary statistics and risk measures about the S&P 500 index.

Download R file

Data file

The R program that you can download above allows you to download the data for the S&P 500 index from the Yahoo! Finance website. The database starts on December 30, 1927. It also computes the returns (logarithmic returns) from closing prices.

Table 3 below represents the top of the data file for the S&P 500 index downloaded from the Yahoo! Finance website with the R program.

Table 3. Top of the data file for the S&P 500 index.
Top of the file for the S&P 500 index data
Source: computation by the author (data: Yahoo! Finance website).

Summary statistics for the S&P 500 index

The R program that you can download above also allows you to compute summary statistics about the returns of the S&P 500 index.

Table 4 below presents the following summary statistics estimated for the S&P 500 index:

  • The mean
  • The standard deviation (the squared root of the variance)
  • The skewness
  • The kurtosis.

The mean, the standard deviation / variance, the skewness, and the kurtosis refer to the first, second, third and fourth moments of statistical distribution of returns respectively.

Table 4. Summary statistics for the S&P 500 index.
Summary statistics for the S&P 500 index
Source: computation by the author (data: Yahoo! Finance website).

Evolution of the S&P 500 index

Figure 1 below gives the evolution of the S&P 500 index from December 30, 1927 to December 30, 2022 on a daily basis.

Figure 1. Evolution of the S&P 500 index.
Evolution of the S&P 500 index
Source: computation by the author (data: Yahoo! Finance website).

Figure 2 below gives the evolution of the S&P 500 index returns from December 30, 1927 to December 30, 2022 on a daily basis.

Figure 2. Evolution of the S&P 500 index returns.
Evolution of the S&P 500 index return
Source: computation by the author (data: Yahoo! Finance website).

Statistical distribution of the S&P 500 index returns

Historical distribution

Figure 3 represents the historical distribution of the S&P 500 index daily returns for the period from December 30, 1927 to December 30, 2022.

Figure 3. Historical distribution of the S&P 500 index returns.
Historical distribution of the daily S&P 500 index returns
Source: computation by the author (data: Yahoo! Finance website).

Gaussian distribution

The Gaussian distribution (also called the normal distribution) is a parametric distribution with two parameters: the mean and the standard deviation of returns. We estimated these two parameters over the period from December 30, 1927 to December 30, 2022. The mean of daily returns is equal to 0.02% and the standard deviation of daily returns is equal to 1.20% (or equivalently 5.88% for the annual mean and 19.38% for the annual standard deviation as shown in Table 3 above).

Figure 4 below represents the Gaussian distribution of the S&P 500 index daily returns with parameters estimated over the period from December 30, 1927 to December 30, 2022.

Figure 4. Gaussian distribution of the S&P 500 index returns.
Gaussian distribution of the daily S&P 500 index returns
Source: computation by the author (data: Yahoo! Finance website).

Risk measures of the S&P 500 index returns

The R program that you can download above also allows you to compute risk measures about the returns of the S&P 500 index.

Table 5 below presents the following risk measures estimated for the S&P 500 index:

  • The long-term volatility (the unconditional standard deviation estimated over the entire period)
  • The short-term volatility (the standard deviation estimated over the last three months)
  • The Value at Risk (VaR) for the left tail (the 5% quantile of the historical distribution)
  • The Value at Risk (VaR) for the right tail (the 95% quantile of the historical distribution)
  • The Expected Shortfall (ES) for the left tail (the average loss over the 5% quantile of the historical distribution)
  • The Expected Shortfall (ES) for the right tail (the average loss over the 95% quantile of the historical distribution)
  • The Stress Value (SV) for the left tail (the 1% quantile of the tail distribution estimated with a Generalized Pareto distribution)
  • The Stress Value (SV) for the right tail (the 99% quantile of the tail distribution estimated with a Generalized Pareto distribution)

Table 5. Risk measures for the S&P 500 index.
Risk measures for the S&P 500 index
Source: computation by the author (data: Yahoo! Finance website).

The volatility is a global measure of risk as it considers all the returns. The Value at Risk (VaR), Expected Shortfall (ES) and Stress Value (SV) are local measures of risk as they focus on the tails of the distribution. The study of the left tail is relevant for an investor holding a long position in the S&P 500 index while the study of the right tail is relevant for an investor holding a short position in the S&P 500 index.

Why should I be interested in this post?

For a number of reasons, ESSEC students should learn about the S&P 500 index. The performance of 500 large-cap American companies is tracked by this stock market index, which is first and foremost well-known and respected. Gaining a deeper understanding of the US stock market and the businesses that fuel its expansion requires knowledge of the S&P 500 index. Management students can assess the performance of their own investments and those of their organization by comprehending the S&P 500 index and its components. Last but not least, a lot of businesses base their mutual funds and exchange-traded funds (ETFs) on the S&P 500 index.

Related posts on the SimTrade blog

About financial indexes

   ▶ Nithisha CHALLA Financial indexes

   ▶ Nithisha CHALLA Calculation of financial indexes

   ▶ Nithisha CHALLA The business of financial indexes

   ▶ Nithisha CHALLA Float

About other US financial indexes

   ▶ Nithisha CHALLA The DJIA index

   ▶ Nithisha CHALLA The NASDAQ index

   ▶ Nithisha CHALLA The Russell 2000 index

   ▶ Nithisha CHALLA The Wilshire 5000 index

About portfolio management

   ▶ Jayati WALIA Returns

   ▶ Youssef LOURAOUI Portfolio

About statistics

   ▶ Shengyu ZHENG Moments de la distribution

   ▶ Shengyu ZHENG Mesures de risques

Useful resources

Academic research about risk

Longin F. (2000) From VaR to stress testing: the extreme value approach Journal of Banking and Finance, N°24, pp 1097-1130.

Longin F. (2016) Extreme events in finance: a handbook of extreme value theory and its applications Wiley Editions.

Data: Yahoo! Finance

Yahoo! Finance

Yahoo! Finance Historical data for the S&P 500 index

Data: Bloomberg

Bloomberg

Bloomberg Data for the S&P 500 index

About the author

The article was written in March 2023 by Nithisha CHALLA (ESSEC Business School, Grande Ecole Program – Master in Management, 2021-2023).