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

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.

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

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).

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?

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: 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.