Automation in Audit

April 4, 2023 by Federico MARTINETTO

Automation in Audit

In this article, Federico MARTINETTO (ESSEC Business School, Exchange Global BBA, 2021) explains about the importance of the data automation in the audit process.

Why is intelligent automation important for the audit processes?

Traditional auditing has the following problems, for which intelligent automation can provide a solution:

It relies on manual labor of intensive data collection and examination, which makes traditional auditing costly, time-consuming, and error-prone.
It relies on sampling, where a representative sample of the data is selected to identify risks. This is because examining the entire data is expensive and time-consuming. If the selected data is not representative of the population being tested, auditors may conclude that there are more or fewer problems than actually exist. This problem is referred to as sampling risk.

By leveraging RPA and AI, intelligent automation:

Reduces the time spent on repetitive and tedious auditing tasks such as data collection, data extraction, or reporting. Human intelligence and talent can then be deployed in more value-added processes.
Enables a more granular data analysis by reviewing all available data automatically instead of sampling. As a result, auditors will gain a better understanding of an organization’s risk and be able to focus on high-risk documents and anomalies.

PwC, one of the world’s leading providers of audit, consulting, tax and advisory services, created RPA bots to streamline report development for monthly management, accounts receivable and travel expense reports. Report development time was reduced from one week to minutes with a suite of IBM RPA bots.

How does intelligent automation improve the audit processes?

Faster and more comprehensive data collection and cleaning.

Whether it is an internal or external audit, auditors gather evidence about business processes from a variety of sources such as process documents, invoices, system logs, or reports. Gathering data from unstructured sources is burdensome when executed manually. Intelligent automation tools can read and understand the context of documents with NLP and intelligent document processing technologies. This enables intelligent bots to:

Automatically convert unstructured data to a structured format
Perform calculations with extracted data
Combine data from different sources and input it into a target file.

As a result, auditors can review the entire population instead of just a sample in a fraction of the time it would take to perform a manual audit.

In addition to statistical analysis and visualizations, intelligent bots can perform analyses on gathered data with machine learning algorithms and identify anomalies such as potential fraud or suspicious IT logs, according to predetermined rules. By flagging these anomalies, auditors can focus on high-risk areas throughout the population.

Moreover, AI-enabled bots can learn and adapt to datasets so they can improve the accuracy of anomaly detection over time.
For instance, researchers from Rutgers University implemented an RPA bot for a public accounting firm. While testing the deployed bot, the researchers overstated the loan amount balance of some transactions, and the bot could detect all the anomalies.

Reduction in manual work can allow auditors to conduct audits more often. This can help businesses to adapt to the ever-changing business environment and provide a higher level of assurance. Intelligent bots can also continuously monitor determined controls in real-time and flag issues for further examination by auditors.

Three steps for implementing intelligent automation in audit

Step 1: Identify processes suitable for automation

It is important to understand how different audit processes are carried out in order to determine which ones should be automated. By using event logs and other process-related data, auditors can leverage process mining to identify process patterns and deviations and create full visualizations of processes. Most major intelligent automation vendors also provide process mining capabilities.

This higher-level understanding enabled by process mining helps auditors to determine which audit processes:

are repetitive, rule-based, and time-consuming. These processes are low-hanging fruits for automation.
require human judgment and professional skepticism. Auditors can define the rules governing human judgment for these processes and have bots flag cases that deviate from them for further examination.

Step 2: Test your bots to ensure that they function as desired

After determining the processes for automation and building bots for them, auditors should test the bots in a controlled environment to ensure:

They carry out the tasks they are designed for without issues
They handle exceptions well and route the exception to relevant staff.

Step 3: Monitor your automated processes and identify areas for improvement

Auditors should monitor the deployed bots to ensure that they continue functioning as expected. This is because:

You may discover areas for improvement after deployment
Bots can encounter data or exceptions that were not included in the test phase
The business environment is constantly changing, so bots’ performance could degrade over time.

Why should I be interested in this post?

You should be fascinated in this post if the audit process and the analysis of data and their transformation into essential information fascinates you. Technology and all the most innovative tools are a puzzle to solve.

About the author

The article was written in April 2023 by Federico MARTINETTO (ESSEC Business School, Exchange Global BBA, 2021).

The investment ecosystem

March 31, 2024March 22, 2023 by Nithisha CHALLA

The investment ecosystem

In this article, Nithisha CHALLA (ESSEC Business School, Grande Ecole Program – Master in Management, 2021-2023) explains the investment ecosystem in financial markets.

Introduction

In the investment ecosystem, there are several blocks to understand: market participants, market products, and market organization.

Market participants

Market participants are individuals, companies, financial institutions, and governments. Some of these participants may issue assets like companies (stocks, commercial paper, and bonds) and governments (bonds). Some of these participants may invest in these assets like individuals or pension funds.

Based on the amount they invest, market participants are segregated as big players and small players. Big players are mostly institutional investors which collect the funds and then invest them. Few examples of institutional investors are mutual funds, pension funds, hedge funds, trusts, charities etc. Big players may also be wealthy individuals (high net worth individuals or HNWI) or family offices. Small players are other individual investors.

Corporates run businesses, including manufacturing, service, and technology firms, and they need capital to expand and maintain their operations. On the other side, we have institutions that consist of fund managers that could be institutional investors but also retail investors as well. These are the people that have capital so the capital flows from the institutions or investment managers who have the money to the corporations that need that money to grow and run their business. The cycle between the two parties is completed when the firms issue back to the investor’s bonds, which are classified as debt, or shares, which are classified as equity.

In the middle of these two groups sit the investment banks they are often referred to as the sell side and they have contacts on both sides of these players. They have corporate clients, and they have institutional investor clients, their job is to match up the institutional investors with the corporates based on risk and return assessments and expectations and investment style to get the deal done. In addition, we have public accounting firms which are the fourth player in the market.

Market Products

Assets

What are assets? In financial language, an asset is that which has some economic value. And assuming that its value increases in the future market participants buy them and that is how it is a part of the investment ecosystem. Few examples for assets are fixed deposit, land, gold, stock, etc.

Asset classes are made up of those investments or securities whose characteristics are the same. Few major asset classes are equity, bonds (fixed income), commodities, and real estate.

Instruments

What are Instruments? Instruments are the ways through which we can invest in different asset classes.

Some of the major instruments we see in markets are direct investing, mutual funds, and exchange-traded funds (ETFs).

Direct investing is nothing but investing cash physically in different asset classes or we can digitally buy assets through our accounts
Mutual funds are the funds collected by multiple investors and then those are invested in different asset classes. To manage these mutual funds, we have fund managers who will invest on behalf of investors.
ETFs are nothing but a basket of securities just like mutual funds, but the only difference is they are traded on stock exchanges.

Market organization

Primary and secondary markets

The primary markets: the initial issuance of assets

The primary market is where new securities, including stocks, bonds, and other financial assets, are first issued by governments or corporations. The primary market is also referred to as the market for new issues.

Companies and governments raise money in the primary market by offering their securities to retail or institutional investors. The securities may be sold through a private placement or an initial public offering (IPO).

There are four main players in the primary market mainly for issuance of securities.
1) Corporates
2) Investors: institutional investors and individual investors
3) Corporate banks
4) Public accounting firms

The secondary markets: the exchange of assets

In the secondary market, fund managers and banks collaborate to trade securities between investors after they have already been issued. On one side, a fund manager may want to purchase securities of a public company, while on the other, a different fund manager may wish to sell those same securities. Investment bankers come between these clients to help facilitate these trades, and this trade is facilitated over the stock exchange. They provide equity research coverage to help fund managers make decisions about buying and selling those securities. And this secondary market trading makes markets liquid. This is what allows you to get in and out of security very easily.

Market infrastructure

Infrastructure providers are the companies which enable the transactions and functioning of different instruments. It means all the digital and physical infrastructure required for the investor is provided by the infrastructure provider. The few common examples of an infrastructure provider are the stock exchange, depositories, and registrar and transfer of agents.

Stock exchange: It is the platform where you can sell and buy securities. Here, with the help of a broker and the stock exchange two investors can buy and sell stocks without knowing each other. For example, The TSE is the largest stock exchange in Asia by market capitalization. It is located in Tokyo, Japan and has over 3,500 listed companies.
Depositories: These are the companies that store the stocks we buy in electronic form. We can store these stocks through our demat accounts. Depositories help you transfer stock and various other functions like checking the statements, portfolio holdings and transaction information etc. Generally investors directly do not interact with depositories but they approach through a broker who would invest on their behalf. For example: The DTC is one of the largest depositories in the world. It is located in New York City and holds over 3.5 million securities worth trillions of dollars.
Registrar and Transfer of Agents (RTA): just like depositories in case of stocks, RTA’s in case of mutual funds. All trades of mutual funds like subscription, redemption, and transfer, are recorded by an RTA. An RTA also helps mutual fund investors in providing their portfolio and statements to them.

Why should I be interested in this post?

As a student and prospective business management graduate, I think it is important to know the investment ecosystem. Firstly, investments play a vital role in the growth and success of companies. Companies need investments to fund their operations, expand their businesses, and create value for their shareholders. Therefore, understanding the investment ecosystem will enable management students to make informed decisions regarding investments that can help drive the growth of the companies they work for or manage in the future.

Useful resources

McKinsey (2017) Capital Markets Infrastructure: An Industry Reinventing Itself

Black rock The Investment Stewardship Ecosystem

About the author

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

High-frequency trading and limit orders

February 16, 2025March 22, 2023 by Clara PINTO

High-frequency trading and limit orders

In this article, Clara PINTO (ESSEC Business School, Master in Strategy & Management of International Business (SMIB), 2020-2023) explains about high frequency trading in a dynamic limit order market.

What is High-frequency trading (HFT)?

While the adage “time is money” applies to almost all economic operations, the rapid spread of computerized trading has carried this quote to its final extreme. High-frequency trading (HFT) is a type of algorithmic trading that relies on advanced computer programs to make trading decisions and execute trades in a matter of milliseconds. HFT has become increasingly popular in recent years, particularly in dynamic limit order markets (“A dynamic limit order market with fast and slow traders”, European Central Bank), where the bid and ask prices of securities are constantly changing. This allows them to take advantage of small price discrepancies in the market and generate profits on a large scale, this method known as statistical arbitrage, involves traders looking for temporary pricing inconsistencies across different exchanges and capitalize on it, using ultra-fast transactions.

What Exactly Is a Limit Order?

A limit order is an instruction to buy or sell a security at a specified price or better. For example, a trader may place a buy limit order for a stock at $50, meaning he or she is willing to buy the stock only if it is available at that price or lower. Similarly, a sell limit order may be placed at $60, meaning the trader will sell the stock only if the price is at that level or higher.

HTF and Limit Order

High-frequency trading (HFT) and limit orders are closely linked, as HFT traders often rely on limit orders to execute their trades. In fact, limit orders are a key component of many HFT trading strategies. HFT traders often use limit orders in conjunction with advanced algorithms to identify market trends and execute trades at lightning-fast speeds. They may place many limit orders at various prices to take advantage of small price movements in the market and use sophisticated algorithms to determine the best time to execute their trades.

However, the use of limit orders in HFT trading can also have downsides. For example, the large number of limit orders placed by HFT traders can lead to increased volatility in the market, as these orders can cause sudden price movements, for example flash crash when the prices of stocks or commodities suddenly plunges but then quickly recovers. Hence, the use of limit orders in HFT trading can also have downsides, and it is important for regulators to monitor HFT activity and ensure that it does not cause market instability or unfair trading practices.

Why should I be interested in this post?

For many business school students, finance and trading are part of the most preferred jobs. Understanding the trends in high-frequency trading is now a requirement for future institutional investors. Being quick allows traders to adjust outstanding limit orders in response to news arrivals when working with “slow” market players who experience a relative loss in bargaining power, leading them to strategically submit limit orders with a lower execution probability, limiting trade.

Useful resources

SimTrade course Trade orders

Hoffmann P. (2013) A dynamic limit order market with fast and slow traders European Central Bank Working Paper Series.

Lewis M. (2015) Flash boys Norton & Company.

About the author

The article was written in March 2023 by Clara PINTO (ESSEC Business School, Master in Strategy & Management of International Business (SMIB), 2020-2023).

Strategy and Tactics: From military to trading

March 22, 2023 by Clara PINTO

Strategy and Tactics: From military to trading

In this article, Clara PINTO (ESSEC Business School, Master in Strategy & Management of International Business (SMIB), 2020-2023) shares her insights as a former military analyst on strategy and tactics applied to trading.

IRSEM: The Institute for Strategic Research at the Military School

Created in 2009, IRSEM is the strategic research institute of the French Ministry of Armed Forces and operates under the supervision of the Directorate General for International Relations and Strategy (DGRIS) operating under the umbrella of the Ministry for the Armed Forces. IRSEM is home to a staff of about forty civilian and military permanent researchers. The Institute seeks to foster the emergence of a new generation of researchers specialized in security and defense issues.

Logo of IRSEM.

Source: IRSEM.

From military to Finance: Strategy and tactics applied to trading

My experience as an analyst in a military Think tank required me to learn the basics of military strategy and tactics. The distinction between strategy and tactics is frequently stated as “strategy is long-term, whereas tactics are short-term.” While the two terms may exhibit similar qualities at times, it is an erroneous and partial explanation of their definitions.

Chinese General Sun Tzu wrote the difference this way: “All the men can see the tactics I use to conquer, but what none can see is the strategy out of which great victory is evolved.”

However, even if strategy and tactics are also used in business, their principles still apply in the trading context. Indeed, successful trading requires a solid understanding of both strategy and tactics. In this article, we will explore the differences between these two concepts and how they can be applied to trading.

Strategy refers to a long-term plan that outlines how you will achieve your trading goals. It involves identifying your objectives, assessing the risks and opportunities in the market, and deciding on a plan of action. A good trading strategy should be flexible enough to adapt to changing market conditions, but also structured enough to provide a clear path forward. One key aspect of a trading strategy is risk management. This involves identifying the potential risks associated with a particular trade and taking steps to mitigate them. This might involve setting stop-loss orders to limit potential losses or diversifying your portfolio to reduce the overall risk. A good trading strategy should also take into account the amount of capital you have available to trade with, as well as your risk tolerance and investment goals.

Tactic, on the other hand, refers to the specific actions you take to implement your trading strategy. These might include analyzing technical indicators to identify trends and patterns to assess the value of a particular asset. A successful trading tactic will depend on a number of factors, including the specific asset you are trading, and the current market conditions.

Ultimately, the success of your trading will depend on how well you are able to combine strategy and tactics. A strong strategy will provide a clear framework for making decisions and managing risk, while effective tactics will allow you to execute that strategy in a way that maximizes your returns. In order to develop a successful trading strategy, it is important to conduct thorough research and analysis of the markets you are interested in. This might involve studying historical market trends, analyzing economic and political factors that could impact the markets, or keeping up to date with news and events that could affect the value of specific assets. It is also important to remember that trading involves a degree of risk, and no strategy or tactic can guarantee success. However, by developing a strong strategy and using effective tactics to execute that strategy, you can improve your chances of making profitable trades over the long term.

In conclusion, strategy and tactics are both essential components of successful trading. A strong trading strategy provides a clear framework for decision-making and risk management, while effective tactics allow you to execute that strategy in a way that maximizes your returns. By combining careful research and analysis with disciplined execution, you can increase your chances of success in the complex and ever-changing world of trading.

Why should I be interested in this post?

Unfortunately, the concepts of strategy and tactics are often mixed up and not entirely understood. However, they provide a good framework to trade in the long term and structure your choices in the decision-making process.

Useful resources

IRSEM – The Institute for Strategic Research

About the author

The article was written in March 2023 by Clara PINTO (ESSEC Business School, Master in Strategy & Management of International Business (SMIB), 2022-2023).

The business of financial indexes

March 18, 2023 by Nithisha CHALLA

The business of financial indexes

In this article, Nithisha CHALLA (ESSEC Business School, Grande Ecole Program – Master in Management, 2021-2023) explains the business of financial indexes.

Introduction

Indexes are frequently used in the financial sector to measure the evolution of market prices for a set of financial assets over time. These sets of assets can be defined to represent an asset class, country or geographical zone, or sector of the economy, and provide a comprehensive and accurate overview of the market.

Financial indexes serve as a benchmark for assessing the performance of an investor’s asset portfolio and give investors a way to monitor the performance of a given set of assets. By using financial indexes, investors can gain knowledge of market trends and conditions and make informed investment decisions. Index providers are responsible for creating and maintaining financial indexes.

Financial indexes can be developed to track particular geographical areas or market segments and can be created for a variety of asset classes, including equities, bonds, commodities, and currencies. Financial indexes are primarily provided by specialized companies with experience in data compilation and index value calculation, such as S&P Dow Jones Indices, MSCI, and FTSE Russell. Overall, the business of financial indexes is a critical component of the financial industry, providing valuable data and insights to investors.

Key Players

Index providers

An index provider is a specialized business that specializes in developing and computing market indices as well as licensing its intellectual property to be used as the foundation of passive products. The index providers are essential to the investment professionals in charge of looking after these assets because they provide reliable data distribution, sound index construction, and strict index maintenance. The primary activities of an index provider are product development, licensing, distribution, and related service and support.

Index Industry Association (IIA)

The production of indexes has become an industry! And every industry has a professional association. The index industry is no exception. The Index Industry Association (IIA) was founded in 2012. Some of the founding members are MSCI and S&P Dow Jones Indexes.

As stated on the IIA website, the association mandate is “to educate investors on the attributes and role of indexes within the investment process, to advocate for the interests of index users and providers worldwide, and to push for industry standards of best practice, independence and transparency”.

Business models

Index providers typically employ one of the following business models to make money from their indexes: licensing, creating index-linked products, getting charged for index inclusion, and selling data for index-related research and analysis.

Licensing

Index providers make money by licensing financial institutions like asset managers, banks, and insurance companies to use their indexes. These financial institutions pay a fee to the index provider for the right to use the indexes as a benchmark for their investment products, such as exchange-traded funds (ETFs) and index funds.

Creation of index-linked products

Index providers make money by developing their own index-linked products, such as index funds and ETFs. The investors that are invested in the product pay a management fee to the index provider.

Selling data

By selling the data that has been produced from the history, research, and analysis, the index providers make money.

Regulation of indexes

Index providers build and maintain indexes. In order to ensure that the index accurately reflects the performance of the market or sector it is meant to represent, they are in charge of defining the methodology used to construct the index, choosing the stocks or bonds included in the index, and performing routine index rebalancing.

Beyond the activity of index providers, financial authorities play a role to authorize indexes. The main objective of authorization is to safeguard investors who use the index as a benchmark for their investment decisions and to make sure that the index accurately reflects the performance of the market or sector it is meant to represent. In the United States, the US Securities and Exchange Commission (SEC) has the power to approve specific indexes that serve as the foundation for exchange-traded funds (ETFs) and other investment products. This is done to make sure that these products operate in the best interests of investors and are compliant with SEC regulations.

Why should I be interested in this post?

A wide range of professionals, including portfolio managers, investment advisors, and financial analysts, use financial indexes, which are a crucial part of the financial sector. Financial indexes change over time to take into account adjustments to the economy and market conditions.

You can stay on top of the curve and adjust to changes in the industry by staying informed of the most recent financial index developments. So, in my opinion, studying the business of financial indexes can give business students useful skills and knowledge that they can use in a variety of fields and jobs.

Useful resources

Index Industry Association (IIA)

S&P Global Who’s Behind the Index?

Committee for Economic Development of The Conference Board (CED) The Financial Index Industry

K&L Gates SEC solicits comments on whether index providers, model portfolio providers, and pricing services are investment advisers: seeking a problem for a “solution”

About the author

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

The S&P 500 index

January 17, 2025March 18, 2023 by Nithisha CHALLA

The S&P 500 index

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.

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.

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, P^k the market price of asset k, N^k 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).

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.

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.

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.

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.

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.

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.

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.

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).

Calculation of financial indexes

March 18, 2023 by Nithisha CHALLA

Calculation of financial indexes

In this article, Nithisha CHALLA (ESSEC Business School, Grande Ecole Program – Master in Management, 2021-2023) explains the calculation of financial indexes.

Introduction

A stock market index keeps tabs on the gains and losses made by a specific selection of stocks or other assets. In other words, the index determines how share prices for various companies have changed. The performance of a market index can be quickly evaluated to ascertain the state of the stock market. It also serves as a template for financial institutions to use when creating index funds and exchange-traded funds (ETFs).

Definition

What is an index? In financial markets, there are many sectors, segments and business lines, and if you have to statistically measure the performance of these sectors we need a reference which is called an index. Simply, it is a group of securities or financial instruments which represents the performance of a specific segment of the market.

Calculation

Then the index value has to be calculated with a specific formula. There are different calculation methods for financial indexes: price-weighted index, market-capitalization-weighted index, equal-weighted index and fundamentals-weighted index.

The general formula for a financial index is given by

Index value

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

Note: the index I_t at time t is divided by the value of the index at the beginning I₀ and multiplied by 100.

Price-Weighted Index

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, P^k 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.

In a price-weighted index, the higher-priced stocks move the index more than the lower-priced stocks.

The most popular price-weighted index in the world is likely the Dow Jones Industrial Average (DJIA). It consists of 30 different stocks in the US market.

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

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, P^k the market price of asset k, N^k the number of issued shares for asset k, F^k 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

Fundamental-weighted Index

A fundamental-weighted index is calculated based on specific financial metrics, such as revenue or earnings, rather than market capitalization or price. The weightings of each asset in the index are determined by its financial metrics, so that the companies with the strongest financial performance have the greatest impact on the overall performance of the index.

The formula for a fundamental-weighted index is given by

Fundamental Weighted Index value

where I is the index value, k a given asset, K the number of assets in the index, P^k the market price of asset k, F^k the financial metric of asset k, and t the time of calculation of the index.

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

Fundamental Weighted Index Weight

which clearly shows that the weight of each asset in the index is the value of the fundamental variable of the asset divided by the sum of the values of the fundamental variable of all assets.

Equal-weighted Index

An equal-weighted index is calculated by dividing the total value of the index by the number of securities in the index, and then allocating the same weighting to each security. This method gives each security an equal influence on the overall performance of the index, regardless of its market capitalization.

The formula for an equal-weighted index is given by

Equal Weighted Index value

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

Equal Weighted Index Weight

Which clearly shows that the weight of each asset in the index, one divided by the number of assets, is constant over time.

Examples of financial indexes

The Dow Jones Industrial Average: an equal-weighted index

The Dow Jones Industrial Average, or DJIA (Dow), was the first index, appearing in 1896. The 30 largest and most prosperous American companies make up the Dow. The experts have carefully chosen these businesses to represent a wide range of industries. Companies with higher prices are given more weight in the Dow. Even though it is the most established and performs similarly to the S&P 500, it is occasionally thought to be less indicative of the entire market.

The S&P 500 index: a market-capitalization-weighted index

S&P 500 – The performance of 500 of the biggest American publicly traded companies is measured. Some people think the S&P 500, which is weighted by market capitalization and has a wider scope, is the best indicator of the American stock market. Because of this, the S&P 500’s average is most significantly impacted by the companies with the highest total market value.

Why should I be interested in this post?

Learning about the calculation of financial indices is important to understand the behavior of an index. It can assist you in managing risk in your portfolio, understanding the overall performance of various markets, and making wise investment decisions. Financial indices can offer insightful data on how various markets, sectors, and economies are performing. Investors can determine whether their investments are outperforming or underperforming the overall market by comparing the returns to the returns of a relevant financial index.

Useful resources

Weight priced index Indice

Equity Indexes Indice

Security market index Indice

Value weighted index Indice

Evolution of indexes Indice

About the author

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

Financial indexes

March 18, 2023 by Nithisha CHALLA

Financial indexes

In this article, Nithisha CHALLA (ESSEC Business School, Grande Ecole Program – Master in Management, 2021-2023) explains financial indexes, their construction and their use in the finance.

Definition

What is an index? An index can be defined as a measure of a quantity.

An index is a measure of quantity that can be defined as the ratio between the value of the quantity during a current period and its value during a base period. The use of a ration makes it easy to calculate and compare changes in one or more quantities between two given periods. This ratio is often multiplied by 100 or 1,000. Indexes are frequently used in the financial sector to measure the evolution of market prices for a set of financial assets over time. These sets of assets can be defined to represent an asset class, country or geographical zone, or sector of the economy, and provide a comprehensive and accurate overview of the market.

History

The Dow Jones Industrial Average was first created in 1896 by Charles Dow, a co-founder of the Dow Jones Company, and is widely regarded as the first index. Who is creating the index? The Dow Jones Industrial Average, which included 12 companies at the time that were emblematic of the US Market. Currently, there are 30 companies that make it up even though none of the original 12 companies are still included. As interest in indices increased, financial publications like the Financial Times or exchange owners like the Deutsche Borse in Germany developed their own equity indices, while investment banks took the lead in developing indices for bonds. Since then, numerous other financial indexes have been developed, including the NASDAQ Composite, FTSE 100, Nikkei 225, S&P 500, and others.

Evolution over time

Stock market indexes were initially just simple arithmetic averages of the prices of a small number of chosen stocks; they did not take the entire market into account. The daily averages were first published in the newspapers in the 1800s. Later, they began to use market capitalization weighting, which was well-liked because it assigned weights based on the size of the company. Following that, various indexes based on sectors, nationalities, etc. were assigned. A significant trend recently has been the use of passive index funds and the addition of ESG criteria to the indexes.

Providers of financial indexes

Financial indexes are typically provided by financial data and research firms. As mentioned earlier, though there are several providers in the financial services industry, there are few most prominent index providers – S&P Global, MSCI, FTSE Russell, Dow Jones Indices and Nasdaq. With a combined market share of about 90% for equity indexes, these firms are thought to dominate the world index market.

Index Industry Association (IIA)

The production of indexes has become an industry! And every industry has a professional association. The index industry is no exception. The Index Industry Association was founded in 2012. Some of the founding members are MSCI and S&P Dow Jones Indexes.

Composition of an index

The composition of an index is a crucial factor in determining its representation, and it is important for investors to understand the criteria used by the index provider to select the assets included in the index, as well as the weightings assigned to each asset. The composition of an index is designed to represent a specific market or sector, and the index provider selects the assets to be included based on specific criteria, such as market capitalization, liquidity (float), and sector representation.

There are several steps in the process of creating an index. As we all know, index providers use a variety of companies to create the index, but how are they selected? Specific eligibility requirements must be met, such as the size of the business and the industry it belongs to, etc. After the eligible companies have been narrowed down, they are properly evaluated before being included in the index. This evaluation includes looking at the company’s earnings, market capitalization, and other factors. Additionally, they conduct index balancing with regard to various industries, segments, etc. Last but not least the index’s potential market impact is cross-checked as the index stands as a benchmark for the investors to make decisions. Different index providers may have different selection criteria and processes.

The index provider regularly reviews and updates the composition of the index to ensure that it remains representative of the market or sector it is tracking.

For example, the S&P 500 index is designed to represent the performance of the U.S. stock market, and the securities included in the index are chosen based on market capitalization, liquidity, and sector representation. Since each security’s weight in the index is based on its market capitalization, the largest and most powerful corporations have the biggest effects on the index’s overall performance.

Calculation of financial indexes

Once the index provider has chosen the assets to be included in the index based on predetermined criteria, such as market capitalization, liquidity, and sector representation. Then the index value has to be calculated with a specific formula. There are different calculation methods for financial indexes: price-weighted index, market-capitalization-weighted index, equal-weighted index and fundamentals-weighted index.

Classifications of financial indexes

By having a solid understanding of the various classifications of financial indexes, investors can select the most suitable indexes for their investment goals and strategies. Market coverage, calculation method, geographic region, asset class, investment approach, and security type are used to categorize financial indexes.

The criteria for classifying financial indexes include:

Asset class: equity, bond, crypto, etc.
Geography: US, Asia-Pacific, Europe
Sector: Information Technology, Health Care, Financials, Consumer Discretionary, Communication Services, Industrials, Consumer Staples, Energy, Utilities, Real Estate, and Materials.
Weighting methodology: price-weighted, market-capitalization-weighted, float-adjusted market-capitalization-weighted, fundamental-weighted
Objectives: market representation, risk factor representation

Most popular financial indexes

The Dow Jones Industrial Average

The Dow Jones Industrial Average (DJIA) was established in 1896, is the country’s first stock market index. Thirty large-cap companies that are leaders in their fields are included in this price-weighted index. The index is frequently used as a gauge for the American stock market and the overall economy. ▶ More about the DJIA index

S&P 500

The S&P 500 index is a market capitalization-weighted index that monitors the progress of 500 large-cap U.S. businesses operating in various industries. It was established in 1957, and many people consider it to be one of the most significant benchmarks for the American stock market. The index is widely used as a benchmark by fund managers and investors and is frequently used as a stand-in for the overall health of the American economy. ▶ More about the S&P 500 index

Nasdaq Composite

Composed of all the companies listed on the Nasdaq stock market, the Nasdaq Composite is a market capitalization-weighted index. It was founded in 1971 and is renowned for the prominence of technology firms, even though it also includes businesses from the consumer goods, healthcare, and finance sectors. The index is frequently used as a yardstick for growth and technology stock performance. ▶ More about the Nasdaq Composite index

FTSE 100

The performance of the top 100 companies listed on the London Stock Exchange is tracked by the FTSE 100, a market capitalization-weighted index. Since its creation in 1984, it has gained widespread recognition as the top benchmark for the UK stock market. Companies from the financial, energy, and mining sectors make up the majority of the index, and each company is weighted according to its market capitalization. ▶ More about the FTSE 100 index

MSCI World

The MSCI World Index tracks the performance of businesses in 23 developed markets around the world, including the United States, Canada, Japan, and Europe. It is a market capitalization-weighted index. It was developed in 1969 and is frequently used as a yardstick for performance in the global equity market. The weighting of each company in the index, which consists of more than 1,600 large- and mid-cap stocks, is determined by its market capitalization.

Health Care Select Sector Index

The Health Care Select Sector Index is based on the companies of the S&P 500’s health care sector. It was established in 1998 with the purpose of monitoring the performance of businesses involved in the health care sector, such as those producing pharmaceuticals, biotechnology, medical devices, and healthcare providers.

Use of indexes in finance

Financial indexes play an important role for market participants like investors, traders, and asset managers. Some of the ways indexes are used in finance include:

Gauges of the market evolution

Indexes can offer insightful information about the state of the financial markets. An index helps to measure the market returns of a given set of securities.

The best part of the stock index is that just by tracking the simple indicator we get a general idea of how the stock market is performing. A stock index clearly shows how the market is performing, or at least the market that it represents, despite the fact that individual stocks may perform differently, making it challenging to determine whether the market is strong or weak.

Benchmarks

Indexes are frequently used as a benchmark to assess the performance of investment portfolios, especially actively managed portfolios.

Proxies for modeling

In academic studies, indexes are used as proxies for the market portfolio to capture systematic risk and to compute risk-adjusted performance.

Portfolio Asset allocation

Because they offer a way to gain exposure to particular asset classes, industries, or geographic areas, indices serve as the foundation for asset allocation strategies.

Risk management

Indexes can assist investors in comprehending the risks related to particular asset classes or geographical areas.

Building of investment vehicles

Exchange-traded funds (ETFs), mutual funds, options and structured products, among others, use indexes as their underlying assets. These investment vehicles make it easy and affordable for investors to become exposed to the index’s performance.

Rebalancing

Some indexes imply frequent and even continuous rebalancing (buying and selling assets). For example, for a fund tracking an equally-weighted index, the fund manager will have to sell assets whose price increased and buy assets whose price decreased.

Change in index composition and impact on asset prices

When an asset is included in an index, its price usually increases as fund managers need to buy it to include it in their portfolio. Conversely, when an asset is excluded from an index, its price usually decreases as fund managers need to sell it to exclude it from their portfolio.

Empirical results confirming these propositions can be found in a study by McKinsey (2004). The prices of the assets included in a financial index may change as a result of changes in the composition of the index over time.

It is crucial to remember that depending on the specifics of the change, the effect of a change in index composition on asset prices may be either short-lived or long-lasting. The effect of a change in index composition on asset prices can also be challenging to forecast because it depends on a variety of variables, such as investor sentiment, fund flows, and market sentiment.

Link with academic research

The performance of a particular sector of the stock market, such as large-cap stocks, small-cap stocks, or a specific sector or industry, is measured by an equity index, a type of financial index.

On the other hand, market factors are factors that account for a significant amount of the variation in stock prices. Market variables include both macroeconomic ones like interest rates and GDP and market-specific ones like market volatility and liquidity.

The relationship between equity indexes and market factors is that changes in market factors can have an impact on equity index performance, and equity index performance can be influenced by market factor changes. For instance, adjustments in interest rates may have an effect on the performance of the stock market as a whole and, consequently, on the performance of an equity index that monitors the stock market. Factor-based indexes that seek to capture the performance of particular market factors, such as value, growth, and momentum, have been developed as a result of research into the effects of market factors on equity indexes. These factor-based indexes can be employed to examine the effects of market factors on the performance of equity indexes and to base investment choices on the exposure to market factors.

Why should I be interested in this post?

I frequently come across news-related stocks, bonds, and indices in publications like newspapers, financial journals, and business magazines. We require a fundamental understanding of indices in order to even understand what is happening in the business world. It’s also crucial to have a thorough understanding of markets and financial indices because we need to comprehend these financial indices in order to assess a company’s performance and compare it to previous years.

Useful resources

Insee Indice

Russel How are indexes weighted?

Financial Index Industry Presentation of the association

Index Industry Association Presentation of the association

Marc H. Goedhart and Regis Huc (2004) What is stock index membership worth? McKinsey & Company.

About the author

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

Capital Guaranteed Products

March 15, 2023 by Shengyu ZHENG

Capital Guaranteed Products

In this article, Shengyu ZHENG (ESSEC Business School, Grande Ecole Program – Master in Management, 2020-2023) explains how capital guaranteed products are built.

Motivation for investing in capital-guaranteed products

In order to invest the surplus of the firm liquid assets, corporate treasurers take into account the following characteristics of the financial instruments: performance, risk and liquidity. It is a common practice that some corporate investment strategies require that the investment capital should at least be guaranteed. The sacrifice of this no-loss guarantee is limited return in case of appreciation of the underlying asset price.

Capital-guaranteed (or capital-protected) products are one of the most secure forms of investment, usually in the form of certificates. They provide a guarantee that a specified minimum amount (usually 100 per cent of the issuance price) will be repaid at maturity. They are suitable particularly for risk-averse investors who wish to hold the products through to maturity and are not prepared to bear any loss that might exceed the level of the guaranteed repayment.

Performance

Let us consider a capital-guaranteed product with the following characteristics:

Table 1. Characteristics of the capital-guaranteed products

Notional amount	EUR 1,000,000.00
Underlying asset	CAC40 index
Participation rate	40%
Minimum amount guarantee	100% of the initial level
Effective date	February 01, 2022
Maturity date	July 30, 2022

We also have the following information about the market:

Table 2. Market information

Risk-free rate (annual rate)	8%
Implied volatility (annualized)	10%

In case of depreciation of the underlying index, the return of the product remains zero, which means the original capital invested is guaranteed (or protected). In case of appreciation of the underlying index, the product only yields 40% of the return of the underlying index. The following chart is a straightforward illustration of the performance structure of this product.

Performance of the capital guaranteed product

Construction of a capital guaranteed product

We can decompose a capital-guaranteed product into three parts:

Investment in the risk-free asset that would yield the guaranteed capital at maturity
Investment in a call option that guarantees participation in the appreciation of the underlying asset
Margin of the bank

Decomposition of the capital guaranteed product

Investment in the risk-free asset

The essence of the capital guarantee is realized by investing a part of the initial capital in the risk-free asset and obtaining the amount of the guaranteed capital at maturity. Given the amount of the capital to be guaranteed and the risk-free rate, we can calculate the amount to be invested in risk-free asset: 1,000,000/(1+0.08)^0.5 =962,250.45 €

Investment in the call option

To realize the upside exposure, call options are a perfect vehicle. With a notional amount of 1,000,000 € and a maturity of 6 months, an at-the-money call option would cost 41,922.70 € (calculated with the Black-Scholes-Merton formula). Since the participation rate is 40%, the amount to be invested in the call option would be 16,769.08 € (= 40% * 41,922.70 €).

Margin of the bank

The margin of the bank is equal to the difference between the original capital and the two parts of the investment. In this case, the margin is 20,980.47 € (= 1,000,000.00 € – 962,250.45 € – 16,769.08 €)
If we compress the margin, there would be more capital available to invest in the call option, thus increasing the participation rate. In the case of zero margin, we obtain the maximum participation rate. In this scenario, the maximum participation rate would be 90.05% (= (1,000,000.00 € – 962,250.45 €) / 41,922.70 €).

Sensitivity to variations of the marketplace

Considering the two parts of the investment constituting the capital-guaranteed product, we can see that the risk-free rate and the volatility of the underlying asset are the two major factors influencing the pricing of this product. Here let us focus on the maximum participation rate as a proxy of the value of the product to the buyer of the product.

The effect of the risk-free rate could be ambiguous at the first glance. On one hand, if the risk-free rate rises, there needs to be less capital invested in the risk-free asset and there would be therefore more capital to be placed in purchasing the call options. On the other hand, if the risk-free rate rises, the call option value rises as well. With the same amount of capital, fewer call options could be purchased. However, the largest portion of the original capital is invested in the risk-free asset and the impact on this regard is more important. Overall, a rising risk-free rate has a positive impact on the participation rate.

The effect of the volatility of the underlying asset, however, is clear. Rising volatility has no impact on the risk-free investment in the framework of our hypotheses. It, however, raises the value of the call options, which means that fewer options could be purchased with the same amount of capital. Overall, rising volatility has a negative impact on the participation rate.

Statistical distribution of the return

The statistical distribution of the return of the instrument is mixed by two parts: the discrete part equal to 0 corresponding to the case of depreciation of the underlying asset; and the continuous part of positive return. Based on a Gaussian assumption for the statistical distribution, we can calculate the probability mass of the depreciation of the underlying asset is 33.70%. In the continuous part, the return follows a Gaussian statistical distribution, with a mean equal to the periodic return over the participation rate and a standard deviation equal to periodic implied volatility over the participation rate, if the Gaussian assumption prevails.

Statistical distribution of the return of the capital guaranteed product

Risks and constraints

Liquidity risk

Being exotic financial instruments, capital-guaranteed products are not traded in standard exchanges. By construction, these products can normally only be redeemed at maturity and therefore are less liquid. There could be, however, early redemption clauses involved to mitigate the long-term liquidity risks. Investors should be aware of their liquidity needs before entering into a position in this product.

Counterparty risk

Similar to all other over-the-counter (OTC) transactions, there is no mechanism such as a central clearing counterparty (CCP) to ensure the timeliness and integrity of due payments. In case of financial difficulty including the bankruptcy of the issuer, the capital guarantee would be rendered worthless. It is therefore highly recommended to enter into such transactions with issuers of higher ratings.

Limited return

It is worth noting that capital-guaranteed products have weak exposure to the appreciation of the underlying asset. In this case, for a probability of 33.70%, there would be a return of zero, which is lower than investing directly in the risk-free security.

In order to mitigate this limit, the issuer could modify the level of guarantee to a lower level than 100%. This allows the product to have more exposure to the upside movement of the underlying asset with a relatively low risk of capital loss. To realize this involves entering positions of out-of-the-money call options.

Taxation and fees

In many countries, the return of capital-guaranteed products is considered as ordinary income, instead of capital gains or tax-advantaged dividends. For example, in Switzerland, it is not recommended to buy such a product with a long maturity, since the tax burden, in this case, could be higher than the “impaired” return of the product.

Moreover, fees for such products could be higher than exchange-traded funds (ETFs) or mutual funds. This part of investment cost should also be taken into account in making investment decisions.

Download the Excel file to analyze capital-guaranteed products

You can find below an Excel file to analyze capital-guaranteed products.

Why should I be interested in this post?

As a family of investments that is often used in corporate treasury management, it is important to understand the mechanism and structure of capital-guaranteed products. It would be conducive for future asset managers, treasurer managers, or structurers to make the appropriate and optimal investment decisions.

Resources

Books

Cox J. C. & M. Rubinstein (1985) “Options Markets” Prentice Hall.

Hull J. C. (2005) “Options, Futures and Other Derivatives” Prentice Hall, 6th edition.

Articles

Black F. and M. Scholes (1973) The Pricing of Options and Corporate Liabilities Journal of Political Economy, 81(3): 637-654.

Lacoste V. and Longin F. (2003) Term guaranteed fund management: the option method and the cushion method Proceeding of the French Finance Association, Lyon, France.

Merton R. (1974) On the Pricing of Corporate Debt Journal of Finance, 29(2): 449-470.

Websites

longin.fr Pricer for standard equity options – Call and put

Euronext www.euronext.com: website of the Euronext exchange where the historical data of the CAC 40 index can be downloaded

Euronext CAC 40 Index Option: website of the Euronext exchange where the option prices of the CAC 40 index are available

Six General information about capital protection without a cap: website of the Swiss stock exchange where information of various financial products are available.

About the author

The article was written in February 2023 by Shengyu ZHENG (ESSEC Business School, Grande Ecole Program – Master in Management, 2020-2023).

Understanding the Order Book: How It Impacts Trading

February 16, 2025March 2, 2023 by Federico DE ROSSI

Understanding the Order Book: How It Impacts Trading

In this article, Federico DE ROSSI (ESSEC Business School, Master in Strategy & Management of International Business (SMIB), 2020-2023) talks about the order book and explains its role in financial markets.

Introduction

Understanding the order book is critical when it comes to trading in financial markets. In this article, we’ll go over what an order book is and how it affects trading.

What is an order book?

An order book for a stock, currency, or cryptocurrency is a list of buy and sell limit orders for that asset. It shows the pricing at which buyers and sellers are willing to negotiate, as well as the total number of orders available at each price. The order book is a necessary component of every trading platform since it gives a snapshot of the current market situation, of the price of the assets, and of the liquidity of the market. Thus, it is a crucial tool for traders who want to make informed decisions when entering or exiting deals.

How does an order book work?

The order book is a constantly updated record of buy and sell orders. When a trader puts a limit order, it is placed in the order book at the stated price. As a result, there is a two-sided market with distinct prices for buyers and sellers.

The order book is divided into two sections: bid (buy) and ask (sell). All open buy orders are displayed on the bid side, while all open sell orders are displayed on the ask side. The order book also shows the total volume of buy and sell orders at each price level.

In Tables 1 and 2 below, we give below two examples of order book from online brokers. We can see the two parts of the order book side by side: the “Buy” part and the “Sell” part. Every line of the order book corresponds to a buy or sell proposition for a give price (“Buy” or “Sell” columns) and a given quantity (“Volume” columns). For a given line there may be one or more orders for the same price. When there are several orders, the quantity in the “Volume” column is equal to the sum of the quantities of the different orders. Associated to the order book, there is often a chart which indicates the cumulative quantity of the orders in the order book at a given price. This chart gives an indication of the liquidity of the market in terms of market spread, market breadth, and market depth (see below for more explanations about theses concepts).

The “Buy” and “Sell” parts of the order book can be presented side by side (Table 1) or above each other (Tables 2 and 3) with the “Sell” part (in red) above the “Buy” part (in green) as the price limits of the sell limit orders are always higher than the price limits of the buy limit orders.

Table 1. Example of an order book (buy and sell parts presented side by side).

Source: online broker (Fortuneo).

Table 2. Example of an order book (buy and sell parts presented above each other).

Source: online broker (Cryptowatch).

Table 3. Example of an order book (buy and sell parts presented next to each other).

Source: online broker (Binance).

In a typical order book, the buy side is organized in descending order, meaning that the highest buy orders (i.e., the orders with the highest bid prices) are listed first, followed by the lower buy orders in descending order of price. The highest buy order in the book represents the best bid price, which is the highest price that any buyer is currently willing to pay for the asset.

On the other side of the order book, the sell side is organized in ascending order, with the lowest sell orders (i.e., the orders with the lowest ask prices) listed first, followed by the higher sell orders in ascending order of price. The lowest sell order in the book represents the best ask price, which is the lowest price that any seller is currently willing to accept for the asset.

This organization of the order book makes it easy for traders to see the current market depth and the best available bid and ask prices for an asset. When a buy order is executed at the best ask price or a sell order is executed at the best bid price, the order book is updated in real-time to reflect the new market depth and the new best bid and ask prices.

Table 4 below represents how the order book (limit order book) in trading simulations the SimTrade application.

Table 4. Order book in the SimTrade application.

You can understand how the order book works by launching a trading simulation on the SimTrade application.

The role of the order book in trading

As mentioned before, the order book is incredibly significant in trading. It acts as a market barometer, delivering real-time information about the supply and demand for an asset. Traders can also use the order book to determine market sentiment. If the bid side of the order book is strongly occupied, for example, it could imply that traders are optimistic on the asset. Thanks to the data in the order book, traders can get different information out of it.

Three characteristics of the order book

Market spread

The market spread, also known as the bid-ask spread, is the difference between the highest price a buyer is willing to pay for an asset (the bid price) and the lowest price a seller is willing to accept (the ask price) at a particular point in time.

The market spread is a reflection of the supply and demand for the asset in the market, and it represents the transaction cost of buying or selling the asset. In general, a narrow or tight spread indicates a liquid market with a high level of trading activity and a small transaction cost, while a wider spread suggests a less liquid market with lower trading activity and a higher transaction cost.

Market breadth

Market breadth is a measure of the overall health or direction of a market, sector, or index. It refers to the number of individual stocks that are participating in a market’s movement or trend, and can provide insight into the underlying strength or weakness of the market.

Market breadth is typically measured by comparing the number of advancing stocks (stocks that have increased in price) to the number of declining stocks (stocks that have decreased in price) over a given time period. This ratio is often expressed as a percentage or a ratio, with a higher percentage or ratio indicating a stronger market breadth and a lower percentage or ratio indicating weaker breadth.

For example, if there are 1,000 stocks in an index and 800 of them are increasing in price while 200 are decreasing, the market breadth ratio would be 4:1 or 80%. This would suggest that the market is broadly advancing, with a high number of stocks participating in the upward trend.

Market depth

Finally, market depth is a measure of the supply and demand of a security or financial instrument at different prices. It refers to the quantity of buy and sell orders that exist at different price levels in the market. Market depth is typically displayed in a market depth chart or order book.

It can provide valuable information to traders and investors about the current state of the market. A deep market with large quantities of buy and sell orders at various price levels can indicate a liquid market where trades can be executed quickly and with minimal impact on the market price. On the other hand, a shallow market with few orders at different price levels can indicate a less liquid market where trades may be more difficult to execute without significantly affecting the market price.

Analyzing order book data

Data from order books can be used to gain insight into market sentiment and trading opportunities. For example, traders can use the bid-ask spread to determine an asset’s liquidity. They can also examine the depth of the order book to determine the level of buying and selling interest in the asset. Traders can also use order book data to identify potential trading signals. For example, if the bid side of the order book is heavily populated at a certain price level, this could indicate that the asset’s price is likely to rise. On the other hand, if the ask side is heavily populated at a certain price level, it could indicate that the asset’s price is likely to fall.

Benefits of using order book data for trading

Using order book data can provide traders with a number of advantages.

For starters, it can be used to gauge market sentiment and identify potential trading opportunities.

Second, it can assist traders in more effectively managing risk. Traders can identify areas of support and resistance in order book data, which can then be used to set stop losses and take profits.

Finally, it can aid traders in the identification of potential trading signals. Traders can identify areas of potential buying and selling pressure in order book data, which can then be used to enter and exit trades.

How to use order book data for trading

Traders can use order book data to gain a competitive advantage in the markets. To accomplish this, they must first identify areas of support and resistance that can be used to set stop losses and profit targets.

Traders should also look for indications of buying and selling pressure in the order book. If the bid side of the order book is heavily populated at a certain price level, it could indicate that the asset’s price is likely to rise. On the other hand, if the ask side is heavily populated at a certain price level, it could indicate that the asset’s price is likely to fall.

Finally, traders should use trading software to automate their strategies. Trading bots can be set up to monitor order book data and execute trades based on it. This allows traders to capitalize on trading opportunities more quickly and efficiently.

Conclusion

To summarize, the order book is a vital instrument for financial market traders. It gives real-time information about an asset’s supply and demand, which can be used to gauge market mood and find potential trading opportunities. Traders can also utilize order book data to create stop losses and take profits and to automate their trading techniques. Traders might obtain an advantage in the markets by utilizing the power of the order book.

Useful resources

SimTrade course Trade orders

SimTrade course Market making

SimTrade simulations Market orders Limit orders

About the author

The article was written in March 2023 by Federico DE ROSSI (ESSEC Business School, Master in Strategy & Management of International Business (SMIB), 2020-2023).

Mesures de risques

February 4, 2024February 1, 2023 by Shengyu ZHENG

Mesures de risques

Dans cet article, Shengyu ZHENG (ESSEC Business School, Grande Ecole Program – Master in Management, 2020-2023) présente les mesures de risques basées sur la distribution statistique des rentabilités d’une position de marché, ce qui est une approche possible pour mesurer les risques (comme expliqué dans mon article Catégorie de mesures de risques).

Les mesures de risques basées sur la distribution statistique sont des outils largement utilisés pour la gestion des risques par de nombreux de participants du marché, dont les traders, les teneurs de marché, les gestionnaires d’actifs, les assureurs, les institutions réglementaires et les investisseurs.

Ecart-type / Variance

La variance (moment d’ordre deux de la distribution statistique) est une mesure de la dispersion des valeurs par rapport à la moyenne. La variance est définie par

Var(X) = σ ² = 𝔼[(X-μ)²]

Par construction, la variance est toujours positive (ou nulle pour une variable aléatoire constante).

En finance, l’écart-type (racine carrée de la variance) mesure la volatilité des actifs financiers. Un écart-type (ou une variance élevée) indique une dispersion plus importante, et donc un risque plus important, ce n’est pas apprécié par les investisseurs qui ont de l’aversion au risque. L’écart-type (ou la variance) est un paramètre clef dans la théorie moderne du portefeuille de Markowitz.

La variance a un estimateur non biaisé donné par

Ŝ² = (∑ⁿ_i=1(x_i – X̄)²)/(n-1)

Value at Risque (VaR)

La Value at Risque (VaR, parfois traduite comme valeur en enjeu) est une notion classique pour mesurer les risques de perte d’un actif. Elle correspond au montant de perte d’une position qui ne devrait être dépassé qu’avec une probabilité donnée sur un horizon précisé, ou autrement dit, au montant de la pire perte attendue sur un horizon de temps pour un certain niveau de confiance. Elle est essentiellement le quantile de la probabilité donnée de la distribution de perte (rendement négatif).

Dans le langage mathématique, la VaR est définie comme :

VaR_α = inf{y ∈ : ℙ[L>y] ≤ 1 – α} = inf{ y ∈ : ℙ[L ≤ y] ≥ α }

VaR_α = q_α(F) ≔ F^←(α)

α est la probabilité donnée ; L est une variable aléatoire de montant de perte ; F est la distribution cumulative de perte (rendement négatif), ce qui est continue et strictement croissante ; F^← est l’inverse de F.

Les organismes financiers se servent assez souvent de cette mesure pour la rapidité et la simplicité des calculs. Toutefois, elle présente certaines lacunes. Elle n’est pas une mesure cohérente. Cela dit, l’addition des VaRs de 2 portefeuilles aurait aucun sens. À part cela, basée sur une hypothèse gaussienne, elle ne tient pas compte de la gravité et la possibilité des évènements extrêmes, tant que les distributions du marché financier sont, pour la plupart, leptokurtiques.

Expected Shortfall (ES)

L’Expected shortfall (ES) est la perte espérée pendant N jours conditionnellement au fait de se situer dans la queue (1 – α) de la distribution des gains ou des pertes (N est l’horizon temporel et α est le niveau de confiance). Autrement dit, elle est la moyenne des pertes lors d’un choc qui est pire que α% cas. L’ES est donc toujours supérieure à la VaR. Elle est souvent appelée VaR conditionnelle (CVaR).

ES_α = ∫ ¹_α (VaR_β(L) dβ)/(1 – α)

En comparaison de la VaR, ES est capable de montrer la gravité de perte dans des cas extrêmes. Ce point est primordial pour la gestion moderne de risques qui souligne la résilience surtout en cas d’extrême.

La VaR a été préférée par les participants du marché financier depuis longtemps, mais les défauts importants présentés ci-dessus ont occasionné des reproches, notamment face aux souvenances des crises majeures. L’ES, rendant compte des évènements extrêmes, tend désormais à s’imposer.

Stress Value (SV)

La Stress Value (SV) est un concept similaire à la VaR. Comme la VaR, la SV est définie comme un quantile. Pour la SV, la probabilité associée au quantile est proche de 1 (par exemple, un quantile de 99.5% pour la SV, en comparaison d’un quantile de 95% pour la VaR habituelle). La SV décrit plus précisément les pertes extrêmes.

L’estimation paramétrique de SV normalement s’appuie sur la théorie de valeurs extrêmes (EVT), alors que celle de VaR est basée sur une distribution gaussienne.

Programme R pour calculer les mesures de risques

Vous pouvez télécharger ci-dessous un programme R qui permet de calculer les mesures de risques d’une position de marché (construite à partir d’indices d’actions ou d’autres actifs).

Voici est une liste des symboles d’actif (“tickers”) que nous pouvons intégrer dans le programme R.

Example de calcul des mesures de risque de l’indice S&P 500

Ce programme nous permet de calculer rapidement des mesures de risque pour des actifs financiers dont les données historiques peuvent être téléchargées sur le site Yahoo! Finance. Je vous présente une analyse de risque pour l’indice S&P 500.

En saisissant la date de début comme 01/01/2012 et la date d’arrêté comme 01/01/2022, ce programme est en mesure de calculer les mesures de risque pour toute la période considérée.

Vous trouverez ci-dessous les mesures de risque calculées pour toute la période : la volatilité historique, la volatilité conditionnelle sur les 3 derniers mois, VaR, ES et SV.

risk mesures S&P 500

Autres articles sur le blog SimTrade

▶ Shengyu ZHENG Catégories de mesures de risques

▶ Shengyu ZHENG Moments de la distribution

▶ Shengyu ZHENG Extreme Value Theory: the Block-Maxima approach and the Peak-Over-Threshold approach

▶ Youssef LOURAOUI Markowitz Modern Portfolio Theory

Ressources

Articles académiques

Merton R.C. (1980) On estimating the expected return on the market: An exploratory investigation, Journal of Financial Economics, 8:4, 323-361.

Hull J. (2010) Gestion des risques et institutions financières, Pearson, Glossaire français-anglais.

Données

Yahoo! Finance

A propos de l’auteur

Cet article a été écrit en février 2023 par Shengyu ZHENG (ESSEC Business School, Grande Ecole Program – Master in Management, 2020-2023).

Market Making

January 28, 2023 by Martin VAN DER BORGHT

Market Making

In this article, Martin VAN DER BORGHT (ESSEC Business School, Master in Finance, 2022-2024) explains the activity of market making which is key to bring liquidity in financial markets.

Market Making: What is It and How Does It Work?

Market making is a trading strategy that involves creating liquidity in a security by simultaneously being ready to buy and sell amount of that security. Market makers provide an essential service to the market by providing liquidity to buyers and sellers, which helps to keep stock prices stable (by limiting the price impact of incoming orders). This type of trading is often done by large institutional investors such as banks. In this article, I will explore what market making is, how it works, and provide some real-life examples of market makers in action.

What is Market Making?

Market making is a trading strategy that involves simultaneously being ready to buy and sell amounts of a security in order to create or improve market liquidity for other participants. Market makers are also known as “specialists” or “primary dealers” on the stock market. They act as intermediaries between buyers and sellers, providing liquidity to the market by always being willing to buy and sell a security at a certain price (or more precisely at two prices: a price to buy and a price to sell). The remuneration of a market maker is obtained by making a profit by taking the spread between the bid and ask prices of a security.

How Does Market Making Work?

Market makers create liquidity by always having an inventory of securities that they can buy and sell. They are willing to buy and sell a security at any given time, and they do so at a certain price. The price they buy and sell at may be different from the current market price, as market makers may be trying to influence the price of a security in order to make a profit.

Market makers buy and sell large amounts of a security in order to maintain an inventory, and they use a variety of techniques to do so. For example, they may buy large amounts of a security when the price is low and sell it when the price is high. They may also use algorithms to quickly buy and sell a security in order to take advantage of small price movements.

By providing liquidity to the market, market makers help to keep stock prices stable. They are able to do this by quickly buying and selling large amounts of a security in order to absorb excess demand or supply. This helps to prevent large price fluctuations and helps to keep the price of a security within a certain range.

Market making nowadays

One of the most well-known examples of market making is the role played by Wall Street banks. These banks act as market makers for many large stocks on the NYSE and NASDAQ. They buy and sell large amounts of a security in order to maintain an inventory, and they use algorithms to quickly buy and sell a security in order to take advantage of small price movements.

Another example of market making is the practice of high-frequency trading. In his book Flash Boys, author Michael Lewis examines the impact of high frequency trading (HFT) on market making. HFT uses powerful computers and sophisticated algorithms to rapidly analyze large amounts of data, allowing traders to make trades in milliseconds. This has led to an increased use of HFT for market making activities, which has caused some to argue that it may be harming market liquidity and efficiency. Market makers have begun using HFT strategies to gain an edge over traditional market makers, allowing them to make markets faster and at narrower spreads. This has resulted in tighter spreads and higher trading volumes, but it has also been argued that it has led to increased volatility and decreased liquidity. As a result, some investors have argued that HFT strategies have created an uneven playing field, where HFT firms have an advantage over traditional market makers.

The use of HFT has also raised concerns about the fairness of markets. HFT firms have access to large amounts of data, which they can use to gain an informational advantage over other market participants. This has raised questions about how well these firms are able to price securities accurately, and whether they are engaging in manipulative practices such as front running. Additionally, some argue that HFT firms are able to take advantage of slower traders by trading ahead of them and profiting from their trades.

These concerns have led regulators to take a closer look at HFT and market making activities. The SEC and other regulators have implemented a number of rules designed to protect investors from unfair or manipulative practices. These include Regulation NMS, which requires market makers to post their best bid and ask prices for securities, as well as Regulation SHO, which prohibits naked short selling and other manipulative practices. Additionally, the SEC has proposed rules that would require exchanges to establish circuit breakers and limit the amount of order cancellations that can be done in a certain period of time. These rules are intended to ensure that markets remain fair and efficient for all investors.

Conclusion

In conclusion, market making is a trading strategy that involves creating liquidity in a security by simultaneously being ready to buy and sell large amounts of that security. Market makers provide an essential service to the market by providing liquidity to buyers and sellers, which helps to keep stock prices stable. Wall Street banks and high-frequency traders are two of the most common examples of market makers.

Useful resources

SimTrade course Market making

Michael Lewis (2015) Flash boys.

U.S. Securities and Exchange Commission (SEC) Specialists

About the author

The article was written in January 2023 by Martin VAN DER BORGHT (ESSEC Business School, Master in Finance, 2022-2024).

Evidence of underpricing during IPOs

March 31, 2024January 28, 2023 by Martin VAN DER BORGHT

Evidence of underpricing during IPOs

In this article, Martin VAN DER BORGHT (ESSEC Business School, Master in Finance, 2022-2024) exposes the results of various studies concerning IPO underpricing.

What is IPO Underpricing?

Underpricing is estimated as the percentage difference between the price at which the IPO shares were sold to investors (the offer price) and the price at which the shares subsequently trade in the market. As an example, imagine an IPO for which the shares were sold at $20 and that the first day of trading shows shares trading at $23.5, thus the associated underpricing induced is (23.5 / 20) -1 = 17.5%.

In well-developed capital markets and in the absence of restrictions on how much prices are allowed to fluctuate by from day to day, the full extent of underpricing is evident fairly quickly, certainly by the end of the first day of trading as investor jump on an occasion to reflect the fair value of the asset entering the market, and so most studies use the first-day closing price when computing initial underpricing returns. Using later prices, say at the end of the first week of trading, is useful in less developed capital markets, or in the presence of ‘daily volatility limits’ restricting price fluctuations, because aftermarket prices may take some time before they equilibrate supply and demand.

In the U.S. and increasingly in Europe, the offer price is set just days (or even more typically, hours) before trading on the stock market begins. This means that market movements between pricing and trading are negligible and so usually ignored. But in some countries (for instance, Taiwan and Finland), there are substantial delays between pricing and trading, and so it makes sense to adjust the estimate of underpricing for interim market movements.

As an alternative to computing percentage initial returns, underpricing can also be measured as the (dollar) amount of ‘money left on the table’. This is defined as the difference between the aftermarket trading price and the offer price, multiplied by the number of shares sold at the IPO. The implicit assumption in this calculation is that shares sold at the offer price could have been sold at the aftermarket trading price instead—that is, that aftermarket demand is price-inelastic. As an example, imagine an IPO for which the shares were sold at $20 and that the first day of trading shows shares trading at $23.5, with 20 million shares sold. The initial IPO in dollars was $400,000,000 and at the end of the first trading day this amount goes down to $470,000,000, inducing an amount of money left on the table of $70,000,000.

The U.S. probably has the most active IPO market in the world, by number of companies going public and by the aggregate amount of capital raised. Over long periods of time, underpricing in the U.S. averages between 10 and 20 percent, but there is a substantial degree of variation over time. There are occasional periods when the average IPO is overpriced, and there are periods when companies go public at quite substantial discounts to their aftermarket trading value. In 1999 and 2000, for instance, the average IPO was underpriced by 71% and 57%, respectively. In dollar terms, U.S. issuers left an aggregate of $62 billion on the table in those two years alone. Such periods are often called “hot issue markets”. Given these vast amounts of money left on the table, it is surprising that issuers appear to put so little pressure on underwriters to change the way IPOs are priced. A recent counterexample, however, is Google’s IPO which unusually for a U.S. IPO, was priced using an auction.

Why Has IPO Underpricing Changed over Time?

Underpricing is the difference between the price of a stock when it is first offered on the public market (the offer price) and the price at which it trades after it has been publicly traded (the first-day return). Various authors note that underpricing has traditionally been seen as a way for firms to signal quality to potential investors, which helps them to attract more investors and raise more capital.

In their study “Why Has IPO Underpricing Changed over Time? “, authors Tim Loughran and Jay Ritter discuss how the magnitude of underpricing has varied over time. They note that the average underpricing was particularly high in the 1970s and 1980s, with average first-day returns of around 45%. However, they also find that underpricing has declined significantly since then, with average first-day returns now hovering around 10%.

They then analyze the reasons for this decline in underpricing. They argue that the increased availability of information has made it easier for potential investors to assess a company’s quality prior to investing, thus reducing the need for firms to signal quality through underpricing. Additionally, they suggest that increased transparency and reduced costs of capital have also contributed to the decline in underpricing. Finally, they suggest that improved liquidity has made it easier for firms to raise capital without relying on underpricing.

These changes in underpricing have affected both existing and potential investors. Main arguments are that existing shareholders may benefit from reduced underpricing because it reduces the amount of money that is taken out of their pockets when a company goes public. On the other hand, potential investors may be disadvantaged by reduced underpricing because it reduces the return they can expect from investing in an IPO.

In conclusion we can note that while underpricing has declined significantly over time, there is still some evidence of underpricing in today’s markets. It suggests that further research is needed to understand why this is the case and how it affects investors. Many argue that research should focus on how different types of IPOs are affected by changes in underpricing, as well as on how different industries are affected by these changes. Additionally, they suggest that researchers should investigate how different investor groups are affected by these changes, such as institutional investors versus retail investors.

Overall, studies provide valuable insight into why IPO underpricing has changed so dramatically over the past four decades and how these changes have affected both existing shareholders and potential investors. It provides convincing evidence that increased access to information, greater transparency, reduced costs of capital, and improved liquidity have all contributed to the decline in underpricing. While it is clear that underpricing has declined significantly over time, further research is needed to understand why some IPOs still exhibit underpricing today and what effect this may have on different investor groups.

Useful resources

Ljungqvist A. (2004) IPO Underpricing: A Survey, Handbook in corporate finance: empirical corporate finance, Edited by B. Espen Eckbo.

Loughran T. and J. Ritter (2004) Why Has IPO Underpricing Changed over Time? Financial Management, 33(3), 5-37.

Ellul A. and M. Pagano (2006) IPO Underpricing and After-Market Liquidity The Review of Financial Studies, 19(2), 381-421.

About the author

The article was written in January 2023 by Martin VAN DER BORGHT (ESSEC Business School, Master in Finance, 2022-2024).

Market efficiency

January 28, 2023 by Martin VAN DER BORGHT

Market efficiency

In this article, Martin VAN DER BORGHT (ESSEC Business School, Master in Finance, 2022-2024) explains the key financial concept of market efficiency.

What is Market Efficiency?

Market efficiency is an economic concept that states that financial markets are efficient when all relevant information is accurately reflected in the prices of assets. This means that the prices of assts reflect all available information and that no one can consistently outperform the market by trading on the basis of this information. Market efficiency is often measured by the degree to which prices accurately reflect all available information.

The efficient market hypothesis (EMH) states that markets are efficient and that it is impossible to consistently outperform the market by utilizing available information. This means that any attempt to do so will be futile and that all investors can expect to earn the same expected return over time. The EMH is based on the idea that prices are quickly and accurately adjusted to reflect new information, which means that no one can consistently make money by trading on the basis of this information.

Types of Market Efficiency

Following Fama’s academic works, there are three different types of market efficiency: weak, semi-strong, and strong.

Weak form of market efficiency

The weak form of market efficiency states that asset prices reflect all information from past prices and trading volumes. This implies that technical analysis, which is the analysis of past price and volume data to predict future prices, is not an effective way to outperform the market.

Semi-strong form of market efficiency

The semi-strong form of market efficiency states that asset prices reflect all publicly available information, including financial statements, research reports, and news. This implies that fundamental analysis, which is the analysis of a company’s financial statements and other publicly available information to predict future prices, is also not an effective way to outperform the market.

Strong form of market efficiency

Finally, the strong form of market efficiency states that prices reflect all available information, including private information. This means that even insider trading, which is the use of private information to make profitable trades, is not an effective way to outperform the market.

The Grossman-Stiglitz paradox

If financial markets are informationally efficient in the sense they incorporate all relevant information available, then considering this information is useless when making investment decisions in the sense that this information cannot be used to beat the market on the long term. We may wonder how this information can be incorporate in the market prices if no market participants look at information. This is the Grossman-Stiglitz paradox.

Real-Life Examples of Market Efficiency

The efficient market hypothesis has been extensively studied and there are numerous examples of market efficiency in action.

NASDAQ IXIC 1994 – 2005

One of the most famous examples is the dot-com bubble of the late 1990s. During this time, the prices of tech stocks skyrocketed to levels that were far higher than their fundamental values. This irrational exuberance was quickly corrected as the prices of these stocks were quickly adjusted to reflect the true value of the companies.

NASDAQ IXIC Index, 1994-2005

Source: Wikimedia.

The figure “NASDAQ IXIC Index, 1994-2005” shows the Nasdaq Composite Index (IXIC) from 1994 to 2005. During this time period, the IXIC experienced an incredible surge in value, peaking in 2000 before its subsequent decline. This was part of the so-called “dot-com bubble” of the late 1990s and early 2000s, when investors were optimistic about the potential for internet-based companies to revolutionize the global economy.

The IXIC rose from around 400 in 1994 to a record high of almost 5000 in March 2000. This was largely due to the rapid growth of tech companies such as Amazon and eBay, which attracted huge amounts of investment from venture capitalists. These investments drove up stock prices and created a huge market for initial public offerings (IPOs).

However, this rapid growth was not sustainable, and by the end of 2002 the IXIC had fallen back to around 1300. This was partly due to the bursting of the dot-com bubble, as investors began to realize that many of the companies they had invested in were unprofitable and overvalued. Many of these companies went bankrupt, leading to large losses for their investors.

Overall, the figure “Indice IXIC du NASDAQ, 1994-2005” illustrates the boom and bust cycle of the dot-com bubble, with investors experiencing both incredible gains and huge losses during this period. It serves as a stark reminder of the risks associated with investing in tech stocks. During this period, investors were eager to pour money into internet-based companies in the hopes of achieving huge returns. However, many of these companies were unprofitable, and their stock prices eventually plummeted as investors realized their mistake. This led to large losses for investors, and the bursting of the dot-com bubble.

In addition, this period serves as a reminder of the importance of proper risk management when it comes to investing. While it can be tempting to chase high returns, it is important to remember that investments can go up as well as down. By diversifying your portfolio and taking a long-term approach, you can reduce your risk profile and maximize your chances of achieving successful returns.

U.S. Subprime lending expanded dramatically 2004–2006.

Another example of market efficiency is the global financial crisis of 2008. During this time, the prices of many securities dropped dramatically as the market quickly priced in the risks associated with rising defaults and falling asset values. The market was able to quickly adjust to the new information and the prices of securities were quickly adjusted to reflect the new reality.

U.S. Subprime Lending Expanded Significantly 2004-2006

Source: US Census Bureau.

The figure “U.S. Subprime lending expanded dramatically 2004–2006” illustrates the extent to which subprime mortgage lending in the United States increased during this period. It shows a dramatic rise in the number of subprime mortgages issued from 2004 to 2006. In 2004, less than $500 billion worth of mortgages were issued that were either subprime or Alt-A loans. By 2006, that figure had risen to over $1 trillion, an increase of more than 100%.

This increase in the number of subprime mortgages being issued was largely driven by lenders taking advantage of relaxed standards and government policies that encouraged home ownership. Lenders began offering mortgages with lower down payments, looser credit checks, and higher loan-to-value ratios. This allowed more people to qualify for mortgages, even if they had poor credit or limited income.

At the same time, low interest rates and a strong economy made it easier for people to take on these loans and still be able to make their payments. As a result, many people took out larger mortgages than they could actually afford, leading to an unsustainable increase in housing prices and eventually a housing bubble.

When the bubble burst, millions of people found themselves unable to make their mortgage payments, and the global financial crisis followed. The dramatic increase in subprime lending seen in this figure is one of the primary factors that led to the 2008 financial crisis and is an illustration of how easily irresponsible lending can lead to devastating consequences.

Impact of FTX crash on FTT

Finally, the recent rise (and fall) of the cryptocurrency market is another example of market efficiency. The prices of cryptocurrencies have been highly volatile and have been quickly adjusted to reflect new information. This is due to the fact that the market is highly efficient and is able to quickly adjust to new information.

Price and Volume of FTT

Source: CoinDesk.

FTT price and volume is a chart that shows the impact of the FTX exchange crash on the FTT token price and trading volume. The chart reflects the dramatic drop in FTT’s price and the extreme increase in trading volume that occurred in the days leading up to and following the crash. The FTT price began to decline rapidly several days before the crash, dropping from around $3.60 to around $2.20 in the hours leading up to the crash. Following the crash, the price of FTT fell even further, reaching a low of just under $1.50. This sharp drop can be seen clearly in the chart, which shows the steep downward trajectory of FTT’s price.

The chart also reveals an increase in trading volume prior to and following the crash. This is likely due to traders attempting to buy low and sell high in response to the crash. The trading volume increased dramatically, reaching a peak of almost 20 million FTT tokens traded within 24 hours of the crash. This is significantly higher than the usual daily trading volume of around 1 million FTT tokens.

Overall, this chart provides a clear visual representation of the dramatic impact that the FTX exchange crash had on the FTT token price and trading volume. It serves as a reminder of how quickly markets can move and how volatile they can be, even in seemingly stable assets like cryptocurrencies.

Today, the FTT token price has recovered somewhat since the crash, and currently stands at around $2.50. However, this is still significantly lower than it was prior to the crash. The trading volume of FTT is also much higher than it was before the crash, averaging around 10 million tokens traded per day. This suggests that investors are still wary of the FTT token, and that the market remains volatile.

Conclusion

Market efficiency is an important concept in economics and finance and is based on the idea that prices accurately reflect all available information. There are three types of market efficiency, weak, semi-strong, and strong, and numerous examples of market efficiency in action, such as the dot-com bubble, the global financial crisis, and the recent rise of the cryptocurrency market. As such, it is clear that markets are generally efficient and that it is difficult, if not impossible, to consistently outperform the market.

Useful resources

SimTrade course Market information

Academic research

Fama E. (1970) Efficient Capital Markets: A Review of Theory and Empirical Work, Journal of Finance, 25, 383-417.

Fama E. (1991) Efficient Capital Markets: II Journal of Finance, 46, 1575-617.

Grossman S.J. and J.E. Stiglitz (1980) On the Impossibility of Informationally Efficient Markets The American Economic Review, 70, 393-408.

Chicago Booth Review (30/06/2016) Are markets efficient? Debate between Eugene Fama and Richard Thaler (YouTube video)

Business resources

CoinDesk These Four Key Charts Shed Light on the FTX Exchange’s Spectacular Collapse

Bloomberg Crypto Prices Fall Most in Two Weeks Amid FTT and Macro Risks

About the author

The article was written in January 2023 by Martin VAN DER BORGHT (ESSEC Business School, Master in Finance, 2022-2024).

Special Acquisition Purpose Companies (SPAC)

January 28, 2023 by Martin VAN DER BORGHT

Special Acquisition Purpose Companies (SPAC)

In this article, Martin VAN DER BORGHT (ESSEC Business School, Master in Finance, 2022-2024) develops on the SPACs.

What are SPACs

Special purpose acquisition companies (SPACs) are an increasingly popular form of corporate finance for businesses seeking to go public. SPACs are publicly listed entities created with the objective of raising capital through their initial public offering (IPO) and then using that capital to acquire a private operating business. As the popularity of this financing method has grown, so have questions about how SPACs work, their potential risks and rewards, and their implications for investors. This essay will provide an overview of SPAC structures and describe key considerations for investors in evaluating these vehicles.

How are SPACs created

A special purpose acquisition company (SPAC) is created by sponsors who typically have a specific sector or industry focus; they use proceeds from their IPO to acquire target companies within that focus area without conducting the usual due diligence associated with traditional IPOs. The target company is usually identified prior to the IPO taking place; after it does take place, shareholders vote on whether or not they would like to invest in the acquisition target’s stock along with other aspects such as management compensation packages.

The SPAC process

The process begins when sponsors form a shell corporation that issues share via investment banks’ underwriting services; these shares are then offered in an IPO which typically raises between $250 million-$500 million dollars depending on market conditions at time of launch. Sponsors can also raise additional funds through private placements before going public if needed and may even receive additional cash from selling existing assets owned by company founders prior to launching its IPO. This allows them more flexibility in terms of what targets they choose during search process as well as ability transfer ownership over acquired business faster than traditional M&A processes since no need wait secure regulatory approval beforehand. Once enough capital has been raised through IPO/private placement offerings, sponsor team begins searching for suitable candidate(s) purchase using criteria determined ahead time based off desired sector/industry focus outlined earlier mentioned: things like size revenue generated per quarter/yearly periods competitive edge offered current products compared competitors etcetera all come play here when narrowing down list candidates whose acquisitions could potentially help increase value long-term investments made original shareholders..

Advantages of SPACs

Unlike traditional IPOs where companies must fully disclose financial information related past performance future prospects order comply regulations set forth Securities & Exchange Commission (SEC), there far less regulation involved investing SPACs because purchase decisions already being made prior going public stage: meaning only disclose details about target once agreement reached between both parties – though some do provide general information during pre-IPO phase give prospective buyers better idea what expect once deal goes through.. This type of structure helps lower cost associated taking business public since much due diligence already done before opening up share offer investors thus allowing them access higher quality opportunities at fraction price versus those available traditional stock exchange markets. Additionally, because shareholder votes taken into consideration each step way, risk potential fraud reduced since any major irregularities discovered regarding selected targets become transparent common knowledge everyone voting upon proposed change (i.e., keeping board members accountable).

Disadvantages of SPACs

As attractive option investing might seem, there are still certain drawbacks that we should be aware such the high cost involved structuring and launching successful campaigns and the fact that most liquidation events occur within two years after listing date – meaning there is a lot of money spent upfront without guarantee returns back end. Another concern regards transparency: while disclosure requirements are much stricter than those found regular stocks, there is still lack of full disclosure regarding the proposed acquisitions until the deal is finalized making difficult to determine whether a particular venture is worth the risk taken on behalf investor. Lastly, many believe merging different types of businesses together could lead to the disruption of existing industries instead just creating new ones – something worth considering if investing large sums money into particular enterprise.

Examples of SPACs

VPC Impact Acquisition (VPC)

This SPAC was formed in 2020 and is backed by Pershing Square Capital Management, a leading hedge fund. It had an initial funding of $250 million and made three acquisitions. The first acquisition was a majority stake in the outdoor apparel company, Moosejaw, for $280 million. This acquisition was considered a success as Moosejaw saw significant growth in its business after the acquisition, with its e-commerce sales growing over 50% year-over-year (Source: Business Insider). The second acquisition was a majority stake in the lifestyle brand, Hill City, for $170 million, which has also been successful as it has grown its e-commerce and omnichannel businesses (Source: Retail Dive). The third acquisition was a minority stake in Brandless, an e-commerce marketplace for everyday essentials, for $25 million, which was not successful and eventually shut down in 2020 after failing to gain traction in the market (Source: TechCrunch). In conclusion, VPC Impact Acquisition has been successful in two out of three of its acquisitions so far, demonstrating its ability to identify successful investments in the consumer and retail sector.

Social Capital Hedosophia Holdings Corp (IPOE)

This SPAC was formed in 2019 and is backed by Social Capital Hedosophia, a venture capital firm co-founded by famed investor Chamath Palihapitiya. It had an initial funding of $600 million and has made two acquisitions so far. The first acquisition was a majority stake in Virgin Galactic Holdings, Inc. for $800 million, which has been extremely successful as it has become a publicly traded space tourism company and continues to make progress towards its mission of accessible space travel (Source: Virgin Galactic). The second acquisition was a majority stake in Opendoor Technologies, Inc., an online real estate marketplace, for $4.8 billion, which has been successful as the company has seen strong growth in its business since the acquisition (Source: Bloomberg). In conclusion, Social Capital Hedosophia Holdings Corp has been incredibly successful in both of its acquisitions so far, demonstrating its ability to identify promising investments in the technology sector.

Landcadia Holdings II (LCA)

This SPAC was formed in 2020 and is backed by Landcadia Holdings II Inc., a blank check company formed by Jeffery Hildebrand and Tilman Fertitta. It had an initial funding of $300 million and made one acquisition, a majority stake in Waitr Holdings Inc., for $308 million. Unfortunately, this acquisition was not successful and it filed for bankruptcy in 2020 due to overleveraged balance sheet and lack of operational improvements (Source: Reuters). Waitr had previously been a thriving food delivery company but failed to keep up with the rapid growth of competitors such as GrubHub and DoorDash (Source: CNBC). In conclusion, Landcadia Holdings II’s attempt at acquiring Waitr Holdings Inc. was unsuccessful due to market conditions outside of its control, demonstrating that even when a SPAC is backed by experienced investors and has adequate funding, there are still no guarantees of success.

Conclusion

Despite all these drawbacks, Special Purpose Acquisition Companies remain a viable option for entrepreneurs seeking to take advantage of the rising trend toward the digitalization of global markets who otherwise wouldn’t have access to the resources necessary to fund projects themselves. By providing unique opportunity to access higher caliber opportunities, this type of vehicle serves fill gap left behind many start-up ventures unable to compete against larger organizations given the limited financial capacity to operate self-sufficiently. For reasons stated above, it is clear why SPACs continue to gain traction both among investors entrepreneurs alike looking to capitalize quickly on changing economic environment we live today…

Useful resources

U.S. Securities and Exchange Commission (SEC) Special Purpose Acquisition Companies

U.S. Securities and Exchange Commission (SEC) What are the differences in an IPO, a SPAC, and a direct listing?

U.S. Securities and Exchange Commission (SEC) What You Need to Know About SPACs – Updated Investor Bulletin

PwC Special purpose acquisition companies (SPACs)

Harvard Business Review SPACs: What You Need to Know

Bloomberg

Reuters

About the author

The article was written in January 2023 by Martin VAN DER BORGHT (ESSEC Business School, Master in Finance, 2022-2024).

Catégories de mesures de risques

February 4, 2024January 22, 2023 by Shengyu ZHENG

Catégories de mesures de risque

Dans cet article, Shengyu ZHENG (ESSEC Business School, Grande Ecole Program – Master in Management, 2020-2023) présente les catégories de mesures de risques couramment utilisées en finance.

Selon le type d’actif et l’objectif de gestion de risques, on se sert de mesures de risques de différentes catégories. Techniquement, on distingue trois catégories de mesures de risques selon l’objet statistique utilisé : la distribution statistique, la sensibilité et les scénarios. Généralement, les méthodes des différentes catégories sont employées et combinées, en constituant un système de gestion de risques qui facilite de différents niveaux des besoins managériaux.

Approche basée sur la distribution statistique

Les mesures modernes de risques s’intéressent à la distribution statistiques de la variation de valeur d’une positon de marché (ou de la rentabilité de cette position) à un horizon donné.

Les mesures se divise principalement en deux types, globales et locales. Les mesures globales (variance, beta) rendent compte de la distribution entière. Les mesures locales (Value-at-Risk, Expected Shortfall, Stress Value) se focalisent sur les queues de distribution, notamment la queue où se situent les pertes.

Cette approche n’est toutefois pas parfaite. Généralement un seul indicateur statistique n’est pas suffisant pour décrire tous les risques présents dans la position ou le portefeuille. Le calcul des propriétés statistiques et l’estimation des paramètres sont basés sur les données du passé, alors que le marché financier ne cesse d’évoluer. Même si la distribution reste inchangée entre temps, l’estimation précise de distribution n’est pas évidente et les hypothèses paramétriques ne sont pas toujours fiables.

Approche basée sur les sensibilités

Cette approche permet d’évaluer l’impact d’une variation d’un facteur de risques sur la valeur ou la rentabilité du portefeuille. Les mesures, telles que la duration et la convexité pour les obligations et les Grecques pour les produits dérivés, font partie de cette catégorie.

Elles comportent aussi des limites, notamment en termes d’agrégation de risques.

Approche basée sur les scénarios

Cette approche considère la perte maximale dans tous les scénarios générés sous les conditions de changements majeurs du marché. Les chocs peuvent s’agir, par exemple, d’une hausse de 10% d’un taux d’intérêt ou d’une devise, accompagnée d’une chute de 20% des indices d’actions importants.

Un test de résistance est un dispositif souvent mis en place par les banques centrales afin d’assurer la solvabilité des acteurs importants et la stabilité du marché financier. Un test de résistance, ou en anglicisme un « stress test », est un exercice consistance à simuler des conditions économiques et financières extrêmes mais effectivement plausibles, dans le but d’étudier les conséquences majeures apportées surtout aux établissements financiers (par exemple, les banques ou les assureurs), et de quantifier la capacité de résistance de ces établissements.

Autres article sur le blog SimTrade

▶ Shengyu ZHENG Mesures de risques

▶ Shengyu ZHENG Moments de la distribution

▶ Shengyu ZHENG Extreme Value Theory: the Block-Maxima approach and the Peak-Over-Threshold approach

▶ Youssef LOURAOUI Markowitz Modern Portfolio Theory

Resources

Academic research (articles)

Aboura S. (2009) The extreme downside risk of the S&P 500 stock index. Journal of Financial Transformation, 2009, 26 (26), pp.104-107.

Gnedenko, B. (1943). Sur la distribution limite du terme maximum d’une série aléatoire. Annals of mathematics, 423–453.

Hosking, J. R. M., Wallis, J. R., & Wood, E. F. (1985) “Estimation of the generalized extreme-value distribution by the method of probability-weighted moments” Technometrics, 27(3), 251–261.

Longin F. (1996) The asymptotic distribution of extreme stock market returns Journal of Business, 63, 383-408.

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

Longin F. et B. Solnik (2001) Extreme correlation of international equity markets Journal of Finance, 56, 651-678.

Mises, R. v. (1936). La distribution de la plus grande de n valeurs. Rev. math. Union interbalcanique, 1, 141–160.

Pickands III, J. (1975). Statistical Inference Using Extreme Order Statistics. The Annals of Statistics, 3(1), 119– 131.

Academic research (books)

Embrechts P., C. Klüppelberg and T Mikosch (1997) Modelling Extremal Events for Insurance and Finance.

Embrechts P., R. Frey, McNeil A. J. (2022) Quantitative Risk Management, Princeton University Press.

Gumbel, E. J. (1958) Statistics of extremes. New York: Columbia University Press.

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

Other materials

Extreme Events in Finance

Rieder H. E. (2014) Extreme Value Theory: A primer (slides).

A propos de l’auteur

Cet article a été écrit en janvier 2023 par Shengyu ZHENG (ESSEC Business School, Grande Ecole Program – Master in Management, 2020-2023).

Hedge fund diversification

January 13, 2023 by Youssef LOURAOUI

In this article, Youssef LOURAOUI (Bayes Business School, MSc. Energy, Trade & Finance, 2021-2022) discusses the notion of hedge fund diversification by analyzing the paper “Hedge fund diversification: how much is enough?” by Lhabitant and Learned (2002).

This article is organized as follows: we describe the primary characteristics of the research paper. Then, we highlight the research paper’s most important points. This essay concludes with a discussion of the principal findings.

Introduction

The paper discusses the advantages of investing in a set of hedge funds or a multi-strategy hedge fund. It is a relevant subject in the field of alternative investments since it has attracted the interest of institutional investors seeking to uncover the alternative investment universe and increase their portfolio return. The paper’s primary objective is to determine the appropriate number of hedge funds that an portfolio manager should combine in its portfolio to maximise its (expected) returns. The purpose of the paper is to examine the impact of adding hedge funds to a traditional portfolio and its effect on the various statistics (average return, volatility, skewness, and kurtosis). The authors consider basic portfolios (randomly chosen and equally-weighted portfolios). The purpose is to evaluate the diversification advantage and the dynamics of the diversification effect of hedge funds.

Key elements of the paper

The pioneering work of Henry Markowitz (1952) depicted the effect of diversification by analyzing the portfolio asset allocation in terms of risk and (expected) return. Since unsystematic risk (specific risk) can be neutralized, investors will not receive an additional return. Systematic risk (market risk) is the component that the market rewards. Diversification is then at the heart of asset allocation as emphasized by Modern Portfolio Theory (MPT). The academic literature has since then delved deeper on the analysis of the optimal number of assets to hold in a well-diversified portfolio. We list below some notable contributions worth mentioning:

Elton and Gruber (1977), Evans and Archer (1968), Tole (1982) and Statman (1987) among others delved deeper into the optimal number of assets to hold to generate the best risk and return portfolio. There is no consensus on the optimal number of assets to select.
Evans and Archer (1968) depicted that the best results are achieved with 8-10 assets, while raising doubts about portfolios with number of assets above the threshold. Statman (1987) concluded that at least thirty to forty stocks should be included in a portfolio to achieve the portfolio diversification.

Lhabitant and Learned (2002) also mention the concept of naive diversification (also known as “1/N heuristics”) is an allocation strategy where the investor split the overall fund available is distributed into same. Naive diversification seeks to spread asset risk evenly in the portfolio to reduce overall risk. However, the authors mention important considerations for naïve/Markowitz optimization:

Drawback of naive diversification: since it doesn’t account for correlation between assets, the allocation will yield a sub-optimal result and the diversification won’t be fully achieved. In practice, naive diversification can result in portfolio allocations that lie on the efficient frontier. On the other hand, mean-variance optimisation, the framework revolving he Modern Portfolio Theory is subject to input sensitivity of the parameters used in the optimization process. On a side note, it is worth mentioning that naive diversification is a good starting point, better than gut feeling. It simplifies allocation process while also benefiting by some degree of risk diversification.
Non-normality of distribution of returns: hedge funds exhibit non-normal returns (fat tails and skewness). Those higher statistical moments are important for investors allocation but are disregarded in a mean-variance framework.
Econometric difficulties arising from hedge fund data in an optimizer framework. Mean-variance optimisers tend to consider historical return and risk, covariances as an acceptable point to assess future portfolio performance. Applied in a construction of a hedge fund portfolio, it becomes even more difficult to derive the expected return, correlation, and standard deviation for each fund since data is scarcer and more difficult to obtain. Add to that the instability of the hedge funds returns and the non-linearity of some strategies which complicates the evaluation of a hedge fund portfolio.
Operational risk arising from fund selection and implementation of the constraints in an optimiser software. Since some parameters are qualitative (i.e., lock up period, minimum investment period), these optimisers tool find it hard to incorporate these types of constraints in the model.

Conclusion

Due to entry restrictions, data scarcity, and a lack of meaningful benchmarks, hedge fund investing is difficult. The paper analyses in greater depth the optimal number of hedge funds to include in a diversified portfolio. According to the authors, adding funds naively to a portfolio tends to lower overall standard deviation and downside risk. In this context, diversification should be improved if the marginal benefit of adding a new asset to a portfolio exceeds its marginal cost.

The authors reiterate that investors should not invest “naively” in hedge funds due to their inherent risk. The impact of naive diversification on the portfolio’s skewness, kurtosis, and overall correlation structure can be significant. Hedge fund portfolios should account for this complexity and examine the effect of adding a hedge fund to a well-balanced portfolio, taking into account higher statistical moments to capture the allocation’s impact on portfolio construction. Naive diversification is subject to the selection bias. In the 1990s, the most appealing hedge fund strategy was global macro, although the long/short equity strategy acquired popularity in the late 1990s. This would imply that allocations will be tilted towards these two strategies overall.

The answer to the title of the research paper? Hedge funds portfolios should hold between 15 and 40 underlying funds, while most diversification benefits are reached when accounting with 5 to 10 hedge funds in the portfolio.

Why should I be interested in this post?

The purpose of portfolio management is to maximise returns on the entire portfolio, not just on one or two stocks. By monitoring and maintaining your investment portfolio, you can accumulate a substantial amount of wealth for a range of financial goals, such as retirement planning. This article facilitates comprehension of the fundamentals underlying portfolio construction and investing. Understanding the risk/return profiles, trading strategy, and how to incorporate hedge fund strategies into a diversified portfolio can be of great interest to investors.

Useful resources

Academic research

Elton, E., and M. Gruber (1977). “Risk Reduction and Portfolio Size: An Analytical Solution.” Journal of Business, 50. pp. 415-437.

Evans, J.L., and S.H. Archer (1968). “Diversification and the Reduction of Dispersion: An Empirical Analysis”. Journal of Finance, 23. pp. 761-767.

Lhabitant, François S., Learned Mitchelle (2002). “Hedge fund diversification: how much is enough?” Journal of Alternative Investments. pp. 23-49.

Markowitz, H.M (1952). “Portfolio Selection.” The Journal of Finance, 7, pp. 77-91.

Statman, M. (1987). “How many stocks make a diversified portfolio?”, Journal of Financial and Quantitative Analysis , pp. 353-363.

Tole T. (1982). “You can’t diversify without diversifying”, Journal of Portfolio Management, 8, pp. 5-11.

About the author

The article was written in January 2023 by Youssef LOURAOUI (Bayes Business School, MSc. Energy, Trade & Finance, 2021-2022).

Managed futures strategy

January 13, 2023 by Youssef LOURAOUI

In this article, Youssef LOURAOUI (Bayes Business School, MSc. Energy, Trade & Finance, 2021-2022) presents the managed futures strategy (also called CTAs or Commodity Trading Advisors). The objective of the managed futures strategy is to look for market trends across different markets.

This article is structured as follow: we introduce the managed futures strategy principle. Then, we present the different types of managed futures strategies available. We also present a performance analysis of this strategy and compare it a benchmark representing all hedge fund strategies (Credit Suisse Hedge Fund index) and a benchmark for the global equity market (MSCI All World Index).

Introduction

According to Credit Suisse (a financial institution publishing hedge fund indexes), a managed futures strategy can be defined as follows: “Managed Futures funds (often referred to as CTAs or Commodity Trading Advisors) focus on investing in listed bond, equity, commodity futures and currency markets, globally. Managers tend to employ systematic trading programs that largely rely upon historical price data and market trends. A significant amount of leverage is employed since the strategy involves the use of futures contracts. CTAs do not have a particular biased towards being net long or net short any particular market.”

Managed futures funds make money based on the points below:

Exploit market trends: trending markets tend to keep the same direction over time (either upwards or downwards)
Combine short-term and long-term indicators: use of short-term and long-term moving averages
Diversify across different markets: at least one market should move in trend
Leverage: the majority of managed futures funds are leveraged in order to get increased exposures to a certain market

Types of managed futures strategies

Managed futures may contain varying percentages of equity and derivative investments. In general, a diversified managed futures account will have exposure to multiple markets, including commodities, energy, agriculture, and currencies. The majority of managed futures accounts will have a trading programme that explains their market strategy. The market-neutral and trend-following strategies are two main methods.

Market-neutral strategy

Market-neutral methods look to profit from mispricing-induced spreads and arbitrage opportunities. Investors that utilise this strategy usually attempt to limit market risk by taking long and short positions in the same industry to profit from both price increases (for long positons) and decreases (for short positions).

Trend-following strategy

Trend-following strategies seek to generate profits by trading long or short based on fundamental and/or technical market indicators. When the price of an asset is falling, trend traders may decide to enter a short position on that asset. On the opposite, when the price of an asset is rising, trend traders may decide to enter a long position. The objective is to collect gains by examining multiple indicators, deciding an asset’s direction, and then executing the appropriate trade.

Methodolgical isuses

The methodology to define a managed futures strategy is described below:

Identify appropriate markets: concentrate on the markets that are of interest for this style of trading strategy
Identify technical indicators: use key technical indicators to assess if the market is trading on a trend
Backtesting: the hedge fund manager will test the indicators retained for the strategy on the market chosen using historical data and assess the profitability of the strategy across a sample data frame. The important point to mention is that the results can be prone to errors. The results obtained can be optimized to historical data, but don’t offer the returns computed historically.
Execute the strategy out of sample: see if the in-sample backtesting result is similar out of sample.

This strategy makes money by investing in trending markets. The strategy can potentially generate returns in both rising and falling markets. However, understanding the market in which this strategy is employed, coupled with a deep understanding of the key drivers behind the trending patterns and the rigorous quantitative approach to trading is of key concern since this is what makes this strategy profitable (or not!).

Performance of the managed futures strategy

Overall, the performance of the managed futures strategy was overall not correlated from equity returns, but volatile (Credit Suisse, 2022). To capture the performance of the managed futures strategy, we use the Credit Suisse hedge fund strategy index. To establish a comparison between the performance of the global equity market and the managed futures strategy, we examine the rebased performance of the Credit Suisse managed futures index with respect to the MSCI All-World Index.

Over a period from 2002 to 2022, the managed futures strategy index managed to generate an annualized return of 3.98% with an annualized volatility of 10.40%, leading to a Sharpe ratio of 0.077. Over the same period, the Credit Suisse Hedge Fund Index managed to generate an annualized return of 5.18% with an annualized volatility of 5.53%, leading to a Sharpe ratio of 0.208. The managed futures strategy had a negative correlation with the global equity index, just about -0.02 overall across the data analyzed. The results are in line with the idea of global diversification and decorrelation of returns derived of the managed futures strategy from global equity returns.

Figure 1 gives the performance of the managed futures funds (Credit Suisse Managed Futures Index) compared to the hedge funds (Credit Suisse Hedge Fund index) and the world equity funds (MSCI All-World Index) for the period from July 2002 to April 2021.

Figure 1. Performance of the managed futures strategy.

Source: computation by the author (Data: Bloomberg)

You can find below the Excel spreadsheet that complements the explanations about the Credit Suisse managed futures strategy.

Why should I be interested in this post?

Understanding the profits and risks of such a strategy might assist investors in incorporating this hedge fund strategy into their portfolio allocation.

Useful resources

Academic research

Pedersen, L. H., 2015. Efficiently Inefficient: How Smart Money Invests and Market Prices Are Determined. Princeton University Press.

Business Analysis

Credit Suisse Hedge fund strategy

Credit Suisse Hedge fund performance

Credit Suisse Managed futures strategy

Credit Suisse Managed futures performance benchmark

About the author

The article was written in January 2023 by Youssef LOURAOUI (Bayes Business School, MSc. Energy, Trade & Finance, 2021-2022).

Dedicated short bias strategy

January 13, 2023 by Youssef LOURAOUI

In this article, Youssef LOURAOUI (Bayes Business School, MSc. Energy, Trade & Finance, 2021-2022) presents the dedicated short bias strategy. The strategy holds a net short position, which implies more shorts (selling) than long (buying) positions. The objective of the dedicated bias strategy is to profit from shorting overvalued equities.

This article is structured as follow: we introduce the dedicated short bias strategy. Then, we present a practical case study to grasp the overall methodology of this strategy. We also present a performance analysis of this strategy and compare it a benchmark representing all hedge fund strategies (Credit Suisse Hedge Fund index) and a benchmark for the global equity market (MSCI All World Index).

Introduction

According to Credit Suisse (a financial institution publishing hedge fund indexes), a dedicated short bias strategy can be defined as follows: “Dedicated Short Bias funds take more short positions than long positions and earn returns by maintaining net short exposure in long and short equities. Detailed individual company research typically forms the core alpha generation driver of dedicated short bias managers, and a focus on companies with weak cash flow generation is common. To affect the short sale, the manager borrows the stock from a counter-party and sells it in the market. Short positions are sometimes implemented by selling forward. Risk management consists of offsetting long positions and stop-loss strategies”.

This strategy makes money by short selling overvalued equities. The strategy can potentially generate returns in falling markets but would underperform in rising equity market. The interesting characteristic of this strategy is that it can potentially offer to investors the added diversification by being non correlated with equity market returns.

Example of the dedicated short bias strategy

Jim Chanos (Kynikos Associates) short selling trade: Enron

In 2000, Enron dominated the raw material and energy industries. Kenneth Lay and Jeffrey Skilling were the two leaders of the group that disguised the company’s financial accounts for years. Enron’s directors, for instance, hid interminable debts in subsidiaries in order to create the appearance of a healthy parent company whose obligations were extremely limited because they were buried in the subsidiary accounts. Enron filed for bankruptcy on December 2, 2001, sparking a big scandal, pulling down the pension funds intended for the retirement of its employees, who were all laid off simultaneously. Arthur Andersen, Enron’s auditor, failed to detect the scandal, and the scandal ultimately led to the dissolution of one of the five largest accounting and audit firms in the world (restructuring the sector from the Big 5 to the Big 4). Figure 1 represents the share price of Enron across time.

Figure 1. Performance Enron across time.
img_SimTrade_Enron_performance
Source: Computation by the author

Fortune magazine awarded Enron Corporation “America’s Most Innovative Company” annually from 1996 to 2000. Enron Corporation was a supposedly extremely profitable energy and commodities company. At the beginning of 2001, Enron had around 20,000 employees and a market valuation of $60 billion, approximately 70 times its earnings.

Short seller James Chanos gained notoriety for identifying Enron’s problems early on. This trade was dubbed “the market call of the decade, if not the past fifty years” (Pederssen, 2015).

Risk of the dedicated short bias strategy

The most significant risk that can make this strategy loose money is a short squeeze. A short seller can borrow shares through a margin account if he/she believes a stock is overvalued and its price is expected to decline. The short seller will then sell the stock and deposit the money into his/her margin account as collateral. The seller will eventually have to repurchase the shares. If the price of the stock has decreased, the short seller gains money owing to the difference between the price of the stock sold on margin and the price of the stock paid later at the reduced price. Nonetheless, if the price rises, the buyback price may rise the initial sale price, and the short seller will be forced to sell the security quickly to avoid incurring even higher losses.

We illustrate below the risk of a dedicated short bias strategy with Gamestop.

Gamestop short squeeze

GameStop is best known as a video game retailer, with over 3,000 stores still in operation in the United States. However, as technology in the video game business advances, physical shops faced substantial problems. Microsoft and Sony have both adopted digital game downloads directly from their own web shops for their Xbox and Playstation systems. While GameStop continues to offer video games, the company has made steps to diversify into new markets. Toys and collectibles, gadgets, apparel, and even new and refurbished mobile phones are included.

However, given the increased short pressure by different hedge funds believing that the era of physical copies was dead, they started positioning in Gamestop stock and traded short in order to profit from the decrease in value. In this scenario, roughly 140% of GameStop’s shares were sold short in January 2021. In this case, investors have two choices: keep the short position or cover it (to buy back the borrowed securities in order to close out the open short position at a profit or loss). When the stock price rises, covering a short position means purchasing the shares at a loss since the stock price is now higher than what was sold. And when 140% of a stock’s float is sold short, a large number of positions are (have to be) closed. As a result, short sellers were constantly buying shares to cover their bets. When there is that much purchasing pressure, the stock mechanically continued to rise. From the levels reached in early 2020 to the levels reached in mid-2021, the stock price climbed by a factor of a nearly a hundred times (Figure 2).

Figure 2. Performance of Gamestop stock price.
Gamestop performance
Source: (Data: Tradingview)

In the Gamestop story, the short sellers lost huge amount of money. Especially, the hedge fund Melvin Capital lost billions of dollars after being on the wrong side of the GameStop short squeeze.

Why should I be interested in this post?

Understanding the profits and risks of such a strategy might assist investors in incorporating this hedge fund strategy into their portfolio allocation.

Useful resources

Academic research

Pedersen, L. H., 2015. Efficiently Inefficient: How Smart Money Invests and Market Prices Are Determined. Princeton University Press.

Business Analysis

Credit Suisse Hedge fund strategy

Credit Suisse Hedge fund performance

Wikipedia Gamestop short squeeze

TradingView, 2023 Gamestop stock price historical chart

About the author

The article was written in January 2023 by Youssef LOURAOUI (Bayes Business School, MSc. Energy, Trade & Finance, 2021-2022).

Hedging of the crude oil price

January 11, 2023 by Youssef LOURAOUI

In this article, Youssef Louraoui (Bayes Business School, MSc. Energy, Trade & Finance, 2021-2022) discusses the concept of hedging and its application in the crude oil market.

This article is structured as follow: we introduce the concept of hedging in the first place. Then, we present the mathematical foundation of the Minimum Variance Hedging Ratio (MVHR). We wrap up with an empirical analysis applied to the crude oil market with a conclusion.

Introduction

Hedging is a strategy that considers taking both positions in the physical as well as the futures market to offset market movement and lock-in the price. When an individual or a corporation decides to hedge risk using futures markets, the objective is to take the opposite position to neutralize the risk as far as possible. If the company is long on the physical side (say a producer), they will mitigate the hedging by taking a short exposure in the future market. The opposite is true for a market player who is short physical. He will seek to have a long exposure in the futures market to offset the risk (Hull, 2006).

Short hedge

Selling futures contracts as insurance against an expected decrease in spot prices is known as a short hedge. For instance, an oil producer might sell crude futures or forwards if they anticipate a decline in the price of the commodity.

Long hedge

A long hedge involves purchasing futures as insurance against an increase in price. For instance, an aluminum smelter will purchase electricity futures and forward contracts, allowing the business to secure its electricity needs in the event that the physical market rises in value.

Mathematical foundations

Linear regression model

We can consider the hedge ratio as the slope of the following linear regression representing the relationship between the spot and futures price changes:

doc_SimTrade_MVHR_formula_4

where

∆S_t the change in the spot price at time t
β represents the hedging parameter
∆F_t the change in the futures price at time t

The linear regression model above can also be expressed with returns instead of price changes:

doc_SimTrade_MVHR_formula_5

R^Spot the return in the spot market at time t
R^Futures the return in the futures market at time t

Hedge ratio

We can derive the following formula for the Minimum Variance Hedging Ratio (MVHR) denoted by the Greek letter beta β:

doc_SimTrade_MVHR_formula_3

where

Cov(∆S_t,∆F_t) the co movement of the change in spot price and futures price at time t
Var(∆F_t) represents the variance of the change in price of the future price at time t

The variance and covariance of spot and futures prices are time-varying due to the changing distributional features of these values across time. Accordingly, taking into consideration such dynamics in the variance and covariance term of asset prices is a more acceptable method of establishing the minimal variance hedge ratio. There is a number of different methods that account for the dynamic nature of the minimal variance hedge ratio estimation (Alizadeh, 2022):

Simple Rolling OLS
Rolling VAR or VECM
GARCH models
Markov Regime Switching
Minimising VaR and CVaR methods

Empirical approach to hedging analysis

Periods

We downloaded ten-year worth of weekly data for the WTI crude oil spot and futures contract from the US Energy Information Administration (EIA) website. We decompose the data into two periods to assess the effectiveness of the different hedging strategies: 1st period from 23rd March 2012 to 24th March 2017 and 2nd period from 31st March 2017 to 22nd March 2022.

First period: March 2012 – March 2017

The first five years are used to estimate the Minimum Variance Hedging Ratio (Ederington, 1979). We can approach this question by using the “=slope(known_ys, known_xs)” function in Excel to obtain the gamma coefficient that would represent the MVHR. When computing the slope for the first period of the sample from 23rd March 2012 to 24th March 2017, we get a MVHR equal to 0.985. We obtain a correlation (ρ) using the Excel formula “=correl(array_1, array_2)” highlighting the logarithmic return of WTI spot and futures contract price, which yields 0.986. We can see from the figure 1 how the spot and futures prices converge closely and track each other in a very tight corridor, with very minor divergence. The regression plot between spot and futures contract returns for the first period is shown in Figure 2. This suggests that the hedger should take an opposite position in the futures market equal to 0.985 contract for each spot contract in order to minimise risk when using futures contracts as a hedging tool.

Figure 1. WTI spot and futures (1 month) prices
March 2012 – March 2017
WTI spot and futures prices
Source: computation by the author (data: EIA & Refinitiv Eikon).

Figure 2. Linear regression of WTI spot return on futures (1 month) return
March 2012 – March 2017

Source: computation by the author (data: EIA & Refinitiv Eikon).

A one-to-one hedge ratio (also known as naïve hedge) means that for every dollar of exposure in the physical market, we take one dollar exposure in the futures market. The effectiveness of this strategy is tied closely to how the spot/futures market correlation behaves. The effectiveness of this strategy would be equal to the correlation of the spot and the futures market prices in the second period.

Second period: March 2017 – March 2022

We compute the MVHR for the second period with the same approach retained in the first part by using the “=slope(known_ys, known_xs)” function in Excel to obtain the gamma coefficient that would represent the MVHR. When computing the slope for the first period of the sample from 23rd March 2017 to 24th March 2022, we get a MVHR equal to 1.095. This means that for every spot contract that we own, we need to buy 0.985 futures contracts to hedge our market risk. As previously stated, the same trend can be seen in figure 3, where spot and futures prices converge closely and track each other with just little deviation. Figure 4 represents the regression plot between spot and futures contract returns for the second period. This means that in order to reduce risk to the minimum possible amount when futures contract used as hedging instrument, for each spot contract the hedger should take an opposite position equivalent to 1.05 contract in the futures market.

Figure 3. WTI spot and futures (1 month) prices
March 2017 – March 2022.
WTI spot and futures prices
Source: computation by the author (data: EIA & Refinitiv Eikon).

Figure 4. Linear regression of WTI spot return on futures (1 month) return
March 2017 – March 2022

Source: computation by the author (data: EIA & Refinitiv Eikon).

We can approach this hedging exercise in a time-varying framework. Some academics consider that covariance and correlation are not static parameters, so they came up with models to accommodate for the time-varying nature of these two parameters. We can compute the rolling regression as the rolling slope by changing the timeframe to allow for dynamic coefficients. For this example, we computed rolling regression for one month, three-month, one year and two years. We can plot the rolling regression in the graph below (Figure 5). We can average the rolling gammas and obtain an average for each rolling period (Table 1):

Table 1. Table capturing the rolling hedge ratio for WTI across different horizons.
Hedging strategy
Source: computation by the author (data: EIA & Refinitiv Eikon).

Figure 5. WTI hedge ratio for different rolling window sizes.
Hedge ratio for WTI for rolling window sizes
Source: computation by the author (data: EIA & Refinitiv Eikon).

Conclusion

In an realistic setting, these results may be oversimplified. In some instances, cross hedging is required to calculate this strategy. This technique is used to hedge an asset’s value by relying on another asset to replicate its behaviour. Let’s use an airline as an example of a corporation seeking to hedge its jet fuel expenditures. As there is currently no jet fuel futures contract, the airline can hedge its basis risk with heating oil (an equivalent product with a valid futures market). As stated previously, the degree of correlation between the spot price and the futures price impacts the precision of cross-hedging (and hedging in general). To get the desired results and avoid instances in which we overhedge or underhedge our exposure, hedging must finally be performed appropriately.

You can find below the Excel spreadsheet that complements the explanations about of this article.

Why should I be interested in this post?

Understanding hedging techniques can be a valuable tool to implement to reduce the downside risk of an investment. Implementing a good hedging strategy can help professionals to better monitor and modify their trading strategies based different market environments.

Useful resources

Academic research

Adler M. and B. Dumas (1984) “Exposure to Currency Risk: Definition and Measurement” Financial Management 13(2) 41-50.

Alizadeh A. (2022) Volatility of energy prices: Estimation and modelling. Oil and Energy Trading module at Bayes Business School. 46-51.

Ederington L.H. (1979). The Hedging Performance of the New Futures Markets. Journal of Finance, 34(1) 157-170.

Hull C.J. (2006). Options, futures and Other Derivatives, sixth edition. Pearson Prentice Hall. 99-373.

Business

US Energy Information Administration (EIA)

About the author

The article was written in January 2023 by Youssef LOURAOUI (Bayes Business School, MSc. Energy, Trade & Finance, 2021-2022).

Automation in Audit

Why is intelligent automation important for the audit processes?

How does intelligent automation improve the audit processes?

Three steps for implementing intelligent automation in audit

Step 1: Identify processes suitable for automation

Step 2: Test your bots to ensure that they function as desired

Step 3: Monitor your automated processes and identify areas for improvement

Why should I be interested in this post?

Related posts on the SimTrade blog

About the author

The investment ecosystem

Introduction

Market participants

Market Products

Assets

Instruments

Market organization

Primary and secondary markets

Market infrastructure

Why should I be interested in this post?

Related posts on the SimTrade blog

Useful resources

About the author

High-frequency trading and limit orders

What is High-frequency trading (HFT)?

What Exactly Is a Limit Order?

HTF and Limit Order

Why should I be interested in this post?

Related posts on the SimTrade blog

Useful resources

About the author

Strategy and Tactics: From military to trading

IRSEM: The Institute for Strategic Research at the Military School

From military to Finance: Strategy and tactics applied to trading

Why should I be interested in this post?

Related posts on the SimTrade blog

Useful resources

About the author

The business of financial indexes

Introduction

Key Players

Index providers

Index Industry Association (IIA)

Business models

Licensing

Creation of index-linked products

Selling data

Regulation of indexes

Why should I be interested in this post?

Related posts on the SimTrade blog

About financial indexes

Examples of financial indexes

Useful resources

About the author

The S&P 500 index

The S&P 500 index

Calculation of the S&P 500 index value

Use of the S&P 500 index in asset management

Benchmark for equity funds

Financial products around the S&P 500 index

Historical data for the S&P 500 index

How to get the data?

R program

Data file

Summary statistics for the S&P 500 index

Evolution of the S&P 500 index

Statistical distribution of the S&P 500 index returns

Historical distribution

Gaussian distribution

Risk measures of the S&P 500 index returns

Why should I be interested in this post?

Related posts on the SimTrade blog

About financial indexes

About other US financial indexes

About portfolio management

About statistics

Useful resources

Academic research about risk

Data: Yahoo! Finance

Data: Bloomberg