Quantitative equity investing

December 19, 2022 by Youssef LOURAOUI

In this article, Youssef LOURAOUI (Bayes Business School, MSc. Energy, Trade & Finance, 2021-2022) elaborates on the concept of quantitative equity investing, a type of investment approach in the equity trading space.

This article follows the following structure: we introduce the quantitative equity investing. We present a review of the major types of quantitative equity strategies and we finish with a conclusion.

Introduction

Quantitative equity investing refers to funds that uses model-driven decision making when trading in the equity space. Quantitative analysts program their trading rules into computer systems and use algorithmic trading, which is overseen by humans.

Quantitative investing has several advantages and disadvantages over discretionary trading. The disadvantages are that the trading rule cannot be as personalized to each unique case and cannot be dependent on “soft” information such human judgment. These disadvantages may be lessened as processing power and complexity improve. For example, quantitative models may use textual analysis to examine transcripts of a firm’s conference calls with equity analysts, determining whether certain phrases are commonly used or performing more advanced analysis.

The advantages of quantitative investing include the fact that it may be applied to a diverse group of stocks, resulting in great diversification. When a quantitative analyst builds an advanced investment model, it can be applied to thousands of stocks all around the world at the same time. Second, the quantitative modeling rigor may be able to overcome many of the behavioral biases that commonly impact human judgment, including those that produce trading opportunities in the first place. Third, using past data, the quant’s trading principles can be backtested (Pedersen, 2015).

Types of quantitative equity strategies

There are three types of quantitative equity strategies: fundamental quantitative investing, statistical arbitrage, and high-frequency trading (HFT). These three types of quantitative investing differ in various ways, including their conceptual base, turnover, capacity, how trades are determined, and their ability to be backtested.

Fundamental quantitative investing

Fundamental quantitative investing, like discretionary trading, tries to use fundamental analysis in a systematic manner. Fundamental quantitative investing is thus founded on economic and financial theory, as well as statistical data analysis. Given that prices and fundamentals only fluctuate gradually, fundamental quantitative investing typically has a turnover of days to months and a high capacity (meaning that a large amount of money can be invested in the strategy), owing to extensive diversification.

Statistical arbitrage

Statistical arbitrage aims to capitalize on price differences between closely linked stocks. As a result, it is founded on a grasp of arbitrage relations and statistics, and its turnover is often faster than that of fundamental quants. Statistical arbitrage has a lower capacity due to faster trading (and possibly fewer stocks having arbitrage spreads).

High Frequency Trading (HFT)

HFT is based on statistics, information processing, and engineering, as the success of an HFT is determined in part by the speed with which they can trade. HFTs focus on having superfast computers and computer programs, as well as co-locating their computers at exchanges, actually trying to get their computer as close to the exchange server as possible, using fast cables, and so on. HFTs have the fastest trading turnover and, as a result, the lowest capacity.

The three types of quants also differ in how they make trades: Fundamental quants typically make their deals ex ante, statistical arbitrage traders make their trades gradually, and high-frequency traders let the market make their transactions. A fundamental quantitative model, for example, identifies high-expected-return stocks and then buys them, almost always having their orders filled; a statistical arbitrage model seeks to buy a mispriced stock but may terminate the trading scheme before completion if prices have moved adversely; and, finally, an HFT model may submit limit orders to both buy and sell to several exchanges, allowing the market to determine which ones are hit. Because of this trading structure, fundamental quant investing can be simulated with some reliability via a backtest; statistical arbitrage backtests rely heavily on assumptions on execution times, transaction costs, and fill rates; and HFT strategies are frequently difficult to simulate reliably, so HFTs must rely on experiments.

Table 1. Quantitative equity investing main categories and characteristics.

Source: Source: Pedersen, 2015.

Conclusion

Quants run their models on hundreds, if not thousands, of stocks. Because diversification eliminates most idiosyncratic risk, firm-specific shocks tend to wash out at the portfolio level, and any single position is too tiny to make a major impact in performance.

An equity market neutral portfolio eliminates total stock market risk by being equally long and short. Some quants attempt to establish market neutrality by ensuring that the long side’s dollar exposure equals the dollar worth of all short bets. This technique, however, is only effective if the longs and shorts are both equally risky. As a result, quants attempt to balance market beta on both the long and short sides. Some quants attempt to be both dollar and beta neutral.

Why should I be interested in this post?

It may provide an opportunity for investors to diversify their global portfolios. Including hedge funds in a portfolio can help investors obtain absolute returns that are uncorrelated with typical bond/equity returns.

For practitioners, learning how to incorporate hedge funds into a standard portfolio and understanding the risks associated with hedge fund investing can be beneficial.

Understanding if hedge funds are truly providing “excess returns” and deconstructing the sources of return can be beneficial to academics. Another challenge is determining whether there is any “performance persistence” in hedge fund returns.

Getting a job at a hedge fund might be a profitable career path for students. Understanding the market, the players, the strategies, and the industry’s current trends can help you gain a job as a hedge fund analyst or simply enhance your knowledge of another asset class.

Useful resources

Academic research

Pedersen, L. H., 2015. Efficiently Inefficient: How Smart Money Invests and Market Prices Are Determined. Chapter 9 : 133 – 164. Princeton University Press.

About the author

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

Optimal portfolio

December 19, 2022 by Youssef LOURAOUI

In this article, Youssef LOURAOUI (Bayes Business School, MSc. Energy, Trade & Finance, 2021-2022) presents the concept of optimal portfolio, which is central in portfolio management.

This article is structured as follows: we first define the notion of an optimal portfolio (in the mean-variance framework) and we then illustrate the concept of optimal portfolio with an example.

Introduction

An investor’s investment portfolio is a collection of assets that he or she possesses. Individual assets such as bonds and equities can be used, as can asset baskets such as mutual funds or exchange-traded funds (ETFs). When constructing a portfolio, investors typically evaluate the expected return as well as the risk. A well-balanced portfolio contains a diverse variety of investments.

An optimal portfolio is a collection of assets that maximizes the trade-off between expected return and risk: the portfolio with the highest expected return for a given level of risk, or the portfolio with the lowest risk for a given level of expected return.

To obtain the optimal portfolio, Markowitz sought to optimize the following dual program:

The first optimization seeks to maximize expected return with respect to a specific level of risk, subject to the short-selling constraint (weights of the portfolio should be equal to one).

img_SimTrade_implementing_Markowitz_2

The second optimization seeks to minimize the variance of the portfolio with respect to a specific level of expected return, subject to the short-selling constraint (weights of the portfolio should be equal to one).

img_SimTrade_implementing_Markowitz

Mathematical foundations

The investment universe is composed of N assets characterized by their expected returns μ and variance-covariance matrix V. For a given level of expected return μ_P, the Markowitz model gives the composition of the optimal portfolio. The vector of weights of the optimal portfolio is given by the following formula:

With the following notations:

w_P = vector of asset weights of the portfolio
μ_P = desired level of expected return
e = identity vector
μ = vector of expected returns
V = variance-covariance matrix of returns
V^-1 = inverse of the variance-covariance matrix
t = transpose operation for vectors and matrices

A, B and C are intermediate parameters computed below:

img_SimTrade_implementing_Markowitz_2

The variance of the optimal portfolio is computed as follows

img_SimTrade_implementing_Markowitz_3

To calculate the standard deviation of the optimal portfolio, we take the square root of the variance.

Optimal portfolio application: the case of two assets

To create the optimal portfolio, we first obtain monthly historical data for the last two years from Bloomberg for two stocks that will comprise our portfolio: Apple and CMS Energy Corporation. Apple is in the technology area, but CMS Energy Corporation is an American company that is entirely in the energy sector. Apple’s historical return for the two years covered was 41.86%, with a volatility of 35.11%. Meanwhile, CMS Energy Corporation’s historical return was 13.95% with a far lower volatility of 15.16%.

According to their risk and return profiles, Apple is an aggressive stock pick in our example, but CMS Energy is a much more defensive stock that would serve as a hedge in our example. The correlation between the two stocks is 0.19, indicating that they move in the same direction. In this example, we will consider the market portfolio, defined as a theoretical portfolio that reflects the return of the whole investment universe, which is captured by the wide US equities index (S&P500 index).

As captured in Figure 1, CMS Energy suffered less severe losses than Apple. When compared to the red bars, the blue bars are far more volatile and sharp in terms of the size of the move in both directions.

Figure 1. Apple and CMS Energy Corporation return breakdown.
Time-series regression
Source: computation by the author (Data: Bloomberg)

After analyzing the historical return on both stocks, as well as their volatility and covariance (and correlation), we can use Mean-Variance portfolio optimization to find the optimal portfolio. According to Markowitz’ foundational study on portfolio construction, the optimal portfolio will attempt to achieve the best risk-return trade-off for an investor. After doing the computations, we discover that the optimal portfolio is composed of 45% Apple stock and 55% CMS Energy corporation stock. This portfolio would return 26.51% with a volatility of 19.23%. As captured in Figure 2, the optimal portfolio is higher on the efficient frontier line and has a higher Sharpe ratio (1.27 vs 1.23 for the theoretical market portfolio).

Figure 2. Optimal portfolio.
Optimal portfolio plot 2 asset
Source: computation by the author (Data: Bloomberg)

You can find below the Excel spreadsheet that complements the example above.

Optimal portfolio application: the general case

We generated a large time series to obtain useful results by downloading the equivalent of 23 years of market data from a data provider (in this example, Bloomberg). We generate the variance-covariance matrix after obtaining all necessary statistical data, which includes the expected return and volatility indicated by the standard deviation of the returns for each stock during the provided period. Table 1 depicts the expected return and volatility for each stock retained in this analysis.

Table 1. Asset characteristics of Apple, Amazon, Microsoft, Goldman Sachs, and Pfizer.
img_SimTrade_implementing_Markowitz_spreadsheet_1
Source: computation by the author.

We can start the optimization task by setting a desirable expected return after computing the expected return, volatility, and the variance-covariance matrix of expected return. With the data that is fed into the appropriate cells, the model will complete the optimization task. For a 20% desired expected return, we get the following results (Table 2).

Table 2. Asset weights for an optimal portfolio.
Optimal portfolio case 1
Source: computation by the author.

To demonstrate the effect of diversification in the reduction of volatility, we can form a Markowitz efficient frontier by tilting the desired anticipated return with their relative volatility in a graph. The Markowitz efficient frontier is depicted in Figure 1 for various levels of expected return. We highlighted the portfolio with 20% expected return with its respective volatility in the plot (Figure 3).

Figure 3. Optimal portfolio plot for 5 asset case.
Optimal portfolio case 1
Source: computation by the author.

You can download the Excel file below to use the Markowitz portfolio allocation model.

Why should I be interested in this post?

The purpose of portfolio management is to maximize the (expected) returns on the entire portfolio, not just on one or two stocks. By monitoring and maintaining your investment portfolio, you can build a substantial amount of wealth for a variety of financial goals such as retirement planning. This post facilitates comprehension of the fundamentals underlying portfolio construction and investing.

Useful resources

Academic research

Pamela, D. and Fabozzi, F., 2010. The Basics of Finance: An Introduction to Financial Markets, Business Finance, and Portfolio Management. John Wiley and Sons Edition.

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

About the author

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

Long-short equity strategy

December 17, 2022 by Youssef LOURAOUI

In this article, Youssef LOURAOUI (Bayes Business School, MSc. Energy, Trade & Finance, 2021-2022) presents the long-short equity strategy, one of pioneer strategies in the hedge fund industry. The goal of the long-short equity investment strategy is to buy undervalued stocks and sell short overvalued ones.

This article is structured as follow: we introduce the long-short strategy principle. Then, we present a practical case study to grasp the overall methodology of this strategy. We conclude with a performance analysis of this strategy in comparison with a global benchmark (MSCI All World Index).

Introduction

According to Credit Suisse, a long-short strategy can be defined as follows: “Long-short equity funds invest on both long and short sides of equity markets, generally focusing on diversifying or hedging across particular sectors, regions, or market capitalizations. Managers have the flexibility to shift from value to growth; small to medium to large capitalization stocks; and net long to net short. Managers can also trade equity futures and options as well as equity related securities and debt or build portfolios that are more concentrated than traditional long-only equity funds.”

This strategy has the particularity of potentially generate returns in both rising and falling markets. However, stock selection is key concern, and the stock picking ability of the fund manager is what makes this strategy profitable (or not!). The trade-off of this approach is to reduce market risk but exchange it for specific risk. Another key characteristic of this type of strategy is that overall, funds relying on long-short are net long in their trading exposure (long bias).

Equity strategies

In the equity universe, we can separate long-short equity strategies into discretionary long-short equity, dedicated short bias, and quantitative.

Discretionary long-short

Discretionary long-short equity managers typically decide whether to buy or sell stocks based on a basic review of the value of each firm, which includes evaluating its growth prospects and comparing its profitability to its valuation. By visiting managers and firms, these fund managers also evaluate the management of the company. Additionally, they investigate the accounting figures to judge their accuracy and predict future cash flows. Equity long-short managers typically predict on particular companies, but they can also express opinions on entire industries.

Value investors, a subset of equity managers, concentrate on acquiring undervalued companies and holding these stocks for the long run. A good illustration of a value investor is Warren Buffett. Since companies only become inexpensive when other investors stop investing in them, putting this trading approach into practice frequently entails being a contrarian (buy assets after a price decrease). Because of this, cheap stocks are frequently out of favour or purchased while others are in a panic. Traders claim that deviating from the standard is more difficult than it seems.

Dedicated short bias

Like equity long-short managers, dedicated short bias is a trading technique that focuses on identifying companies to sell short. Making a prediction that the share price will decline is known as short selling. Similar to how purchasing stock entails profiting if the price increases, holding a short position entail profiting if the price decreases. Dedicated short-bias managers search for companies that are declining. Since dedicated short-bias managers are working against the prevailing uptrend in markets since stocks rise more frequently than they fall (this is known as the equity risk premium), they make up a very small proportion of hedge funds.

Most hedge funds in general, as well as almost all equity long-short hedge funds and dedicated short-bias hedge funds, engage in discretionary trading, which refers to the trader’s ability to decide whether to buy or sell based on his or her judgement and an evaluation of the market based on past performance, various types of information, intuition, and other factors.

Quantitative

The quantitative investment might be seen as an alternative to this traditional style of trading. Quants create systems that methodically carry out the stated definitions of their trading rules. They use complex processing of ideas that are difficult to analyse using non-quantitative methods to gain a slight advantage on each of the numerous tiny, diversified trades. To accomplish this, they combine a wealth of data with tools and insights from a variety of fields, including economics, finance, statistics, mathematics, computer science, and engineering, to identify relationships that market participants may not have immediately fully incorporated in the price. Quantitative traders use computer systems that use these relationships to generate trading signals, optimise portfolios considering trading expenses, and execute trades using automated systems that send hundreds of orders every few seconds. In other words, data is fed into computers that execute various programmes under the supervision of humans to conduct trading (Pedersen, 2015).

Example of a long-short equity strategy

The purpose of employing a long-short strategy is to profit in both bullish and bearish markets. To measure the profitability of this strategy, we implemented a long-short strategy from the beginning of January 2022 to June 2022. In this time range, we are long Exxon Mobile stock and short Tesla. The data are extracted from the Bloomberg terminal. The strategy of going long Exxon Mobile and short Tesla is purely educational. This strategy’s basic idea is to profit from rising oil prices (leading to a price increase for Exxon Mobile) and rising interest rates (leading to a price decrease for Tesla). Over the same period, the S&P 500 index has dropped 23%, while the Nasdaq Composite has lost more than 30%. The Nasdaq Composite is dominated by rapidly developing technology companies that are especially vulnerable to rising interest rates.

Overall, the market’s net exposure is zero because we are 100% long Exxon Mobile and 100% short Tesla stock. This strategy succeeded to earn significant returns in both the long and short legs of the trade over a six-month timeframe. It yielded a 99.5 percent return, with a 36.8 percent gain in the value of the Exxon Mobile shares and a 62.8 percent return on the short Tesla position. Figure 1 shows the overall performance of each equity across time.

Figure 1. Long-short equity strategy performance over time
Time-series regression
Source: computation by the author (Data: Bloomberg)

You can find below the Excel spreadsheet that complements the example above.

Performance of the long-short equity strategy

To capture the performance of the long-short equity strategy, we use the Credit Suisse hedge fund strategy index. To establish a comparison between the performance of the global equity market and the long-short hedge fund strategy, we examine the rebased performance of the Credit Suisse index with respect to the MSCI All-World Index. Over a period from 2002 to 2022, the long-short equity strategy index managed to generate an annualised return of 5.96% with an annualised volatility of 7.33%, leading to a Sharpe ratio of 0.18. Over the same period, the MSCI All World Index managed to generate an annualised return of 6.00% with an annualised volatility of 15.71%, leading to a Sharpe ratio of 0.11. The low correlation of the long-short equity strategy with the MSCI All World Index is equal to 0.09, which is closed to zero. Overall, the Credit Suisse hedge fund strategy index performed somewhat slightly worse than the MSCI All World Index, but presented a much lower volatility leading to a higher Sharpe ratio (0.18 vs 0.11).

Figure 2. Performance of the long-short equity strategy compared to the MSCI All-World Index across time.
Time-series regression
Source: computation by the author (Data: Bloomberg)

You can find below the Excel spreadsheet that complements the explanations about the Credit Suisse hedge fund strategy index.

Why should I be interested in this post?

Long-short funds seek to reduce negative risk while increasing market upside. They might, for example, invest in inexpensive stocks that the fund managers believe will rise in price while simultaneously shorting overvalued stocks to cut losses. Other strategies used by long-short funds to lessen market volatility include leverage and derivatives. 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

BlackRock Long-short strategy

BlackRock Investment Outlook

Credit Suisse Hedge fund strategy

Credit Suisse Hedge fund performance

Credit Suisse Long-short strategy

Credit Suisse Long-short performance benchmark

About the author

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

Fama-MacBeth two-step regression method: the case of K risk factors

December 12, 2022 by Youssef LOURAOUI

Fama-MacBeth two-step regression method: the case of K risk factors

This article is structured as follows: we introduce the Fama-MacBeth two-step regression method. Then, we present the mathematical foundation that underpins their approach for K risk factors. We provide an illustration for the 3-factor mode developed by Fama and French (1993).

Introduction

Risk factors are frequently employed to explain asset returns in asset pricing theories. These risk factors may be macroeconomic (such as consumer inflation or unemployment) or microeconomic (such as firm size or various accounting and financial metrics of the firms). The Fama-MacBeth two-step regression approach found a practical way for measuring how correctly these risk factors explain asset or portfolio returns. The aim of the model is to determine the risk premium associated with the exposure to these risk factors.

The first step is to regress the return of every asset against one or more risk factors using a time-series approach. We obtain the return exposure to each factor called the “betas” or the “factor exposures” or the “factor loadings”.

The second step is to regress the returns of all assets against the asset betas obtained in Step 1 using a cross-section approach. We obtain the risk premium for each factor. Then, Fama and MacBeth assess the expected premium over time for a unit exposure to each risk factor by averaging these coefficients once for each element.

Mathematical foundations

We describe below the mathematical foundations for the Fama-MacBeth regression method for a K-factor application. In the analysis, we investigated the Fame-French three factor model in order to understand their significance as a fundamental driver of returns for investors under the Fama-MacBeth framework.

The model considers the following inputs:

The return of N assets denoted by R_i for asset i observed every day over the time period [0, T].
The risk factors denoted by F_k for k equal from 1 to K.

Step 1: time-series analysis of returns

For each asset i from 1 to N, we estimate the following linear regression model:

Fama-French time-series regression

From this model, we obtain the β_{i, Fk} which is the beta associated with the k^th risk factor.

Step 2: cross-sectional analysis of returns

For each period t from 1 to T, we estimate the following linear regression model:

Fama-French cross-sectional regression

Application: the Fama-French 3-Factor model

The Fama-French 3-factor model is an illustration of Fama-MacBeth two-step regression method in the case of K risk factors (K=3). The three factors are the market (MKT) factor, the small minus big (SMB) factor, and the high minus low (HML) factor. The SMB factor measures the difference in expected returns between small and big firms (in terms of market capitalization). The HML factor measures the difference in expected returns between value stocks and growth stock.

The model considers the following inputs:

The return of N assets denoted by R_i for asset i observed every day over the time period [0, T].
The risk factors denoted by F_MKT associated to the MKT risk factor, F_SMB associated to the MKT risk factor which measures the difference in expected returns between small and big firms (in terms of market capitalization) and F_HML associated to 𝐻𝑀𝐿 (“High Minus Low”) which measures the difference in expected returns between value stocks and growth stock

Step 1: time-series regression

img_SimTrade_Fama_French_time_series_regression

Step 2: cross-sectional regression

img_SimTrade_Fama_French_cross_sectional_regression

Figure 1 represents for a given period the cross-sectional regression of the return of all individual assets with respect to their estimated individual beta for the MKT factor.

Figure 1. Cross-sectional regression for the market factor.
Cross-section regression for the MKT factor Source: computation by the author.

Figure 2 represents for a given period the cross-sectional regression of the return of all individual assets with respect to their estimated individual beta for the SMB factor.

Figure 2. Cross-sectional regression for the SMB factor.
Cross-section regression for the SMB factor Source: computation by the author.

Figure 3 represents for a given period the cross-sectional regression of the return of all individual assets with respect to their estimated individual beta for the SMB factor.

Figure 3. Cross-sectional regression for the HML factor.
Cross-section regression for the HML factor Source: computation by the author.

Empirical study of the Fama-MacBeth regression

Fama-MacBeth seminal paper (1973) was based on an analysis of the market factor by assessing constructed portfolios of similar betas ranked by increasing values. This approach helped to overcome the shortcoming regarding the stability of the beta and correct for conditional heteroscedasticity derived from the computation of the betas for individual stocks. They performed a second time the cross-sectional regression of monthly portfolio returns based on equity betas to account for the dynamic nature of stock returns, which help to compute a robust standard error and assess if there is any heteroscedasticity in the regression. The conclusion of the seminal paper suggests that the beta is “dead”, in the sense that it cannot explain returns on its own (Fama and MacBeth, 1973).

Empirical study: Stock approach for a K-factor model

We collected a sample of 440 significant firms’ end-of-day stock prices in the US economy from January 3, 2012 to December 31, 2021. We calculated daily returns for each stock as well as the factor used in this analysis. We chose the S&P500 index to represent the market since it is an important worldwide stock benchmark that captures the US equities market.

Time-series regression

To assess the multi-factor regression, we used the Fama-MacBeth 3-factor model as the main factors assessed in this analysis. We regress the average returns for each stock against their factor betas. The first regression is statistically tested. This time-series regression is run on a subperiod of the whole period from January 03, 2012, to December 31, 2018. We use a t-statistic to explain the regression’s behavior. Because the p-value is in the rejection zone (less than the significance level of 5%), we can conclude that the factors can first explain an investor’s returns. However, as we will see later in the article, when we account for a second regression as proposed by Fama and MacBeth, the factors retained in this analysis are not capable of explaining the return on asset returns on its own. The stock approach produces statistically significant results in time-series regression at 10%, 5%, and even 1% significance levels. As shown in Table 1, the p-value is in the rejection range, indicating that the factors are statistically significant.

Table 1. Time-series regression t-statistic result.
Cross-section regression Source: computation by the author.

Cross-sectional regression

Over a second period from January 04, 2019, to December 31, 2021, we compute the dynamic regression of returns at each data point in time with respect to the betas computed in Step 1.

That being said, when the results are examined using cross-section regression, they are not statistically significant, as indicated by the p-value in Table 2. We are unable to reject the null hypothesis. The premium investors are evaluating cannot be explained solely by the factors assessed. This suggests that factors retained in the analysis fail to adequately explain the behavior of asset returns. These results are consistent with the Fama-MacBeth article (1973).

Table 2. Cross-section regression t-statistic result.
Source: computation by the author.

Excel file

You can find below the Excel spreadsheet that complements the explanations covered in this article.

Why should I be interested in this post?

Fama-MacBeth made a significant contribution to the field of econometrics. Their findings cleared the way for asset pricing theory to gain traction in academic literature. The Capital Asset Pricing Model (CAPM) is far too simplistic for a real-world scenario since the market factor is not the only source that drives returns; asset return is generated from a range of factors, each of which influences the overall return. This framework helps in capturing other sources of return.

Useful resources

Academic research

Brooks, C., 2019. Introductory Econometrics for Finance (4th ed.). Cambridge: Cambridge University Press. doi:10.1017/9781108524872

Fama, E. F., MacBeth, J. D., 1973. Risk, Return, and Equilibrium: Empirical Tests. Journal of Political Economy, 81(3), 607–636.

Roll R., 1977. A critique of the Asset Pricing Theory’s test, Part I: On Past and Potential Testability of the Theory. Journal of Financial Economics, 1, 129-176.

American Finance Association & Journal of Finance (2008) Masters of Finance: Eugene Fama (YouTube video)

About the author

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

Fama-MacBeth regression method: the stock approach vs the portfolio approach

December 12, 2022 by Youssef LOURAOUI

Fama-MacBeth regression method: the stock approach vs the portfolio approach

In this article, Youssef LOURAOUI (Bayes Business School, MSc. Energy, Trade & Finance, 2021-2022) presents the Fama-MacBeth regression method used to test asset pricing models and addresses the difference when applying the regression method on individual stocks or portfolios composed of stocks with similar betas.

This article is structured as follow: we introduce the Fama-MacBeth testing method. Then, we present the mathematical foundation that underpins their approach. We conduct an empirical analysis on both the stock and the portfolio approach. We conclude with a discussion on econometric issues.

Introduction

As a reminder, the Fama-MacBeth regression method is composed on two steps: step 1 with a time-series regression and step 2 with a cross-section regression.

The first step is to regress the return of every stock against one or more risk factors using a time-series regression. We obtain the return exposure to each factor called the “betas” or the “factor exposures” or the “factor loadings”.

The second step is to regress the returns of all stocks against the asset betas obtained in the first step using a cross-section regression for different periods. We obtain the risk premium for each factor used to test the asset pricing model.

The implementation of this method can be done with individual stocks or with portfolios of stocks as proposed by Fama and MacBeth (1973). Their argument is the better stability of the beta when considering portfolios. In this article we illustrate the difference with the two implementations.

Fama and MacBeth (1973) implemented with individual stocks

We downloaded a sample of daily prices of stocks composing the S&P500 index over the period from January 03, 2012, to December 31, 2021 (we selected the stocks present from the beginning to the end of the period reducing our sample from 500 to 440 stocks). We computed daily returns for each stock and for the market factor retained in this study. To represent the market, we chose the S&P500 index, an important global stock benchmark capturing the US equity market.

The procedure to derive the Fama-MacBeth regression using the stock approach can be achieved as follow:

Step 1: time-series regression

We compute the beta of the stocks with respect to the market factor for the period covered (time-series regression). We estimate the beta of each stock related to the S&P500 index. The beta is computed as the slope of the linear regression of the stock return on the market return (S&P500 index return). This time-series regression is run on a subperiod of the whole period from January 03, 2012, to December 31, 2018.

Step 2: cross-sectional regression

Over a second period from January 04, 2019, to December 31, 2021, we compute the dynamic regression of returns at each data point in time with respect to the betas computed in Step 1.

With this procedure, we obtain a risk premium that would represent the relationship between the stock returns at each data point in time with their respective beta for the sample analyzed.

Test the statistical significance of the results obtained from the regression

Results in the time-series regression using the stock approach are statistically significant. As shown in Table 1, the p-value is in the rejection area, which implies that the factor that the market factor can be considered as a driver of return.

Table 1. Time-series regression t-statistic result.
img_SimTrade_Fama_MacBeth_cross_sectional_regression_stat_result Source: computation by the author.

However, when analyzed in the cross-section regression, the results are not statistically significant anymore. As shown in Table 2, the p-value is not in the rejection area. We cannot reject the null hypothesis (H0: non significance of the market factor). Market factor alone cannot explain the premium investors are considering.
This means that the market factor fails to explain properly the behavior of asset returns, which undermines the validity of the CAPM framework. These results are in line with the Fama-MacBeth paper (1973).

Table 2. Cross-section regression t-statistic result.
img_SimTrade_Fama_MacBeth_cross_sectional_regression_stat_result Source: computation by the author.

You can find below the Excel spreadsheet that complements the explanations covered in this part of the article (implementation of the Fama and MacBeth (1973) method with individual stocks).

Fama and MacBeth (1973) implemented with portfolios of stocks

The procedure to derive the Fama-MacBeth regression using the portfolio approach can be achieved as follow:

Step 1: time-series regression

We first compute the beta of the stocks with respect to the market factor for the period covered (time-series regression). We estimate the beta of each stock related to the S&P500 index. The beta is computed as the slope of the linear regression of the stock return on the market return (S&P500 index return). This time-series regression is run on a subperiod of the whole period from January 03, 2012, to December 31, 2015. We build twenty portfolios based on stock betas ranked in ascending order. The betas of the portfolios are then estimated again on a subperiod from January 04, 2016, to December 31, 2018.

It is challenging to maintain beta stability over time. Fama-MacBeth aimed to remedy this shortcoming through its novel technique. However, some issues must be addressed. When betas are calculated using a monthly time series, the statistical noise in the time series is significantly reduced in comparison to shorter time frames (i.e., daily observation). When portfolio betas are constructed, the coefficient becomes considerably more stable than when individual betas are evaluated. This is due to the diversification impact that a portfolio can produce, which considerably reduces the amount of specific risk.

Step 2: cross-sectional regression

Over a second period from January 03, 2019, to December 31, 2021, we compute the dynamic regression of portfolio returns at each data point in time with respect to the betas computed in Step 1.

With this procedure, we obtain a risk premium that would represent the relationship between the portfolio returns at each data point in time with their respective beta for the sample analyzed.

Test the statistical significance of the results obtained from the regression

Results in the cross-section regression using the portfolio approach are not statistically significant. As captured in Table 3, the p-value is not in the rejection area, which implies that the factor is statistically insignificant and that the market factor cannot be considered as a driver of return.

Table 3. Cross-section regression with portfolio approach t-statistic result.
img_SimTrade_Fama_MacBeth_Portfolio_cross_sectional_regression_stat_result Source: computation by the author.

You can find below the Excel spreadsheet that complements the explanations covered in this part of the article (implementation of the Fama and MacBeth (1973) method with portfolios of stocks).

Econometric issues

Errors in data measurement

Because regression uses a sample instead of the entire population, a certain margin of error must be accounted for since the authors derive estimated betas for the sample.

Asset return heteroscedasticity

In econometrics, heteroscedasticity is an important concern since it results in unequal residual variance. This indicates that a time series exhibiting some heteroscedasticity has a non-constant variance, which renders forecasting ineffective because the time series will not revert to its long-run mean.

Asset return autocorrelation

Standard errors in Fama-MacBeth regressions are solely corrected for cross-sectional correlation. This method does not fix the standard errors for time-series autocorrelation. This is typically not a concern for stock trading, as daily and weekly holding periods have modest time-series autocorrelation, whereas autocorrelation is larger over long horizons. This suggests that Fama-MacBeth regression may not be applicable in many corporate finance contexts where project holding durations are typically lengthy.

Why should I be interested in this post?

Useful resources

Academic research

Brooks, C., 2019. Introductory Econometrics for Finance (4th ed.). Cambridge: Cambridge University Press. doi:10.1017/9781108524872

Fama, E. F., MacBeth, J. D., 1973. Risk, Return, and Equilibrium: Empirical Tests. Journal of Political Economy, 81(3), 607–636.

Roll R., 1977. A critique of the Asset Pricing Theory’s test, Part I: On Past and Potential Testability of the Theory. Journal of Financial Economics, 1, 129-176.

American Finance Association & Journal of Finance (2008) Masters of Finance: Eugene Fama (YouTube video)

About the author

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

Fama-MacBeth regression method: Analysis of the market factor

December 12, 2022 by Youssef LOURAOUI

In this article, Youssef LOURAOUI (Bayes Business School, MSc. Energy, Trade & Finance, 2021-2022) presents the Fama-MacBeth two-step regression method used to test asset pricing models. The seminal paper by Fama and MacBeth (1973) was based on an investigation of the market factor by evaluating portfolios of stocks with similar betas. In this article I will elaborate on the methodology and assess the statistical significance of the market factor as a fundamental driver of return.

This article is structured as follow: we introduce the Fama-MacBeth testing method used in asset pricing. Then, we present the mathematical foundation that underpins their approach. I then apply the Fama-MacBeth to recent US stock market data. Finally, I expose the limitations of their approach and conclude to discuss the generalization of the original study to other risk factors.

Introduction

The two-step regression method proposed by Fama-MacBeth was originally used in asset pricing to test the Capital Asset Pricing Model (CAPM). In this model, there is only one risk factor determining the variability of returns: the market factor.

The first step is to regress the return of every asset against the risk factor using a time-series approach. We obtain the return exposure to the factor called the “beta” or the “factor exposure” or the “factor loading”.

The second step is to regress the returns of all assets against the asset betas obtained in Step 1 during a given time period using a cross-section approach. We obtain the risk premium associated with the market factor. Then, Fama and MacBeth (1973) assess the expected premium over time for a unit exposure to the risk factor by averaging these coefficients once for each element.

Mathematical foundations

We describe below the mathematical foundations for the Fama-MacBeth two-step regression method.

Step 1: time-series analysis of returns

The model considers the following inputs:

The return of N assets denoted by R_i for asset i observed over the time period [0, T].
The risk factor denoted by F for the market factor impacting the asset returns.

For each asset i (for i varying from 1 to N) we estimate the following time-series linear regression model:

Fama MacBeth time-series regression

From this model, we obtain the following coefficients: α_i and β_i which are specific to asset i.

Figure 1 represents for a given asset (Apple stocks) the regression of its return with respect to the S&P500 index return (representing the market factor in the CAPM). The slope of the regression line corresponds to the beta of the regression equation.

Figure 1. Step 1: time-series regression for a given asset (Apple stock and the S&P500 index).
Source: computation by the author.

Step 2: cross-sectional analysis of returns

For each period t (from t equal 1 to T), we estimate the following cross-section linear regression model:

Fama MacBeth cross-section regression

Figure 2 plots for a given period the cross-sectional returns and betas for a given point in time.

Figure 2 represents for a given period the regression of the return of all individual assets with respect to their estimated individual market beta.

Figure 2. Step 2: cross-section regression for a given time-period.

Source: computation by the author.

We average the gamma obtained for each data point. This is the way the Fama-MacBeth method is used to test asset pricing models.

Empirical study of the Fama-MacBeth regression

The seminal paper by Fama and MacBeth (1973) was based on an analysis of the market factor by assessing constructed portfolios of similar betas ranked by increasing values. This approach helped to overcome the shortcoming regarding the stability of the beta and correct for conditional heteroscedasticity derived from the computation of the betas for individual stocks. They performed a second time the cross-sectional regression of monthly portfolio returns based on equity betas to account for the dynamic nature of stock returns, which help to compute a robust standard error and assess if there is any heteroscedasticity in the regression. The conclusion of the seminal paper suggests that the beta is “dead”, in the sense that it cannot explain returns on its own (Fama and MacBeth, 1973).

Empirical study: Stock approach

We downloaded a sample of end-of-month stock prices of large firms in the US economy over the period from March 31, 2016, to March 31, 2022. We computed monthly returns. To represent the market, we chose the S&P500 index.

We then applied the Fama-MacBeth two-step regression method to test the market factor (CAPM).

Figure 3 depicts the computation of average returns and the betas and stock in the analysis.

Figure 3. Computation of average returns and betas of the stocks.
Source: computation by the author.

Figure 4 represents the first step of the Fama-MacBeth regression. We regress the average returns for each stock with their respective betas.

Figure 4. Step 1 of the regression: Time-series analysis of returns
Source: computation by the author.

The initial regression is statistically evaluated. To describe the behavior of the regression, we employ a t-statistic. Since the p-value is in the rejection area (less than the significance limit of 5 percent), we can deduce that the market factor can at first explain the returns of an investor. However, as we are going deal in the later in the article, when we account for a second regression as formulated by Fama and MacBeth (1973), the market factor is not capable of explaining on its own the return of asset returns.

Figure 5 represents Step 2 of the Fama-MacBeth regression, where we perform for a given data point a regression of all individual stock returns with their respective estimated market beta.

Figure 5. Step 2: cross-sectional analysis of return.
Source: computation by the author.

Figure 6 represents the hypothesis testing for the cross-sectional regression. From the results obtained, we can clearly see that the p-value is not in the rejection area (at a 5% significance level), hence we cannot reject the null hypothesis. This means that the market factor fails to explain properly the behavior of asset returns, which undermines the validity of the CAPM framework. These results are in line with Fama-MacBeth (1973).

Figure 6. Hypothesis testing of the cross-sectional regression.
Source: computation by the author.

Excel file for the Fama-MacBeth two-step regression method

You can find below the Excel spreadsheet that complements the explanations covered in this article to implement the Fama-MacBeth two-step regression method.

Limitations of the Fama-McBeth approach

Selection of the market index

For the CAPM to be valid, we need to determine if the market portfolio is in the Markowitz efficient curve. According to Roll (1977), the market portfolio is not observable because it cannot capture all the asset classes (human capital, art, and real estate among others). He then believes that the returns cannot be captured effectively and hence makes the market portfolio, not a reliable factor in determining its efficiency.

Furthermore, the coefficients estimated in the time-series regressions are sensitive to the market index chosen for the study. These shortcomings must be taken into account when assessing CAPM studies.

Stability of the coefficients

The beta of individual assets are not stable over time. Fama and MacBeth attempted to address this shortcoming by implementing an innovative approach.

When betas are computed using a monthly time-series, the statistical noise of the time series is considerably reduced as opposed to shorter time frames (i.e., daily observation).

Using portfolio betas makes the coefficient much more stable than using individual betas. This is due to the diversification effect that a portfolio can achieve, reducing considerably the amount of specific risk.

Conclusion

Why should I be interested in this post?

Useful resources

Academic research

Brooks, C., 2019. Introductory Econometrics for Finance (4th ed.). Cambridge: Cambridge University Press. doi:10.1017/9781108524872

Fama, E. F., MacBeth, J. D., 1973. Risk, Return, and Equilibrium: Empirical Tests. Journal of Political Economy, 81(3), 607–636.

Roll R., 1977. A critique of the Asset Pricing Theory’s test, Part I: On Past and Potential Testability of the Theory. Journal of Financial Economics, 1, 129-176.

American Finance Association & Journal of Finance (2008) Masters of Finance: Eugene Fama (YouTube video)

Business Analysis

NEDL. 2022. Fama-MacBeth regression explained: calculating risk premia (Excel). [online] Available at: [Accessed 29 May 2022].

About the author

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

Forex exchange markets

December 2, 2022 by Nakul PANJABI

Forex exchange markets

In this article, Nakul PANJABI (ESSEC Business School, Grande Ecole Program – Master in Management, 2021-2024) explains how the foreign exchange markets work.

Forex Market

Forex trading can be simply defined as exchange of a unit of one currency for a certain unit of another currency. It is the act of buying one currency while simultaneously selling another.

Foreign exchange markets (or Forex) are markets where currencies of different countries are traded. Forex market is a decentralised market in which all trades take place online in an over the counter (OTC) format. By trading volume, the forex market is the largest financial market in the world with a daily turnover of 6.6 trillion dollars in 2019. At present, it is worth 2,409 quadrillion dollars. Major currencies traded are USD, EUR, GBP, JPY, and CHF.

Players

The main players in the market are Central Banks, Commercial banks, Brokers, Traders, Exporters and Importers, Immigrants, Investors and Tourists.

Central banks

Central banks are the most important players in the Forex Markets. They have the monopoly in the supply of currencies and therefore, tremendous influence on the prices. Central Banks’ policies tend to protect aggressive fluctuations in the Forex Markets against the domestic currency.

Commercial banks

The second most important players of the Forex market are the Commercial Banks. By quoting, on a daily basis, the foreign exchange rates for buying and selling they “Make the Market”. They also function as Clearing Houses for the Market.

Brokers

Another important group is that of Brokers. Brokers do not participate in the market but acts as a link between Sellers and Buyers for a commission.

Types of Transactions in Forex Markets

Some of the transactions possible in the Forex Markets are as follows:

Spot transaction

As spot transaction uses the spot rate and the goods (currencies) are exchanges over a two-day period.

Forward transaction

A forward transaction is a future transaction where the currencies are exchanged after 90 days of the deal a fixed exchange rate on a defined date. The exchange rate used is called the Forward rate.

Future transaction

Futures are standardized Forward contracts. They are traded on Exchanges and are settled daily. The parties enter a contract with the exchange rather than with each other.

Swap transaction

The Swap transactions involve a simultaneous Borrowing and Lending of two different currencies between two investors. One investor borrows the currency and lends another currency to the second investor. The obligation to repay the currencies is used as collateral, and the amount is repaid at forward rate.

Option transaction

The Forex Option gives an investor the right, but not the obligation to exchange currencies at an agreed rate and on a pre-defined date.

Peculiarities of Forex Markets

Trading of Forex is not much different from trading of any other asset such as stocks or bonds. However, it might not be as intuitive as trading of stocks or bonds because of its peculiarities. Some peculiarities of the Forex market are as follows:

Going long and short simultaneously

Since the goods traded in the market are currencies themselves, a trade in the Forex market can be considered both long and short position. Buying dollars for euros can be profitable in cases of both dollar appreciation and euro depreciation.

High liquidity and 24-hour market

As mentioned above, the Forex market has the largest daily trading volume. This large volume of trading implies the highly liquid feature of Forex Assets. Moreover, Forex market is open 24 hours 5 days a week for retail traders. This is due to the fact that Forex is exchanged electronically over the world and anyone with an internet connection can exchange currencies in any Forex market of the world. In fact for Central banks and related organisations can trade over the weekends as well. This can cause a change in the price of currencies when the market opens to retail traders again after a gap of 2 days. This risk is known as Gapping risk.

High leverage and high volatility

Extremely high leverage is a common feature of Forex trades. Using high leverage can result in multiple fold returns in favourable conditions. However, because of high trading volume, Forex is very volatile and can go in either upward or downward spiral in a very short time. Since every position in the Forex market is a short and long position, the exposure from one currency to another is very high.

Hedging

Hedging is one of the main reasons for a lot of companies and corporates to enter into a Forex Market. Forex hedging is a strategy to reduce or eliminate risk arising from negative movement in the Exchange rate of a particular currency. If a French wine seller is about to receive 1 million USD for his wine sales then he can enter into a Forex futures contract to receive 900,000 EUR for that 1 million USD. If, at the date of payment, the rate of 1 million USD is 800,000 EUR the French wine seller will still get 900,000 EUR because he hedged his forex risk. However, in doing so, he also gave up any gain on any positive movement in the EUR-USD exchange rate.

Useful resources

Academic resources

Solnik B. (1996) International Investments Addison-Wesley.

Business resources

DailyFX / IG The History of Forex

DailyFX / IG Benefits of forex trading

DailyFX / IG Foreign Exchange Market: Nature, Structure, Types of Transactions

About the author

The article was written in December 2022 by Nakul PANJABI (ESSEC Business School, Grande Ecole Program – Master in Management, 2021-2024).

Exchange-traded funds and Tracking Error

November 16, 2022 by Micha FISCHER

Exchange-traded funds and Tracking Error

In this article, Micha FISHER (University of Mannheim, MSc. Management, 2021-2023) explains the concept of Tracking Error in the context of exchange traded funds (ETF).

This article will offer a short introduction to the concept of exchange-traded funds, will then describe several reasons for the existence of tracking errors and finish with a concise example on how tracking error can be calculated.

Exchange-traded funds

An exchange-traded fund is conceptionally very close to classical mutual funds, with the key difference being, that ETFs are traded on a stock exchange during the trading day. Most ETFs are so-called index funds and thus they try to replicate an existing index like the S&P 500 or the CAC 40. This sort of passive investing is aimed at following or tracking the underlying index as closely as possible. However, actively managed ETFs with the aim of outperforming the market do exist as well and typically come with higher management fees. There are several types of ETFs covering equity index funds, commodities or currencies with classical equity index funds being the most prominent.

The total volume of global ETF portfolios has increased substantially over the last two decades. At the beginning of the century total asset volume was in the low triple digit billions measured in USD. According to research by the Wall Street Journal total assets in ETF investments surpassed nine trillion USD in 2021.

The continuing attractiveness of exchange-traded index funds can be explained with the very low management fees, the clarity of the product objective, and the high liquidity of the investment vehicle. However, although especially the market leaders like BlackRock, the Vanguard Group or State Street offer products that come extremely close to mirroring their underlying index, exchange-traded funds do not perfectly track the evolution of the underlying index. This phenomenon is known as tracking error and will be discussed in detail below.

Theoretical measure of the Tracking Error

Simply speaking, the tracking error of an ETF is the difference in the returns of the underlying index (I for index) and the returns of the ETF itself (E for ETF). For a specific period, it is computed by taking the standard deviation of the differences between the two time-series.

Formula for tracking error

Theoretically, it is possible to fully replicate an index in a portfolio and thus reach a tracking error of zero. However, there are several reasons why this is not achievable in practice.

Origins of the Tracking Error

The most important and obvious reason is that the Net Asset Value (NAV) of index funds is necessarily lower than the NAV of its underlying index. An index itself has no liabilities, as it is strictly speaking an instrument of measurement. On the other hand, even a passively managed index fund comes with expenses to pay for infrastructure, personnel, and marketing. These liabilities decrease the Net Asset Value of the fund. In general, a higher tracking error could indicate that the fund is not working efficiently compared to products of competitors with the same underlying index.

Another origin of tracking error can be found in specific sector ETFs and more niche markets with not enough liquidity. When the trading volume of a stock is very low, buying / selling the stock would increase / decrease the price (price impact). In this case an ETF could buy more liquid stocks with the aim to mirror the value development of the illiquid stock, which in turn could lead to a higher tracking error.

Another source of tracking error that occurs more severely in dividend-focused ETFs is the so-called cash drag. High dividend payments that are not instantly reinvested drag down the fund performance in contrast to the underlying index.

Of course, transaction fees of the marketplaces can reduce the fund performance as well. This is especially true if large rebalancing efforts are necessary due to a change of the index composition.

Lastly, there are also ways to reduce the effects described above. Funds can engage in security lending to earn additional money. In this case, the fund lends individual assets within the portfolio to other investors (mostly short sellers) for an agreed period in return for lending fees and possible interest. It should be noted, that while this might reduce tracking error, it also exposes the fund to additional counterparty risk.

Tracking Error: An Example

The sheet posted below shows a simple example of how the tracking error can be computed. To not include hundreds of individual shares, the example transformed the top ten positions within the Nasdaq-100 index into an artificial “Nasdaq-10” index. Although the data for the 23rd of September is accurate, the future data is of course randomly simulated.

By using the individual weights of the index components and their corresponding weights, the index returns for the next three months can be computed.

Figure 1: Three-months simulation of “Nasdaq-10” index.
Three-months simulation of Nasdaq-10 index
Source: computation by the author.

At this point our made-up ETF is introduced with an initial investment of 100 million USD. This ETF fully replicates the Nasdaq-10 index by holding shares in the same proportion as the index. In this example only the management and marketing fees are incorporated. Security lending, index changes and transaction fees and dividends are omitted. Also, all the portfolio shares are highly liquid and allow for full replication. The fund works with small expenses for personnel of only ten thousand USD per month. Additionally, once per quarter, a marketing campaign costs additionally fifty thousand USD.

Figure 2: Computation of ETF return and tracking error.
Computation of ETF-return and Tracking Error
Source: computation by the author.

Calculating the net asset value (NAV) gives us the monthly returns of the fund which in turn allows us to calculate the three-month standard deviation of the tracking difference. Additionally, the Total Expense Ratio can be calculated as the percentage of expenses per year divided by the total asset value of the fund.

This example gives us a Total Expense Ratio of nearly 0.3 percent per annum which is within the competitive area of real passive funds. Vanguard is able to replicate the FTSE All-World index with 0.2 percent. However, the calculated tracking error is obviously smaller than most real tracking errors with only 0.0002, as only management fees were considered. Exemplary, Vanguards FTSE All-World ETF had an historical tracking error of 0.042 in 2021, due to the reasons mentioned in the section above.

Excel file for computing the tracking error of an ETF

You can also download below the Excel file for the computation of the tracking error of an ETF.

Why should I be interested in this post?

ETFs in all forms are one of the major developments in the area of portfolio management over the last two decades. They are also a very interesting option for private investments.

Although they are conceptually very simple it is important to understand the finer metrics that vary between different service providers as even small differences can have a large impact over a longer investment period.

Useful resources

Academic articles

Roll R. (1992) A Mean/Variance Analysis of Tracking Error, The Journal of Portfolio Management, 18 (4) 13-22.

Business

ET Money What is Tracking Error in Index Funds and How it Impacts Investors?

About the author

The article was written in November 2022 by Micha FISHER (University of Mannheim, MSc. Management, 2021-2023).

Approaches to investment

November 14, 2022 by Henri VANDECASTEELE

Approaches to investment

In this article, Henri VANDECASTEELE (ESSEC Business School, Master in Strategy & Management of International Business (SMIB), 2021-2022) explains the two main approaches to investment: fundamental analysis and technical analysis.

Fundamental analysis

Fundamental analysis (FA) is a way of determining the fundamental value of a securities by looking at linked economic and financial elements. Fundamental analysts look at everything that might impact the value of a security, from macroeconomic issues like the state of the economy and industry circumstances to microeconomic elements like management performance. All stock analysis attempts to evaluate if a security’s value in the larger market is right. Fundamental research is often conducted from a macro to micro viewpoint in order to find assets that the market has not valued appropriately. To get at a fair market valuation for the stock, analysts often look at the overall status of the economy, then the strength of the specific industry, before focusing on individual business performance.

Fundamental analysis evaluates the value of a stock or any other form of investment using publicly available data. An investor, for example, might undertake fundamental research on a bond’s value by looking at economic variables like interest rates and the overall status of the economy, then reviewing information about the bond issuer, such as probable changes in its credit rating.

The aim is to arrive at a figure that can be compared to the present price of an asset to determine whether it is undervalued or overpriced.

Fundamental analysis is based on both qualitative and quantitative publicly available historical and current data. This includes company statements, historical stock market data, company press releases, financial year statements, investor presentations, information found on internet fora, media articles, and broker/analyst reports.

Technical analysis

Technical analysis (TA) is a trading discipline that analyzes statistical trends acquired from trading activity, such as price movement and volume, to evaluate investments and uncover trading opportunities.

Technical analysis, as opposed to fundamental analysis, focuses on the examination of price and volume. Fundamental analysis aims to estimate a security’s worth based on business performance such as sales and earnings. Technical analysis methods are used to examine how variations in price, volume, and implied volatility are affected by supply and demand for a security. Any security with past trading data can benefit from technical analysis. This includes stocks, futures, commodities, bonds, currencies and other securities. In fact, technical analysis is much more common in commodities and forex markets where traders focus on short-term price fluctuations.

Technical analysis is commonly used to generate short-term trading signals from various charting tools, but it also helps to improve the assessment of securities strengths or weaknesses compared to one of the broader markets or sectors increase. This information helps analysts improve their overall rating estimates.

Technical analysis is performed on quantitative data only that recent and historical, but publicly available. It leverages mainly market information, namely daily transaction volumes, stock price, spread, volatility, … and performs trend analyses.

Link with market efficiency

When linking both approaches to investment to the market efficiency theory, we can state that fundamental analysis assumes that financial markets are not efficient in the semi-strong sense, whereas technical analysis assumes that financial markets are not efficient in the weak sense. But the trading activity of both fundamental analysts and technical analysts make the markets more efficient.

Useful resources

SimTrade course Market information

About the author

The article was written in November 2022 by Henri VANDECASTEELE (ESSEC Business School, Master in Strategy & Management of International Business (SMIB), 2021-2022).

Understand the mechanism of inflation in a few minutes?

November 1, 2022 by Louis DETALLE

Understand the mechanism of inflation in a few minutes?

In this article, Louis DETALLE (ESSEC Business School, Grande Ecole Program – Master in Management, 2020-2023) explains everything you have to know about inflation.

What is inflation and how can it make us poorer?

In a liberal economy, the prices of goods and services consumed vary over time. In France, for example, when the price of wheat rises, the price of wheat flour rises and so the price of a loaf of bread may also rises as a consequence of the rise in the price of the raw materials used for its production… This small example is only designed to make the evolution of prices concrete for one good only. It helps us understand what happens when the increase in price happens not only for a loaf of bread, but for all the goods of an economy.

Inflation is when prices rise overall, not just the prices of a few goods and services. When this is the case, over time, each unit of money buys fewer and fewer products. In other words, inflation gradually erodes the value of money (purchasing power).

If we take the example of a loaf of bread which costs €1 in year X, while the price of the 20g of wheat flour contained in a loaf is 20 cents. In year X+1, if the 20g of wheat flour now costs 22 cents, i.e., a 10% increase over one year, the price of the loaf of bread will have to reflect this increase, otherwise the baker will be the only one to suffer the increase in the price of his raw material. The price of a loaf of bread will then be €1.02.

We can see that here, with one euro, i.e., the same amount of the same currency, from one year to the next, it is not possible for us to buy a loaf of bread because it costs €1.02 and not €1 anymore.

This is a very schematic way of understanding the mechanism of inflation and how it destroys the purchasing power of consumers in an economy.

How is the inflation computed and what does a x% inflation mean?

In France, Insee (Institut national de la statistique et des études économiques in French) is responsible for calculating inflation. It obtains it by comparing the price of a basket of goods and services each month. The content of this basket is updated once a year to reflect household consumption patterns as closely as possible. In detail, the statistics office uses the distribution of consumer expenditure by item as assessed in the national accounts, and then weights each product in proportion to its weight in household consumption expenditure.

What is important to understand is that Insee calculates the price of an overall household expenditure basket and evaluates the variation of its price over time.

When inflation is announced at X%, this means that the overall value spent in the year by a household will increase by X%.

However, if the price of goods increases but wages remain the same, then purchasing power deteriorates, and this is why low-income households are the most affected by the rise in the price of everyday goods. Indeed, low-income households can’t easily cope with a 10% increase in price of their daily products, whereas the middle & upper classes can better deal with such a situation.

What can we do to reduce inflation?

It is the regulators who control inflation through major macroeconomic levers. It is therefore central banks and governments that can act and they do so in various ways (as an example, we use the context of the War in Ukraine in 2022):

They raise interest rates: when inflation is too high, central banks raise interest rates to slow down the economy and bring inflation down. This is what the European Central Bank (ECB) has just done because of the economic consequences of the War in Ukraine. The economic sanctions have seen the price of energy commodities soar, which has pushed up inflation.

Blocking certain prices: This is what the French government is still doing on energy prices. Thus, in France, the increase in gas and electricity tariffs will be limited to 15% for households, compared to a freeze on gas prices and an increase limited to 4% for electricity in 2022. Without this “tariff shield”, the French would have had to endure an increase of 120%.

Distribute one-off aid: These measures are often considered too costly and can involve an increase in salaries.

Bear in mind that “miracle” methods do not exist, otherwise inflation would never be a subject discussed in the media. However, these three methods are the most used by governments and central banks but only time will tell us whether they succeed.

Figure 1. Inflation in France.

Source: Insee / Les Echos.

Useful resources

Inflation rates across the World

Insee’s forecast of the French inflation rate

About the author

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

What are LBOs and how do they work?

November 1, 2022 by Louis DETALLE

What are LBOs and how do they work?

In this article, Louis DETALLE (ESSEC Business School, Grande Ecole Program – Master in Management, 2020-2023) explains why LBOs are so trendy and what they consist in.

What does a LBO consist in & how is it built?

LBO stands for a Leverage Buy-Out. It means a company acquisition which is funded with a lot of debt. Often, when an LBO is performed, 70% of the funds used for the acquisition come from debt, the 30% left being equity.

Figure 1. Schematic plan of the organization of an LBO.

Source: the author.

To perform an LBO, the company wishing to buy the company called Target in this example will have to create a Holding company specially for this purpose. The holding will then take on some debt with specific lenders (banks, debt funds) under the form of loan or bonds. After that, the holding will have both some initial equity from the company wishing to acquire Target and some debt to buy Target.

What happens after the target has been bought?

Well, after the target has been bought, since the target company has an operating activity which motivated the acquiring company to buy it, this means that the target company had great financial performance. And it better to be the case! Otherwise, the large amount of debt taken for the operation will never be reimbursed to the lenders.

The principle is that target’s financial cash flows will be redistributed to the holding in the form of dividends, and the holding will use these dividends to pay back the debt to the lenders until all debt is reimbursed.

What makes a company a good LBO target?

A good LBO target should respect a few conditions related to the target company: important operating cashflows, a mature market, A company whose development cycle is over.

Important operating cashflows

First & foremost, without great cashflows, the holding will never be able to reimburse the debt taken with the dividend if they are insufficient. For that matter, the company targeted for the LBO should have both regular & important cashflows.

A mature market

When looking at the bigger picture, the company willing to acquire a target with a LBO must make sure that the market in which the potential target evolves is stabilized. Because LBO means major financial risk due to the amount of debt involved, a company cannot also add operational risk.

A company whose development cycle is over

Once again, the target company will ensure the reimbursement of a high debt. This is why all capital expenditures (CAPEX) and major investments such as machines, fleets of vehicles should have been already done.

Useful resources

Vernimmen’s book chapters on LBOs

Youtube video on a LBO Case Study

About the author

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

Time Series Forecasting: Applications and Artificial Neural Networks

October 21, 2022 by Micha FISCHER

Time Series Forecasting: Applications and Artificial Neural Networks

In this article, Micha FISHER (University of Mannheim, MSc. Management, 2021-2023) discusses on the applications of time series forecasting and the use of artificial neural networks for this purpose.

This article will offer a short introduction to the different applications of time-series forecasting and forecasting in general, will then describe the theoretical aspects of simple artificial neural networks and finish with a practical example on how to implement a forecast based on these networks.

Overview

The American economist and diplomat John Kenneth Galbraith once said: “The function of economic forecasting is to make astrology look respectable”. Certainly, the failure of mainstream economics to predict several financial crises is testimony to this quote.

However, on a smaller scale, forecast can be very useful in different applications and this article describes several use cases for the forecasting of time series data and a special method to perform such analyses.

Different Applications of Time Series Forecasting

Different methods of forecasting are used in various settings. Central banks and economic research institutes use complex forecasting methods with a vast amount of input factors to forecast GDP growth and other macroeconomic figures. Technical analysts forecast the evolution of asset prices based on historical patterns to make trading gains. Businesses forecast the demand for their products by including seasonal trends (e.g., utility providers) and economic developments.

This article will deal with the latter two applications of forecasting that is focused on the analysis of historical patterns and seasonality. Using different input factors to come up with a prediction, like for example a multivariate regression analysis does, can be a successful way of making prediction. However, it also inherently includes the problem of determining those input factors as well in the first place.

The practical methods described in this article circumvent this problem by exclusively using historical time series data (e.g., past sales per month, historical electricity demand per hour of the day, etc.). This makes the use of those methods easy and both methods can be used to predict helpful input parameters of DCF models for example.

Artificial neural networks

Artificial Intelligence (AI) is a frequently used buzzword in the advertising of products and services. However, the concept of artificial intelligence is going back to the 1940s, when mathematicians McCulloch and Pitts first presented a mathematical model that was based on the neural activity of the human brain.

Before delving into the practical aspects of an exemplary simple artificial neural network, it is important to understand the terminology. These networks are one – although not the only one – of the key aspects of “Machine Learning”. Machine Learning itself is in turn a subtopic of Artificial Intelligence, which itself employs different tools besides Machine Learning.

Figure 1. Neural network.

Source: internet.

To give a simple example of an artificial neural network we will focus on a so-called feedforward neural network. Those networks deliver and transform information from the left side to the right side of the schematic picture below without using any loops. This process is called Forward Propagation. Historic time series data is simply put into the first layer of neurons. The actual transformation of the data is done by the individual neurons of the network. Some neurons simply put different weights on the input parameter. Neurons of the hidden layers then use several non-linear functions to manipulate the data given to them by the initial layer. Eventually the manipulated data is consolidated in the output layer.

This sounds all very random and indeed it is. At the beginning, a neural network is totally unaware of its actual best solution and the first computations are done via random weights and functions. But after a first result is compiled, the algorithm compares the result with the actual true value. Of course, this is not possible for values that lye in the future. Therefore, the algorithm divides the historic time series into a section used for training (data that is put into the network) and into a section for testing (data that can be compared to the transformed training data). The deviation between compiled value and true value is then minimized via the process of so-called backpropagation. Weights and functions are changed iteratively until an optimal solution is reached and the network it sufficiently trained. This optimal solution then servers to compute the “real” future values.

This description is a very theoretical presentation of such an artificial neural network and the question arises, how to handle such complex algorithms. Therefore, the last part of this article focuses on the implementation of such a forecasting tool. One very useful tool for statistical forecasting via artificial neural networks is the programming language R and the well-known development environment RStudio. RStudio enables the user to directly download user-created packages, to import historical data from Excel sheets and to export graphical presentations of forecasts.

A very easy first approach is the nnetar function of R. This function can be simply used to analyze existing time series data and it will automatically define an artificial neural network (number of layers, neurons etc.) and train it. Eventually it also allows to use the trained model to forecast future data points.

The chart below is a result of this function used on simulated sales data between 2015 and 2021 to forecast the sales of 2022. In this case the nnetar function used one layer of hidden neurons and correctly recognized a 12-month seasonality in the data.

Figure 2. Simulated sales data.

Source: internet.

Why should I be interested in this post?

Artificial neural networks are a powerful tool to forecast time-series data. By using development environments like RStudio, even users without a sophisticated background in data science can make apply those networks to forecast data they might need for other purposes like DCF models, logistical planning, or internal financial modelling.

Useful resources

RStudio Official Website

Rob Hyndman and George Athanasopoulos Forecasting: Principles and Practice

About the author

The article was written in October 2022 by Micha FISHER (University of Mannheim, MSc. Management, 2021-2023).

Simple interest rate and compound interest rate

October 16, 2022 by Sébastien PIAT

Simple interest rate and compound interest rate

In this article, Sébastien PIAT (ESSEC Business School, Grande Ecole Program – Master in Management, 2021-2024) explains the difference between simple interest rate and compound interest rate.

Introduction

When dealing with interest rates, it can be useful to be able to switch from a yearly rate to a period rate that is used to compute interests on a period for an investment or a loan. But you should be aware that the computation is different when working with simple interests and compounded interests.

Below is the method to switch back and forth between a period rate and a yearly rate.

With simple interests

If you think of an investment that generates yearly incomes at a rate of 6%, you might want to know what your monthly return is.

As we deal with simple interests, the monthly rate of this investment will be 0.5% (=6/12).

With simple interests, the interests on a given period are computed with the initial capital:

Interests computed a simple rate

Assuming that the interests are computed over p periods during the year, the capital of the investment at the end of the year is equal to

Interests computed a simple rate

The equivalent yearly rate of return R_y gives the same capital value at the end of the year

Interests computed a simple rate

By equating the two formulas for the capital at the end of the year, we obtain a relation between the period rate R_p and the equivalent yearly rate R_y:

Formula to switch from a period rate to the equivalent yearly rate with simple interests

Formula to switch from a yearly rate to the corresponding period rate with simple interests

With compound interests

Things get a little trickier when dealing with compound interests as interests get reinvested period after period.

Compounded interests can be considered by the following equation:

Interests computed a compound rate

Where R_p is the period rate of the investment and C_n is your capital at the end of the n_th period.

Assuming that the interests are computed over p periods during the year, the capital of the investment at the end of the year is equal to

Interests computed a compound rate

The equivalent yearly rate of return R_y gives the same capital value at the end of the year

Interests computed a compound rate

By equating the two formulas for the capital at the end of the year, we obtain a relation between the period rate R_p and the equivalent yearly rate R_y:

Formula to switch from a period rate to the equivalent yearly rate with compound interests

Formula to switch from a yearly rate to the corresponding period rate with compound interests

Excel file to compute interests of an investment

You can download below the Excel file for the computation of interests with simple and compound interests and the equivalent yearly interest rate.

You can download below the Excel file to switch from a period interest rate to a yearly interest rate and vice versa.

Why should I be interested in this post?

This post should help you switch between a period rate and the equivalent yearly rate of an investment.

This is particularly useful when we deal with cash flows that do not appear with a yearly frequency but with a monthly or quarterly frequency. With non-yearly cash flows, it is necessary to consider a period rate to compute the present value (PV), net present value (NPV) and internal rate of return (IRR).

Useful resources

longin.fr website Cours Gestion financière (in French).

About the author

The article was written in October 2022 by Sébastien PIAT (ESSEC Business School, Grande Ecole Program – Master in Management, 2021-2024) .

Enjeux de la pratique de la pleine conscience et de l’intelligence émotionnelle dans la fonction de contrôle de gestion

October 11, 2022 by Jessica BAOUNON

Enjeux de la pratique de la pleine conscience et de l’intelligence émotionnelle dans la fonction de contrôle de gestion

Dans cet article, Jessica BAOUNON (ESSEC Business School, Executive Master in Direction Financière et Contrôle de Gestion, 2020-2022) explique les enjeux de la pratique de la pleine conscience et de l’intelligence émotionnelle dans la fonction contrôle de gestion. Le monde de l’entreprise s’est considérablement transformé avec la crise du COVID-19. L’appel à l’intelligence émotionnelle n’a jamais été aussi important pour faire face aux situations les plus complexes.

La fonction contrôle de gestion est en pleine évolution. Ses missions ne portent plus uniquement sur la production et la communication d’indicateurs financiers. Son rôle consiste désormais à accompagner dirigeants et managers dans l’amélioration de la performance financière, c’est-à-dire à les conseiller sur les décisions d’orientations stratégiques.

La crise Covid-19 a projeté le contrôle de gestion davantage vers un rôle de « coach. En effet, en étant proche de ceux qui ont dû garantir la continuité des activités, le contrôle de gestion a dû se pencher sur l’empathie dans sa relation établie avec dirigeants et managers. On attend de lui une attitude d’écoute, de disponibilité, une capacité à se placer dans le contexte de son interlocuteur pour agir avec efficacité et désamorcer des situations de crise.

En d’autres termes, acquérir des compétences relationnelles et se doter d’un capital émotionnel sont aujourd’hui des qualités recherchées. L’action d’un contrôleur de gestion s’inscrit de plus en plus dans un état d’esprit collaboratif. Il remplit une fonction de business partner.

Or comment imaginer qu’un contrôleur de gestion puisse construire une relation de partenariat pérenne s’il n’est lui-même pas pleinement conscient de l’environnement dans lequel il évolue ? Sa prise de conscience de soi et des autres doit faciliter ses interactions sociales.

A ce titre, s’exercer à une pratique régulière de méditation de pleine conscience peut s’avérer efficace pour travailler son intelligence émotionnelle. En effet, l’exercice de la pleine conscience implique avant tout de ressentir et comprendre les émotions en portant une qualité d’attention sur une expérience vécue. C’est une attitude qui propose d’ouvrir un espace d’observation sans filtre, sans attente, de ses sensations, pensées, émotions d’une action, d’un évènement dans l’acceptation et sans jugement.

Ce processus d’observation permet ainsi de mieux aller vers l’autre en apportant une réponse adaptée et clairvoyante dans des dialogues de gestion. Elle permet notamment de reprendre possession de soi dans des situations de stress ou de gestion de conflit.

Origines et impact de la pratique de la pleine conscience dans la fonction contrôle de gestion

Jon Kabat Zin, professeur de médecine à l’Université du Massachussetts et docteur en biologie, est le père-fondateur de la méditation de pleine conscience. Intitulé Mindfullness-Based Stress Reduction (MBSR), ce programme laïque inspiré du bouddhisme, offre une initiation à la méditation sur une période de huit semaines.

Cette pratique, à l’origine millénaire, s’est progressivement répandue avec succès dans les écoles scientifiques, philosophiques et psychologiques. Elle émerge depuis quelques années dans les entreprises telle que chez EDF, Google ou L’Oréal au travers de formations certifiées.

Google, précurseur, propose à ses collaborateurs depuis 2007 un programme de méditation nommé « Search Inside Yourself ». Chade-Meng Tan, ingénieur chez Google, a réuni une équipe d’experts en technique de pleine conscience et intelligence émotionnelle pour construire cette formation. L’objectif est de développer des compétences d’intelligence émotionnelle pour créer une cohésion sociale favorable à l’épanouissement individuelle et collectif chez Google. Ces cours ont été dispensés auprès de plus de 10 000 personnes et dans plus de 50 pays.

Cette pratique se démocratise et est perçue de moins en moins comme une bizarrerie. Face à un contexte de crises successives, burn out, démotivation des collaborateurs, rééquilibrer les esprits pour évoluer dans un environnement sain devient un enjeu de performance cruciale. Plus que jamais, et en témoigne la récente crise du Covid-19, la responsabilité sociale d’une entreprise est de créer les conditions qui permettront une cohésion sociale durable.

En outre, face à l’ampleur d’imprévisibles changements, la mission du contrôle de gestion consistant à assurer la stabilité des processus de gestion doit s’accompagner d’une réflexion constante sur l’évolution des outils et systèmes d’information. Si les solutions d’automatisation des processus de gestion gagnent du terrain pour répondre à une volonté de rapidité d’exécution, elle ne doit pas pour autant conduire à un mode de pilotage automatique des taches d’un contrôleur de gestion.

Cette approche machinale de la fonction contrôle de gestion doit être signe d’alerte. En effet, le danger de cette posture est de se laisser gouverner, de ne plus observer activement les choses sous un regard nouveau et d’en perdre le sens. Dans un monde où l’humain rivalise de plus en plus avec les machines, développer un état d’esprit créatif et stimuler sa conscience d’esprit est un enjeu essentiel. La pleine conscience, en tant qu’outil, agit comme un accélérateur de créativité. Elle oblige à se libérer d’un mode de fonctionnement mécanique des processus en étant attentif à ce que l’on fait et à ce qui nous entoure pour cheminer vers des nouvelles idées. Avec la montée en puissance des technologies, cette qualité encore absente du langage courant, se retrouvera plus encore demain, dans les exigences de compétences requises en contrôle de gestion.

Innover avec un style de management durable

Dans cette même dynamique de changement, on assiste à une « reconnaissance accrue du rôle des émotions comme action et effet dans les organisations » (1). Celle-ci questionne les modèles de management classiques jugé trop bureaucratique et militaire « dans leur tentative de contrôler, supprimer toute émotion qui interférer la rationalité d’actions souhaitées » (1). L’essoufflement du modèle tayloriste est en train de laisser progressivement place à de nouveaux paradigmes. Cette transformation s’explique par une logique de revalorisation du capital humain subordonnée à celle de l’efficience productive. En outre, la montée en puissance de la Responsabilité Sociale des Entreprises (RSE) a donné lieu à d’importants renversements.

« La recherche de profit n’est pas en soi problématique, ce qui l’est c’est de ne souligner que le profit au détriment de la complexité de réalités humaines » (Bibard Laurent). En témoigne l’affaire Bhopal ou Orange qui ont eu pour effet de révéler une profonde dévalorisation des conditions de travail. Un renversement de rôle qui renvoie également à la question du sens, d’une humanité en prise de conscience sur ce qui ne fonctionne plus, sur la nécessité de l’entreprise à s’ancrer dans un monde durable et servir l’intérêt général.

Pour arriver à cet objectif de durabilité, reconstruire un modèle de management responsable en s’appuyant sur les acquis de la psychologie cognitive et sociale constitue une première solution. Les émotions ont été rejeté pendant très longtemps des visions managériales des entreprises. Or les récentes découvertes en psychologie démontrent que développer des compétences en intelligence émotionnelle permet de développer de réelles qualités relationnelles, de prendre de meilleures décisions et de se montrer bien plus créatif.

Dans un monde incertain rythmé par des crises financières, environnementales et sociales, chaque individu doit être en mesure de pouvoir se défaire de biais cognitifs, en se libérant de ses croyances limitantes pour contribuer à une vision d’un monde juste et responsable. La pratique de la pleine conscience et de l’intelligence émotionnelle contribue à mobiliser une connaissance de soi. Elle permet aux contrôleurs de gestion ainsi qu’à l’ensemble des collaborateurs de questionner la pertinence de leurs actions et décisions sous l’angle de leurs émotions. Cette pratique invite ainsi à nous rappeler ce que nous sommes : des êtres humains.

En quoi ça m’intéresse ?

Dans un monde où l’humain rivalise de plus en plus avec les machines, développer un état d’esprit créatif et stimuler sa conscience d’esprit est essentiel. Cet article présente les bénéfices de la pratique de la pleine conscience et de l’intelligence émotionnelle dans la fonction contrôle de gestion afin d’y apporter d’un éclairage sur ces nouvelles compétences recherchées.

Articles sur le blog SimTrade

▶ POUZOL Chloé Mon expérience de contrôleuse de gestion chez Edgar Suites

Ressources utiles

Teneau, Gilles, Empathie et compassion en entreprise, 2014, ISTE Editions.

Tan, Cheng-Made, Search Inside Yourself, 2015, Harper Collins Libri

Kotsou, Ilios – « Intelligence émotionnelle & management », 2016, De Boeck

Cappelletti, Laurent. Le management de la relation client des professions : un nouveau sujet d’investigation pour le contrôle de gestion, 2010, Revue Management et Avenir.

A propos de l’auteure

Cet article a été écrit en octobre 2022 par Jessica BAOUNON (ESSEC Business School, Executive Master in Direction Financière et Contrôle de Gestion 2020-2022).

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

February 4, 2024October 9, 2022 by Shengyu ZHENG

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

In this article, Shengyu ZHENG (ESSEC Business School, Grande Ecole Program – Master in Management, 2020-2023) presents the extreme value theory (EVT) and two commonly used modelling approaches: block-maxima (BM) and peak-over-threshold (PoT).

Introduction

There are generally two approaches to identify and model the extrema of a random process: the block-maxima approach where the extrema follow a generalized extreme value distribution (BM-GEV), and the peak-over-threshold approach that fits the extrema in a generalized Pareto distribution (POT-GPD):

BM-GEV: The BM approach divides the observation period into nonoverlapping, continuous and equal intervals and collects the maximum entries of each interval. (Gumbel, 1958) Maxima from these blocks (intervals) can be fitted into a generalized extreme value (GEV) distribution.
POT-GPD: The POT approach selects the observations that exceed a certain high threshold. A generalized Pareto distribution (GPD) is usually used to approximate the observations selected with the POT approach. (Pickands III, 1975)

Figure 1. Illustration of the Block-Maxima approach
BM-GEV
Source: computation by the author.

Figure 2. Illustration of the Peak-Over-Threshold approach

POT-GPD
Source: computation by the author.

BM-GEV

Block-Maxima

Let’s take a step back and have a look again at the Central Limit Theorem (CLT):

Illustration of the POT approach

The CLT describes that the distribution of sample means approximates a normal distribution as the sample size gets larger. Similarly, the extreme value theory (EVT) studies the behavior of the extrema of samples.

The block maximum is defined as such:

Illustration of the POT approach

Generalized extreme value distribution (GEV)

Illustration of the POT approach

The GEV distributions have three subtypes corresponding to different tail feathers [von Misès (1936); Hosking et al. (1985)]:

Illustration of the POT approach

POT-GPD

The block maxima approach is under reproach for its inefficiency and wastefulness of data usage, and it has been largely superseded in practice by the peak-over-threshold (POT) approach. The POT approach makes use of all data entries above a designated high threshold u. The threshold exceedances could be fitted into a generalized Pareto distribution (GPD):

Illustration of the POT approach

Illustration of Block Maxima and Peak-Over-Threshold approaches of the Extreme Value Theory with R

We now present an illustration of the two approaches of the extreme value theory (EVT), the block maxima with the generalized extreme value distribution (BM-GEV) approach and the peak-over-threshold with the generalized Pareto distribution (POT-GPD) approach, realized with R with the daily return data of the S&P 500 index from January 01, 1970, to August 31, 2022.

Packages and Libraries

packages and libraries

Data loading, processing and preliminary inspection

Loading S&P 500 daily closing prices from January 01, 1970, to August 31, 2022 and transforming the daily prices to daily logarithm returns (multiplied by 100). Month and year information are also extracted from later use.

data loading

Checking the preliminary statistics of the daily logarithm series.

descriptive stats data

We can get the following basic statistics for the (logarithmic) daily returns of the S&P 500 index over the period from January 01, 1970, to August 31, 2022.

Table 1. Basic statistics of the daily return of the S&P 500 index.

Source: computation by the author.

In terms of daily return, we can observe that the distribution is negatively skewed, which mean the negative tail is longer. The kurtosis is far higher than that of a normal distribution, which means that extreme outcomes are more frequent compared with a normal distribution. the minimum daily return is even more than twice of the maximum daily return, which could be interpreted as more prominent downside risk.

Block maxima – Generalized extreme value distribution (BM-GEV)

We define each month as a block and get the maxima from each block to study the behavior of the block maxima. We can also have a look at the descriptive statistics for the monthly downside extrema variable.

block maxima

With the commands, we obtain the following basic statistics for the monthly minima variable:

Table 2. Basic statistics of the monthly minimal daily return of the S&P 500 index.

Source: computation by the author.

With the block extrema in hand, we can use the fevd() function from the extReme package to fit a GEV distribution. We can therefore get the following parameter estimations, with standard errors presented within brackets.

GEV

Table 3 gives the parameters estimation results of the generalized extreme value (GEV) for the monthly minimal daily returns of the S&P 500 index. The three parameters of the GEV distribution are the shape parameter, the location parameter and the scale parameter. For the period from January 01, 1970, to August 31, 2022, the estimation is based on 632 observations of monthly minimal daily returns.

Table 3. Parameters estimation results of GEV for the monthly minimal daily return of the S&P 500 index.

Source: computation by the author.

With the “plot” command, we are able to obtain the following diagrams.

The top two respectively compare empirical quantiles with model quantiles, and quantiles from model simulation with empirical quantiles. A good fit will yield a straight one-to-one line of points and in this case, the empirical quantiles fall in the 95% confidence bands.
The bottom left diagram is a density plot of empirical data and that of the fitted GEV distribution.
The bottom right diagram is a return period plot with 95% pointwise normal approximation confidence intervals. The return level plot consists of plotting the theoretical quantiles as a function of the return period with a logarithmic scale for the x-axis. For example, the 50-year return level is the level expected to be exceeded once every 50 years.

gev plots

Peak over threshold – Generalized Pareto distribution (POT-GPD)

With respect to the POT approach, the threshold selection is central, and it involves a delicate trade-off between variance and bias where too high a threshold would reduce the number of exceedances and too low a threshold would incur a bias for poor GPD fitting (Rieder, 2014). The selection process could be elaborated in a separate post and here we use the optimal threshold of 0.010 (0.010*100 in this case since we multiply the logarithm return by 100) for stock index downside extreme movement proposed by Beirlant et al. (2004).

POT

With the following commands, we get to fit the threshold exceedances to a generalized Pareto distribution, and we obtain the following parameter estimation results.

Table 4 gives the parameters estimation results of GPD for the daily return of the S&P 500 index with a threshold of -1%. In addition to the threshold, the two parameters of the GPD distribution are the shape parameter and the scale parameter. For the period from January 01, 1970, to August 31, 2022, the estimation is based on 1,669 observations of daily returns exceedances (12.66% of the total number of daily returns).

Table 4. Parameters estimation results of the generalized Pareto distribution (GPD) for the daily return negative exceedances of the S&P 500 index.

Source: computation by the author.

Download R file to understand the BM-GEV and POT-GPD approaches

You can find below an R file (file with txt format) to understand the BM-GEV and POT-GPD approaches.

Why should I be interested in this post

Financial crises arise alongside disruptive events such as pandemics, wars, or major market failures. The 2007-2008 financial crisis has been a recent and pertinent opportunity for market participants and academia to reflect on the causal factors to the crisis. The hindsight could be conducive to strengthening the market resilience faced with such events in the future and avoiding dire consequences that were previously witnessed. The Gaussian copula, a statistical tool used to manage the risk of the collateralized debt obligations (CDOs) that triggered the flare-up of the crisis, has been under serious reproach for its essential flaw to overlook the occurrence and the magnitude of extreme events. To effectively understand and cope with the extreme events, the extreme value theory (EVT), born in the 19th century, has regained its popularity and importance, especially amid the financial turmoil. Capital requirements for financial institutions, such as the Basel guidelines for banks and the Solvency II Directive for insurers, have their theoretical base in the EVT. It is therefore indispensable to be equipped with knowledge in the EVT for a better understanding of the multifold forms of risk that we are faced with.

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).

About the author

The article was written in October 2022 by Shengyu ZHENG (ESSEC Business School, Grande Ecole Program – Master in Management, 2020-2023).

Activist Funds

October 6, 2022 by Akshit GUPTA

Activist Funds

This article written by Akshit GUPTA (ESSEC Business School, Grande Ecole Program – Master in Management, 2019-2022) introduces activist funds which is a type of fund based on shareholder activism to influence a company’s board and top management decisions.

Introduction

Activist funds use an investment strategy where they buy shares in a publicly listed company with the aim to influence a company’s board and top management decisions. A large shareholding provides the activist fund with high power to influence the decision making of these firms at the management level. The aim of an active fund is to push for decisions or changes that would increase the share price and thus, the value of its portfolio.

Activist funds target companies which are poorly managed or have untapped value which if explored, can lead to significant increase in the stock price. They typically buy the equity shares of these companies which provides them with ownership and the rights to vote during the shareholders’ General Meetings to influence the board and top management decisions. Activist funds propose and help implement changes that favourably impact the stock prices and helps them to generate absolute market returns that are generally higher than the market benchmarks. These changes include changes in business strategy, operational decisions, capital structure, corporate governance and the day-to-day practices of the management.

Activist investors are normally seen operating either a private equity firm or a hedge fund and specialising in specific industries or businesses. High-net worth individuals and family offices are majorly involved in activist investing as they have access to huge investments and expertise.

Benefits of activist funds

Like other types of hedge funds and private equity firms, activist funds aim at providing their clients (investors) with investments managed in an efficient manner to optimize expected returns and risk. They try to generate alpha on the clients’ investment by actively participating in company’s board and top management decisions. So, activist funds are often acknowledged as the alternative funds in the asset management industry.

Concerns associated with activist funds

Although the investments in activist funds are handled by professionals and can generate absolute performance, they also come with some concerns for the investors. Some of the commonly associated concerns with activist fund investments are:

Narrow-sighted approach – Activist funds invest in companies with the aim to maximize the shareholder’s wealth. The approach has serious concerns as it doesn’t fully take into account the effects of the decision on the company’s workers and society.
Investment horizon – The investment horizon of activist funds is not very well defined as the changes propose d by the funds can either take shape immediately or may run over a couple of years before the effects are seen.

Example of activist fund

GameStop – Shareholder activism

The infamous GameStop stock rally that happened in 2021 drew people’s attention from around the world and it became the talk of the town. During the same time, the company also went through a change in its management. The event sheds light on the importance and impact of shareholder activism in today’s world.

Ryan Cohen is a famous activist investor who declared 10% stock ownership in GameStop through his investment firm, RC Ventures, in September 2020. This named him amongst the company’s biggest individual investor. He saw a huge opportunity for video games in the e-commerce market and wanted GameStop to evolve from a gaming company to a technology company and also change from traditional brick-and-mortar stores to online channels. To implement the changes, he made efforts to privately engage with the firm to review their strategic vision and change the company’s business model via . But the efforts yielded little success, following which he sent an open letter to the company’s Board of Directors (A copy of the letter can be seen below)

Ryan Cohen Letter to the Board of GameStop in November 2020

The letter was taken seriously by the company’s management and Ryan Cohen was appointed on the Board of Directors of the company in January 2021. Later, he was promoted as the Chairman of the Board to reshape the company’s strategic vision to become a technology-driven business rather than merely a gaming company.

Useful resources

Academic resources

Pedersen, L. H., 2015. Efficiently Inefficient: How Smart Money Invests and Market Prices Are Determined. Princeton University Press, Chapter 7, Discretionary Equity Investing.

Business resources

Business Insider Article on GameStop

Frick W. (2016) The Case for Activist Investors Harvard Business Review, 108–109.

Desjardine M., R. Durand (2021) Activist Hedge Funds: Good for Some, Bad for Others? Knowledge@HEC.

CNBC Article

Forbes Article

About the author

Article written in August 2022 by Akshit GUPTA (ESSEC Business School, Grande Ecole Program – Master in Management, 2019-2022).

Currency overlay

September 4, 2022 by Jayati WALIA

In this article, Jayati WALIA (ESSEC Business School, Grande Ecole Program – Master in Management, 2019-2022) explains currency overlay which is a mechanism to effectively manage currency risk in asset portfolios.

Overview

Currency risk, also known as exchange-rate risk, forex exchange or FX risk, is a kind of market risk that is caused by the fluctuations in currency exchange rates.

Both individual and institutional investors are diversifying their portfolios through assets in international financial markets, but by doing so they also introduce currency risk in their portfolios.

Consider an investor in the US who decides to invest in the French equity market (say in the CAC 40 index). The investor is now exposed to currency risk due to the movements in EURUSD exchange rate. You can download the Excel file below which illustrates the impact of the EURUSD exchange rate on the overall performance of the investor’s portfolio.

This exercise demonstrates the importance of currency risk in managing an equity portfolio with assets dominated in foreign currencies. We can observe that over a one-month time-period (July 19 – August 19, 2022), the annual volatility of the American investor’s portfolio with FX risk included is 12.96%. On the other hand, if he hedges the FX risk (using a currency overlay strategy), the annual volatility of his portfolio is reduced to 10.45%. Thus, the net gain (or loss) on the portfolio is significantly reliant on the EURUSD exchange-rate.

Figure 1 below represents the hedged an unhedged returns on the CAC 40 index. The difference between the two returns illustrates the currency risk for an unhedged position of an investor in the US on a foreign equity market (the French equity market represented by the CAC 40 index.

Figure 1 Hedged and unhedged returns for a position on the CAC 40 index.
Hedged an unhedged return Source : computation by the author.

Currency overlay is a strategy that is implemented to manage currency exposures by hedging against foreign exchange risk. Currency overlay is typically used by institutional investors like big corporates, asset managers, pension funds, mutual funds, etc. For such investors exchange-rate risk is indeed a concern. Note that institutional investors often outsource the implementation of currency overlays to specialist financial firms (called “overlay managers”) with strong expertise in foreign exchange risk. The asset allocation and the foreign exchange risk management are then separated and done by two different persons (and entities), e.g., the asset manager and the overlay manager. This organization explains the origin of the world “overlay” as the foreign exchange risk management is a distinct layer in the management of the fund.

Overlay managers make use of derivatives like currency forwards, currency swaps, futures and options. The main idea is to offset the currency exposure embedded in the portfolio assets and providing hedged returns from the international securities. The implementation can include hedging all or a proportion of the currency exposure. Currency overlay strategies can be passive or active depending on portfolio-specific objectives, risk-appetite of investors and currency movement viewpoint.

Types of currency overlay strategies

Active currency overlay

Active currency overlay focuses on not just hedging the currency exposure, but also profiting additionally from exchange-rate movements. Investors keeps a part of their portfolio unhedged and take up speculative positions based on their viewpoint regarding the currency trends.

Passive currency overlay

A passive overlay focuses only on hedging the currency exposure to mitigate exchange-rate risk. Passive overlay is implemented through derivative contracts like currency forwards which are used to lock-in a specific exchange-rate for a fixed time-period, thus providing stability to asset values and protection against exchange-rate fluctuations.

Passive overlay is a simple strategy to implement and generally uses standardized contracts, however, it also eliminates the scope of generating any additional profits for the portfolio through exchange-rate fluctuations.

Implementing currency overlays

Base currency and benchmark

Base currency is generally the currency in which the portfolio is dominated or the investor’s domestic currency. A meaningful benchmark selection is also essential to analyze the performance and assess risk of the overlay. World market indices such as those published by MSCI, FTSE, S&P, etc. can be appropriate choices.

Hedge ratio

Establishing a strategic hedge ratio is a fundamental step in implementing a currency overlay strategy. It is the ratio of targeted exposure to be currency hedged by the overlay against the overall portfolio position. Different hedge ratios can have different impact on the portfolio returns and determining the optimal hedge ratio can depend on various factors such as investor risk-appetite and objectives, portfolio assets, benchmark selection, time horizon for hedging etc.

Cost of overlay

The focus of overlays is to hedge the fluctuations in foreign exchange rates by generating cashflows to offset the foreign exchange rate movements through derivatives like currency forwards, currency swaps, futures and options. The use of these derivatives products generates additional costs that impacts the overall performance of the portfolio strategy. These costs must be compared to the benefits of portfolio volatility reduction coming from the overlay implementation.

This cost is also an essential factor in the selection of the hedge ratio.

Note that passive overlays are generally cheaper than active overlays in terms of implementation costs.

Useful resources

Academic articles

Black, F. (1989) Optimising Currency Risk and Reward in International Equity Portfolios. Financial Analysts Journal, 45, 16-22.

Business material

Pensions and Lifetime Savings Association Currency overlay: why and how? video.

About the author

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

Reverse Convertibles

August 23, 2022 by Shengyu ZHENG

Reverse Convertibles

In this article, Shengyu ZHENG (ESSEC Business School, Grande Ecole Program – Master in Management, 2020-2023) explains reverse convertibles, which are a structured product with a fixed-rate coupon and downside risk.

Introduction

The financial market has been ever evolving, witnessing the birth and flourish of novel financial instruments to cater to the diverse needs of market participants. On top of plain vanilla derivative products, there are exotic ones (e.g., barrier options, the simplest and most traded exotic derivative product). Even more complex, there are structured products, which are essentially the combination of vanilla or exotic equity instruments and fixed income instruments.

Amongst the structured products, reverse convertible products are one of the most popular choices for investors. Reverse convertible products are non-principal protected products linked to the performance of an underlying asset, usually an individual stock or an index, or a basket of them. Clients can enter into a position of a reverse convertible with the over-the-counter (OTC) trading desks in major investment banks.

In exchange for an above-market coupon payment, the holder of the product gives up the potential upside exposure to the underlying asset. The exposure to the downside risks still remains. Reserve convertibles are therefore appreciated by the investors who are anticipating a stagnation or a slightly upward market trend.

Construction of a reverse convertible

This product could be decomposed in two parts:

On the one hand, the buyer of the structure receives coupons on the principal invested and this could be considered as a “coupon bond”;
On the other hand, the investor is still exposed to the downside risks of the underlying asset and foregoes the upside gains, and this could be achieved by a short position of a put option (either a vanilla put option or a down-and-in barrier put option).

Positions of the parties of the transaction

A reverse convertible involves two parties in the transaction: a market maker (investment bank) and an investor (client). Table 1 below describes the positions of the two parties at different time of the life cycle of the product.

Table 1. Positions of the parties of a reverse convertible transaction

t	Market Maker (Investment Bank)	Investor (Client)
Beginning	Enters into a long position of a put (either a vanilla put or a down-and-in barrier put) Receives the nominal amount for the “coupon” part Invests in the amount (nominal amount plus the premium of the put) in risk-free instruments	Enters into a short position of a put (either a vanilla put or a down-and-in barrier put) Pays the nominal amount for the “coupon” part
Interim	Pays pre-specified interim coupons in respective interim coupon payment dates (if any) Receives interest payment from risk-free investments	Receives the pre-specified interim coupons in respective interim coupon payment dates (if any)
End	Receives the payoff (if any) of the put option component Pays the pre-specified final coupon in the final coupon payment date	Pays the payoff (if any) of the put option component Receives the pre-specified final coupon in the final coupon payment date

Based on the type of the put option incorporated in the product (either plain vanilla put option or down-and-in barrier put option), reserve convertibles could be categorized as plain or barrier reverse convertibles. Given the difference in terms of the composition of the structured product, the payoff and pricing mechanisms diverge as well.

Here is an example of a plain reverse convertible with following product characteristics and market information.

Product characteristics:

Investment amount: USD 1,000,000.00
Underlying asset: S&P 500 index (Bloomberg Code: SPX Index)
Investment period: from August 12, 2022 to November 12, 2022 (3 months)
Coupon rate: 2.50% (quarterly)
Strike level : 100.00% of the initial level

Market data:

Current risk-free rate: 2.00% (annualized)
Volatility of the S&P 500 index: 13.00% (annualized)

Payoff of a plain reverse convertible

As is presented above, a reverse convertible is essentially a combination of a short position of a put option and a long position of a coupon bond. In case of the plain reverse convertible product with the aforementioned characteristics, we have the blow payoff structure:

in case of a rise of the S&P 500 index during the investment period, the return for the reverse convertible remains at 2.50% (the coupon rate);
in case of a drop of the S&P 500 index during the investment period, the return would be equal to 2.50% minus the percentage drop of the underlying asset and it could be negative if the percentage drop is greater than 2.5%.

Figure 1. The payoff of a plain reverse convertible on the S&P 500 index

Source: Computation by author.

Pricing of a plain reverse convertible

Since a reverse convertible is essentially a structured product composed of a put option and a coupon bond, the pricing of this product could also be decomposed into these two parts. In terms of the pricing a vanilla option, the Black–Scholes–Merton model could do the trick (see Black-Scholes-Merton option pricing model) and in terms of pricing a barrier option, two methods, analytical formula method and Monte-Carlo simulation method, could be of help (see Pricing barrier options with analytical formulas; Pricing barrier options with simulations and sensitivity analysis with Greeks).

With the given parameters, we can calculate, as follows, the margin for the bank with respect to this product. The calculated margin could be considered as the theoretical price of this product.

Table 2. Margin for the bank for the plain reverse convertible

Source: Computation by author.

Download the Excel file to analyze reverse convertibles

You can find below an Excel file to analyze reverse convertibles.

Why should I be interested in this post

As one of the most traded structured products, reverse convertibles have been an important instrument used to secure return amid mildly negative market prospect. It is, therefore, helpful to understand the product elements, such as the construction and the payoff of the product and the targeted clients. This could act as a steppingstone to financial product engineering and risk management.

Resources

Academic references

Broadie, M., Glasserman P., Kou S. (1997) A Continuity Correction for Discrete Barrier Option. Mathematical Finance, 7:325-349.

De Bellefroid, M. (2017) Chapter 13 (Barrier) Reverse Convertibles. The Derivatives Academy. Accessible at https://bookdown.org/maxime_debellefroid/MyBook/barrier-reverse-convertibles.html

Haug, E. (1997) The Complete Guide to Option Pricing. London/New York: McGraw-Hill.

Hull, J. (2006) Options, Futures, and Other Derivatives. Upper Saddle River, N.J: Pearson/Prentice Hall.

Merton, R. (1973). Theory of Rational Option Pricing. The Bell Journal of Economics and Management Science, 4:141-183.

Paixao, T. (2012) A Guide to Structured Products – Reverse Convertible on S&P500

Reiner, E. S. (1991) Breaking down the barriers. Risk Magazine, 4(8), 28–35.

Rich, D.R. (1994) The Mathematical Foundations of Barrier Option-Pricing Theory. Advances in Futures and Options Research: A Research Annual, 7, 267-311.

Business references

Six Structured Products. (2022). Reverse Convertibles et barrier reverse Convertibles

About the author

The article was written in August 2022 by Shengyu ZHENG (ESSEC Business School, Grande Ecole Program – Master in Management, 2020-2023).

Macro Funds

August 22, 2022 by Akshit GUPTA

Macro Funds

This article written by Akshit GUPTA (ESSEC Business School, Grande Ecole Program – Master in Management, 2019-2022) explains marco funds which is a type of hedge fund based on the analysis of macroeconomic or political events.

Introduction

Macro funds, also known as global macro funds, are actively managed alternative investment vehicles (hedge funds) whose strategy profits from the broad market movements caused by macroeconomic (economic, fiscal and monetary) or geopolitical events. These funds typically invest in asset classes including equity, fixed income, currencies, and commodities. They invest in both the spot and derivatives markets. They use a mix of long and short positions in these asset classes to implement their market views to achieve superior returns (higher than a given benchmark).

Some key elements impacting the decisions taken by macro funds include:

Economic factors – Macro funds constantly monitor the economic data across different countries including interest rates, inflation rates, GDP growth, unemployment rates and industrial/retail growth rates to make investment decisions.
Mispricing – Macro funds try to arbitrage markets based on perceived mispricing.
Political situations – The political situations in different countries also play a major role in the investment decisions made by macro funds as unstable political situations can lead to low investor confidence and thus cause a decline in the financial markets.

Benefits of a macro funds

Like other types of hedge funds, macro funds aim at providing their clients (investors) with investments managed in an efficient manner to optimize expected returns and risk. Such funds are especially expected to diversify the clients’ portfolios. So, macro funds are often acknowledged as the alternative funds in the industry.

Other characteristics of macro funds

Other characteristics of macro funds (clients, fee structure, investment constraints) are similar to other types of hedge funds (see the posts Introduction to Hedge Funds and Hedge Funds).

Examples of macro funds strategies

A commonly used asset class in macro fund strategy includes currencies. Their exchange rates are affected by several factors including monetary and fiscal policies, economic factors like GDP growth and inflation and geopolitical situation. Black Wednesday is an example of an infamous event, where we can understand the different factors and use of macro fund strategies.

Black Wednesday

During the 1970s, an European Exchange Rate Mechanism (ERM) was set up to reduce exchange rate variability and stabilize the monetary policies across the continent. Also, a stage was being set to introduce a unified common currency named Euro. The United Kingdom joined ERM in 1990 due to political instability in the country raising fears of higher currency fluctuations.

The pound sterling shadowed the German mark but owing to challenges faced by Britain at that point in time, including lower interest rates, higher inflation rates and an unstable economy, the currency traders weren’t satisfied with the decision.

Seeing the economic situation, George Soros, one of the most famous investors, used the macro fund strategy during 1992 when he took a short position in the pound sterling for $10 billion and made a $1 billion profit from his position.

▶ Akshit GUPTA Asset management firms

▶ Akshit GUPTA Hedge Funds

▶ Youssef LOURAOUI Introduction to Hedge Funds

▶ Akshit GUPTA Portrait of George Soros: A famous investor

Useful resources

Academic resources

Pedersen, L. H., 2015. Efficiently Inefficient: How Smart Money Invests and Market Prices Are Determined. Princeton University Press, Chapter 11, Global macro Investing.

Business resources

JP. Morgan Asset Management

DeChesare Brian “Global Macro Hedge Funds: Living in an FX Traders’ Paradise?”

About the author

Article written in August 2022 by Akshit GUPTA (ESSEC Business School, Grande Ecole Program – Master in Management, 2019-2022).

Initial and maintenance margins in stocks

August 15, 2022 by Akshit GUPTA

Initial and maintenance margins in stocks

This article written by Akshit GUPTA (ESSEC Business School, Grande Ecole Program – Master in Management, 2019-2022) explains the mechanisms of initial and maintenance margin used in stocks.

Introduction

In financial markets, margin requirements are present in leveraged positions in stock trading. They refer to a percentage of assets that an investor must put aside with his or her own cash or assets (collateral) as a means of protection against the risk exposure to its potential default for the other counterpart.

Margin requirements serve as a guarantee that the investor providing the margins will fulfill its trade obligations. Many exchanges across the world provide leverage facilities to investors for trading in different assets. For example, an investor can use leverage facilities for trading in equities, bonds, exchange rates, commodities, etc. It usually takes the form of derivatives contracts like futures and options. Whenever an investor buys or sells stocks using leverage, it is called buying or selling on margin.

Margin requirements can be categorized as initial and maintenance margin requirements.

Initial margin

Initial margin (or IM) refers to the initial deposit required when an investor opens a position in an underlying asset and amounts to a percentage of the nominal contract value. The amount for the initial margin requirement is calculated in accordance with approved margin models that are based on the market’s regulatory rules. The determination of the initial margin requirement is essentially based on the volatility of the asset being covered. The more volatile the asset, the higher the initial margin requirement.

You can download below the file to learn about the different initial margin requirements at Euronext Clearing used in stock trading (PDF document).

Maintenance margin

When an investor holds an underlying asset on margin, she is required to maintain a minimum margin amount of that asset position in her portfolio to keep her position open and this is known as the maintenance margin. Maintenance margin requirements aim to protect against excess losses and ensure the broker has enough capital to cover any losses the investor may incur. In case the investor is unable to fulfill the maintenance margin requirements, she receives a margin call initiated from the broker to deposit a further amount in order to keep her position open. If she fails to provide adequate maintenance margins, the broker has the power to close her position.

Mechanism of initial and maintenance margins

Now, we will see how initial and maintenance margins work in the financial markets with the concept of short selling used in equity trading. Since the short sell involves borrowing stock, the investor is required by its broker to post an initial margin at the time the trade is initiated. For instance, this initial margin is set to 50% of the value of the short sale. This money is essentially the collateral on the short sale to protect the lender of the stocks in the future against the default of the borrower (the investor).

Followed by this, a maintenance margin is required at any point of time after the trade is initiated. The maintenance is taken as 30% of the total value of the position. The short seller has to ensure that any time the position falls below this maintenance margin requirement, he will get a margin call and has to increase funds into the margin account.

Example

Here is an example of a typical case of short selling and its margin mechanism:

Margin call on stocks

You can download below the Excel file for the computation of the Intial and Maintenance Margins for the stocks.

Useful resources

Euronext Clearing

Maintenance margin

Initial Margin

Financial Industry Regulatory Authority (FINRA)

▶Akshit GUPTA Initial and Maintenance margin in futures contracts

▶ Youssef LOURAOUI Introduction to Hedge Funds

▶ Akshit GUPTA Analysis of the Big Short movie

▶ Akshit GUPTA Analysis of the Margin call movie

▶ Akshit GUPTA Analysis of the Trading places movie

About the author

Article written in August 2022 by Akshit GUPTA (ESSEC Business School, Grande Ecole Program – Master in Management, 2019-2022).

Introduction

Types of quantitative equity strategies

Fundamental quantitative investing

Statistical arbitrage

High Frequency Trading (HFT)

Conclusion

Why should I be interested in this post?

Related posts on the SimTrade blog

Useful resources

Academic research

About the author

Introduction

Mathematical foundations

Optimal portfolio application: the case of two assets

Optimal portfolio application: the general case

Why should I be interested in this post?

Related posts on the SimTrade blog

Useful resources

Academic research

About the author

Introduction

Equity strategies

Discretionary long-short

Dedicated short bias

Quantitative

Example of a long-short equity strategy

Performance of the long-short equity strategy

Why should I be interested in this post?

Related posts on the SimTrade blog

Useful resources

Academic research

Business Analysis

About the author

Fama-MacBeth two-step regression method: the case of K risk factors

Introduction

Mathematical foundations

Step 1: time-series analysis of returns

Step 2: cross-sectional analysis of returns

Application: the Fama-French 3-Factor model

Empirical study of the Fama-MacBeth regression

Empirical study: Stock approach for a K-factor model

Time-series regression

Cross-sectional regression

Excel file

Why should I be interested in this post?

Related posts on the SimTrade blog

Useful resources

Academic research

About the author

Fama-MacBeth regression method: the stock approach vs the portfolio approach

Introduction

Fama and MacBeth (1973) implemented with individual stocks

Step 1: time-series regression

Step 2: cross-sectional regression

Test the statistical significance of the results obtained from the regression

Fama and MacBeth (1973) implemented with portfolios of stocks

Step 1: time-series regression

Step 2: cross-sectional regression

Test the statistical significance of the results obtained from the regression

Econometric issues

Errors in data measurement

Asset return heteroscedasticity

Asset return autocorrelation

Why should I be interested in this post?

Related posts on the SimTrade blog

Useful resources

Academic research

About the author

Introduction

Mathematical foundations

Step 1: time-series analysis of returns

Step 2: cross-sectional analysis of returns

Empirical study of the Fama-MacBeth regression

Empirical study: Stock approach

Excel file for the Fama-MacBeth two-step regression method

Limitations of the Fama-McBeth approach

Selection of the market index

Stability of the coefficients

Conclusion

Why should I be interested in this post?