Returns

Jayati WALIA

In this article, Jayati WALIA (ESSEC Business School, Grande Ecole Program – Master in Management, 2019-2022) explains how returns of financial assets are computed and their interpretation in the world of finance.

Introduction

The main focus of any investment in financial markets is to make maximum profits within a coherent risk level. Returns in finance is a metric that inherently refers to the change in the value of any investment. Positive values of returns are interpreted as gains whereas negative values are interpreted as losses.

Returns are generally computed over standardized frequencies such as daily, monthly, yearly, etc. They can also be computed for specific time periods such as the holding period for ease of comparison and analysis.

Computation of returns

Consider an asset for a time period [t -1, t] with an initial price Pt-1 at time t-1 and final price Pt at time t (one period, two dates). Different forms of defining returns for the asset over period [t -1, t] are discussed below.

Arithmetic (percentage) returns

This is the simplest way for computation of returns.

The return over the period [t -1, t], denoted by Rt, is expressed as:

Arithmetic returns

Logarithmic returns

Logarithmic returns (or log returns) are also used commonly to express investment returns. The log return over the period [t-1, t], denoted by Rt is expressed as:

Logarithmic returns

Log returns provide the property of time-additivity to the returns which essentially means that the log returns over a given period can be simply added together to compute the total return over subperiods. This feature is particularly useful in statistical analysis and reduction of algorithmic complexity.

Logarithmic returns additivity

Log returns are also known as continuously compounded returns because the rate of log returns is equivalent to the continuously compounding interest rate for the asset at price P0 and time period t.

img_SimTrade_compounded_returns

Link between arithmetic and logarithmic returns

The arithmetic return (Rari) and the logarithmic return (Rlog) are linked by the following formula:

Relation between arithmetic and logarithmic returns

Components of total returns

The total return on an investment is essentially composed of two components: the yield and the capital gain (or loss). The yield refers to the periodic income or cash-flows that may be received on the investment. For example, for an investment in stocks, the yield corresponds to the revenues of dividends while for bonds, it corresponds to interest payments.

On the other hand, capital gain (or loss) refers to the appreciation (or depreciation) in the price of the investment. Thus, the capital gain (or loss) for any asset is essentially the price change in the asset.

Total returns for a stock over the period [t -1, t], denoted by Rt, can hence be expressed as:

Total returns

Where
   Pt: Stock price at time t
   Pt-1: Stock price at time t-1
   Dt-1,t: Dividend obtained over the period [t -1, t]

Price changes and returns

Consider a stock with an initial price of 100€ at time t=0. Suppose the stock price drops to 50€ at time t=1. Thus, there is a change of -50% (minus sign representing the decrease in price) in the initial stock price.

Now for the stock price to reach back to its initial price (100€ in this case) at time t=2 from its price of 50€ at time t=1, it will require an increase of (100€-50€)/50€ = 100%. With arithmetic returns, the increase (+100%) has to be higher than the decrease (-50%).

Similarly, for a price drop of -25% in the initial stock price of 100€, we would require an increase of 33% in the next time period to reach back the initial stock price. Figure 1 illustrates this asymmetry between positive and negative arithmetic returns.

Figure 1. Evolution of price change as a measure of arithmetic returns.
img_SimTrade_price_change_evolution
Source: computation by the author.

If the return is defined as a logarithmic return, there is a symmetry between positive and negative logarithmic returns as illustrated in Figure 2.

Figure 2. Evolution of price change as a measure of logarithmic returns.
img_SimTrade_price_change_evolution
Source: computation by the author.

You can also download below the Excel file for computation of arithmetic returns and visualise the above price change evolution.

Download the Excel file to compute required returns to come back to the initial price

Internal rate of return (IRR)

Internal rate of return (IRR) is the rate at which a project undertaken by the firm break’s even. It is a financial metric used by financial analysts to compute the profitability from an investment and is calculated by equating the initial investment and the discounted value of the future cashflows i.e., making the net present value (NPV) equal to zero. The IRR is the sprecail value of the discount rate which makes the NPV equal to zero.

The IRR for a project can be computed as follows:

IRR formula

Where,
   CFt : Cashflow for time period t

The higher the IRR from a project, the more desirable it is to pursue with the project.

Ex ante and ex post returns

Ex ante and ex post are Latin expressions. Ex ante refers to “before an event” while ex post refers to “after the event”. In context of financial returns, the ex ante return corresponds to prediction or estimation of an asset’s potential future return and can be based on a financial model like the Capital Asset Pricing Model (CAPM). On the other hand, the ex post return corresponds to the actual return generated by an asset historically, and hence are lagging or backward-looking in nature. Ex post returns can be used to forecast ex ante returns for the upcoming period and together, both are used to make sound investment decisions.

Related posts on the SimTrade blog

   ▶ Jayati WALIA Standard deviation

   ▶ Raphaël ROERO DE CORTANZE The Internal Rate of Return

   ▶ Jérémy PAULEN The IRR function in Excel

   ▶ Léopoldine FOUQUES The IRR, XIRR and MIRR functions in Excel

About the author

The article was written in April 2022 by Jayati WALIA (ESSEC Business School, Grande Ecole Program – Master in Management, 2019-2022).

Supply and Demand

Supply and Demand

Diana Carolina SARMIENTO PACHON

In this article, Diana Carolina SARMIENTO PACHON (ESSEC Business School, Master in Strategy & Management of International Business (SMIB), 2021-2022) explains the economic concept of supply and demand, which is key to understand the way markets work.

Supply and demand are the fundamental concepts that shape the way we make business and operate in the world. They construct both simple transactions such as the purchase of coffee or more compounded transactions such as the operations in the financial world. For this reason, it’s crucial to understand and uncover them deeper.

The basic concepts

Supply is referred to the amount available of a product that firms offer, whereas demand is the amount desired by consumers or households. When these quantities are equal, an equilibrium is reached and consequently a transaction takes place, leading to the well-known law of supply & demand which shapes the behavior of daily transactions and shifts in the economy. If price increases, then supply also increases; nonetheless, demand decreases as it’s more expensive for consumers to a buy good; on the contrary, if prices decline then supply also decline since producers would make less revenue whereas demand goes up as it is cheaper to buy. This dynamic takes place until the quantities of supply and demand are equal so that the optimum equilibrium is found.

Figure 1. Supply and demand.
img_Simtrade_risk_reduction_stocks
Source: computation by the author.

From another perspective, if demand escalates then price rises due to the high desirability of the good, meanwhile when demand drops it can create a surplus of supply which can drag the price down. Likewise, this scenario can be applied in financial markets e.g., in the case of a bullish sentiment in the market, there can be a positive speculation which creates a higher desirability for certain stock resulting in a decrease in price; nevertheless, when demand is low the price may drop because of a low or negative speculation on a specific stock.

Furthermore, the fundamental law of supply and demand can also explain the price movements seen in the financial markets. To illustrate, for a commodity such as coffee, if the surface of cultivation expands or if the harvest is good, it is very likely that the coffee price will sink as its supply will be abundant. Therefore, it is essential to consider the information about the market regularly as it can have a significant influence on the speculation of investors which will eventually define their demands and so the price of a stock. Consequently, it is very important to be able to determine how an announcement or any kind of information can affect the demand or even the supply of a stock, commodity, or financial instrument since this will define how markets will behave.

Special cases

However, it’s also important to mention that there are industries and situations in which the law of supply and demand does not apply. An instance of this is the luxury industry, in which the higher the product price set by firms, the higher the demand from consumers. This may be due to the value that costumers perceive by purchasing such items. Alternatively, oil is another example to be mentioned as its price has a low-price sensitivity which means that any change in its price won’t result in any significant demand changes, this could be due to the high necessity of oil in all industries which makes it crucial for daily operations.

Useful resources

Krugman, P. & Wells, R. (2012) Economics. 3rd edition. United States: Macmillan Learning.

Mankiw, G. (2016) The Market Forces of Supply and Demand (table of content) Principles of Economics. 8th edition. Boston: Cengage Learning.

Mankiw, G. (2016) The Market Forces of Supply and Demand (slides) Principles of Economics. 8th edition. Boston: Cengage Learning.

Deskara Supply and Demand: Law, Curves, and Examples

International Energy Agency (IEA) Supply and demand for oil

Sabiou M. Inoua and Vernon L. Smith The Classical Theory of Supply and Demand

About the author

The article was written in April 2022 by Diana Carolina SARMIENTO PACHON (ESSEC Business School, Master in Strategy & Management of International Business (SMIB), 2021-2022)

Risk Aversion

Risk Aversion

Diana Carolina SARMIENTO PACHON

In this article, Diana Carolina SARMIENTO PACHON (ESSEC Business School, Master in Strategy & Management of International Business (SMIB), 2021-2022) explains the economic concept of risk aversion, which is key to understand the behavior of participants in financial markets.

Risk Aversion refers to the level of reluctance that an individual possesses towards risk. Specifically, it refers to the attitude of investors towards the risk underlying investments which will directly determine how portfolios are allocated or even how a stock may behave depending on market conditions. To elaborate, when market participants have higher risk aversion due to unfavorable market shocks e.g., natural disasters, bad news or scandals that affect a company or a security, this situation will cause a perception of higher risk leading to many selling, and thus decreasing prices. Therefore, risk aversion should be analyzed carefully.

Risk aversion and investor’s characteristics

It’s important to note that risk aversion can be highly variable over time as this notion changes along with investor profile, in other words with age, income, culture and other key factors, making it even more complex to evaluate than it appears in the traditional economics literature. To illustrate more accurately some of the factors that define an investor profile are:

Age

The older the person is, the more risk averse he or she is. On the contrary, younger individuals tend to be less risk averse which may be due to their high expectations and eagerness to attempt something new as well as the longer timeframe they have, whereas older people prefer safety and stability in their lives.

Income

Individuals with a smaller budget tend to have a higher risk aversion since they have fewer resources, and a loss would make a greater impact on them than a wealthy individual.

Past Losses

When an individual has already experienced some loss, she or he will be more wary of it since it’s now too costly to bear another loss; therefore, risk aversion will be significantly higher. An example of this is the post-crisis, as people have lost so much and this has had a negative impact on their lives, they tend to become more cautious of risk.

Investment Objective

For crucial events such as retirement or education, risk version tends to be higher as the individual cannot bear to risk for such a fundamental matter of his or her life.

Investment Horizon

Investors focused on short-term horizon tend to be more risk averse as they cannot take too much risk due to the short timeline.

Risk aversion and financial investments

Furthermore, risk aversion also takes into account more factors apart from those mentioned above, for this reason most of the time before creating the respective portfolio for an investor, financial advisors shape their client’s risk preferences in order to adjust the portfolio allocation to them. Many times, these can be conducted by questionnaires and tests that will accordingly assign a risk profile concluding with certain risk categories:

  • A Conservative profile refers to more risk averse individuals, the portfolios assigned for this type are mainly composed by both more secure & less volatile securities such as bonds, meanwhile stocks have a minimal participation.
  • A Moderate profile is attributed to more risk averse individuals who are willing to take more risk, however he or she does not want to step too much further. These portfolios are usually more diversified as they contain more types of securities in different percentages such as government & corporate bonds, and stocks.
  • An aggressive profile which is allocated to portfolios mainly composed in the highest percentage by the risky securities. For instance, the main securities could be stocks, specifically growth stocks or even crypto.

Due to all sensitive and private information used by financial institutions, financial regulatory entities are important to ensure the protection and transparency of information, thereby the Mifid (The Markets in Financial Instruments Directive) has been created in the European Union to fulfill such task through the use of rules and general standards.

Measure of risk of financial assets

Additionally, there are other mathematical metrics that can interfere in the risk profile, and depending on these the portfolio may be constructed:

Standard Deviation

It refers to the volatility of historical data, in other words how dispersed the data is over time which illustrates how risky the security may be. The higher the standard deviation, the higher the risk since this is suggesting that the stock is more variable and there is more uncertainty, thus a risk averse individual prefers a lower standard deviation.

Beta

It is linked with the systematic risk that comes with a stock, that is to say it illustrates the volatility compared to the market. Firstly, a beta equal to 1 indicates a volatility and movement equalizing the market, secondly a beta higher than 1 is referred to a security that is more volatile than the market, to illustrate B= 1.50 specifies 50% more volatility than the market. Thirdly, a beta less than 1 stipulates less volatility than the market. Therefore, the lower the beta the less risk exposure is found.

Modern Portfolio Theory & Risk

Introduced by Harry Markowitz in 1950s, the Modern Portfolio Theory illustrates the optimum portfolio allocation that maximizes return given a specific level of risk, in which risk is measured by the standard deviation and the return by the average mean of the portfolio. This explanation also leads to the one- single period mean-variance theory which suggests various portfolio allocations depending on the trade-off between return and risk. However, there are more advance models which explain this scenario in a multiperiod by rebalancing or diversifying further.

Risk aversion and economic conditions

Risk aversion does not only shape the portfolio allocation and its diversification, but it also may have a significant impact on the market as a result of expectations. When there are booming economic times, individuals usually feel more confident and thus less risk averse as a consequence of positive expectations of future cash flows; however, when a recession is coming investors may shift to a more risk averse behavior making them feel afraid of the future which influences them to sell certain stocks and, in this way, making the price plump. Although it may be seen as a simple emotion that defines the fear of risk, it still impacts in a very large extent the financial market as it dictates the roles and strategies behind investing, and thereby it is crucial analyze it carefully.

Related posts

   ▶ Youssef LOURAOUI Markowitz Modern Portfolio Theory

   ▶ Youssef LOURAOUI Implementing Markowitz asset allocation model

   ▶ Jayati WALIA Capital Asset Pricing Model (CAPM)

Useful resources

Díaz A and Esparcia C (2019) Assessing Risk Aversion From the Investor’s Point of View Frontiers in Psychology, 10:1490

Desjardins Online brokerage The Risk Aversion Coefficient

Coursera course Investment management

Crehana course Trading: How to invest in stocks (Trading: Como invertir en Bolsa)

About the author

The article was written in April 2022 by Diana Carolina SARMIENTO PACHON (ESSEC Business School, Master in Strategy & Management of International Business (SMIB), 2021-2022)

My experience as a junior market research analyst at Procolombia

My experience as a junior market research analyst at Procolombia

Diana Carolina SARMIENTO PACHON

In this article, Diana Carolina SARMIENTO PACHON (ESSEC Business School, Master in Strategy & Management of International Business (SMIB), 2021-2022) shares her experience as a junior market research analyst in the investment department at Procolombia.

The company: Procolombia

Procolombia is the Colombian government entity that promotes direct investment, exports, and tourism into Colombia. The entity has several offices both in Colombia and in different countries around the world in order to reach to other governments, and thus facilitate negotiations. Examples of the locations of these offices are Paris, New York, London, Tokyo, Beijing, Dubai, Mexico, among others.

Procolombia is divided into the three departments: investment, exports and tourism.

Investment

Investment department whose main mission is to promote and bring into Colombia direct foreign investment. Examples of investments executed by the promotion of Procolombia are Amazon, Softbank, and Harley-Davidson.

Exports

Exports department with the main objective of promoting Colombian good across the world, and its main mission is accompanying and support exporters as well as contacting different public and private entities interested in Colombian products.

Tourism

Tourism department main focus is promote tourists into Colombia and expand the market share of the country in the Latin-American tourism.

The investment department organization and execution

Firstly, the investment department is divided into four regional hubs: North-America & the Caribbean, Latin-America, Europe-Middle East & Asia. Each hub is specialized in its respective region and market. Secondly, each hub has a general manager and usually 4/5 advisors specialized in a specific industry (Chemicals, Industries 4.0 which refers to AI/IoT/digitalization, Investment & Real Estate, Agro, Energy, etc.) which would facilitate the operations of the department so that every person is assigned with a specific region and industry.

The process of bringing investment

  • First of all, the investment advisors from Procolombia contact the respective firm/investor to create a very first contact, or the investor may contact Procolombia to obtain the very first information.
  • In the second place, if the investor is interested, he or she will ask for further information and probably require the specific opportunities available. For this purpose, the Colombians firms or projects looking for investing usually provide their basic financial information such as EBITDA, debt ratios, and the amount of money required, so that investors can have the primary financial information.
  • Once the investor shows more interest after having analyzed the basic financial metrics, there will be some factories and free-trade visits alongside meeting with the respective companies in order to gain deeper insight, and if they finally decide to invest, Procolombia will be supporting them in legal and tax matters to facilitate their investment journey in Colombia.

My internship Experience

I was specifically an intern of the North America management team. My main mission was supporting the team by providing market research of the potential investment opportunities as well as the possible investors that could be reached in order to promote the country in North America (US, Canada, and Caribbean countries). Additionally, I provided the consolidation of financial data about different Colombian companies and consolidated such information in such a way that it was understandable by potential investors.

Furthermore, I also had to support the logistics of the various events in which Procolombia looked to promote the country usually with very important high-level guests such as ambassadors, officials or investors looking for large investments, experience that showed how negotiation among different countries were conducted and how was the planning of such plans executed.

Skills needed

This internship required computational abilities with the purpose of comprehending the data and financial information of companies along with rapid analytical skills that can synthetize and summarize such information efficiently.

Regarding soft skills: team oriented and adaptability are crucial as operations are most of the time executed by sharing diverse opinions and agreeing with others which requires the wiliness to work and listen carefully. Besides, confronting different situation which may be one’s out of comfort zone is also a very common situation in the workplace, thereby it’s essential to be open to different challenges and situations as new issues can arise at any moment.

Financial Concepts

Even though my internship was more focused on the promotion of foreign direct investments in Colombia, I was still able to have direct contact with some financial concepts that were used regularly in the running of the entity, such as Ebitda and Debt Ratio.

Foreign direct investment (FDI)

Foreign direct investment (FDI) indicates the transfer of foreign capital into an entity or organization with a long-term vision. For instance, when an American or European multinational corporation invests in Colombia with the aim of opening facilities in this country in order to facilitate the operations in the region, and probably improve profitability. An example of this is P&G, Henkel or L’Oréal, companies that invested in the country in such a way that the performance both in Colombia and Latin America becomes more efficient in addition to providing employment, development and technology .

EBITDA

EBITDA refers to Earnings Before Interest, Taxes, Depreciation & Amortization. In other words, it’s the operating income however the non-cash costs such depreciation & amortization are added. It is usually used because it reflects the earnings from operations and the efficiency of them.

Net debt

All the debt (long-term + shot-term) – all cash & equivalents which would indicate what they company still owed in case of liquidation

Solvency ratios

Solvency ratios were usually used so that the investor could know the debt state of the company such as debt ratio = Total obligations/ Total Liabilities indicating how much financial leveraged the company has. The higher it is, the riskier the company may be, e.g., a 0.5 debt ratio indicated that 50% of the firm assets are financed by debt.

Thus, this experience also helped to shape some basic financial knowledge in real life situations and even taught me the importance of understanding financial concept as even if they are not directly in our expertise, they will always be the base of discussions in the business world.

Related posts on the SimTrade blog

   ▶ All posts about Professional experiences

   ▶ Anna BARBERO Career in finance

   ▶ Akshit GUPTA Green bonds

Useful resources

Procolombia

About the author

The article was written in April 2022 by Diana Carolina SARMIENTO PACHON (ESSEC Business School, Master in Strategy & Management of International Business (SMIB), 2021-2022)

A quick overview of the Bloomberg terminal…

A quick overview of the Bloomberg terminal…

Louis DETALLE

In this article, Louis DETALLE (ESSEC Business School, Grande Ecole Program – Master in Management, 2020-2023) explains everything there is to know about the Bloomberg terminal which is a must-know in finance.

How to use the main functions of the Bloomberg terminal?

One may notice that the keyboard of the Bloomberg terminal is a little strange. Indeed, this keyboard called Starboard, and contains red, blue, green and yellow keys for specific functions in addition to your regular keys.

Functions are unique Bloomberg applications that provide analysis and information on securities,
sectors, regions and more. Each function is accessed by typing in its unique mnemonic (a short, memorable name) and then pressing the key located in the lowest-right sided area of the keyboard.

Let’s review together the different functions of the buttons:

The HELP button is perhaps the most useful button for those just starting out. If you have questions about anything on the terminal, simply press the button once and a Bloomberg specialist will be there to start a live chat with you to resolve your questions.

In order to benefit from the latest news, users can simply type NEWS and press enter to get the latest information on market trends, movements and other relevant news.

Those in the finance industry chat via Bloomberg Messaging, which is essentially equivalent to Facebook Messenger but on Bloomberg. It enables you to send a message to anyone on the device. This means that anyone in the industry can technically contact each other instantly. No need to ask for someone else’s number or find out the best way to get in touch.

Main users of the Bloomberg terminal

Traders, brokers, analysts, portfolio managers, investors and executives are the Terminal’s primary consumer base as they need to access the data provided by Bloomberg easily in order to do their job.

A subscription to the Bloomberg Terminal costs approximately $20,000 a year, but that does not stop its customers from renewing their subscriptions because of its usefulness.

Training webinars

First and foremost, the Bloomberg beginner should work on the document available on Bloomberg website, Getting started on the Bloomberg Terminal, which will give you the main information on the keys and their function.

The best next step to get used to the Bloomberg Terminal is to complete the certification
course: Bloomberg Market Concepts (BMC). BMC is an 8-hour e-learning course that will
provide a visual introduction to the financial markets and covers nearly 70 Terminal functions which is enough for whoever wants to start using Bloomberg.

Related posts on the SimTrade blog

   ▶ Louis DETALLE The importance of data in finance

   ▶ Louis DETALLE Reuters

   ▶ Louis DETALLE Bloomberg

Useful resources

Bloomberg’s website

Capital Markets (BMC) Certification’s website

About the author

The article was written in April 2022 by Louis DETALLE (ESSEC Business School, Grande Ecole Program – Master in Management, 2020-2023).

Bloomberg

Bloomberg

Louis DETALLE

In this article, Louis DETALLE (ESSEC Business School, Grande Ecole Program – Master in Management, 2020-2023) explains everything there is to know about Bloomberg LP, the international leader in the data-providing market…

Quick presentation of the company

Bloomberg LP is an American financial group specialized in services to financial market professionals and in economic and financial information. Bloomberg operates as a news agency and via numerous media such as TV, radio, press, internet, and books. The company was founded in 1981 by Michael Bloomberg, former mayor of New York City.

In its early days, Bloomberg LP’s activities were only based on the exploitation of a historical database of US Treasury yield curves, bought by the founder to its former employer, the investment bank Salomon Brothers. After that, the company added on its terminals a messaging system, retransmissions of financial assets’ prices and developed financial news flows long before the watershed of Internet.
In 1990, Michael Bloomberg installed his 1,000th terminal.

Type of people working at Bloomberg (types of jobs)

The careers available at Bloomberg LP are numerous and very diverse. The Board’s needs in terms of employees mainly consist of software designers to help design the Bloomberg’s terminals, sectorial financial specialists in order to provide precise and adequate analysis.
Finally, the last kind of profiles that Bloomberg needs are journalists and more broadly, people with great writing abilities since Bloomberg LP produces a huge flow of written articles every day. Bloomberg News for instance (one of many Bloomberg LP’s subsidiaries) has over 10 000 employees which gives an idea of the written flow emitted by the company.

Main competitors

As Bloomberg’s activities are very diverse, we will classify the main competitors of the American firm in respect to the activities.
For Bloomberg’s core business, which is the terminals, Thomson Reuters is the most natural competitor in this space (with products like Kobra, Eikon, D3000). The terminal business is built on a fantastic technology platform that provides comprehensive financial information. There are other competitors, such as Dow Jones Industrial Average FX Trader, which have specialized in one type of industry whereas Bloomberg remains a generalist.

Bloomberg’s editorial branch’s main competitors would be Reuters, the FT, the Wall Street Journal, and other traditional financial news companies. The same goes for their TV/radio operation (their competitor would be CNBC).

Use of data in financial markets

The explosion of financial data, enabled by the Internet tremendous potential, caused an explosion of demand for financial data. As evidenced in 2006 by the British mathematician and Tesco marketing mastermind Clive Humby’s quote, “Data is the new oil”, the data market seems to be limitless.

In addition, as Bloomberg acquires many of his competitors, such as BNA and BusinessWeek, this contributes to curbing the number of data providers and improving the monopoly of Bloomberg on the data-providing market.

Useful resources

Bloomberg

Thomson Reuters

Related posts on the SimTrade blog

   ▶ Louis DETALLE Understand the importance of data providers and how they influence global finance…

   ▶ Louis DETALLE Reuters

About the author

The article was written in March 2022 by Louis DETALLE (ESSEC Business School, Grande Ecole Program – Master in Management, 2020-2023).

Specific risk

Youssef_Louraoui

In this article, Youssef LOURAOUI (Bayes Business School, MSc. Energy, Trade & Finance, 2021-2022) explains the specific risk of financial assets, a key concept in asset pricing models and asset management in practice.

This article is structured as follows: we start with a reminder of portfolio theory and the central concept of risk in financial markets. We then introduce the concept of specific risk of an individual asset and especially its sources. We then detail the mathematical foundation of risk. We finish with an insight of the relationship between diversification and risk reduction with a practical example to test this concept.

Portfolio Theory and Risk

Markowitz (1952) and Sharpe (1964) created a framework for risk analysis based on their seminal contributions to portfolio theory and capital market theory. All rational profit-maximizing investors attempt to accumulate a diversified portfolio of risky assets and borrow or lend to achieve a risk level consistent with their risk preferences given a set of assumptions. They established that the key risk indicator for an individual asset in these circumstances is its correlation with the market portfolio (the beta).

The variance of returns of an individual asset can be decomposed as the sum of systematic risk and specific risk. Systematic risk refers to the proportion of the asset return variance that can be attributed to the variability of the whole market. Specific risk refers to the proportion of the asset return variance that is unconnected to the market and reflects the unique nature of the asset. Specific risk is often regarded as insignificant or irrelevant because it can be eliminated in a well-diversified portfolio.

Sources of specific risk

Specific risk can find its origin in business risk (in the assets side of the balance sheet) and financial risk (in the liabilities side of the balance sheet):

Business risk

Internal or external issues might jeopardize a business. Internal risk is directly proportional to a business’s operational efficiency. An internal risk would include management neglecting to patent a new product, so eroding the company’s competitive advantage.

Financial risk

This pertains to the capital structure of a business. To continue growing and meeting financial obligations, a business must maintain an ideal debt-to-equity ratio.

Mathematical foundations

Following the Capital Asset Pricing Model (CAPM), the return on asset i, denoted by Ri can be decomposed as

img_SimTrade_return_decomposition

Where:

  • Ri the return of asset i
  • E(Ri) the risk premium of asset i
  • βi the measure of the risk of asset i
  • RM the return of the market
  • E(RM) the risk premium of the market
  • RM – E(RM) the market factor
  • εi represent the specific part of the return of asset i

The three components of the decomposition are the expected return, the market factor and an idiosyncratic component related to asset only. As the expected return is known over the period, there are only two sources of risk: systematic risk (related to the market factor) and specific risk (related to the idiosyncratic component).

The beta of the asset with the market is computed as:

Beta

Where:

  • σi,m : the covariance of the asset return with the market return
  • σm2 : the variance of market return

The total risk of the asset measured by the variance of asset returns can be computed as:

Decomposition of total risk

Where:

  • βi2 * σm2 = systematic risk
  • σεi2 = specific risk

In this decomposition of the total variance, the first component corresponds to the systematic risk and the second component to the specific risk.

Decomposition of returns

We analyze the decomposition of returns on Apple stocks. Figure 1 gives for every month of 2021 the decomposition of Apple stock returns into three parts: expected return, market factor (systematic return) and an idiosyncratic component (specific return). We used historical price downloaded from the Bloomberg terminal for the period 1999-2022.

Figure 1. Decomposition of Apple stock returns:
expected return, systematic return and specific return.
Decomposition of asset returnsComputation by the author (data: Bloomberg).

You can download below the Excel file which illustrates the decomposition of returns on Apple stocks.

Download the Excel file for the decomposition of Apple stock returns

Why should I be interested in this post?

Investors will be less influenced by single incidents if they possess a range of firm stocks across several industries, as well as other types of assets in a number of asset classes, such as bonds and stocks. 

An investor who only bought telecommunication equities, for example, would be exposed to a high amount of unsystematic risk (also known as idiosyncratic risk). A concentrated portfolio can have an impact on its performance. This investor would spread out telecommunication-specific risks by adding uncorrelated positions to their portfolio, such as firms outside of the telecommunication market.

Related posts on the SimTrade blog

   ▶ Louraoui Y. Systematic risk and specific risk

   ▶ Louraoui Y. Systematic risk

   ▶ Louraoui Y. Beta

   ▶ Louraoui Y. Portfolio

   ▶ Louraoui Y. Markowitz Modern Portfolio Theory

   ▶ Walia J. Capital Asset Pricing Model (CAPM)

Useful resources

Academic research

Evans, J.L., Archer, S.H. 1968. Diversification and the Reduction of Dispersion: An Empirical Analysis. The Journal of Finance, 23(5): 761–767.

Markowitz, H. 1952. Portfolio Selection. The Journal of Finance, 7(1): 77-91.

Mossin, J. 1966. Equilibrium in a Capital Asset Market. Econometrica, 34(4): 768-783.

Sharpe, W.F. 1963. A Simplified Model for Portfolio Analysis. Management Science, 9(2): 277-293.

Sharpe, W.F. 1964. Capital Asset Prices: A Theory of Market Equilibrium under Conditions of Risk. The Journal of Finance, 19(3): 425-442.

Tole T.M. 1982. You can’t diversify without diversifying. The Journal of Portfolio Management. Jan 1982, 8 (2) 5-11.

About the author

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

Systematic risk

Youssef_Louraoui

In this article, Youssef LOURAOUI (Bayes Business School, MSc. Energy, Trade & Finance, 2021-2022) presents the systematic risk of financial assets, a key concept in asset pricing models and investment management theories more generally.

This article is structured as follows: we introduce the concept of systematic risk. We then explain the mathematical foundation of this concept. We present an economic understanding of market risk on recent events.

Portfolio Theory and Risk

Markowitz (1952) and Sharpe (1964) developed a framework on risk based on their significant work in portfolio theory and capital market theory. All rational profit-maximizing investors seek to possess a diversified portfolio of risky assets, and they borrow or lend to get to a risk level that is compatible with their risk preferences under a set of assumptions. They demonstrated that the key risk measure for an individual asset is its covariance with the market portfolio under these circumstances (the beta).

The fraction of an individual asset’s total variance attributable to the variability of the total market portfolio is referred to as systematic risk, which is assessed by the asset’s covariance with the market portfolio. Systematic risk can be decomposed into the following categories:

Interest rate risk

We are aware that central banks, such as the Federal Reserve, periodically adjust their policy rates in order to boost or decrease the rate of money in circulation in the economy. This has an effect on the interest rates in the economy. When the central bank reduces interest rates, the money supply expands, allowing companies to borrow more and expand, and when the policy rate is raised, the reverse occurs. Because this is cyclical in nature, it cannot be diversified.

Inflation risk

When inflation surpasses a predetermined level, the purchasing power of a particular quantity of money reduces. As a result of the fall in spending and consumption, overall market returns are reduced, resulting in a decline in investment.

Exchange Rate Risk

As the value of a currency reduces in comparison to other currencies, the value of the currency’s returns reduces as well. In such circumstances, all companies that conduct transactions in that currency lose money, and as a result, investors lose money as well.

Geopolitical Risks

When a country has significant geopolitical issues, the country’s companies are impacted. This can be mitigated by investing in multiple countries; but, if a country prohibits foreign investment and the domestic economy is threatened, the entire market of investable securities suffers losses.

Natural disasters

All companies in countries such as Japan that are prone to earthquakes and volcanic eruptions are at risk of such catastrophic calamities.

Following the Capital Asset Pricing Model (CAPM), the return on asset i, denoted by Ri can be decomposed as

img_SimTrade_return_decomposition

Where:

  • Ri the return of asset i
  • E(Ri) the risk premium of asset i
  • βi the measure of the risk of asset i
  • RM the return of the market
  • E(RM) the risk premium of the market
  • RM – E(RM) the market factor
  • εi represent the specific part of the return of asset i

The three components of the decomposition are the expected return, the market factor and an idiosyncratic component related to asset only. As the expected return is known over the period, there are only two sources of risk: systematic risk (related to the market factor) and specific risk (related to the idiosyncratic component).

The beta of the asset with the market is computed as:

Beta

Where:

  • σi,m : the covariance of the asset return with the market return
  • σm2 : the variance of market return

The total risk of the asset measured by the variance of asset returns can be computed as:

Decomposition of total risk

Where:

  • βi2 * σm2 = systematic risk
  • σεi2 = specific risk

In this decomposition of the total variance, the first component corresponds to the systematic risk and the second component to the specific risk.

Systematic risk analysis in recent times

The volatility chart depicts the evolution of implied volatility for the S&P 500 and US Treasury bonds – the VIX and MOVE indexes, respectively. Implied volatility is the price of future volatility in the option market. Historically, the two markets have been correlated during times of systemic risk, like as in 2008 (Figure 1).

Figure 1. Volatility trough time (VIX and MOVE index).
Volatility trough time (VIX and MOVE index)
Sources: BlackRock Risk and Quantitative Analysis and BlackRock Investment Institute, with data from Bloomberg and Bank of America Merrill Lynch, October 2021 (BlackRock, 2021).

The VIX index has declined following a spike in September amid the equity market sell-off. It has begun to gradually revert to pre-Covid levels. The periodic, albeit brief, surges throughout the year underscore the underlying fear about what lies beyond the economic recovery and the possibility of a wide variety of outcomes. The MOVE index — a gauge of bond market volatility – has remained relatively stable in recent weeks, despite the rise in US Treasury yields to combat the important monetary policy to combat the effect of the pandemic. This could be a reflection of how central banks’ purchases of government bonds are assisting in containing interest rate volatility and so supporting risk assets (BlackRock, 2021).

The regime map depicts the market risk environment in two dimensions by plotting market risk sentiment and the strength of asset correlations (Figure 2).

Figure 2. Regime map for market risk environment.
Regime map for market risk environment
Source: BlackRock Risk and Quantitative Analysis and BlackRock Investment Institute, October 2021 (BlackRock, 2021).

Positive risk sentiment means that riskier assets, such as equities, are outperforming less risky ones. Negative risk sentiment means that higher-risk assets underperform lower-risk assets.

Due to the risk of fast changes in short-term asset correlations, investors may find it challenging to guarantee their portfolios are correctly positioned for the near future. When asset correlation is higher (as indicated by the right side of the regime map), diversification becomes more difficult and risk increases. When asset prices are less correlated (on the left side of the map), investors have greater diversification choices.

When both series – risk sentiment and asset correlation – are steady on the map, projecting risk and return becomes easier. However, when market conditions are unpredictable, forecasting risk and return becomes substantially more difficult. The map indicates that we are still in a low-correlation environment with a high-risk sentiment, which means that investors are rewarded for taking a risk (BlackRock, 2021). In essence, investors should use diversification to reduce the specific risk of their holding coupled with macroeconomic fundamental analysis to capture the global dynamics of the market and better understand the sources of risk.

Why should I be interested in this post?

Market risks fluctuate throughout time, sometimes gradually, but also in some circumstances dramatically. These adjustments typically have a significant impact on the right positioning of a variety of different types of investment portfolios. Investors must walk a fine line between taking enough risks to achieve their objectives and having the proper instruments in place to manage sharp reversals in risk sentiment.

Related posts on the SimTrade blog

   ▶ Louraoui Y. Systematic risk and specific risk

   ▶ Youssef LOURAOUI Specific risk

   ▶ Youssef LOURAOUI Beta

   ▶ Youssef LOURAOUI Portfolio

   ▶ Youssef LOURAOUI Markowitz Modern Portfolio Theory

   ▶ Jayati WALIA Capital Asset Pricing Model (CAPM)

Useful resources

Academic research

Markowitz, H. 1952. Portfolio Selection. The Journal of Finance, 7(1): 77-91.

Mossin, J. 1966. Equilibrium in a Capital Asset Market. Econometrica, 34(4): 768-783.

Sharpe, W.F. 1963. A Simplified Model for Portfolio Analysis. Management Science, 9(2): 277-293.

Sharpe, W.F. 1964. Capital Asset Prices: A Theory of Market Equilibrium under Conditions of Risk. The Journal of Finance, 19(3): 425-442.

Business analysis

BlackRock, 2021. Market risk monitor

About the author

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