Extreme returns and tail modelling of the S&P 500 index for the US equity market

October 20, 2023 by Shengyu ZHENG

Extreme returns and tail modelling of the S&P 500 index for the US equity market

In this article, Shengyu ZHENG (ESSEC Business School, Grande Ecole Program – Master in Management, 2020-2024) describes the statistical behavior of extreme returns of the S&P 500 index for the US equity market and explains how extreme value theory can be used to model the tails of its distribution.

The S&P 500 index for the US equity market

The S&P 500, or the Standard & Poor’s 500, is a renowned stock market index encompassing 500 of the largest publicly traded companies in the United States. These companies are selected based on factors like market capitalization and sector representation, making the index a diversified and reliable reflection of the U.S. stock market. It is a market capitalization-weighted index, where companies with larger market capitalization represent a greater influence on their performance. The S&P 500 is widely used as a benchmark to assess the health and trends of the U.S. economy and as a performance reference for individual stocks and investment products, including exchange-traded funds (ETF) and index funds. Its historical significance, economic indicator status, and global impact contribute to its status as a critical barometer of market conditions and overall economic health.

Characterized by its diversification and broad sector representation, the S&P 500 remains an essential tool for investors, policymakers, and economists to analyze market dynamics. This index’s performance, affected by economic data, geopolitical events, corporate earnings, and market sentiment, can provide valuable insights into the state of the U.S. stock market and the broader economy. Its rebalancing ensures that it remains current and representative of the ever-evolving landscape of American corporations. Overall, the S&P 500 plays a central role in shaping investment decisions and assessing the performance of the U.S. economy.

In this article, we focus on the S&P 500 index of the timeframe from April 1st, 2015, to April 1st, 2023. Here we have a line chart depicting the evolution of the index level of this period. We can observe the overall increase with remarkable drops during the covid crisis (2020) and the Russian invasion in Ukraine (2022).

Figure 1 below gives the evolution of the S&P 500 index from April 1, 2015 to April 1, 2023 on a daily basis.

Figure 1. Evolution of the S&P 500 index.

Source: computation by the author (data: Yahoo! Finance website).

Figure 2 below gives the evolution of the daily logarithmic returns of S&P 500 index from April 1, 2015 to April 1, 2023 on a daily basis. We observe concentration of volatility reflecting large price fluctuations in both directions (up and down movements). This alternation of periods of low and high volatility is well modeled by ARCH models.

Figure 2. Evolution of the S&P 500 index logarithmic returns.

Source: computation by the author (data: Yahoo! Finance website).

Summary statistics for the S&P 500 index

Table 1 below presents the summary statistics estimated for the S&P 500 index:

Table 1. Summary statistics for the S&P 500 index.
summary statistics of the S&P 500 index returns
Source: computation by the author (data: Yahoo! Finance website).

The mean, the standard deviation / variance, the skewness, and the kurtosis refer to the first, second, third and fourth moments of statistical distribution of returns respectively. We can conclude that during this timeframe, the S&P 500 index takes on a slight upward trend, with relatively important daily deviation, negative skewness and excess of kurtosis.

Tables 2 and 3 below present the top 10 negative daily returns and top 10 positive daily returns for the S&P 500 index over the period from April 1, 2015 to April 1, 2023.

Table 2. Top 10 negative daily returns for the S&P 500 index.
Top 10 negative returns of the S&P 500 index
Source: computation by the author (data: Yahoo! Finance website).

Table 3. Top 10 positive daily returns for the S&P 500 index.
Top 10 positive returns of the S&P 500 index
Source: computation by the author (data: Yahoo! Finance website).

Modelling of the tails

Here the tail modelling is conducted based on the Peak-over-Threshold (POT) approach which corresponds to a Generalized Pareto Distribution (GPD). Let’s recall the theoretical background of this approach.

The POT approach takes into account all data entries above a designated high threshold u. The threshold exceedances could be fitted into a generalized Pareto distribution:

Illustration of the POT approach

An important issue for the POT-GPD approach is the threshold selection. An optimal threshold level can be derived by calibrating the tradeoff between bias and inefficiency. There exist several approaches to address this problematic, including a Monte Carlo simulation method inspired by the work of Jansen and de Vries (1991). In this article, to fit the GPD, we use the 2.5% quantile for the modelling of the negative tail and the 97.5% quantile for that of the positive tail.

Based on the POT-GPD approach with a fixed threshold selection, we arrive at the following modelling results for the GPD for negative extreme returns (Table 4) and positive extreme returns (Table 5) for the S&P 500 index:

Table 4. Estimate of the parameters of the GPD for negative daily returns for the S&P 500 index.

Source: computation by the author (data: Yahoo! Finance website).

Table 5. Estimate of the parameters of the GPD for positive daily returns for the S&P 500 index.

Source: computation by the author (data: Yahoo! Finance website).

Figure 3. GPD for the left tail of the S&P 500 index returns.

Source: computation by the author (data: Yahoo! Finance website).

Figure 4. GPD for the right tail of the S&P 500 index returns.

Source: computation by the author (data: Yahoo! Finance website).

Applications in risk management

Extreme Value Theory (EVT) as a statistical approach is used to analyze the tails of a distribution, focusing on extreme events or rare occurrences. EVT can be applied to various risk management techniques, including Value at Risk (VaR), Expected Shortfall (ES), and stress testing, to provide a more comprehensive understanding of extreme risks in financial markets.

Why should I be interested in this post?

Extreme Value Theory is a useful tool to model the tails of the evolution of a financial instrument. In the ever-evolving landscape of financial markets, being able to grasp the concept of EVT presents a unique edge to students who aspire to become an investment or risk manager. It not only provides a deeper insight into the dynamics of equity markets but also equips them with a practical skill set essential for risk analysis. By exploring how EVT refines risk measures like Value at Risk (VaR) and Expected Shortfall (ES) and its role in stress testing, students gain a valuable perspective on how financial institutions navigate during extreme events. In a world where financial crises and market volatility are recurrent, this post opens the door to a powerful analytical framework that contributes to informed decisions and financial stability.

Download R file to model extreme behavior of the index

You can find below an R file (file with txt format) to study extreme returns and model the distribution tails for the S&P 500 index.

Useful resources

Academic resources

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

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 resources

Extreme Events in Finance

Chan S. Statistical tools for extreme value analysis

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

About the author

The article was written in October 2023 by Shengyu ZHENG (ESSEC Business School, Grande Ecole Program – Master in Management, 2020-2024).

Les distributions statistiques

October 16, 2023 by Shengyu ZHENG

Distributions statistiques : variable discrète vs variable continue

Dans cet article, Shengyu ZHENG (ESSEC Business School, Grande Ecole – Master in Management, 2020-2024) explique les distributions statistiques pour des variables aléatoires discrètes et continues.

Variables aléatoires discrète et continue

Une variable aléatoire est une variable dont la valeur est déterminée d’après la réalisation d’un événement aléatoire. Plus précisément, la variable (X) est une fonction mesurable depuis un ensemble de résultats (Ω) à un espace mesurable (E).

X : Ω → E

On distingue principalement deux types de variables aléatoires : discrètes et continues.

Une variable aléatoire discrète prend des valeurs dans un ensemble dénombrable comme l’ensemble des entiers naturels. Par exemple, le nombre de points marqués lors d’un match de basket est une variable aléatoire discrète, car elle ne peut prendre que des valeurs entières telles que 0, 1, 2, 3, etc. Les probabilités associées à chaque valeur possible de la variable aléatoire discrète sont appelées probabilités de masse.

En revanche, une variable aléatoire continue prend des valeurs dans un ensemble non dénombrable comme l’ensemble des nombres réels. Par exemple, la taille ou le poids d’une personne sont des variables aléatoires continues, car elles peuvent prendre n’importe quelle valeur réelle positive. Les probabilités associées à une variable aléatoire continue sont déterminées par une fonction de densité de probabilité. Cette fonction permet de mesurer la probabilité que la variable aléatoire se situe dans un intervalle donné de valeurs.

Méthodes pour décrire des distributions statistiques

Afin de mieux comprendre une variable aléatoire, il y a plusieurs moyens pour décrire la distribution de la variable.

Calcul des statistiques

Une statistique est le résultat d’une suite d’opérations appliquées à un ensemble d’observations appelé échantillon et une mesure numérique qui résume une caractéristique de cet ensemble. Par exemple, la moyenne est un exemple de statistiques.
Les statistiques peuvent être divisées en deux types principaux : les statistiques descriptives et les statistiques inférentielles.

Les statistiques descriptives sont utilisées pour résumer et décrire les caractéristiques de base d’un ensemble de données. Elles comprennent des mesures telles que les moments d’une distribution (la moyenne, la variance, le skewness, le kurtosis, …). Une explication plus détaillée est disponible dans l’article Moments de la distribution.

Les statistiques inférentielles, quant à elles, sont utilisées pour faire des inférences sur une population à partir d’un échantillon de données. Elles incluent des tests d’hypothèses, des intervalles de confiance, des analyses de régression, des modèles prédictifs, etc.

Histogramme

Un histogramme est un type de graphique qui permet de représenter la distribution des données d’un échantillon. Il est constitué d’une série de rectangles verticaux, où chaque rectangle représente une plage de valeurs de la variable étudiée (appelée classe), et dont la hauteur correspond à la fréquence des observations de cette classe.

L’histogramme est un outil très utilisé pour visualiser la distribution des données et pour identifier les tendances et les formes dans les données pour les variables discrètes ainsi que continues discrétisées.

Fonction de masse et fonction de densité

Une fonction de masse de probabilité est une fonction mathématique qui permet de décrire la distribution de probabilité d’une variable aléatoire discrète.

La fonction de masse de probabilité associe à chaque valeur possible de la variable aléatoire discrète une probabilité. Par exemple, si X est une variable aléatoire discrète prenant les valeurs 1, 2, 3 et 4 avec des probabilités respectives de 0,2, 0,3, 0,4 et 0,1, alors la fonction de masse de probabilité de X (loi multinomiale) est donnée par :
P(X=1) = 0,2
P(X=2) = 0,3
P(X=3) = 0,4
P(X=4) = 0,1

Il est important de noter que la somme des probabilités pour toutes les valeurs possibles de la variable aléatoire doit être égale à 1, c’est-à-dire, pour toute variable aléatoire discrète X :
∑ P(X=x) = 1

Figure 1. Fonction de masse d’une loi multinomiale (pour une variable discrète).

Source : calcul par l’auteur

Par contre, une fonction de densité représente la distribution de probabilité d’une variable aléatoire continue. La fonction de densité permet de calculer la probabilité que la variable aléatoire prenne une valeur dans un intervalle donné.
Graphiquement, l’aire sous la courbe de la fonction de densité entre deux valeurs a et b correspond à la probabilité que la variable aléatoire prenne une valeur dans l’intervalle [a, b].

Il est important de noter que la fonction de densité est une fonction continue, positive et intégrable sur tout son domaine. L’intégrale de la fonction de densité sur l’ensemble des valeurs possibles de la variable aléatoire est égale à 1.

Figure 2. Fonction de densité d’une loi normale (pour une variable continue).

Source : calcul par l’auteur

Fonction de répartition

La fonction de répartition (ou fonction de distribution cumulative) est une fonction mathématique qui décrit la probabilité qu’une variable aléatoire prenne une valeur inférieure ou égale à une certaine valeur donnée. Elle est définie pour toutes les variables aléatoires, qu’elles soient continues ou discrètes.
Pour une variable aléatoire discrète, la fonction de répartition F(x) est définie comme la somme des probabilités des valeurs inférieures ou égales à x :

F(x) = P(X ≤ x) = Σ P(X = xi) pour xi ≤ x

Pour une variable aléatoire continue, la fonction de répartition F(x) est définie comme l’intégrale de la densité de probabilité f(x) de -∞ à x :
F(x)=P(X≤x)= ∫_-∞^xf(t)dt

Exemples

Dans cette partie, nous allons prendre deux exemples d’analyse de distribution statistique, l’un d’une variable aléatoire discrète et l’autre d’une variable continue.

Variable discrète : résultat du lancer d’un dé à six faces

Le jeu de lancer de dé à six faces consiste à lancer un dé pour obtenir un résultat aléatoire entre 1 et 6, correspondant aux six faces du dé. Les résultats ne prennent que les valeurs entières (1, 2, 3, 4, 5 et 6) et ils ont tous une probabilité identique de 1/6.

Dans cet exemple, le code R permet de simuler N lancers de dé et de visualiser la distribution des N résultats à l’aide d’un histogramme. En utilisant ce code, il est possible de simuler des parties de lancer de dé et d’analyser les résultats pour mieux comprendre la distribution des probabilités.

Si cette expérience aléatoire est répétée 1 000 fois, nous arrivons à un résultat dont l’histogramme est comme :

Figure 3. Histogramme des résultats de lancers d’un dé à six faces.

Source : calcul par l’auteur

Nous constatons que les résultats sont distribués d’une manière équilibrée et ont la tendance de converger vers la probabilité théorique 1/6.

Variable continue : rendments de l’indice CAC40

Le rendement d’un indice d’actions comme le CAC 40 pour le marché français est une variable aléatoire continue parce qu’elle peut prendre toutes les valeurs réelles.

Nous utilisons un historique de l’indice boursier journalier pour des cours de clôture de l’indice CAC 40 du 1^er avril 2021 au 1^er avril 2023 pour calculer des rendements journalières (rendements logarithmiques).

En finance, la distribution des rendements journalières de l’indice CAC 40 est souvent modélisée par une loi normale, même si la loi normale ne modélise pas forcément bien la distribution observée, surtout les queues de distributions observées. Dans le graphique ci-dessous, nous voyons que la distribution normale ne décrit pas bien la distribution réelle.

Figure 4. Fonction de densité des rendements journalières de l’indice CAC 40 (variable continue).

Source : calcul par l’auteur

Pour des observations issues pour une variable continue, il est toujours possible de regrouper les observations dans des intervalles et de représenter dans un histogramme.

La table 1 ci-dessous donne les statistiques descriptives pour les rendements journalières de l’indice CAC 40.

Table 1. Statistiques descriptives pour les rendements journalières de l’indice CAC 40.

Statistiques descriptives	Valeur
Moyenne	0.035
Médiane	0.116
Écart-type	1.200
Skewness	-0.137
Kurtosis	6.557

Les résultats du calcul des statistiques descriptives correspondent bien à ce que nous pouvons remarquer du graphique. La distribution des rendements a une moyenne légèrement positive. La queue de la distribution empirique est plus épaisse que celle de la distribution normale vu les survenances des rendements (positives ou négatives) extrêmes.

Fichier R pour cet article

A propos de l’auteur

Cet article a été écrit en octobre 2023 par Shengyu ZHENG (ESSEC Business School, Grande Ecole Program – Master in Management, 2020-2024).

My experience as Actuarial Apprentice at La Mutuelle Générale

October 9, 2023 by Shengyu ZHENG

My experience as Actuarial Apprentice at La Mutuelle Générale

In this article, Shengyu ZHENG (ESSEC Business School, Grande Ecole Program – Master in Management, 2020-2024) shares his professional experience as Actuarial Apprentice at La Mutuelle Générale .

About the company

La Mutuelle Générale is a major French mutual insurance company that has established itself as a trusted provider of health and social protection solutions. With a history dating back to its foundation in 1945 as the mutual health insurance provider for La Poste et France Télécom, La Mutuelle Générale has grown to become a key player in the mutual health insurance sector in France.

Unlike private insurance companies, mutual insurance companies are based on the concept of solidarity and not for lucrative purposes. As a mutual insurance company, La Mutuelle Générale has no shareholders but only member clients who also contribute to the decision making of the company.

Specializing in health insurance and complementary health coverage, La Mutuelle Générale offers a comprehensive range of insurance products and services designed to meet the diverse needs of both individual and collective clients. On top of the coverage offered by the French social security system, la Mutuelle Générale’s health insurance offerings encompass a wide array of guarantees, including medication reimbursement, hospitalization coverage, dental care, optical care, and so forth. The company strives to provide flexible and tailored solutions to suit the specific requirements of the member clients.

The core business of the mutual insurance company is composed of health insurance and social protection (short-term incapacity, long-term invalidity, dependency and death). For the purpose of providing a more comprehensive healthcare service, in 2020, the company launched its Flex service platform, which enables partner companies to access services such as home care or personal assistance.

Overall, La Mutuelle Générale stands as a reliable and reputable insurance company, driven by the mission to provide quality healthcare coverage and social protection to individuals and businesses across France. They combine their extensive expertise, expansive coverage, and a dedicated workforce to promote well-being, financial security in face of healthcare needs, and peace of mind for their members.

Logo of La Mutuelle Générale

Source: website of La Mutuelle Générale

My position

Since September 2022, I have been engaged in a one-year apprenticeship contract for the position of Actuarial Analyst in the Technical Department that englobes all the actuarial missions. Specifically, I was in the team of Studies and Products Collective Health Insurance and Social Protection. This team takes charge of the actuarial studies of social protections and collective health insurance contracts.

My missions

Within the team, I had the chance to assist my colleagues to conduct actuarial studies in various subjects:

Monitor the profitability and risk of different insurance portfolios

We continually evaluate the financial performance and risk exposure associated with individual and group Health Insurance and Life Insurance policies. We assess factors such as claims experience, investment returns, and expenses to gauge the profitability and financial health of the portfolios. By closely monitoring these aspects, the management can make informed decisions to ensure the sustainability and growth of the company.

Calculate and provide rates for group Health Insurance and Life Insurance products

We are responsible for developing the pricing structure and tools for group Health Insurance and Life Insurance products. According to the size of the clients, we deploy different pricing strategies.

We model factors such as the demographics and health profiles of the insured individuals, expected claims frequency and severity, and desired profit margins. Through mathematical models and statistical analysis, we determine appropriate premia for corresponding products.

Here I introduce brief the key idea of insurance pricing. The mechanism of insurance is that the insured person pays for a premium beforehand to get guarantee against a certain risk for a period in the future. Insurance works on the basis of mutualisation, explained by the Law of Large Numbers. For example, for automobile insurance against the risk of theft. The risk does not befall everyone (the probability of occurrence is relatively low). Whereas, when it happens, the owner has to endure a loss amount that is relatively high and it is in this case that insurance companies accompany the car owner to cover part or all of the loss if the owner is insured.

Let’s denote X_i as the loss amount for insured person i (X_i equals 0 if the risk does not take place). If an insurance company has n insured persons, and we assume all X_i are independent and identically distributed. According to the Law of Large Numbers, we have:

1/n ∑ ⁿ_{i =1} X_i → 𝔼[ X_i]

If n is large enough, the total claim amount will converge to 𝔼[ X₁]. Therefore, if every insured person pays individually a premium of 𝔼[ X₁], the insurance company as a whole would be able to pay off all the possible claims.

Ensure the implementation of the underwriting policy:

The Underwriting Department relies on a tool to assess and price group insurance contracts. Actuaries play a crucial role in guaranteeing the consistency and accuracy of the pricing scales used within this tool. We review and validate the formulas and algorithms used to calculate premia, to make sure that they are aligned with the company’s underwriting guidelines and principles and with our calculations.

We work closely with the underwriting team to enforce the company’s underwriting policy. This involves establishing guidelines and criteria for accepting or rejecting insurance applications, determining coverage limits, and setting appropriate pricing. We provide insights and recommendations based on their analyses to ensure the underwriting policy is effectively implemented, balancing risk management and business objectives.

Conduct studies related to the current political and economic conditions

Given the dynamic nature of the insurance sector, we conduct studies to assess the impact of external factors, such as economic conditions, on insurance products. For example, we analyze the effects of the 100% Santé reform on insurance premia and claim payouts. We also conduct theoretical research of the impact of the 2023 retirement reform on our social protection portfolio.

By understanding these impacts, actuaries can adapt pricing strategies, adjust risk models, and make informed decisions to address emerging challenges and provide appropriate coverage to policyholders in conformity with the framework of regulations.

Required skills and knowledge

First and foremost, the position pivoted on actuarial studies requires solid understanding of actuarial and insurance concepts and theories. For example, it is indispensable to understand the contractual aspects of insurance policies, pricing theories and accounting rules of insurance products. Actuary is a profession that requires high-level specified expertise, and the title of Actuary is recognized by actuarial associations in respective countries after passing the credentialing process.

Besides, statistical and information techniques are highly needed. The professions of Actuary could be in a way considered as a combination of Statistician, Informatician and Marketer. Making use of statistical and information techniques, actuaries delve deep into data to uncover useful information that would aid the pricing of insurance policies and the decision-making process.

Last but not least, since the insurance sector is highly regulated and insurance offerings are mostly homogeneous, a solid and comprehensive knowledge of the local regulatory environment and business landscape is a must to make sure efficient development and management of the product portfolio. In my case, a thorough understanding of the French social security system and product specificities is crucial.

What I have learned

This apprenticeship experience takes place in parallel with my double curriculum in Actuarial Science at Institut de Statistique de Sorbonne Université (ISUP). I had the opportunities to apply the theoretical aspects in actual projects and work on various subjects with the guidance of experienced professionals. I had the chance to deepen my understanding in insurance pricing, health insurance & social protection and risk management for insurers.

Financial concepts related my internship

Insurance pricing

Health insurance pricing involves the application of theoretical concepts and statistical analysis to assess risk, project future claims, and determine suitable premiums. Insurers utilize statistical models to evaluate factors such as age, gender, pre-existing conditions, and healthcare utilization patterns to estimate the likelihood and cost of potential claims. By considering risk pooling, loss ratios, and health economic studies, insurers strive to set premiums that balance financial sustainability while providing adequate coverage to policyholders. Regulatory guidelines and statistical modeling further contribute to the development of pricing strategies in health insurance.

Solvency II

Solvency II is a regulatory framework for insurance companies in the European Union (EU) that aims to ensure financial stability and solvency. It establishes risk-based capital requirements, governance standards, and disclosure obligations for insurers. Under Solvency II, insurers are required to assess and manage their risks, maintain sufficient capital to withstand potential losses, and regularly report their financial and risk positions to regulatory authorities. The framework promotes a comprehensive approach to risk management, aligning capital requirements with the underlying risks of insurance activities and enhancing transparency and accountability in the insurance sector.

Useful resources

La Mutuelle Générale

Institut des Actuaires

Pricing Insurance #1: Pure Premium Method

About the author

The article was written in October 2023 by Shengyu ZHENG (ESSEC Business School, Grande Ecole Program – Master in Management, 2020-2024).

Application de la théorie des valeurs extrêmes en finance de marchés

February 4, 2024October 6, 2023 by Gabriel FILJA

Dans cet article, Gabriel FILJA (ESSEC Business School, Executive Master in Senior Bank Management, 2022-2023 & Head of Hedging à Convera) présente des applications de la théorie des valeurs extrêmes en finance de marchés et notamment en gestion des risques de marchés.

Principe

La théorie des valeurs extrêmes (TVE), appelé théorème de Fisher-Tippet-Gnedenko tente de fournir une caractérisation complète du comportement de la queue pour tous les types de distributions de probabilités.

La théorie des valeurs extrêmes montre que la loi asymptotique des rentabilités minimale et maximale a une forme bien déterminée qui est largement indépendante du processus de rentabilités lui-même (le lien entre les deux distributions apparaît en particulier dans la valeur de l’indice de queue qui reflète le poids des queues de distribution). L’intérêt de la TVE dans la gestion du risque c’est de pouvoir calculer le quantile au-delà de 99% du seuil de confiance dans le cadre des stress tests ou de la publication des exigences réglementaires.

Gnedenko a démontré en 1943 par la Théorie des valeurs extrêmes la propriété qui s’applique à des nombreuses distributions de probabilités. Soit F(x) la fonction de répartition d’une variable x. u est une valeur de x située dans la partie droite de la queue de distribution.

La probabilité que x soit compris entre u et u+y est de F(y+u) – F(u) et la probabilité que x soit supérieur à u est 1-F(u). Soit F_u(y) la probabilité conditionnelle que x soit compris entre u et u+y sachant que x>u∶

Probabilité conditionnelle

Estimation des paramètres

Selon les résultats de Gnedenko, pour un grand nombre de distribution, cela converge vers une distribution généralisée de Pareto au fur et à mesure que u augmente :

Distribution_généralisée_Pareto

β est le paramètre d’échelle représente la dispersion de la loi des extrêmes
ξ est l’indice de queue qui mesure l’épaisseur de la queue et la forme

Selon la valeur de l’indice de queue, on distingue trois formes dedistribiution d’extrêmes :

Frechet ξ > 0
Weibull ξ < 0
Gumbel ξ = 0

L’indice de queue ξ reflète le poids des extrêmes dans la distribution des rentabilités. Une valeur positive de l’indice de queue signifie que les extrêmes n’ont pas de rôle important puisque la variable est bornée. Une valeur nulle donne relativement peu d’extrêmes alors qu’une valeur négative implique un grand nombre d’extrêmes (c’est le cas de la loi normale).

Figure 1 : Densité des lois des valeurs extrêmes

Source : auteur.

Tableau 1 : Fonctions de distribution des valeurs extrêmes pour un ξ > 0, loi de Frechet, ξ < 0 loi de Weibull et ξ = 0, loi de Gumbel.
Source : auteur.

Les paramètres β et ξ sont estimés par la méthode de maximum de vraisemblance. D’abord il faut définir u (valeur proche du 95e centile par exemple). Une des méthodes pour déterminer ce seuil, c’est la technique appelée Peak Over Threshold (POT), ou méthode des excès au-delà d’un seuil qui se focalise sur les observations qui dépassent un certain seuil donné. Au lieu de considérer les valeurs maximales ou les plus grandes valeurs, cette méthode consiste à examiner toutes les observations qui franchissent un seuil élevé préalablement fixé.
L’objectif est de sélectionner un seuil adéquat et d’analyser les excès qui en découlent. Ensuite nous trions les résultats par ordre décroissant pour obtenir les observations telles que x>u et leur nombre total.

Nous étudions maintenant les rentabilités extrêmes pour l’action Société Générale sur la période 2011-2021. La Figure 2 représentes rentabilités journalières de l’action et les rentabilités extrêmes négatives obtenues avec l’approche des dépassements de seuil (Peak Over Threshold ou POT). Avec le seuil retenu de -7%, on obtient 33 dépassements sur 2 595 rentabilités journalières de la période 2011 à 2021.

Figure 2 : Sélection des rentabilités extrêmes négatives pour l’action Société Générale selon l’approche Peak Over Threshold (POT)

Source : auteur.

Méthode d’estimation statistique

Nous allons maintenant voir comment déterminer les β et ξ en utilisant la fonction de maximum de vraisemblance qui s’écrit :

Fonction de vraisemblance

Pour un échantillon de n observations, l’estimation de 1-F(u) est n_u/n. Dans ce cas, la probabilité inconditionnelle de x>u+y vaut :

Fonction de vraisemblance

Et l’estimateur de la queue de distribution de probabilité cumulée de x (pour un grand) est :

Estimateur queue distribution

Mon travail personnel a consisté à estimer le paramètre d’échelle β et le paramètre de queue ξ à partir de la formule par le maximum de vraisemblance en utilisant le solveur Excel. Nous avons précédemment déterminé n=0,07 par la méthode de POT en Figure 2, et n_u= 2595

Ainsi nous obtenons β=0,0378 et ξ=0,0393 ce qui maximise par la méthode du maximum de vraisemblance la somme du logarithme des valeurs extrêmes à un total de 73,77.

Estimation de la VaR TVE

Pour calculer le VaR au seuil q, nous obtenons F(VaR) = q

VaR TVE

Mon travail personnel a consisté à estimer la VaR du titre de la Société Générale de la période de 2011 à 2021 sur un total de 2595 cotations avec 33 dépassements de seuil (-7%). En appliquant les données obtenues à la formule nous obtenons :

VaR 99% Société Générale

Puis nous estimons la VaR à 99,90% et 99,95% :

VaR 99,90% Société Générale

Il n’est pas surprenant que l’extrapolation à la queue d’une distribution de probabilité soit difficile, pas parce qu’il est difficile d’identifier des distributions de probabilité possibles qui pourraient correspondre aux données observées (il est relativement facile de trouver de nombreuses distributions possibles différentes), mais parce que l’éventail des réponses qui peuvent vraisemblablement être obtenues peut être très large, en particulier si nous voulons extrapoler dans la queue lointaine où il peut y avoir peu ou pas de points d’observation directement applicables.

La théorie des valeurs extrêmes, si elle est utilisée pour modéliser le comportement de la queue au-delà de la portée de l’ensemble de données observées, est une forme d’extrapolation. Une partie de la cause du comportement à queue épaisse (fat tail) est l’impact que le comportement humain (y compris le sentiment des investisseurs) a sur le comportement du marché.

En quoi ça peut m’intéresser ?

Nous pouvons ainsi mener des stress tests en utilisant la théorie des valeurs extrêmes et évaluer les impacts sur le bilan de la banque ou encore déterminer les limites de risques pour le trading et obtenir ainsi une meilleure estimation du worst case scenario.

Autres articles sur le blog SimTrade

▶ Shengyu ZHENG Catégories de mesures de risques

▶ Shengyu ZHENG Moments de la distribution

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

Ressources

Articles académiques

Falk M., J. Hüsler, et R.-D. Reiss, Laws of Small Numbers: Extremes and Rare Events. Basel: Springer Basel, 2011. doi: 10.1007/978-3-0348-0009-9.

Gilli M. et E. Këllezi, « An Application of Extreme Value Theory for Measuring Financial Risk », Comput Econ, vol. 27, no 2, p. 207‑228, mai 2006, doi: 10.1007/s10614-006-9025-7.

Gkillas K. and F. Longin (2018) Financial market activity under capital controls: lessons from extreme events Economics Letters, 171, 10-13.

Gnedenko B., « Sur La Distribution Limite Du Terme Maximum D’Une Serie Aleatoire », Annals of Mathematics, vol. 44, no 3, p. 423‑453, 1943, doi: 10.2307/1968974.

Hull J.et A. White, « Optimal delta hedging for options », Journal of Banking & Finance, vol. 82, p. 180‑190, sept. 2017, doi: 10.1016/j.jbankfin.2017.05.006.

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

Longin F. and B. Solnik (2001) Extreme Correlation of International Equity Markets, The Journal of Finance, 56, 649-676.

Roncalli T. et G. Riboulet, « Stress testing et théorie des valeurs extrêmes : une vision quantitée du risque extrême ».

Sites internet

Extreme Events in Finance

A propos de l’auteur

Cet article a été écrit en juillet 2023 par Gabriel FILJA (ESSEC Business School, Executive Master in Senior Bank Management, 2022-2023 & Head of Hedging à Convera).

How to get crypto data

March 25, 2024October 4, 2023 by Snehasish CHINARA

How to get crypto data

In this article, Snehasish CHINARA (ESSEC Business School, Grande Ecole Program – Master in Management, 2022-2024) explains how to get crypto data.

Types of data

Number of coins

The information on the number of coins in circulation for a given currency is important to compute its market capitalization. Market capitalization is calculated by multiplying the current price of the cryptocurrency by its circulating number of coins (supply). This metric gives a rough estimate of the cryptocurrency’s total value within the market and its relative size compared to other cryptocurrencies. A lower circulating supply often implies a greater level of scarcity and rarity.

For cryptocurrencies (unlike fiat money), the number of coins in circulation is given by a mathematical formula. The number of coins may be limited (like the Bitcoin) or unlimited (like Ethereum and Dogecoin) over time.

Cryptocurrencies with limited supplies, such as Bitcoin’s maximum supply of 21 million coins, can be perceived as more valuable due to their finite nature. Scarcity can contribute to investor interest and potential price appreciation over time. A lower circulating supply might indicate the potential for future adoption and value appreciation, as the limited supply can create scarcity-driven demand, especially if the cryptocurrency gains more utility and usage.

Bitcoin’s blockchain also relies on a key equation to steadily allow new BTC to be introduced. The equation below gives the total supply of bitcoins:

Total supply of bitcoins

Figure 1 below represents the evolution of the supply of Bitcoins.

Figure 1. Evolution of the supply of Bitcoins

Source: computation by the author.

Market price of a coin

The market price of a cryptocurrency in the market holds crucial insights into how well the cryptocurrency is faring. Although not the sole factor, the market price significantly contributes to evaluating the cryptocurrency’s performance and its prospects. The market price of a cryptocurrency is a dynamic and intricate element that reflects a multitude of factors, both intrinsic and extrinsic. The gradual rise in market value over time indicates a willingness among investors and traders to offer higher prices for the cryptocurrency. This signifies a rising interest and strong belief in the project’s potential for the future. The market price reflects the collective sentiment of investors and traders. Comparing the market price of a cryptocurrency to other similar cryptocurrencies or benchmark assets like Bitcoin can provide insights into its relative strength and performance within the market. A rising market price can indicate increasing adoption of the cryptocurrency for various use cases. Successful projects tend to attract more users and real-world applications, which can drive up the price.

The value of cryptocurrencies in the market is influenced by a variety of elements, with each factor contributing uniquely to their pricing. One of the most significant influences is market sentiment and investor psychology. These factors can cause prices to shift based on positive news, regulatory changes, or reactive selling due to fear. Furthermore, the real-world implementation and usage of a cryptocurrency are crucial for its prosperity. Concrete use cases such as Decentralized Finance (DeFi), Non-Fungible Tokens (NFTs), and international transactions play a vital role in creating demand and propelling price appreciation. Meanwhile, adherence to basic economic principles is evident in the supply-demand dynamics, where scarcity due to limited issuance, halving events, and token burns interact with the balance between supply and demand.

With the number of coins in circulation, the information on the price of coins for a given currency is also important to compute its market capitalization.

Figure 2 below represents the evolution of the price of Bitcoin in US dollar over the period October 2014 – August 2023. The price corresponds to the “closing” price (observed at 10:00 PM CET at the end of the month).

Figure 2. Evolution of the Bitcoin price

Source: computation by the author (data source: Yahoo! Finance).

Trading volume

Trading volume is crucial when assessing the health, reliability, and potential price movements of a cryptocurrency. Trading volume refers to the total amount of a cryptocurrency that is bought and sold within a specific time frame, typically measured in units of the cryptocurrency (e.g., BTC) or in terms of its equivalent value in another currency (e.g., USD).

Trading volume directly mirrors market liquidity, with higher volumes indicative of more liquid markets. This liquidity safeguards against drastic price fluctuations when trading, contrasting with low-volume scenarios that can breed volatility, where even a single substantial trade may disproportionately shift prices. Price alterations are most reliable and meaningful when accompanied by substantial trading volume. Price movements upheld by heightened volume often hold greater validity, potentially pointing to more pronounced market sentiment. When price surges parallel rising trading volume, it suggests a sustainable upward trajectory. Conversely, low trading volume amid rising prices may hint at a forthcoming correction or reversal. Scrutinizing the correlation between price oscillations and trading volume can uncover potential divergences. For instance, ascending prices coupled with dwindling trading volume may suggest a weakening trend.

Figure 3 below represents the evolution of the monthly trading volume of Bitcoin over the period October 2014 – July 2023.

Figure 3. Evolution of the trading volume of Bitcoin

Source: computation by the author (data source: Yahoo! Finance).

Bitcoin data

You can download the Excel file with Bitcoin data used in this post as an illsutration.

Python code

You can download the Python code used to download the data from Yahoo! Finance.

Python script to download Bitcoin historical data and save it to an Excel sheet:

import yfinance as yf
import pandas as pd

# Define the ticker symbol and date range
ticker_symbol = “BTC-USD”
start_date = “2020-01-01”
end_date = “2023-01-01”

# Download historical data using yfinance
data = yf.download(ticker_symbol, start=start_date, end=end_date)

# Create a Pandas DataFrame
df = pd.DataFrame(data)

# Create a Pandas Excel writer object
excel_writer = pd.ExcelWriter(‘bitcoin_historical_data.xlsx’, engine=’openpyxl’)

# Write the DataFrame to an Excel sheet
df.to_excel(excel_writer, sheet_name=’Bitcoin Historical Data’)

# Save the Excel file
excel_writer.save()

print(“Data has been saved to bitcoin_historical_data.xlsx”)

# Make sure you have the required libraries installed and adjust the “start_date” and “end_date” variables to the desired date range for the historical data you want to download.

APIs

Calculating the total number of Bitcoins in circulation over time
Access – Bitcoin Blockchain data
By running a Bitcoin node or by using blockchain data providers like Blockchain.info, Blockchair, or a similar service.

Extract Block Data: Once you have access to the blockchain data, you would need to extract information from each block. Each block contains a record of the transactions that have occurred, including the creation (mining) of new Bitcoins in the form of a “Coinbase” transaction.

Calculate Cumulative Supply: You can calculate the cumulative supply of Bitcoins by adding up the rewards from each block’s Coinbase transaction. Initially, the block reward was 50 Bitcoins, but it halves approximately every four years due to the Bitcoin halving events. So, you’ll need to account for these halving in your calculations.

Code – python

import requests

# Replace ‘YOUR_API_KEY’ with your CoinMarketCap API key
api_key = ‘YOUR_API_KEY’

# Define the endpoint URL for CoinMarketCap’s API
url = ‘https://pro-api.coinmarketcap.com/v1/cryptocurrency/quotes/latest’

# Define the parameters for the request
params = {
‘symbol’: ‘BTC’,
‘convert’: ‘USD’,
‘CMC_PRO_API_KEY’: api_key
}

# Send the request to CoinMarketCap
response = requests.get(url, params=params)

# Parse the response JSON
data = response.json()

# Extract the circulating supply from the response
circulating_supply = data[‘data’][‘BTC’][‘circulating_supply’]

print(f”Current circulating supply of Bitcoin: {circulating_supply} BTC”)

## Replace ‘YOUR_API_KEY’ with your actual CoinMarketCap API key.

Why should I be interested in this post?

Cryptocurrency data is becoming increasingly relevant in these fields, offering opportunities for research, data analysis skill development, and even career prospects. Whether you’re aiming to conduct research, stay informed about the evolving financial landscape, or simply enhance your data analysis abilities, understanding how to access and work with crypto data is an asset. Plus, as the cryptocurrency industry continues to grow, this knowledge can open new career paths and improve your personal finance decision-making. In a rapidly changing world, diversifying your knowledge with cryptocurrency data acquisition skills can be a wise investment in your future.

Useful resources

APIs

CoinMarketCap Source of API keys and program

CoinGecko Source of API keys and Programs

CryptoNews Source of API keys and Programs

Data sources

Yahoo! Finance Historical data for Bitcoin

Coinmarketcap Historical data for Bitcoin

Blockchain.com Market Data and charts on Bitcoin history

About the author

The article was written in October 2023 by Snehasish CHINARA (ESSEC Business School, Grande Ecole Program – Master in Management, (2022-2024).

My Experience as an External Junior Consultant with Eurogroup Consulting

August 2, 2023 by Snehasish CHINARA

My Experience as an External Junior Consultant with Eurogroup Consulting

In this article, Snehasish CHINARA (ESSEC Business School, Grande Ecole Program – Master in Management, 2022-2024) shares his experience as an External Junior Consultant with Eurogroup Consulting, which is a consulting company specialized in organization and operations (supply chain).

About Eurogroup Consulting

Eurogroup Consulting, founded in 1982, is a French consulting firm with a European approach to management, strategy and organization. With a focus on freedom to take risks, requirements of the clients and the projects, and solidarity to the success of their entrepreneurial partners, Eurogroup consulting has been able to expand its network to 16 countries and clientele to all sectors of activity. They have grown significantly in the areas of banking and finance, business, insurance and welfare, logistics and transportation, retail, energy and the environment, and public sector, including healthcare. Today, Eurogroup Consulting stands out as a highly reputable and able partner for companies seeking all-encompassing solutions and knowledgeable advisory in the areas of Digital, Operational Excellence, and Transitions.

Eurogroup Consulting Logo

Source: Eurogroup Consulting.

Junior Consultant Experience

As a part of my Master in Management program at ESSEC Business School, I and a few other students a ESSEC (my team) collaborated as an External Junior Consultant with Eurogroup Consulting for a consulting project in the aviation sector based in Singapore. With my team, I closely worked with the managing partner of Eurogroup Consulting in Singapore to offer strategic recommendations to one of the firm’s clients in the aviation sector dealing with logistics (for the maintenance, repair and overhaul (MRO) of airplanes). Our focus was on addressing the real-world challenges faced by the aviation industry in the post-Covid era in the Asia-Pacific region.

My project with Eurogroup Consulting dealt with logistics and supply chain within the aviation sector. Efficient logistics and supply chain management are vital for businesses to remain competitive in today’s globalized marketplace as they ensure the efficient flow of goods, services and information from the point of origin to the point of consumption.

Our focus was on Contract Logistics in the aviation sector, which is a type of third-party logistics (3PL) service where a company delegates certain aspects of its supply chain operations to a specialized provider. This provider, known as the contract logistics provider, oversees a portion or all the company’s supply chain, which includes transportation, distribution, and related activities, as per the contractual agreement. The primary objective of contract logistics is to enhance the efficiency of the customer’s supply chain, reduce expenses, and optimize overall performance. By leveraging expertise, resources, and technology, contract logistics providers enable clients to concentrate on core business activities while entrusting the management of their logistics operations to the specialized service. Contract logistics providers provide services such as warehouse management, inventory management, order fulfillment, distribution and transportation management. In the aviation sector, contract logistics play an important role in offering services like space part logistics. Airlines face challenges with “Inoperable parts” (INOPs), which necessitate costly replacements or risk grounding the aircraft indefinitely. Major companies provide essential services to address this spare parts availability issue, such as Order Tracking & Tracing, spare parts storage management, advanced stock organization, and repair logistics management.

My missions

The objective my project was to achieve the following:

Identify the post-Covid supply chain strategies of major multinational corporations (MNCs) in the aviation sector, including the evolution of their supply chain footprints and their expectations from contract logistics providers (an intermediary between the different manufacturers and an airline company).
Evaluate the current positioning and services offered by prominent contract logistics providers and anticipate how their positioning and offerings might evolve in the future.
Recommend new potential offerings and analyze their suitability and key factors for success.

Required skills and knowledge

As a part of a cross-functional team of ESSEC students to achieve the shared project objectives through efficient cooperation, and decision-making, I gained an understanding of the aerospace Third Party Logistic (3PL) and Maintenance, Repair and Overhaul (MRO) industry in the Asia-Pacific region as we conducted comprehensive market research. We gathered and analysed large sets of data related to the aviation contract-logistics market, customers, competitors, and industry trends to identify growth opportunities. Following the analysis, we had weekly meetings with the managing partner of Eurogroup consulting, a professor-mentor of the team at ESSEC and the client to discuss our approach to the problem statement, challenges faced by the team to gather access to information, since aviation industry is well-known for its confidentiality norms, and the assessments produced after detailed analysis of the data. Attending the weekly team-mentor meetings was vital to our learning, providing us with first-hand exposure to the real-life operations within a consulting firm. In these meeting we decided upon the objective targets for the coming weeks and how to address the challenges faced this week.

As a junior consultant, I engaged with subject matter experts in the region in order to gain a holistic understanding of the impact of Covid-19 on the aviation contract-logistics industry. I conducted detailed financial statement analysis to understand how the larger players and competition were leveraging their cash flows, and debt to counter the crisis caused on the industry by the pandemic. In order to measure the risk of the competitors of the client, we conducted a fundamental calculation of Altman’s Z-Score and developed a credit rating model based on key financial indicators, both quantitative and qualitative, in Excel. This allowed us to scrutinize the key players in the current market and identify competitors to be focused on. Based on our discussions with experts, and analysis conducted, we identified the gap in the service offerings which allowed us to provide strategic recommendations for the client company. This 3-month long learning-by-doing experience gave me immense exposure to the operations of a consulting firm and the way they respect the needs of the stakeholders of the project.

What I learned

Key Learning Outcomes of this project :

To utilise evidence-based conclusions and strategic thinking to propose new strategic initiatives that aligned with industry innovations and key success factors.
To analyse corporate information and financial statements, preparing pitch-books and presentations while collaborating with stakeholders.
To define the value chain of aviation contract-logistics industry in Asia-Pacific region and observe potential channels to expand.
To develop custom credit rating tool based on key performance indicators.

Concepts related my internship

Third-Party Logistics in Aviation Sector

Third-Party Logistics (3PL) is a crucial aspect of Logistics and Supply Chain Management, that has transformed how businesses handle the transportation and storage of products and services. Through strategic outsourcing, companies delegate specific logistics tasks to external service providers, known as 3PL providers. These service providers streamline supply chain processes, resulting in increased efficiency, cost reduction, and improved overall performance. Within the aviation sector, 3PL is crucial for aiding airlines, aircraft manufacturers, and associated enterprises with intricate global logistics. Due to the complexity and time-sensitivity of aviation operations, 3PL providers offer customized solutions to address the unique demands and challenges of the industry. 3PL companies in the aviation industry offer a range of essential services to streamline operations. These include arranging the transportation of aviation-related cargo and goods, managing efficient warehousing and inventory systems for quick access to items, handling customs clearance for international shipments, ensuring prompt last-mile delivery to designated destinations, managing the distribution of critical spare parts for airlines’ maintenance facilities worldwide, and facilitating smooth transportation of large components and sub-assemblies for aircraft manufacturers. These services contribute significantly to the industry’s efficiency and help reduce aircraft downtime, making them indispensable partners for aviation businesses.

Aviation 3PL Services:

Freight Transportation: 3PL companies arrange timely transport of aviation cargo to airports, maintenance facilities, and aircraft assembly lines.
Efficient Warehousing: These providers manage aviation-related inventory in well-organized warehouses, reducing lead times.
Customs Compliance: 3PLs handle international shipments’ customs documentation, ensuring smooth clearance.
Last-Mile Delivery: They ensure prompt delivery of aviation components to their destinations.
Spare Parts Distribution: Airlines rely on 3PLs for critical spare parts distribution, minimizing aircraft downtime.
Aircraft Manufacturing Support: Specialized 3PLs facilitate smooth production by transporting large components for aircraft manufacturers.

Aviation companies benefit from the expertise of 3PL providers in handling complex logistics. Outsourcing these services saves on capital investments and allows them greater flexibility in scaling services based on demand. 3PL providers’ extensive network aids in smoother international operations for the customers.

Credit risk

The evaluation of credit risk holds significant importance in financial risk management, especially concerning lending and investment activities. It pertains to the potential financial loss that a lender or investor might encounter in the event of non-payment or failure of a borrower or counterparty to fulfil their financial commitments. Credit risk occurs when people, companies, or governmental entities take loans or offer credit with the possibility that they might be unable to repay the borrowed amount according to the agreed terms.

Several key concepts allow us to gauge the risk involved with an investment and make better decisions. The Probability of Default (PD) is a measure that evaluates the probability of a borrower being unable to fulfil their contractual obligations and defaulting. Although defaulting doesn’t always result in immediate losses, it can raise the risk of bankruptcy and eventual losses. PD is expressed as a percentage, with higher percentages indicating a higher risk of default. Loss Given Default (LGD) is a commonly used expression to describe the ‘loss severity’ of an investment. It calculates the proportion of an exposure (such as a bond or loan equivalent) that is expected to remain unrecovered if a default occurs. It is a percentage of the outstanding debt or investment that is not recoverable after a default occurs.

Credit agencies are responsible for assigning credit ratings to both corporations and governments based on their ability to fulfil financial obligations. These credit ratings serve as indicators for lenders regarding the entity’s capacity to repay loans. Each credit agency employs slightly varied approaches in determining credit ratings. On the other hand, credit scores pertain to individuals and reflect their creditworthiness, considering their credit history and financial conduct. Credit risk models play a vital role in the financial industry as they employ mathematical techniques to foresee the probability of default, evaluate potential losses, and handle credit risk. These sophisticated tools aid both financial institutions and investors in making well-informed choices concerning lending and investment matters. As the global economy continues to evolve, understanding and managing credit risk will remain paramount for safeguarding financial stability and ensuring sustainable growth in lending and investment sectors. By employing comprehensive credit risk analysis, stakeholders can navigate potential challenges, capitalize on opportunities, and foster a resilient financial landscape for the future.

The evaluation of credit risk had a vital role in the extensive market research conducted for the top players in the aviation contract logistics segment. Although credit risk analysis mainly concentrates on appraising the creditworthiness of potential collaborators or customers, it offered valuable insights that prove beneficial for competitive intelligence and market research objectives. Conducting credit risk analysis on companies within the industry allowed for the identification of major players and their market position. Assessing financial stability, including liquidity, profitability, and debt levels, helped evaluate potential investment opportunities and market disruptions. Additionally, studying competitors’ credit risk provided insights into their market share, customer base, and potential risks of default or bankruptcy. Understanding their financial strength aided in formulating effective strategies for competitive positioning in the aviation contract logistics niche.

Corporate Risk Management

In order to mitigate various types of financial risks, such as credit risk, market risk, liquidity risk, and operational risk, investors and management can use risk analysis to identify, measure, and mitigate these risks effectively. Instabilities and losses in financial markets generally caused by fluctuations in stock prices, currencies, interest rates and more lead to rise in financial risks. Market risk reflects the fluctuations of interest rates, currencies, and prices of raw materials. Probability of failing to pay creditors such as banks or lenders leads to credit risk. Liquidity risk is the inability of a company to meet its short-term financial obligations (to pay the salaries of its employees, to settle the invoices to its suppliers, to pay back the capital and interests to the bank, to pay the taxes to the State, etc.) and is generally signs of cashflow inefficiencies. Flawed policies, processes, events or systems disrupt business operations and are known to cause operational risks. Financial risks are measured by calculating specific ratios that indicate the overall health of a company, which are then compared against the industry benchmark.

The following table provides some of the important financial ratios used to estimate the risk of a company. High financial risk is implied by high or low measure according to the ratio.

Table 1. Financial ratios

Source: The author.

Ratios are most useful when compared between companies in similar sectors and over time. Multiple measurements may be necessary for each given firm to fully comprehend the financial risk.

Why should I be interested in this post?

Working closely with subject matter experts and engaging in financial statement analysis to assess the impact of Covid-19 on the various industries equipped us with valuable skills and knowledge in financial analysis and risk assessment. Additionally, learning to calculate Altman’s Z-Score and developing a credit score model allowed us to evaluate the financial health of companies, a crucial skill in the finance industry. The exposure to strategic decision-making, data analysis, and client interactions during this consulting project helped me develop problem-solving capabilities and communication skills, which are highly sought-after attributes in the finance job market. Overall, this hands-on experience provided me with practical experience for finance roles, especially in consulting firms.

Useful resources

Eurogroup Consulting

Financial Risk – Allianz Trade

Financial Risk – Deloitte

About the author

The article was written in August 2023 by Snehasish CHINARA (ESSEC Business School, Grande Ecole Program – Master in Management, 2022-2024).

Netflix 'Billions' Analysis of characters through CFA Code and Standards

July 24, 2023 by William LONGIN

Netflix ‘Billions’ Analysis of characters through CFA Code of Ethics and Standards of Professional Conduct

In this article, William LONGIN (EDHEC Business School, Global BBA 2020-2024) analyzes the show “Billions” through the lens of the Code of Ethics and Standards of Professional Conduct developed by the CFA Institute. I wrote this post while I prepared for the Level 1 of the CFA exam.

Overview of ‘Billions’ and ethics

The Netflix show “Billions,” set in New York City, portrays the intense story between three individuals: Bobby Axelrod, CEO of hedge fund ‘Axe Capital’, Chuck Rhoades, a tenacious US Attorney, and Wendy Rhoades, the wife of Chuck Rhoades and a talented performance coach working at Axe Capital. Bobby Axelrod and Chuck Rhoades fight for their honor and survival throughout the series with sometimes questionnable actions. Wendy Rhoades often plays the role of a middle person to find compromise and communication between Bobby Axelrod and Chuck Rhoades. The main characters insatiable greed has led them to indulge in misconduct, disregarding the ethical rules that govern investment and legal professionals in the real world.

Billions
Source: Showtime / Netflix.

CFA Institute’s Code of Ethics and Standards of Professional Conduct

The CFA Institute’s Code of Ethics and Professional Standards defines a comprehensive canvas for ethical and professional behavior. It states that it is for “investment professionals globally, regardless of job function, cultural differences, or local laws and regulations.” The Code places a strong emphasis on honesty to ensure that investment professionals operate in clients’ best interests. In “Billions”, the characters’ choices and actions often cross paths with these moral guidelines. In this article we will explore the three main characters Bobby Axelrod, Chuck and Wendy Rhoades through the lens of the CFA Code of Ethics and Standards of Professional Conduct.

“Billions” main characters: Bobby Axelrod, Chuck and Wendy Rhoades
Billions main characters: Bobby Axelrod, Chuck and Wendy Rhoades
Source: Netflix.

Bobby Axelrod: the hedge fund manager

Bobby Axelrod is the main character of the series “Billions”. He is the CEO of the hedge fund Axe Capital. Bobby Axelrod possesses exceptional financial acumen (the ability to make good judgements and take quick decisions) but his actions often push the boundaries of ethical behavior. These actions are driven by the drive to always beat the market at whatever cost.

Insider trading

By definition, insider trading is the illegal practice of trading on the stock exchange to one’s own advantage using material non-public information (confidential information).

One important ethical concern surrounding Bobby is his open willingness to engage in insider trading for himself and his firm. Despite having a legal department at Axe Capital, insider trading has been normalized throughout the series and undetected in most cases by the Securities and Exchange Commission (SEC) – the US authority in charge of regulating the financial markets. Bobby Axelrod gets his information through his extensive professional network and from his spies. Insider trading is forbidden by CFA standards of professional conduct as it violates point II.A. of CFA standards of professional conduct.

II.A. Material Nonpublic Information. Members and Candidates who possess material nonpublic information that could affect the value of an investment must not act or cause others to act on the information.

Insider trading is also forbidden by law in the United States. According to Cornell Law School “Courts impose liability for insider trading with Rule 10b-5 under the classical theory of insider trading and, since U.S. v. O’Hagan, 521 U.S. 642 (1997), under the misappropriation theory of insider trading”.

An example of insider trading is in the Episode 1 Season 1: “Pilot”. Bobby Axelrod approves a short-sell on Superior Automotive based on insider information. In this scene, Bobby Axelrod listens to two points of view: a deduction based on public information from one of his employees and another point of view based on confidential information from the character Dollar-Bill. When Axe asks Dollar-Bill “his level of certainty” about the excess supply that wasn’t disclosed by the company, there is a cut scene that shows the bribing with cash & watches of an employee of Superior Automotive and Dollar-Bill directly looking at the physical inventories of the company. To which Dollar-Bills answers famously “I am not uncertain”. When in possession of insider information, professionals cannot share, or influence action based on that information according to CFA Code of Professional Standards. Although Dollar-Bill is the one that actively tried to act on insider information, Axelrod is also in fault because of his lack of due diligence and supervision of his employee.

Independence and Objectivity

Bobby Axelrod has been found to use financial incentives to influence other people’s decisions in his favor. For example, Axelrod tipped the policeman that was going to arrest his employee. This tip avoided legal charges for his employee and bad image for the firm. Axelrod is found to disregard point I.B of the CFA standards of professional conduct.

I.B. Independence and Objectivity. (…) Members and Candidates must not offer, solicit, or accept any gift, benefit, compensation, or consideration that reasonably could be expected to compromise their own or another’s independence and objectivity.

In season 1 episode 7 “The Punch”, Bobby Axelrod pays a police officer named Lonnie Watley to prevent the arrest of one of his employees, Donnie Caan. Donnie Caan is a key member of Axe Capital, and Bobby Axelrod takes measures to protect him from legal troubles related to an insider trading investigation. In a later episode this incident was discovered by Raul Gomez, New York City Police and Fire Department Pension Fund Manager that asks him to not “greed” his colleagues in the future.

Unethical behavior

Axelrod frequently engages in aggressive tactics to push his personal agenda. A major example of unethical behavior is the Ice Juice Scheme from Season 2. In this case Bobby Axelrod sabotaged the initial public offering (IPO) of a company called “Ice Juice.” He used insider information to short the stock and profit immensely when the stock price immediate crash due to his scheme. His plan was to have some people get instantly sick after drinking Ice Juice and profit from media coverage. His scheme tampered with the public opinion and destabilised the fair consideration of Ice Juice on its IPO day. This also impacted his colleagues in the investment profession and their clients. According to point 1 of the CFA Code of Ethics this behaviour is unethical.

Act with integrity, competence, diligence, respect and in an ethical manner with the public, clients, prospective clients, employers, employees, colleagues in the investment profession, and other participants in the global capital markets.

Chuck Rhoades: the US Attorney for Southern district of New York

Chuck Rhoades is the United States Attorney for the Southern district of New York. During the first season Chuck attempts to take down Bobby Axelrod to protect fair competition in the markets. Bobby and Chuck both used their network to try and destabilize the other but ended in a stalemate in the 1rst season. It is important to note that Chuck Rhoades is not an investment professional, but the Code and Standards promotes ethical guidelines that can be interpreted in various professions.

Fraud

Chuck’s methods and ethical choices also raise concern. Chuck often bends the rules, manipulates evidence, and employs coercion to secure convictions and survive in his industry. Manipulating evidence goes against point II.D of the Code of standards of professional conduct regarding misconduct.

II.D. Misconduct. Members and Candidates must not engage in any professional conduct involving dishonesty, fraud, or deceit or commit any act that reflects adversely on their professional reputation, integrity, or competence.

Conflicts of interests

Additionally, Chuck’s relationship with Wendy Rhoades, who works as a performance coach for Axe Capital, raises ethical concerns regarding conflicts of interest and the appropriate boundaries between personal and professional relationships. While Chuck initially recuses himself from the Axe Capital case, he continued to work on the case behind the scene. This goes against the interest of the American people because he is biased in his work. Point VI.A. of CFA standards of professional conduct on conflicts of interests states the following.

VI.A. Disclosure of Conflicts. Members and Candidates must make full and fair disclosure of all matters that could reasonably be expected to impair their independence and objectivity or interfere with respective duties to their clients, prospective clients, and employer. Members and Candidates must ensure that such disclosures are prominent, are delivered in plain language, and communicate the relevant information effectively.

Wendy Rhoades: the middle woman

Wendy Rhoades is a performance coach at Axe Capital. She plays a key role in the series and is a powerful woman that often plays a role in resolving the fights between Axe and Chuck. Wendy tries to balance her professional responsibilities at Axe Capital while managing her personal relationship with Chuck Rhoades. Since Wendy Rhoades works in the finance industry she is therefore directly concerned by the Code of Ethics and Standards.

Whistleblowing

Wendy Rhoades is entrusted with confidential information, serving as a confidante to many within the organization. This fiduciary (involving trust) duty requires her to prioritize the interests and welfare of these individuals, acting with integrity and avoiding any conflicts that could compromise their trust. Across Season 2 we see that the information that Wendy has on the company is compromising and therefore we may ask ourselves if under national law she would be required to play a role of whistleblower. Indeed, Wendy has had knowledge of criminal activity and refused to whistle blow mostly due to her friendship with Bobby. This goes against point I.A of CFA standards of professional conduct.

I.A. Knowledge of the Law. Members and Candidates must understand and comply with all applicable laws, rules, and regulations (including the CFA Institute Code of Ethics and Standards of Professional Conduct) of any government, regulatory organization, licensing agency, or professional association governing their professional activities. (…) Members and Candidates must not knowingly participate or assist in and must dissociate from any violation of such laws, rules, or regulations.

Wendy’s loyalty to Bobby Axelrod adds another layer of complexity. Bobby relies heavily on Wendy’s expertise and guidance, seeking her advice on critical business decisions and relying on her insight into the minds of Axe Capital employees.

Wendy’s dual loyalties place her in a delicate position, as her duty to uphold the best interests of Axe Capital and with her personal relationship with her husband Chuck Rhoades.

Importance of ethics in the investment industry and popular media’s influence

Ethics play an important role in the investment industry as it gives it reputation and trust. A Code of Ethics and Professional Standards as proposed by the CFA Institute helps to work towards a stable financial system while reducing the likelihood of wrongdoings.

The Netflix series “Billions” that started in 2016, almost 10 years after the financial crisis of 2007 portrays traders as greedy and unethical in many cases. “Billions” stays nonetheless a fictional representation of the financial industry. However, this portrayal could badly influence and create false impressions, especially for future analysts and viewers who aspire to these positions.

Television shows and movies have the power to shape public opinion. “Billions” contributes to the overall perception of the financial sector along with other films like the Wolf of Wall Street and The Big Short. The financial sector is often a sector that is unknown or known very little by the average person. The portrayal of ethical dilemmas in popular media could raise awareness and generate important discussions about the role of ethics in finance. It encourages critical thinking and prompts viewers to question the ethical boundaries they would be willing to cross in pursuit of success.

Useful resources

U.S Securities Exchange Commission (SEC)

Cornell Law School Insider trading

CFA Code of Ethics and Professional Standards

About the author

Article written in July 2023 by William LONGIN (EDHEC Business School, Global BBA, 2020-2024).

Top 5 companies by market capitalization in India

January 29, 2024July 23, 2023 by Nithisha CHALLA

Top 5 companies by market capitalization in India

In this article, Nithisha CHALLA (ESSEC Business School, Grande Ecole Program – Master in Management, 2021-2023) presents the top 5 companies by market capitalization in India.

Introduction to market capitalization

Market capitalization is a crucial factor in investment analysis. Learning about the market capitalization of companies helps you evaluate their size, growth potential, and overall value in the market. This knowledge can assist you in making informed investment decisions and assessing the financial health of companies.

Top 5 companies by market capitalization in India

The top 5 companies in India according to market capitalization by 2023 are as follows:

Stock chart for Hindustan Unilever

Source: Yahoo! Finance.

The historical data for Hindustan Unileverstock prices can be downloaded from Yahoo! Finance website: Download the data for Hindustan Unilever

Why should I be interested in this post?

As a management student, understanding the top companies in different markets and their market capitalization holds significant value. It provides you with industry insights, allowing you to comprehend the competitive landscape and trends within specific sectors.

Analyzing market capitalization aids in investment analysis, enabling you to assess the size, growth potential, and financial health of companies. Moreover, studying successful companies (success being measured by their market capitalization) provides valuable lessons in competitive strategy, organizational management, and leadership practices.

Useful resources

Companies Market Cap Largest Indian companies by market capitalization

Yahoo! 15 Biggest Indian State-Owned Companies

Wikipedia List of largest companies in India

About the author

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

Top 5 companies by market capitalization in Europe

January 30, 2024July 23, 2023 by Nithisha CHALLA

Top 5 companies by market capitalization in the Europe

In this article, Nithisha CHALLA (ESSEC Business School, Grande Ecole Program – Master in Management, 2021-2023) presents the top 5 companies by market capitalization in Europe.

Introduction to market capitalization

Market capitalization, often referred to as “market cap,” is a key metric used in the financial world to assess the size and value of a publicly traded company. Market capitalization provides insights into a company’s position in the market and its relative size compared to other companies. It is a measure of a company’s total market value, calculated by multiplying its current stock price by the total number of outstanding shares. It is an important indicator for investors, analysts, and market participants as it reflects the perceived worth of a company by the investing public. Note that market capitalization assesses the size of the company in the equity market, but the total value of the company measured by its assets or the sum of its liabilities and shareholders’ equity may be larger if the company uses debt (financial leverage).

Top 5 companies by market capitalization in Europe

The top 5 companies in the European market according to market capitalization by 2023 are as follows:

Stock chart for SAP

Source: Yahoo! Finance.

The historical data for SAP stock prices can be downloaded from Yahoo! Finance website: Download the data for SAP

Why should I be interested in this post?

Useful resources

Companies Market Cap Largest European companies by market capitalization

Statista Market capitalization of leading companies on Euronext stock exchange as of February 2023

Yahoo! 10 Best European Companies To Invest In

About the author

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

Top 5 companies by market capitalization in China

January 30, 2024July 23, 2023 by Nithisha CHALLA

Top 5 companies by market capitalization in China

In this article, Nithisha CHALLA (ESSEC Business School, Grande Ecole Program – Master in Management, 2021-2023) presents the top 5 companies by market capitalization in China.

Introduction to market capitalization

Top 5 companies by market capitalization in China

The top 5 companies in the Chinese market according to market capitalization by 2023 are as follows:

Stock chart for Ping An Insurance

Source: Yahoo! Finance.

The historical data for Ping An Insurance prices can be downloaded from Yahoo! Finance website: Download the data for Ping An Insurance

Why should I be interested in this post?

Useful resources

Companies Market Cap Largest Chinese companies by market capitalization

Yahoo! 15 Biggest Chinese State-Owned Companies

About the author

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

Introduction to convertible bonds

December 31, 2023June 30, 2023 by Tanguy TONEL

Introduction to convertible bonds

In this article, Tanguy TONEL (ESSEC Business School, Global BBA, 2019-2023) explains about convertible bonds.

Introduction

In the ever-evolving financial landscape, investors are constantly seeking new opportunities to diversify their portfolios and maximize returns. One such investment vehicle that has gained traction in recent years is the convertible bond. As a hybrid security, convertible bonds offer a unique blend of debt and equity features, providing investors with the potential for capital appreciation and income generation. In this article, we will delve into the world of convertible bonds, exploring their characteristics, types, and the benefits they offer to both investors and issuers.

What are Convertible Bonds

A convertible bond is a type of corporate bond that can be converted into a predetermined number of shares of common stock in the issuing company upon or before its maturity.

Like traditional corporate bonds, convertible bonds entitle their holders to coupon (interest) payments at regular intervals and can usually be redeemed for their par value (original price) upon maturity, assuming they were not already converted into shares.

Technically, convertible bonds are considered debt instruments until they are converted into shares. However, due to their ability to be converted into equity, most investors consider them hybrid securities.

Types of Convertible Bonds

Vanilla Convertible Bonds

These are the most common type of convertible bonds, allowing investors the option to convert their bonds into shares at a predetermined conversion price and rate during the bond’s lifetime.

Mandatory Convertible Bonds

Unlike vanilla convertible bonds, mandatory convertible bonds require the bondholder to convert their bonds into shares at the maturity date. This feature makes them more equity-like in nature.

Reverse Convertible Bonds

These bonds give the issuer the option to either buy back the bond in cash or convert the bond into equity at a predetermined conversion price and rate at the maturity date.

Risks

Also known as Public Investment in Private Equity (PIPE), convertible bonds allow companies that have difficulties securing financing with a more traditional approach to get funding more easily.

Nevertheless, convertible bonds can lead to significant dilution for investors if the funds holding them decide, or are forced, to convert the debt into equity as they usually purchase the debt at a discount. Convertible bonds can be seen as debt combined to an already “in the money” option for newly emitted shares. Through “OCEANE” bonds in France, companies might refund the bondholders with existing shares, but it happens less often than a refund with newly emitted shares.

The Hull precises that “When these instruments are exercised, the company issues more shares of its own stock and sells them to the option holder for the strike price. The exercise of the instruments therefore leads to an increase in the number of shares of the company’s stock that are outstanding.”. Indeed, a major risk for the old shareholders is dilution and an important decrease in the value of their shares if the bond issuance is used as a form of credit line rather than funding growth.

As it is a common source of funding for companies in difficulties, that risk tends to be significative.

Indeed, according to Les Echos, the AMF (Autorité des marchés financiers) scrutinized a sample of 69 companies, and among them 57 companies, or 83% of the sample, saw their stock prices decline, with an average decrease of 72%. The stock price of 20 of them, or 29% of the sample, has even lost more than 90%.Only 12 companies, or 17% of the sample, saw their stock price rise.

Conditions of exercise

Convertible bonds come with specific conditions for exercise, offering investors the flexibility to convert their bonds into a predetermined number of common shares of the issuing company.

The conditions typically include a conversion ratio, which specifies the number of shares the bondholder will receive for each convertible bond converted.

Additionally, there is usually a conversion price, which is the predetermined price at which the conversion occurs. Investors can choose to exercise their convertible bonds if the market price of the company’s common stock exceeds the conversion price, enabling them to benefit from the appreciation in the stock value.

The issuing company may also impose restrictions on when and how the conversion can take place, such as waiting until a certain period has passed since the issuance of the bonds. These conditions are designed to balance the interests of both the bondholder and the issuing company and provide a mechanism for investors to participate in potential upside movements in the company’s stock.

Example

A convertible bond is issued at a value of €1,000 at a ratio of 1 bond to 5 shares.

Five years later, the number of shares associated to this bond are worth €3,000, the bondholder claims his five shares. His benefit is €2,000 plus the yield of the bond for the 5 years.

If, five years later, the 5 shares are worth €200, the bondholder claims a refund in cash and his benefit is the yield of the bond.

It is to be noted that the investor is granted no voting rights before claiming shares against his bond.

Also, in the case of mandatory convertible bonds, the investor will incur a loss of (1000-200) €800 and will get 5 shares now worth €200.

Why should I be interested in this post?

Small caps can offer larger returns than large caps which may attract the retail investor desiring to beat the market. Nevertheless, some companies abuse this financing method, generating unwanted risk that mainly hurts the investors. Therefore, it is important to be aware of the opportunities offered by those alternative investment vehicles while keeping in mind the associated risks.

Useful resources

Hull J.C. (2021) Options, Futures, and Other Derivatives Pearson, 11^th Edition.

Elbadraoui, Khalid & Lilti, Jean-Jacques & Mzali, Bouchra. (2008) La Performance Opérationnelle à Long Terme des Entreprises Françaises Émettrices d’Obligations Convertibles. Revue Finance Contrôle Stratégie 11, 125-154.

U.S. Securities and Exchange Commission (SEC) Private Investment in Public Equity (PIPE).

C.P. (18 octobre 2022) L’AMF met à nouveau en garde contre les OCABSA.

About the author

The article was written in June 2023 by Tanguy TONEL (ESSEC Business School, Global BBA, 2019-2023).

Top 5 companies by market capitalization in the US

March 26, 2024June 28, 2023 by Nithisha CHALLA

Top 5 companies by market capitalization in the US

In this article, Nithisha CHALLA (ESSEC Business School, Grande Ecole Program – Master in Management, 2021-2023) presents the top 5 companies by market capitalization in the US.

Introduction to market capitalization

Market capitalization is an important indicator for investors, analysts, and market participants as it reflects the perceived worth of a company by the investing public. Note that market capitalization assesses the size of the company in the equity market, but the total value of the company measured by its assets or the sum of its liabilities and shareholders’ equity may larger if the company uses debt (financial leverage).

The top 5 corporations in the US market according to market capitalization by 2023 are as follows:

Stock chart for Meta Platforms

Source: the company.

The historical data for Meta Platforms stock prices can be downloaded from Yahoo! Finance website: Download the data for Meta Platforms

Why should I be interested in this post?

Useful resources

Companies Market Cap Largest American companies by market capitalization

Yahoo! The 30 Largest Companies on the Stock Market

About the author

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

Market Capitalization

June 28, 2023 by Nithisha CHALLA

Market Capitalization

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

What is Market Capitalization?

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

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

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

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

Mathematical formula?

The general formula for calculating market capitalization:

Market Capitalization = Current Share Price x Number of Outstanding Shares

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

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

The Significance of Stock Price

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

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

How is the Number of Shares Computed?

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

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

Which Shares are Included?

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

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

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

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

Why should I be interested in this post?

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

Useful resources

Fidelity Investments Market capitalization

Wikipedia Market capitalization

Motley Fool An Example of Market Capitalization

About the author

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

My experience as a trading floor intern at CIC Market Solutions

June 22, 2023 by Tanguy TONEL

My experience as a trading floor intern at CIC Market Solutions

In this article, Tanguy TONEL (ESSEC Business School, Global BBA, 2019-2023) shares his professional experience as an intern at the Bordeaux trading floor of CIC.

About CIC Market Solutions

Logo of the CIC Market Solutions.
Logo of CIC Market Solutions
Source: CIC Market Solutions

My internship

I joined the trading floor of CIC Sud-Ouest (the South-West branch of CIC) which is divided in two desks (FICC – Fixed Income, Currencies and Commodities, and asset management) to provide personalized advice to local corporate clients for their investments and risk management. There, I assisted sales and asset managers in their daily duties.

My missions

As an intern, my tasks were very diverse as I have been assisting both FICC and asset management desks. In a day, I would operate the trades reconciliation, monitor the limit orders execution for the sales traders, research and analyze data for the asset managers in preparation of client meetings and do reporting to track the performance of investments. Finally, I helped with management control and middle office tasks such as new clients’ registration.

Required skills and knowledge

While some technical skills such as Excel/VBA are welcomed, the most important skill to have is curiosity. Indeed, as financial markets are constantly evolving it is important to look for anything that can help explain any change, whether in the products’ performances, in the regulatory environment or in clients’ demand to react proactively.

What I learned

During the internship, I learned about the financial solutions provided by a trading floor. On the FICC desk, I was exposed to derivatives and other complex products. On the asset management desk, I discovered the world of EMTNs (Euro Medium Term Notes) which are structured products.

Overall, the internship allowed me to get a broader understanding of the financial markets as I could see the impacts of the markets and the broader economy on clients’ needs, and the impact of client’s needs on the type of products offered by the bank.

Financial concepts related my internship

EMTNs

Euro Medium Term Notes (EMTNs) are a type of debt security that is issued by large corporations, financial institutions, and sovereign governments to raise funds for financing purposes (so the bank can loan money). EMTNs are similar to traditional bonds in that they pay a fixed or floating rate of interest and have a maturity date. One of the key advantages of EMTNs is their flexibility. They can indeed be tailored to meet the specific needs of investors. In practice, the structurers can work on guaranteeing the capital, on the yield… They usually obey rules (such as “The EMTN pays 7% per year for 3 years, then the spread between a rate and another. When the EMTN has paid 22% or at the end of the seventh year, the product ends, and the investor gets his or her capital back.”).

Derivatives

Financial derivatives are financial instruments used to manage risk. They derive their value from an underlying asset or group of assets. Derivatives can be sold for a wide range of assets such as interest rates, currencies and commodities, which are traded by the FICC desk.

There are several types of financial derivatives. The best-known include futures contracts, options contracts, swaps, and forwards.

Futures contracts are agreements to buy or sell an asset at a predetermined price and date in the future.
Options contracts give the holder the right, but not the obligation, to buy or sell an asset at a predetermined price and date in the future.
Swaps are agreements to exchange cash flows based on different financial instruments, such as interest rates or currencies.
Forwards are similar to futures contracts, but they are customized agreements between two parties rather than standardized contracts traded on an exchange.

Structured products

Structured products are financial instruments that are created by combining multiple financial assets, such as stocks, bonds, and derivatives, into a single investment product. These products are designed to meet specific investment objectives, such as providing income, capital protection, or exposure to a particular market or asset class.

Structured products are typically created by financial institutions, such as banks or investment firms, and are sold to investors. They can be customized to meet the specific needs of individual investors and can be structured to provide a range of risk and return profiles.

Some common types of structured products include:

Principal-protected notes: These products provide investors with a guaranteed return of their initial investment, while also offering exposure to the performance of an underlying asset or index.
Autocallable notes: These products provide investors with a fixed income stream, while also offering the potential for higher returns if an underlying asset or index meets certain performance criteria.
Reverse convertibles: These products provide investors with a fixed income stream, while also exposing them to the risk of a decline in the value of an underlying asset or index.

Why should I be interested in this post?

The trading floor is the link between the financial markets and the rest of the business world. Understanding the products offered allows one to get a better grasp on both sides of the economy.

Useful resources

Academic resources

Hull J.C. (2021) Options, Futures, and Other Derivatives Pearson, 11^th Edition.

Business resources

CIC Market Solutions

About the author

The article was written in June 2023 by Tanguy TONEL (ESSEC Business School, Global BBA, 2019-2023).

My experience as an Investment Specialist at Amundi Asset Management

June 22, 2023 by Tanguy TONEL

My experience as an Investment Specialist at Amundi Asset Management

In this article, Tanguy TONEL (ESSEC Business School, Global BBA, 2019-2023) shares his professional experience as an investment specialist in the ETF, Smart Beta & Indexing division of Amundi Asset Management.

About Amundi Asset Management

Amundi Asset Management is a leading global asset manager with over €1.7 trillion in assets under management as of December 31, 2022. The company was founded in 2010 as a joint venture between Crédit Agricole and Société Générale and has since grown to become one of the largest asset managers in Europe.

Amundi offers a wide range of investment solutions across all major asset classes, including equities, fixed income, multi-asset, and alternative investments. The company serves a diverse client base, including institutional investors, corporations, and individual investors.

Logo of Amundi.

Source: Amundi

My internship

I joined the Investment Specialist team of the ETF, Smart Beta & Indexing division which works as a facilitator for the asset management and the sales teams. The team answers clients on the most technical questions and their due diligence inquiries, applies to calls for tenders, monitors the market and does the reporting of the funds.

My missions

During my internship, I shadowed the team, helping them on a broad variety of their tasks.
Among those, I worked on the reporting of the funds, researching data to answer clients’ questions and on drafting sales offers for calls for bids. Additionally, I documented the tools used by the team in their daily activity which allowed me to get involved in nearly all the team’s duties.

Required skills and knowledge

While some technical skills such as Excel/VBA are welcomed, the most important skill to have is curiosity. Indeed, as financial markets are constantly evolving it is important to look for anything that can help explain any change, whether in fund performance, in the regulatory environment or in clients’ demand to react proactively. The ability to adapt is crucial, tools change.

What I learned

During the internship, I have been able to learn a lot about passive management. Indeed, the funds offered by Amundi are very diverse and allowed me to discover the concept of Smart Beta, how indices are built and replicated by asset managers, how ESG rules are incorporated into funds…

Financial concepts related my internship

Passive asset management

Passive asset management is an investment strategy that seeks to replicate the performance of a market index or benchmark. It involves investing in a diversified portfolio of securities that closely mirrors the composition of a particular index.

Usually replicated by index funds or ETFs, the indices follow different kind of rules in their composition while the asset managers work to replicate them without getting involved in the composition.

Physical and Synthetic ETFs

There are two main ways that an ETF can replicate an index: physically and synthetically.

A physically replicated ETF holds all or a representative sample of the securities in the index it tracks. For example, if an ETF tracks the S&P 500 index, it will hold all 500 stocks in the index or a representative sample of those stocks. The ETF’s performance would then closely track the performance of the index.

A synthetically replicated ETF, on the other hand, does not hold the underlying securities in the index. Instead, it uses derivatives, such as swaps, to replicate the index performance. The ETF enters into an agreement with a counterparty, such as a bank, to receive the returns of the index in exchange for paying the counterparty a fee. The counterparty holds the underlying securities and takes on the risk of holding them.

Physical replication tends to be more straightforward and transparent, as investors can see exactly what securities the ETF holds. However, it can also be more expensive, as the ETF incurs costs associated with buying and selling the underlying securities.

Synthetic replication can be cheaper, as the ETF does not need to buy and sell the underlying securities. However, it also introduces counterparty risk, as the ETF is reliant on the counterparty to fulfill its obligations. Additionally, synthetic ETFs may be less transparent, as investors may not know exactly what securities the counterparty is holding.

Smart Beta

Smart Beta is a strategy used in asset management that seeks to outperform traditional market-cap weighted indices by selecting stocks based on factors other than their market capitalization. These factors can include value, momentum, quality, and low volatility, among others.

Using Smart Beta, investors will seek to lower the variance of their portfolio, reducing risk or try to improve returns.

Indeed, one of the flaws of passive funds such as ETFs is that by following the indices, they might bear unrewarded risk or miss rewarded risk. This is due to the fact that for market-cap weighted funds, when a company’s market cap rises as a share of the index, it will also rise as a share of the fund, even if it yields less returns to the holder than another stock.

This has lately been seen with tech companies that grew exponentially as money flowed into those funds.

Why should I be interested in this post?

As passive management is taking a larger share of the asset management industry, understanding this growing trend can provide a valuable edge whether to work inside it or deal with it. Nonetheless, the concepts detailed in this article can also be useful for personal finance decisions.

Useful resources

Amundi ETF, Gestion indicielle et Smart Beta

Amundi ETF

About the author

The article was written in June 2023 by Tanguy TONEL (ESSEC Business School, Global BBA, 2019-2023).

Can technical analysis actually help to make better trading decisions?

June 14, 2023 by Theo SCHWERTLE

Can technical analysis actually help to make better trading decisions?

In this article, Theo SCHWERTLE (Maastricht University, School of Business and Economics, Bachelor in International Business, 2023) explains how technical analysis can actually help to make better trading decisions (or not).

Market efficiency

Let’s take a look at the different levels of market efficiency and their implications for a trader.

The efficient market hypothesis (EMH) posits that market prices fully incorporate all available information. If this hypothesis is verified, it is infeasible to consistently achieve higher returns than the market on a risk-adjusted basis. According to the EMH, stocks are believed to consistently trade at their fair value on exchanges, precluding the possibility of purchasing undervalued stocks or selling overvalued ones, thus implicitly dismissing the efficiency of technical analysis (TA) and fundamental analysis. As such, the EMH suggests that outperforming the overall market through security selection or market timing is infeasible, and the only way for investors to attain higher returns is by taking on increased risk in their investments.

Definitions

The EMH has three forms: the weak form, the semi-strong form and the strong form. The weak form of the EMH asserts that historical market data (transaction prices and volumes) cannot be used to predict future price movements. The semi-strong form of the EMH asserts that publicly available information (historical market data, financial account published by firms, reports written by financial analysts, etc.) cannot be used to predict future price movements. The strong form of the EMH asserts that both public and private information cannot be used to predict future movements.

Tests of the EMH

Though the strong form of the EMH is generally rejected, scholars are less consistent with evidence for or against the weak or semi-strong form of the EMH. Focusing on technical analysis, a significant body of literature has examined the relationship between EMH and technical analysis (TA), with many scholars rejecting the weak form (Leigh et al., 2002; Eugster and Uhl, 2022). The results of the tests seem to depend on the length of the investment period, the EMH being less rejected for a longer investment period.

Technical analysis

In the world of finance, Technical Analysis serves as an essential tool for investors and traders alike. The methodology involves forecasting future price movements based on the historical data of financial instruments. This strategy pivots on two core principles: the market discounts everything, and prices move in trends (Kirkpatrick & Dahlquist, 2010).

Chartism is one of the oldest techniques in technical analysis. It rests on the identification and analysis of chart patterns and price formations, with chartists meticulously studying these patterns to anticipate future market trends (Lo, Mamaysky, & Wang, 2000). This form of analysis operates on the principle that certain patterns are recurring and that understanding these patterns can provide insights into future price movements.

Another time-tested tool is Moving Averages, a technique that seeks to smooth out price data by creating a consistently updated average price. This approach comes in several variants, with the Simple Moving Average (SMA) and the Exponential Moving Average (EMA) being the most prevalent. These techniques help to clear out the ‘noise’ from random short-term price fluctuations and allow analysts to focus on the overall trend direction.

In stark contrast to these conventional methods stands the modern, technology-driven approach of High Frequency Trading (HFT). This innovative form of trading capitalizes on the power of advanced algorithms and high-speed data processing to execute trades at astonishing speeds. Unlike traditional technical analysis, which primarily focuses on transaction prices and volumes, HFT leverages real-time data from the order-flow and the order-book, exploring minute market discrepancies that might otherwise go unnoticed (Aldridge, 2010).

All we need is short-term market inefficiencies

Hirshleifer and Shumway (2003) gave meaningful insight into the relationship between the weather and daily market index return, demonstrating that sunshine is strongly and significantly correlated with stock returns. In line with that argumentation, Edmans et al. (2007) investigate the stock market reaction to sudden changes in investor mood, using international soccer results as the primary mood variable. The results show a significant market decline after soccer losses in equity markets of the losing teams, with a loss in the World Cup elimination stage leading to a next-day abnormal stock return of −49 basis points. This effect is more substantial in small stocks and more meaningful games and is robust to methodological changes. The same loss effect could also be documented for other international tournaments.

So what does that mean? There are human biases that make humans so different from the rational being many financial theories suggest we are.

Discussion about the feasibility of technical analysis for hedge funds

Hedge funds are also using technical analysis in their decision-making process; however, the degree of utilization varies significantly. The main area where TA is used by hedge funds is to find areas of liquidity to full big positions.

Kavajecz und Odders-White (2004) explored the relationship between TA and liquidity by testing the hypotheses that support and resistance levels coincide with peaks in depth on the limit order book and that moving-average forecasts reveal information about the relative position of depth on the book. They found that technical support/resistance levels, as well as moving average indicators, are significantly related to the state of liquidity on the limit order book and concluded that it is tied to the strategic behavior of limit order traders. This provides a reliable method for practitioners to locate liquidity in the book and reduce transaction costs.

The main advantage of TA is the low cost to construct a market perspective as it requires only market data. The implementation of TA is lower than acquiring and analyzing public or private information. So, if used adequately it is in face the cheaper and more accessible investment approach compared to traditional financial analysis tools.

Sounds good! Where is the catch?

According to Timmermann and Granger (2004), using new financial prediction methods may lead to short-term gains as the information is rapidly incorporated into market prices making the market the more efficient. As these new financial prediction methods become more widely used by other market participants, their effectiveness decreases over time. This idea is supported by studies showing that many stock market anomalies diminish, vanish, or even reverse after they are documented in academic literature (publication on the Social Science Research Network (SSRN) for example).

A broad study by Yamamoto (2012) investigated the profitability of exploiting short-term market inefficiencies and concluded that one could not generate consistent positive results that outperform a buy-and-hold strategy. Yamamoto (2012) analyzes technical strategies for 207 individual stocks in the Nikkei 225 over a one-year period and use two statistical procedures to reduce data-snooping bias (the data-snooping bias refers to the tendency to make false discoveries or draw incorrect conclusions when repeatedly testing and analyzing a dataset, often due to the increased likelihood of finding seemingly significant patterns or relationships by chance). The results indicate that all 9 technical trading strategies underperform the buy-and-hold strategy, suggesting that information on past prices and demand/supply imbalances are not sufficient for superior technical trading profits.

Conclusion

Short-term market inefficiencies can be exploited to generate positive returns. However, many of the found profitability diminish after introducing real market conditions, transaction fees or adjusting the returns for the increased risk. Generally, TA offers increased benefits over fundamental analysis in the short-term but loses ground with increased time as the market returns to efficiency. The difference in information costs motivates its popularity, but even if a profitable trading strategy is found, its benefits may only be enjoyed for a short time.

Why should I be interested in this post?

Technical analysis offers a different perspective on the market that is rarely touched on by university curriculums. This alternative approach is used by individual traders as well as institutional traders like hedge funds to find good entries and exits in the market. According to a survey by Menkhoff (2010), 77% of all hedge fund managers in their sample rate TA as really important to their decision-making, attributing a value of at least 10% to it in their decision-making process. About 20% of fund managers even indicate to prefer TA over fundamental analysis. So, it seems to offer some value, despite the academic criticism in line the efficiency of the market.

Useful resources

Academic articles

Edmans, A., García, D. & Norli, Y. (2007). Sports Sentiment and Stock Returns The Journal of Finance 62(4), 1967–1998.

Eugster, P. & Uhl, M. W. (2022). Technical analysis: Novel insights on contrarian trading. European Financial Management .

Fama, E. F. (1970). Efficient capital markets: A review of theory and empirical work. The Journal of Finance 25(2), 383-417.

Hirshleifer, D. & Shumway, T. (2003). Good Day Sunshine: Stock Returns and the Weather The Journal of Finance 58(3), 1009–1032.

Kavajecz, K. A. & Odders-White, E. R. (2004). Technical Analysis and Liquidity Provision Review of Financial Studies 17(4), 1043–1071.

Leigh, W., Purvis, R. & Ragusa, J. M. (2002). Forecasting the NYSE composite index with technical analysis, pattern recogniser, neural network, and genetic algorithm: a case study in romantic decision support Decision Support Systems 32(4), 361–377.

Lo, A. W., Mamaysky, H., & Wang, J. (2000). Foundations of technical analysis: Computational algorithms, statistical inference, and empirical implementation. The Journal of Finance 55(4), 1705-1770.

Menkhoff, L. (2010). The use of technical analysis by fund managers: International evidence. Journal of Banking & Finance 34(11), 2573–2586.

Timmermann, A. & Granger, C. W. (2004). Efficient market hypothesis and forecasting International Journal of Forecasting, 20(1), 15–27.

Yamamoto, R. (2012). Intraday technical analysis of individual stocks on the Tokyo Stock Exchange Journal of Banking & Finance, 36(11), 3033–3047.

Books

Aldridge, I. (2010). High-frequency trading: a practical guide to algorithmic strategies and trading systems. John Wiley & Sons.

Kirkpatrick II, C. D., & Dahlquist, J. R. (2010). Technical Analysis: The Complete Resource for Financial Market Technicians. FT press.

Lewis, M. (2014). Flash Boys: A Wall Street Revolt. W. W. Norton & Company.

About the author

The article was written in June 2023 by Theo SCHWERTLE (Maastricht University, School of Business and Economics, Bachelor in International Business, 2018-2023).

The KOSPI 50 index

June 6, 2023 by Nithisha CHALLA

The KOSPI 50 index

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

The KOSPI 50 index

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

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

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

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

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

Table 1. Top 10 stocks in the KOSPI 50 index.

Source: computation by the author (data: Yahoo! Finance website).

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

Table 2. Sector representation in the KOSPI 50 index.

Source: computation by the author (data: Yahoo! Finance website).

Calculation of the KOSPI 50 index value

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

The formula to compute the KOSPI 50 index is given by

Float Adjusted Market Capitalization Index value

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

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

Float Adjusted Market Capitalization Weighted Index Weight

Use of the KOSPI 50 index in asset management

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

Benchmark for equity funds

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

Financial products around the KOSPI 50 index

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

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

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

Historical data for the KOSPI 50 index

How to get the data?

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

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

Source: Yahoo! Finance.

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

R program

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

Data file

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

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

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

Evolution of the KOSPI 50 index

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

Figure 1. Evolution of the KOSPI 50 index.

Source: computation by the author (data: Yahoo! Finance website).

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

Figure 2. Evolution of the KOSPI 50 index returns.

Source: computation by the author (data: Yahoo! Finance website).

Summary statistics for the KOSPI 50 index

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

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

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

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

Table 4. Summary statistics for the KOSPI 50 index.

Source: computation by the author (data: Yahoo! Finance website).

Statistical distribution of the KOSPI 50 index returns

Historical distribution

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

Figure 3. Historical distribution of the KOSPI 50 index returns.

Source: computation by the author (data: Yahoo! Finance website).

Gaussian distribution

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

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

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

Risk measures of the KOSPI 50 index returns

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

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

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

Table 5. Risk measures for the KOSPI 50 index.

Source: computation by the author (data: Yahoo! Finance website).

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

Why should I be interested in this post?

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

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

Useful resources

Academic research about risk

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

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

Business

Wikipedia What is the KOSPI 50 index

PWC A guide to listing on the Korean exchange

Data

Yahoo! Finance

Yahoo! Finance Historical data for the KOSPI 50 index

About the author

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

The OMX Copenhagen 25 (OMXC 25) index

June 6, 2023 by Nithisha CHALLA

The OMX Copenhagen 25 (OMXC 25) index

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

The OMX Copenhagen 25 index

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

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

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

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

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

Table 1. Top 10 stocks in the OMXC 25 index.

Source: computation by the author (data: Yahoo! Finance website).

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

Table 2. Sector representation in the OMXC 25 index.

Source: computation by the author (data: Yahoo! Finance website).

Calculation of the OMXC 25 index value

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

The formula to compute the OMXC 25 index is given by

Float Adjusted Market Capitalization Index value

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

Float Adjusted Market Capitalization Weighted Index Weight

Use of the OMXC 25 index in asset management

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

Benchmark for equity funds

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

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

Financial products around the OMXC 25 index

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

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

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

Historical data for the OMXC 25 index

How to get the data?

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

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

Source: Yahoo! Finance.

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

R program

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

Data file

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

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

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

Evolution of the OMXC 25 index

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

Figure 1. Evolution of the OMXC 25 index.

Source: computation by the author (data: Yahoo! Finance website).

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

Figure 2. Evolution of the OMXC 25 index returns.

Source: computation by the author (data: Yahoo! Finance website).

Summary statistics for the OMXC 25 index

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

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

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

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

Table 4. Summary statistics for the OMXC 25 index.

Source: computation by the author (data: Yahoo! Finance website).

Statistical distribution of the OMXC 25 index returns

Historical distribution

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

Figure 3. Historical distribution of the OMXC 25 index returns.

Source: computation by the author (data: Yahoo! Finance website).

Gaussian distribution

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

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

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

Risk measures of the OMXC 25 index returns

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

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

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

Table 5. Risk measures for the OMXC 25 index.

Source: computation by the author (data: Yahoo! Finance website).

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

Why should I be interested in this post?

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

Useful resources

Academic research about risk

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

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

About the OMXC 25 index

Nasdaq Index Description

Capital.com What is the OMXC20 index?

Data

Yahoo! Finance

Yahoo! Finance Data for the OMXC 25 index

About the author

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

The BEL 20 index

June 6, 2023 by Nithisha CHALLA

The BEL 20 index

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

The BEL 20 index

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

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

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

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

Table 1. Top 10 stocks in the BEL 20 index.

Source: computation by the author (data: Yahoo! Finance website).

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

Table 2. Sector representation in the BEL 20 index.

Source: computation by the author (data: Yahoo! Finance website).

Calculation of the BEL 20 index value

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

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

The formula to compute the BEL 20 index is given by

Float Adjusted Market Capitalization Index value

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

Float Adjusted Market Capitalization Weighted Index Weight

Use of the BEL 20 index in asset management

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

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

Benchmark for equity funds

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

Financial products around the BEL 20 index

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

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

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

Historical data for the BEL 20 index

How to get the data?

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

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

Source: Yahoo! Finance.

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

R program

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

Data file

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

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

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

Evolution of the BEL 20 index

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

Figure 1. Evolution of the BEL 20 index.

Source: computation by the author (data: Yahoo! Finance website).

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

Figure 2. Evolution of the BEL 20 index returns.

Source: computation by the author (data: Yahoo! Finance website).

Summary statistics for the BEL 20 index

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

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

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

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

Table 4. Summary statistics for the BEL 20 index.

Source: computation by the author (data: Yahoo! Finance website).

Statistical distribution of the BEL 20 index returns

Historical distribution

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

Figure 3. Historical distribution of the BEL 20 index returns.

Source: computation by the author (data: Yahoo! Finance website).

Gaussian distribution

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

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

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

Risk measures of the BEL 20 index returns

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

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

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

Table 5. Risk measures for the BEL 20 index.

Source: computation by the author (data: Yahoo! Finance website).

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

Why should I be interested in this post?

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

Useful resources

Academic research about risk

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

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

About the BEL 20 index

Wikipedia What is the BEL 20 index

Currency BEL 20 index explained

Trading economics About Belgium Stock Market Index BEL20

Data

Yahoo! Finance

Yahoo! Finance Data for the BEL 20 index

About the author

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

The IBEX 35 index

June 6, 2023 by Nithisha CHALLA

The IBEX 35 index

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

The IBEX 35 index

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

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

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

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

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

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

Table 1. Top 10 stocks in the IBEX 35 index.

Source: computation by the author (data: Yahoo! Finance financial website).

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

Table 2. Sector representation in the IBEX 35 index.

Source: computation by the author (data: Yahoo! Finance website).

Calculation of the IBEX 35 index value

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

The formula to compute the IBEX 35 index is given by

Float Adjusted Market Capitalization Index value

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

Float Adjusted Market Capitalization Weighted Index Weight

Use of the IBEX 35 index in asset management

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

Benchmark for equity funds

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

Financial products around the IBEX 35 index

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

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

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

Historical data for the IBEX 35 index

How to get the data?

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

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

Source: Yahoo! Finance.

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

R program

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

Data file

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

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

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

Evolution of the IBEX 35 index

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

Figure 1. Evolution of the IBEX 35 index.

Source: computation by the author (data: Yahoo! Finance website).

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

Figure 2. Evolution of the IBEX 35 index returns.

Source: computation by the author (data: Yahoo! Finance website).

Summary statistics for the IBEX 35 index

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

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

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

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

Table 4. Summary statistics for the IBEX 35 index.

Source: computation by the author (data: Yahoo! Finance website).

Statistical distribution of the IBEX 35 index returns

Historical distribution

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

Figure 3. Historical distribution of the IBEX 35 index returns.

Source: computation by the author (data: Yahoo! Finance website).

Gaussian distribution

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

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

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

Risk measures of the IBEX 35 index returns

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

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

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

Table 5. Risk measures for the IBEX 35 index.

Source: computation by the author (data: Yahoo! Finance website).

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

Why should I be interested in this post?

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

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

Useful resources

About the IBEX 35 index

Wikipedia What is the IBEX 35 index

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

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

Academic research about risk

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

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

Data

Yahoo! Finance

Yahoo! Finance Data for the IBEX 35 index

About the author

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

Extreme returns and tail modelling of the S&P 500 index for the US equity market

The S&P 500 index for the US equity market

Summary statistics for the S&P 500 index

Modelling of the tails

Applications in risk management

Why should I be interested in this post?

Download R file to model extreme behavior of the index

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Exemples

Variable discrète : résultat du lancer d’un dé à six faces

Variable continue : rendments de l’indice CAC40

Table 1. Statistiques descriptives pour les rendements journalières de l’indice CAC 40.

Fichier R pour cet article

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Monitor the profitability and risk of different insurance portfolios

Calculate and provide rates for group Health Insurance and Life Insurance products

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