Fixed-income arbitrage strategy

January 10, 2023 by Youssef LOURAOUI

Fixed-income arbitrage strategy

In this article, Youssef LOURAOUI (Bayes Business School, MSc. Energy, Trade & Finance, 2021-2022) presents the fixed-income arbitrage strategy which is a well-known strategy used by hedge funds. The objective of the fixed-income arbitrage strategy is to benefit from trends or disequilibrium in the prices of fixed-income securities using systematic and discretionary trading strategies.

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

Introduction

According to Credit Suisse (a financial institution publishing hedge fund indexes), a fixed-income arbitrage strategy can be defined as follows: “Fixed-income arbitrage funds attempt to generate profits by exploiting inefficiencies and price anomalies between related fixed-income securities. Funds limit volatility by hedging out exposure to the market and interest rate risk. Strategies include leveraging long and short positions in similar fixed-income securities that are related either mathematically or economically. The sector includes credit yield curve relative value trading involving interest rate swaps, government securities and futures, volatility trading involving options, and mortgage-backed securities arbitrage (the mortgage-backed market is primarily US-based and over-the-counter)”.

Types of arbitrage

Fixed-income arbitrage makes money based on two main underlying concepts:

Pure arbitrage

Identical instruments should have identical price (this is the law of one price). This could be the case, for instance, of two futures contracts traded on two different exchanges. This mispricing could be used by going long the undervalued contract and short the overvalued contract. This strategy uses to work in the days before the rise of electronic trading. Now, pure arbitrage is much less obvious as information is accessible instantly and algorithmic trading wipe out this kind of market anomalies.

Relative value arbitrage

Similar instruments should have a similar price. The fundamental rationale of this type of arbitrage is the notion of reversion to the long-term mean (or normal relative valuations).

Factors that influence fixed-income arbitrage strategies

We list below the sources of market inefficiencies that fixed-income arbitrage funds can exploit.

Market segmentation

Segmentation is of concern for fixed-income arbitrageurs. In financial institutions, the fixed-income desk is split into different traders looking at specific parts of the yield curve. In this instance, some will focus on very short, dated bonds, others while concentrate in the middle part of the yield curve (2-5y) while other while be looking at the long-end of the yield curve (10-30y).

Regulation

Regulation has an implication in the kind of fixed-income securities a fund can hold in their books. Some legislations regulate actively to have specific exposure to high yield securities (junk bonds) since their probability of default is much more important. The diminished popularity linked to the tight regulation can make the valuation of those bonds more attractive than owning investment grade bonds.

Liquidity

Liquidity is also an important concern for this type of strategy. The more liquid the market, the easier it is to trade and execute the strategy (vice versa).

Volatility

Large market movements in the market can have implications to the profitability of this kind of strategy.

Instrument complexity

Instrument complexity can also be a reason to have fixed-income securities. The events of 2008 are a clear example of how banks and regulators didn’t manage to price correctly the complex instruments sold in the market which were highly risky.

Application of a fixed-income arbitrage

Fixed-income arbitrage strategy makes money by focusing on the liquidity and volatility factors generating risk premia. The strategy can potentially generate returns in both rising and falling markets. However, understanding the yield curve structure of interest rates and detecting the relative valuation differential between fixed-income securities is the key concern since this is what makes this strategy profitable (or not!).

We present below a case study related tot eh behavior of the yield curves in the European fixed-income markets inn the mid 1990’s

The European yield curve differential during in the mid 1990’s

The case showed in this example is the relative-value trade between Germany and Italian yields during the period before the adoption of the Euro as a common currency (at the end of the 1990s). The yield curve should reflect the future path of interest rates. The Maastricht treaty (signed on 7th February 1992) obliged most EU member states to adopt the Euro if certain monetary and budgetary conditions were met. This would imply that the future path of interest rates for Germany and Italy should converge towards the same values. However, the differential in terms of interest rates at that point was nearly 350 bps from 5-year maturity onwards (3.5% spread) as shown in Figure 1.

Figure 1. German and Italian yield curve in January 1995.

Source: Motson (2022) (Data: Bloomberg).

A fixed-income arbitrageur could have profited by entering in an interest rate swap where the investor receives 5y-5y forward Italian rates and pays 5y-5y German rates. If the Euro is introduced, then the spread between the two yield curves for the 5-10y part should converge to zero. As captured in Figure 2, the rates converged towards the same value in 1998, where the spread between the two rates converged to zero.

Figure 2. Payoff of the fixed-income arbitrage strategy.

Source: Motson (2022) (Data: Bloomberg).

Performance of the fixed-income arbitrage strategy

Overall, the performance of the fixed-income arbitrage between 1994-2020 were smaller on scale, with occasional large drawdowns (Asian crisis 1998, Great Financial Crisis of 2008, Covid-19 pandemic 2020). This strategy is skewed towards small positive returns but with important tail-risk (heavy losses) according to Credit Suisse (2022). To capture the performance of the fixed-income arbitrage strategy, we use the Credit Suisse hedge fund strategy index. To establish a comparison between the performance of the global equity market and the fixed-income arbitrage strategy, we examine the rebased performance of the Credit Suisse index with respect to the MSCI All-World Index.

Over a period from 2002 to 2022, the fixed-income arbitrage strategy index managed to generate an annualized return of 3.81% with an annualized volatility of 5.84%, leading to a Sharpe ratio of 0.129. Over the same period, the Credit Suisse Hedge Fund index Index managed to generate an annualized return of 5.04% with an annualized volatility of 5.64%, leading to a Sharpe ratio of 0.197. The results are in line with the idea of global diversification and decorrelation of returns derived from the global macro strategy from global equity returns. Overall, the Credit Suisse fixed-income arbitrage strategy index performed better than the MSCI All World Index, leading to a higher Sharpe ratio (0.129 vs 0.08).

Figure 3 gives the performance of the fixed-income arbitrage funds (Credit Suisse Fixed-income Arbitrage Index) compared to the hedge funds (Credit Suisse Hedge Fund index) and the world equity funds (MSCI All-World Index) for the period from July 2002 to April 2021.

Figure 3. Performance of the fixed-income arbitrage strategy.
Global macro performance
Source: computation by the author (Data: Bloomberg).

You can find below the Excel spreadsheet that complements the explanations about the fixed-income arbitrage strategy.

Why should I be interested in this post?

The fixed-income arbitrage strategy aims to profit from market dislocations in the fixed-income market. This can be implemented, for instance, by investing in inexpensive fixed-income securities that the fund manager predicts that it will increase in value, while simultaneously shorting overvalued fixed-income securities to mitigate losses. Understanding the profits and risks associated with such a strategy may aid investors in adopting this hedge fund strategy into their portfolio allocation.

Useful resources

Academic research

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

Motson, N. 2022. Hedge fund elective. Bayes (formerly Cass) Business School.

Business Analysis

Credit Suisse Hedge fund strategy

Credit Suisse Hedge fund performance

Credit Suisse Fixed-income arbitrage strategy

Credit Suisse Fixed-income arbitrage performance benchmark

About the author

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

Global macro strategy

January 9, 2023 by Youssef LOURAOUI

In this article, Youssef LOURAOUI (Bayes Business School, MSc. Energy, Trade & Finance, 2021-2022) presents the global macro equity strategy, one of the most widely known strategies in the hedge fund industry. The goal of the global macro strategy is to look for trends or disequilibrium in equity, bonds, currency or alternative assets based on broad economic data using a top-down approach.

This article is structured as follow: we introduce the global macro strategy principle. Then, we present a famous case study to grasp the overall methodology of this strategy. We conclude with a performance analysis of this strategy in comparison with a global benchmark (MSCI All World Index and the Credit Suisse Hedge Fund index).

Introduction

According to Credit Suisse, a global macro strategy can be defined as follows: “Global Macro funds focus on identifying extreme price valuations and leverage is often applied on the anticipated price movements in equity, currency, interest rate and commodity markets. Managers typically employ a top-down global approach to concentrate on forecasting how political trends and global macroeconomic events affect the valuation of financial instruments. Profits are made by correctly anticipating price movements in global markets and having the flexibility to use a broad investment mandate, with the ability to hold positions in practically any market with any instrument. These approaches may be systematic trend following models, or discretionary.”

This strategy can generate returns in both rising and falling markets. However, asset screening is of key concern, and the ability of the fund manager to capture the global macro picture that is driving all asset classes is what makes this strategy profitable (or not!).

The greatest trade in history

The greatest trade in history (before Michael Burry becomes famous for anticipating the Global financial crisis of 2008 linked to the US housing market) took place during the 1990’s when the UK was intending to join the Exchange Rate Mechanism (ERM) founded in 1979. This foreign exchange (FX) system involved eight countries with the intention to move towards a single currency (the Euro). The currencies of the countries involved would be adjustably pegged with a determined band in which they can fluctuate with respect to the Deutsche Mark (DEM), the currency of Germany considered as the reference of the ERM.

Later in 1992, the pace at which the countries adhering to the ERM mechanism were evolving at different rate of growth. The German government was in an intensive spending following the reunification of Berlin, with important stimulus from the German Central Bank to print more money. However, the German government was very keen on controlling inflation to satisfactory level, which was achieved by increasing interest rates in order to curb the inflationary pressure in the German economy.

In the United Kingdom (UK), another macroeconomic picture was taking place: there was a high unemployment coupled with already relatively high interest rates compared to other European economies. The Bank of England was put in a very tight spot because they were facing two main market scenarios:

To increase interest rates, which would worsen the economy and drive the UK into a recession
To devalue the British Pound (GBP) by defending actively in the FX market, which would cause the UK to leave the ERM mechanism.

The Bank of England decided to go with the second option by defending the British Pound in the FX market by actively buying pounds. However, this strategy would not be sustainable over time. Soros (and other investors) had seen this disequilibrium and shorted British Pound and bought Deutsche Mark. The situation got completely off control for the Bank of England that in September 1992, they decided to increase interest rates, which were already at 10% to more than 15% to calm the selling pressure. Eventually, the following day, the Bank of England announced the exit of the UK from the ERM mechanism and put a hold on the increase of interest rate to the 12% until the economic conditions get better. Figure 1 gives the evolution of the exchange rate between the British Pound (GBP) and the Deutsche Mark (DEM) over the period 1991-1992.

Figure 1. Evolution of the GBP-DEM (British Pound / Deutsche Mark FX rate).
Global macro performance
Source: Bloomberg.

It was reported that Soros amassed a position of $10 billion and gained a whopping $1 billion for this trade. This event put Soros in the scene as the “man who broke the Bank of England”. The good note about this market event is that the UK economy emerged much healthier than the European countries, with UK exports becoming much more competitive as a result of the pound devaluation, which led the Bank of England to cut rates cut down to the 5-6% level the years following the event, which ultimately helped the UK economy to get better.

Performance of the global macro strategy

Overall, the performance of the global macro funds between 1994-2020 was steady, with occasional large drawdowns (Asian crisis 1998, Dot-com bubble 2000’s, Great Financial Crisis of 2008, Covid-19 pandemic 2020). On a side note, the returns seem smaller and less volatile since 2000 onwards (Credit Suisse, 2022).

To capture the performance of the global macro strategy, we use the Credit Suisse hedge fund strategy index. To establish a comparison between the performance of the global equity market and the global macro hedge fund strategy, we examine the rebased performance of the Credit Suisse index with respect to the MSCI All-World Index. Over a period from 2002 to 2022, the global macro strategy index managed to generate an annualized return of 7.85% with an annualized volatility of 5.77%, leading to a Sharpe ratio of 0.33. Over the same period, the MSCI All World Index managed to generate an annualized return of 6.00% with an annualized volatility of 15.71%, leading to a Sharpe ratio of 0.08. The low correlation of the long-short equity strategy with the MSCI All World Index is equal to -0.02, which is close to zero. The results are in line with the idea of global diversification and decorrelation of returns derived from the global macro strategy from global equity returns. Overall, the Credit Suisse hedge fund strategy index performed better worse than the MSCI All World Index, leading to a higher Sharpe ratio (0.33 vs 0.08).

Figure 2 gives the performance of the global macro funds (Credit Suisse Global Macro Index) compared to the hedge funds (Credit Suisse Hedge Fund index) and the world equity funds (MSCI All-World Index) for the period from July 2002 to April 2021.

Figure 2. Performance of the global macro strategy.

Source: computation by the author (data: Bloomberg).

You can find below the Excel spreadsheet that complements the explanations about the global macro hedge fund strategy.

Why should I be interested in this post?

Global macro funds seek to profit from market dislocations across different asset classes. reduce negative risk while increasing market upside. They might, for example, invest in inexpensive assets that the fund managers believe will rise in price while simultaneously shorting overvalued assets to cut losses. Other strategies used by global macro funds to lessen market volatility can include leverage and derivatives. Understanding the profits and risks of such a strategy might assist investors in incorporating this hedge fund strategy into their portfolio allocation.

Useful resources

Academic research

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

Business Analysis

Credit Suisse Hedge fund strategy

Credit Suisse Hedge fund performance

Credit Suisse Global macro strategy

Credit Suisse Global macro performance benchmark

About the author

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

Interest rate term structure and yield curve calibration

January 9, 2023 by Youssef LOURAOUI

Interest rate term structure and yield curve calibration

In this article, Youssef LOURAOUI (Bayes Business School,, MSc. Energy, Trade & Finance, 2021-2022) presents the usage of a widely used model for building the yield curve, namely the Nelson-Seigel-Svensson model for interest rate calibration.

This article is structured as follows: we introduce the concept of the yield curve. Next, we present the mathematical foundations of the Nelson-Siegel-Svensson model. Finally, we illustrate the model with practical examples.

Introduction

Fine-tuning the term structure of interest rates is the cornerstone of a well-functioning financial market. For this reason, the testing of various term-structure estimation and forecasting models is an important topic in finance that has received considerable attention for several decades (Lorenčič, 2016).

The yield curve is a graphical representation of the term structure of interest rates (i.e. the relationship between the yield and the corresponding maturity of zero-coupon bonds issued by governments). The term structure of interest rates contains information on the yields of zero-coupon bonds of different maturities at a certain date (Lorenčič, 2016). The construction of the term structure is not a simple task due to the scarcity of zero-coupon bonds in the market, which are the basic elements to estimate the term structure. The majority of bonds traded in the market carry coupons (regular paiement of interests). The yields to maturity of coupon bonds with different maturities or coupons are not immediately comparable. Therefore, a method of measuring the term structure of interest rates is needed: zero-coupon interest rates (i.e. yields on bonds that do not pay coupons) should be estimated from the prices of coupon bonds of different maturities using interpolation methods, such as polynomial splines (e.g. cubic splines) and parsimonious functions (e.g. Nelson-Siegel).

As explained in an interesting paper that I read (Lorenčič, 2016), the prediction of the term structure of interest rates is a basic requirement for managing investment portfolios, valuing financial assets and their derivatives, calculating risk measures, valuing capital goods, managing pension funds, formulating economic policy, making decisions about household finances, and managing fixed income assets . The pricing of fixed income securities such as swaps, bonds and mortgage-backed securities depends on the yield curve. When considered together, the yields of non-defaulting government bonds with different characteristics reveal information about forward rates, which are potentially predictive of real economic activity and are therefore of interest to policy makers, market participants and economists. For instance, forward rates are often used in pricing models and can indicate market expectations of future inflation rates and currency appreciation/depreciation rates. Understanding the relationship between interest rates and the maturity of securities is a prerequisite for developing and testing the financial theory of monetary and financial economics. The accurate adjustment of the term structure of interest rates is the backbone of a well-functioning financial market, which is why the refinement of yield curve modelling and forecasting methods is an important topic in finance that has received considerable attention for several decades (Lorenčič, 2016).

The most commonly used models for estimating the zero-coupon curve are the Nelson-Siegel and cubic spline models. For example, the central banks of Belgium, Finland, France, Germany, Italy, Norway, Spain and Switzerland use the Nelson-Siegel model or a type of its improved extension to fit and forecast yield curves (BIS, 2005). The European Central Bank uses the Sonderlind-Svensson model, an extension of the Nelson-Siegel model, to estimate yield curves in the euro area (Coroneo, Nyholm & Vidova-Koleva, 2011).

Mathematical foundation of the Nelson-Siegel-Svensson model

In this article, we will deal with the Nelson-Siegel extended model, also known as the Nelson-Siegel-Svensson model. These models are relatively efficient in capturing the general shapes of the yield curve, which explains why they are widely used by central banks and market practitioners.

Mathematically, the formula of Nelson-Siegel-Svensson is given by:

img_SimTrade_NSS_equation

where

τ = time to maturity of a bond (in years)
β₀ = parameter to capture for the level factor
β₁= parameter to capture the slope factor
β₂ = parameter to capture the curvature factor
β₃ = parameter to capture the magnitude of the second hump
λ₁ and λ₂ = parameters to capture the rate of exponential decay
exp = the mathematical exponential function

The parameters β₀, β₁, β₂, β₃, λ₁ and λ₂ can be calculated with the Excel add-in “Solver” by minimizing the sum of squared residuals between the dirty price (market value, present value) of the bonds and the model price of the bonds. The dirty price is a sum of the clean price, retrieved from Bloomberg, and accrued interest. Financial research propose that the Svensson model should be favored over the Nelson-Siegel model because the yield curve slopes down at the very long end, necessitating the second curvature component of the Svensson model to represent a second hump at longer maturities (Wahlstrøm, Paraschiv, and Schürle, 2022).

Application of the yield curve structure

In financial markets, yield curve structure is of the utmost importance, and it is an essential market indicator for central banks. During my last internship at the Central Bank of Morocco, I worked in the middle office, which is responsible for evaluating risk exposures and profits and losses on the positions taken by the bank on a 27.4 billion euro foreign reserve investment portfolio. Volatility evaluated by the standard deviation, mathematically defined as the deviation of a random variable (asset prices or returns in my example) from its expected value, is one of the primary risk exposure measurements. The standard deviation reveals the degree to which the present return deviates from the expected return. When analyzing the risk of an investment, it is one of the most used indicators employed by investors. Among other important exposures metrics, there is the VaR (Value at Risk) with a 99% confidence level and a 95% confidence level for 1-day and 30-day positions. In other words, the VaR is a metric used to calculate the maximum loss that a portfolio may sustain with a certain degree of confidence and time horizon.

Every day, the Head of the Middle Office arranges a general meeting in which he discusses a global debriefing of the most significant overnight financial news and a debriefing of the middle office desk for “watch out” assets that may present an investment opportunity. Consequently, the team is tasked with adhering to the investment decisions that define the firm, as it neither operates as an investment bank nor as a hedge fund in terms of risk and leverage. As the central bank is tasked with the unique responsibility of safeguarding the national reserve and determining the optimal mix of low-risk assets to invest in, it seeks a good asset strategy (AAA bonds from European countries coupled with American treasury bonds). The investment mechanism is comprised of the segmentation of the entire portfolio into three principal tranches, each with its own features. The first tranche (also known as the security tranche) is determined by calculating the national need for a currency that must be kept safe in order to establish exchange market stability (mostly based on short-term positions in low-risk profile assets) (Liquid and high rated bonds). The second tranche is based on a buy-and-hold strategy and a market approach. The first entails taking a long position on riskier assets than the first tranche until maturity, with no sales during the asset’s lifetime (riskier bonds and gold). The second strategy is based on the purchase and sale of liquid assets with the expectation of better returns.

Participants in the market are accustomed to categorizing the debt of eurozone nations. Germany and the Netherlands, for instance, are regarded as “core” nations, and their debt as safe-haven assets (Figure 1). Due to the stability of their yield spreads, France, Belgium, Austria, Ireland, and Finland are “semi-core” nations (Figure 1). Due to their higher bond yields and more volatile spreads, Spain, Portugal, Italy, and Greece are called “peripheral” (BNP Paribas, 2019) (Figure 2). The 10-year gap represents the difference between a country’s 10-year bond yield and the yield on the German benchmark bond. It is a sign of risk. Therefore, the greater the spread, the greater the risk. Figure 3 represents the yield curve for the Moroccan bond market.

Figure 1. Yield curves for core countries (Germany, Netherlands) and semi-core (France, Austria) of the euro zone.

Source: computation by the author.

Figure 2. Yield curves for peripheral countries of the euro zone
(Spain, Italy, Greece and Portugal).
Yield curves for semi-core countries of the euro zone
Source: computation by the author.

Figure 3. Yield curve for Morocco.

Source: computation by the author.

This example provides a tool comparable to the one utilized by central banks to measure the change in the yield curve. It is an intuitive and simplified model created in an Excel spreadsheet that facilitates comprehension of the investment process. Indeed, it is capable of continuously refreshing the data by importing the most recent quotations (in this case, retrieved from investing.com, a reputable data source).

One observation can be made about the calibration limits of the Nelson-Seigel-Svensson model. In this sense, when the interest rate curve is in negative levels (as in the case of the structure of the Japanese curve), the NSS model does not manage to model negative values, obtaining a result with substantial deviations from spot rates. This can be interpreted as a failure of the NSS calibration approach to model a negative interest rate curve.

In conclusion, the NSS model is considered as one of the most used and preferred models by central banks to obtain the short- and long-term interest rate structure. Nevertheless, this model does not allow to model the structure of the curve for negative interest rates.

Excel file for the calibration model of the yield curve

You can download an Excel file with data to calibrate the yield curve for different countries. This spreadsheet has a special macro to extract the latest data pulled from investing.com website, a reliable source for time-series data.

Why should I be interested in this post?

Predicting the term structure of interest rates is essential for managing investment portfolios, valuing financial assets and their derivatives, calculating risk measures, valuing capital goods, managing pension funds, formulating economic policy, deciding on household finances, and managing fixed income assets. The yield curve affects the pricing of fixed income assets such as swaps, bonds, and mortgage-backed securities. Understanding the yield curve and its utility for the markets can aid in comprehending this parameter’s broader implications for the economy as a whole.

Useful resources

Academic research

Lorenčič, E., 2016. Testing the Performance of Cubic Splines and Nelson-Siegel Model for Estimating the Zero-coupon Yield Curve. NGOE, 62(2), 42-50.

Wahlstrøm, Paraschiv, and Schürle, 2022. A Comparative Analysis of Parsimonious Yield Curve Models with Focus on the Nelson-Siegel, Svensson and Bliss Versions. Springer Link, Computational Economics, 59, 967–1004.

Business Analysis

BNP Paribas (2019) Peripheral Debt Offers Selective Opportunities

About the author

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

Minimum Volatility Portfolio

January 9, 2023 by Youssef LOURAOUI

In this article, Youssef LOURAOUI (Bayes Business School, MSc. Energy, Trade & Finance, 2021-2022) elaborates on the concept of Minimum Volatility Portfolio, which is derived from Modern Portfolio Theory (MPT) and also in practice to build investment funds.

This article is structured as follows: we introduce the concept of Minimum Volatility Portfolio. Next, we present some interesting academic findings, and we finish by presenting a theoretical example to support the explanations given in this article.

Introduction

The minimum volatility portfolio represents a portfolio of assets with the lowest possible risk for an investor and is located on the far-left side of the efficient frontier. Note that the minimum volatility portfolio is also called the minimum variance portfolio or more precisely the global minimum volatility portfolio (to distinguish it from other optimal portfolios obtained for higher risk levels).

Modern Portfolio Theory’s fundamental notion had significant implications for portfolio construction and asset allocation techniques. In the late 1970s, the portfolio management business attempted to capture the market portfolio return. However, as financial research progressed and some substantial contributions were made, new factor characteristics emerged to capture extra performance. The financial literature has long encouraged taking on more risk to earn a higher return. However, this is a common misconception among investors. While extremely volatile stocks can produce spectacular gains, academic research has repeatedly proved that low-volatility companies provide greater risk-adjusted returns over time. This occurrence is known as the “low volatility anomaly,” and it is for this reason that many long-term investors include low volatility factor strategies in their portfolios. This strategy is consistent with Henry Markowitz’s renowned 1952 article, in which he embraces the merits of asset diversification to form a portfolio with the maximum risk-adjusted return.

Academic Literature

Markowitz is widely regarded as a pioneer in financial economics and finance due to the theoretical implications and practical applications of his work in financial markets. Markowitz received the Nobel Prize in 1990 for his contributions to these fields, which he outlined in his 1952 Journal of Finance article titled “Portfolio Selection.” His seminal work paved the way for what is now commonly known as “Modern Portfolio Theory” (MPT).

In 1952, Harry Markowitz created modern portfolio theory with his work. Overall, the risk component of MPT may be evaluated using multiple mathematical formulations and managed through the notion of diversification, which requires building a portfolio of assets that exhibits the lowest level of risk for a given level of expected return (or equivalently a portfolio of assets that exhibits the highest level of expected return for a given level of risk). Such portfolios are called efficient portfolios. In order to construct optimal portfolios, the theory makes a number of fundamental assumptions regarding the asset selection behavior of individuals. These are the assumptions (Markowitz, 1952):

The only two elements that influence an investor’s decision are the expected rate of return and the variance. (In other words, investors use Markowitz’s two-parameter model to make decisions.) .
Investors are risk averse. (That is, when faced with two investments with the same expected return but two different risks, investors will favor the one with the lower risk.)
All investors strive to maximize expected return at a given level of risk.
All investors have the same expectations regarding the expected return, variance, and covariances for all hazardous assets. This assumption is known as the homogenous expectations assumption.
All investors have a one-period investment horizon.

Only in theory does the minimum volatility portfolio (MVP) exist. In practice, the MVP can only be estimated retrospectively (ex post) for a particular sample size and return frequency. This means that several minimum volatility portfolios exist, each with the goal of minimizing and reducing future volatility (ex ante). The majority of minimum volatility portfolios have large average exposures to low volatility and low beta stocks (Robeco, 2010).

Example

To illustrate the concept of the minimum volatility portfolio, we consider an investment universe composed of three assets with the following characteristics (expected return, volatility and correlation):

Asset 1: Expected return of 10% and volatility of 10%
Asset 2: Expected return of 15% and volatility of 20%
Asset 3: Expected return of 22% and volatility of 35%

Correlation between Asset 1 and Asset 2: 0.30
Correlation between Asset 1 and Asset 3: 0.80
Correlation between Asset 2 and Asset 3: 0.50

The first step to achieve the minimum variance portfolio is to construct the portfolio efficient frontier. This curve represents all the portfolios that are optimal in the mean-variance sense. After solving the optimization program, we obtain the weights of the optimal portfolios. Figure 1 plots the efficient frontier obtained from this example. As captured by the plot, we can see that the minimum variance portfolio in this three-asset universe is basically concentrated on one holding (100% on Asset 1). In this instance, an investor who wishes to minimize portfolio risk would allocate 100% on Asset 1 since it has the lowest volatility out of the three assets retained in this analysis. The investor would earn an expected return of 10% for a volatility of 10% annualized (Figure 1).

Figure 1. Minimum Volatility Portfolio (MVP) and the Efficient Frontier.

Source: computation by the author.

Excel file to build the Minimum Volatility Portfolio

You can download below an Excel file in order to build the Minimum Volatility portfolio.

Why should I be interested in this post?

Portfolio management’s objective is to optimize the returns on the entire portfolio, not just on one or two stocks. By monitoring and maintaining your investment portfolio, you can accumulate a sizable capital to fulfil a variety of financial objectives, including retirement planning. This article helps to understand the grounding fundamentals behind portfolio construction and investing.

Useful resources

Academic research

Lintner, John. 1965a. Security Prices, Risk, and Maximal Gains from Diversification. Journal of Finance, 20, 587-616.

Lintner, John. 1965b. The Valuation of Risk Assets and the Selection of Risky Investments in Stock Portfolios and Capital Budgets.Review of Economics and Statistics 47, 13-37.

Markowitz, H., 1952. Portfolio Selection. The Journal of Finance, 7, 77-91.

Sharpe, William F. 1963. A Simplified Model for Portfolio Analysis. Management Science, 19, 425-442.

Sharpe, William F. 1964. Capital Asset Prices: A Theory of Market Equilibrium under Conditions of Risk. Journal of Finance, 19, 425-442.

Business analysis

Robeco, 2010 Ten things you should know about minimum volatility investing.

About the author

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

Moments d’une distribution statistique

April 8, 2024January 7, 2023 by Shengyu ZHENG

Moments d’une distribution statistique

Dans cet article, Shengyu ZHENG (ESSEC Business School, Grande Ecole Program – Master in Management, 2020-2023) présente les quatre premiers moments d’une distribution statistique : la moyenne, la variance, la skewness et la kurtosis.

Variable aléatoire

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

X est une variable aléatoire réelle à condition que l’espace mesurable (E) soit, ou fasse partie de, l’ensemble des nombres réels (ℝ).

Je présente un exemple avec la rentabilité d’un investissement dans l’action Apple. La figure 1 ci-dessous représente la série temporelle de la rentabilité journalière de l’action Apple sur la période allant de novembre 2017 à novembre 2022.

Figure 1. Série temporelle de rentabilités de l’action Apple.
Série de rentabilité
Source : calcul par l’auteur (données : Yahoo Finance).

Figure 2. Histogramme des rentabilités de l’action Apple.
Histogramme de rentabilité
Source : calcul par l’auteur (données : Yahoo Finance).

Moments d’une distribution statistique

Le moment d’ordre r ∈ ℕ est un indicateur de la dispersion de la variable aléatoire X. Le moment ordinaire d’ordre r est défini, s’il existe, par la formule suivante :

m_r = 𝔼 (X^r)

Nous avons aussi le moment centré d’ordre r défini, s’il existe, par la formule suivante :

c_r = 𝔼([X-𝔼(X)]^r)

Moment d’ordre un : la moyenne

Définition

La moyenne ou l’espérance mathématique d’une variable aléatoire est la valeur attendue en moyenne si la même expérience aléatoire est répétée un grand nombre de fois. Elle correspond à une moyenne pondérée par probabilité des valeurs que peut prendre cette variable, et elle est donc connue comme la moyenne théorique ou la vraie moyenne.

Si une variable X prend une infinité de valeurs x₁, x₂,… avec les probabilités p₁, p₂,…, l’espérance de X est définie comme :

Μ = m₁= 𝔼(X) = ∑^∞_i=1p_ix_i

L’espérance existe à condition que cette somme soit absolument convergente.

Estimation statistique

La moyenne empirique est un estimateur de l’espérance. Cet estimateur est sans biais, convergent (selon la loi des grands nombres), et distribué normalement (selon le théorème centrale limite).

A partir d’un échantillon de variables aléatoire réelles indépendantes et identiquement distribuées (X₁,…,X_n), la moyenne empirique est donc :

X̄ = (∑ⁿ_i=1x_i)/n

Pour une loi normale centrée réduite (μ = 0 et σ = 1), la moyenne est égale à zéro.

Moment d’ordre deux : la variance

Définition

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

Var(X) = σ ² = 𝔼[(X-μ)²]

Elle exprime l’espérance du carré de l’écart à la moyenne théorique. Elle est donc toujours positive.

Pour une loi normale centrée réduite (μ = 0 et σ = 1), la variance est égale à un.

Estimation statistique

A partir d’un échantillon (X₁,…,X_n), nous pouvons estimer la variance théorique à l’aide de la variance empirique :

S² = (∑ⁿ_i=1(x_i – X̄)²)/n

Cependant, cet estimateur est biaisé, parce que 𝔼(S²) = (n-1)/(n) σ². Nous avons donc un estimateur non-biaisé Š² = (∑ⁿ_i=1(x_i – X̄)²)/(n-1)

Application en finance

La variance correspond à la volatilité d’un actif financier. Une variance élevée indique une dispersion plus importante, et ce n’est pas favorable du regard des investisseurs rationnels qui présentent de l’aversion au risque. Ce concept est un paramètre clef dans la théorie moderne du portefeuille de Markowitz.

Moment d’ordre trois : la skewness

Définition

La skewness (coefficient d’asymétrie en bon français) est le moment d’ordre trois, défini comme ci-dessous :

γ₁ = 𝔼[((X-μ)/σ)³]

La skewness mesure l’asymétrie de la distribution d’une variable aléatoire. On distingue trois types de distributions selon que la distribution est asymétrique à gauche, symétrique, ou asymétrique à droite. Un coefficient d’asymétrie négatif indique une asymétrie à gauche de la distribution, dont la queue gauche est plus importante que la queue droite. Un coefficient d’asymétrie nul indique une symétrie, les deux queues de la distribution étant aussi importante l’une que l’autre. Enfin, un coefficient d’asymétrie positif indique une asymétrie à droite de la distribution, dont la queue droite est plus importante que la queue gauche.

Pour une loi normale, la skewness est égale à zéro car cette loi est symétrique par rapport à la moyenne.

Moment d’ordre quatre : la kurtosis

Définition

La kurtosis (coefficient d’acuité en bon français) est le moment d’ordre quatre, défini par :

β₂ = 𝔼[((X-μ)/σ)⁴]

Il décrit l’acuité d’une distribution. Un coefficient d’acuité élevé indique que la distribution est plutôt pointue en sa moyenne, et a des queues de distribution plus épaisses (fatter tails en anglais).

Le coefficient d’une loi normale est de 3, autrement dit, une distribution mésokurtique. Au-delà de ce seuil, une distribution est appelée leptokurtique. Les distributions présentes au marché financier sont principalement leptokurtique, impliquant que les valeurs anormales et extrêmes sont plus fréquentes que celles d’une distribution gaussienne. Au contraire, un coefficient d’acuité de moins de 3 indique une distribution platykurtique, dont les queues sont plus légères.

Pour une loi normale, la kurtosis est égale à trois.

Exemple : distribution des rentabilités d’un investissement dans l’action Apple

Nous donnons maintenant un exemple en finance en étudiant la distribution des rentabilités de l’action Apple. Dans les données récupérées de Yahoo! Finance pour la période allant de novembre 2017 à novembre 2022, on se sert de la colonne du cours de clôture pour calculer les rentabilités journalières. Nous utilisons des fonctions Excel afin de calculer les quatre premiers moments de la distribution empirique des rentabilités de l’action Apple comme indiqué dans la table ci-dessous.

Moments de l’action Apple

Pour une distribution normale standard (centrée réduite), la moyenne est de zero, la variance est de 1, le skewness est de zéro, et le kurtosis est de 3. À comparaison avec une distribution normale, la distribution de rentabilité de l’action Apple a une moyenne légèrement positive. Cela signifie qu’à long terme, la rentabilité de l’investissement dans cet actif est positive. Son skewness est négatif, indiquant l’asymétrie vers la gauche (les valeurs négatives). Son kurtosis est supérieur de 3, ce qui indique que les extrémités sont plus épaisses que la distribution normale.

Fichier Excel pour calculer les moments

Vous pouvez télécharger le ficher Excel d’analyse des moments de l’action Apple en suivant le lien ci-dessous :

Autres article sur le blog SimTrade

▶ Shengyu ZHENG Catégories de mesures de risques

▶ Shengyu ZHENG Mesures de risques

Ressources

Articles académiques

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

Données

Yahoo! Finance Données de marché pour l’action Apple

A propos de l’auteur

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

The effect of Elon Musk's Tweets on the Cryptocurrency Market

January 5, 2023 by Ines ILLES MEJIAS

The effect of Elon Musk’s Tweets on the Cryptocurrency Market

In this article, Ines ILLES MEJIAS (ESSEC Business School, Global BBA, 2020-2024) analyzes the effect of Elon Musk’s tweets on the cryptocurrency market and its link with the concept of market efficiency.

Who is Elon Musk?

Founder of SpaceX and Tesla, Elon Musk, is known to be one of the richest and most famous people in the world. He is known to be a “technological visionary”, especially working in companies which focus on innovation and technology. Elon Musk has currently over 120 million followers on Twitter, a social media platform which he is regularly active on to speak about his life, his business or give his opinion on a wide variety of topics, one of them being cryptocurrency. No surprises he likes Twitter so much that he chose to purchase this one for US$ 44 billion not so long time ago in 2022.

Why does Elon Musk have an impact on the crypto market?

The effect of Elon Musk on the crypto market seems to be explained by his tweets due to his persona, as he is also known to be a successful investor and one of the wealthiest people in the world in 2022.

His activity on Twitter seems to affect the prices and volumes of cryptocurrencies on the short-term, by looking at the price changes or volatility following his tweets. This is called the “Elon Musk Effect”. The two most known cryptocurrencies having been influenced by Elon Musk are the Bitcoin and the Dogecoin. Likewise, we know thanks to his tweets and affirmation in conferences that he currently owns three cryptocurrencies: Bitcoin, Ethereum, and Dogecoin.

Examples of the positive impact of Elon Musk’s tweets on the crypto market

Elon Musk’s tweets seem to have an influence in the variation of cryptocurrency prices.

December 2021: “Bitcoin is my safe word”

In December 2021, Elon Musk positively tweeted about the Bitcoin saying that it is his “safe word”. This made the value of Bitcoin increase largely as the graph below shows.

Figure 1. Elon Musk’s tweet effect on Bitcoin
Tweet of Elon Musk 2021
Source: Source: Reuters

January 2022: Elon Musk shows he’s a Bitcoin supporter.

In January 2022, Elon Musk changed his Twitter bio by adding “#bitcoin” which caused the Bitcoin to increase its value by 20%.

Figure 2. Elon Musk’s tweet effect on Bitcoin
Tweet of Elon Musk 2021
Source: Source: Blockchain Research Lab

Figure 3. Elon Musk’s tweet effect on Bitcoin

Source: Source: Blockchain Research Lab

Moreover, the price of Dogecoin raised by more than 500% after he tweeted that it was his favorite cryptocurrency. For this he is also known to be the “Dogefather” or “King of Dogecoin”. He also tweeted that SpaceX will accept Dogecoin payments which again, made the value of one of his cryptocurrencies raise largely.

Figure 4. Elon Musk’s tweet effect on Dogecoin

Source: Source: Blockchain Research Lab

Figure 5. Elon Musk’s tweet effect on Dogecoin

Source: Source: Blockchain Research Lab

Examples of the negative impact of Elon Musk’s tweets on the crypto market

Elon Musk can have a positive but also a negative impact on the crypto market by creating its own up and downs. For instance, after his presence on Saturday Night Live in May 2021, the Dogecoin’s value fell 34%. This was shocking considering that it was predicted by many crypto enthusiasts that it would increase the Dogecoin’s value to US$ 1.

Also, after Musk called Dodgecoin to be a “hustle”, its price went down by more than 30%.

A last example I will add is of when Elon Musk tweeted a meme about breaking up with bitcoin on June 3. This caused the price of Bitcoin to decrease by 5%.

Figure 6. Tweet of Elon Musk on June 4, 2021

Source: Twitter.

Impact of Elon Musk’s tweets on the cryptocurrency market

Figure 7. Impact of Elon Musk’s tweets on the cryptocurrency market

Source: Coinjournal.

Why did it interest me?

This topic really caught my attention as I’ve always been very interested in investing, although never had the courage to do so due to the potential loss of real money. So, when I heard about this virtual currency, I became interested in knowing more about it, and after some research I found out about the news regarding Elon Musk and his effect on these. It was surprising and shocking seeing how an individual can have so much power over something, especially the power of social media.

Link with market efficiency

There are three types of market efficiency: weak efficiency related to market data (prices and transaction volumes), semi-strong efficiency related to all public information (company accounts, analyst reports, etc.) and strong efficiency (all public as well as private information).

Given the market reaction after Elon Musk’s tweets, the market is definitely efficient in the semi-strong sense. By observing the market reaction before Elon Musk’s tweets, we may wonder if the market is also efficient in the strong sense…

Useful resources

Academic articles

Gupta, R.R., Arya, R.K., Kumar, J., Gururani, A., Dugh, R., Dugh, A. (2022). The Impact of Elon Musk Tweets on Bitcoin Price. In: Mandal, J.K., Hsiung, PA., Sankar Dhar, R. (eds) Topical Drifts in Intelligent Computing. ICCTA 2021. Lecture Notes in Networks and Systems, vol 426. Springer, Singapore. https://doi.org/10.1007/978-981-19-0745-6_44

Business resources

Twitter Elon Musk

Bitcoin

DodgeCoin

Blockchain Research Lab

Joe Khalique-Brown (15/06/2021) The Elon Musk Bitcoin saga continues: BTC rallies 10% Coin Journal

Noel Randewich (08/02/2021) Musk’s Bitcoin investment follows months of Twitter talk Reuters.

About the author

The article was written in December 2022 by Ines ILLES MEJIAS (ESSEC Business School, Global BBA, 2020-2024).

Arbitrage Pricing Theory (APT)

April 18, 2025January 2, 2023 by Youssef LOURAOUI

Arbitrage Pricing Theory (APT)

In this article, Youssef LOURAOUI (Bayes Business School, MSc. Energy, Trade & Finance, 2021-2022) presents the concept of arbitrage portfolio, a pillar concept in asset pricing theory.

This article is structured as follows: we present an introduction for the notion of arbitrage portfolio in the context of asset pricing, we present the assumptions and the mathematical foundation of the model and we then illustrate a practical example to complement this post.

Introduction

Arbitrage pricing theory (APT) is a method of explaining asset or portfolio returns that differs from the capital asset pricing model (CAPM). It was created in the 1970s by economist Stephen Ross. Because of its simpler assumptions, arbitrage pricing theory has risen in favor over the years. However, arbitrage pricing theory is far more difficult to apply in practice since it requires a large amount of data and complicated statistical analysis.The following points should be kept in mind when understanding this model:

Arbitrage is the technique of buying and selling the same item at two different prices at the same time for a risk-free profit.
Arbitrage pricing theory (APT) in financial economics assumes that market inefficiencies emerge from time to time but are prevented from occurring by the efforts of arbitrageurs who discover and instantly remove such opportunities as they appear.
APT is formalized through the use of a multi-factor formula that relates the linear relationship between the expected return on an asset and numerous macroeconomic variables.

The concept that mispriced assets can generate short-term, risk-free profit opportunities is inherent in the arbitrage pricing theory. APT varies from the more traditional CAPM in that it employs only one factor. The APT, like the CAPM, assumes that a factor model can accurately characterize the relationship between risk and return.

Assumptions of the APT model

Arbitrage pricing theory, unlike the capital asset pricing model, does not require that investors have efficient portfolios. However, the theory is guided by three underlying assumptions:

Systematic factors explain asset returns.
Diversification allows investors to create a portfolio of assets that eliminates specific risk.
There are no arbitrage opportunities among well-diversified investments. If arbitrage opportunities exist, they will be taken advantage of by investors.

To have a better grasp on the asset pricing theory behind this model, we can recall in the following part the foundation of the CAPM as a complementary explanation for this article.

Capital Asset Pricing Model (CAPM)

William Sharpe, John Lintner, and Jan Mossin separately developed a key capital market theory based on Markowitz’s work: the Capital Asset Pricing Model (CAPM). The CAPM was a huge evolutionary step forward in capital market equilibrium theory, since it enabled investors to appropriately value assets in terms of systematic risk, defined as the market risk which cannot be neutralized by the effect of diversification. In their derivation of the CAPM, Sharpe, Mossin and Litner made significant contributions to the concepts of the Efficient Frontier and Capital Market Line. The seminal contributions of Sharpe, Litner and Mossin would later earn them the Nobel Prize in Economics in 1990.

The CAPM is based on a set of market structure and investor hypotheses:

There are no intermediaries
There are no limits (short selling is possible)
Supply and demand are in balance
There are no transaction costs
An investor’s portfolio value is maximized by maximizing the mean associated with projected returns while reducing risk variance
Investors have simultaneous access to information in order to implement their investment plans
Investors are seen as “rational” and “risk averse”.

Under this framework, the expected return of a given asset is related to its risk measured by the beta and the market risk premium:

CAPM risk beta relation

Where :

E(r_i) represents the expected return of asset i
r_f the risk-free rate
β_i the measure of the risk of asset i
E(r_m) the expected return of the market
E(r_m)- r_f the market risk premium.

In this model, the beta (β) parameter is a key parameter and is defined as:

CAPM beta formula

Where:

Cov(r_i, r_m) represents the covariance of the return of asset i with the return of the market
σ²(r_m) is the variance of the return of the market.

The beta is a measure of how sensitive an asset is to market swings. This risk indicator aids investors in predicting the fluctuations of their asset in relation to the wider market. It compares the volatility of an asset to the systematic risk that exists in the market. The beta is a statistical term that denotes the slope of a line formed by a regression of data points comparing stock returns to market returns. It aids investors in understanding how the asset moves in relation to the market. According to Fama and French (2004), there are two ways to interpret the beta employed in the CAPM:

According to the CAPM formula, beta may be thought in mathematical terms as the slope of the regression between the asset return and the market return. Thus, beta quantifies the asset sensitivity to changes in the market return.
According to the beta formula, it may be understood as the risk that each dollar invested in an asset adds to the market portfolio. This is an economic explanation based on the observation that the market portfolio’s risk (measured by σ²(r_m)) is a weighted average of the covariance risks associated with the assets in the market portfolio, making beta a measure of the covariance risk associated with an asset in comparison to the variance of the market return.

Mathematical foundations

The APT can be described formally by the following equation

APT expected return formula

Where

E(r_p) represents the expected return of portfolio p
r_f the risk-free rate
β_k the sensitivity of the return on portfolio p to the k^th factor (f_k)
λ_k the risk premium for the k^th factor (f_k)
K the number of risk factors

Richard Roll and Stephen Ross found out that the APT can be sensible to the following factors:

Expectations on inflation
Industrial production (GDP)
Risk premiums
Term structure of interest rates

Furthermore, the researchers claim that an asset will have varied sensitivity to the elements indicated above, even if it has the same market factor as described by the CAPM.

Application

For this specific example, we want to understand the asset price behavior of two equity indexes (Nasdaq for the US and Nikkei for Japan) and assess their sensitivity to different macroeconomic factors. We extract a time series for Nasdaq equity index prices, Nikkei equity index prices, USD/CHY FX spot rate and US term structure of interest rate (10y-2y yield spread) from the FRED Economics website, a reliable source for macroeconomic data for the last two decades.

The first factor, which is the USD/CHY (US Dollar/Chinese Renminbi Yuan) exchange rate, is retained as the primary factor to explain portfolio return. Given China’s position as a major economic player and one of the most important markets for the US and Japanese corporations, analyzing the sensitivity of US and Japanese equity returns to changes in the USD/CHY Fx spot rate can help in understanding the market dynamics underlying the US and Japanese equity performance. For instance, Texas Instrument, which operates in the sector of electronics and semiconductors, and Nike both have significant ties to the Chinese market, with an overall exposure representing approximately 55% and 18%, respectively (Barrons, 2022). In the example of Japan, in 2017 the Japanese government invested 117 billion dollars in direct investment in northern China, one of the largest foreign investments in China. Similarly, large Japanese listed businesses get approximately 18% of their international revenues from the Chinese market (The Economist, 2019).

The second factor, which is the 10y-2y yield spread, is linked to the shape of the yield curve. A yield curve that is inverted indicates that long-term interest rates are lower than short-term interest rates. The yield on an inverted yield curve decreases as the maturity date approaches. The inverted yield curve, also known as a negative yield curve, has historically been a reliable indicator of a recession. Analysts frequently condense yield curve signals to the difference between two maturities. According to the paper of Yu et al. (2017), there is a significant link between the effects of varying degrees of yield slope with the performance of US equities between 2006 and 2012. Regardless of market capitalization, the impact of the higher yield slope on stock prices was positive.

The APT applied to this example can be described formally by the following equation:

APT expected return formula example

Where

E(r_p) represents the expected return of portfolio p
r_f the risk-free rate
β_{p, Chinese FX} the sensitivity of the return on portfolio p to the USD/CHY FX spot rate
β_{p, US spread} the sensitivity of the return on portfolio p to the US term structure
λ_{Chinese FX} the risk premium for the FX risk factor
λ_{US spread} the risk premium for the interest rate risk factor

We run a first regression of the Nikkei Japanese equity index returns onto the macroeconomic variables retained in this analysis. We can highlight the following: Both factors are not statistically significant at a 10% significance level, indicating that the factors have poor predictive power in explaining Nikkei 225 returns over the last two decades. The model has a low R2, equivalent to 0.48%, which indicates that only 0.48% of the behavior of Nikkei performance can be attributed to the change in USD/CHY FX spot rate and US term structure of the yield curve (Table 1).

Table 1. Nikkei 225 equity index regression output.
Time-series regression
Source: computation by the author (Data: FRED Economics)

Figure 1 and 2 captures the linear relationship between the USD/CHY FX spot rate and the US term structure with respect to the Nikkei equity index.

Figure 1. Relationship between the USD/CHY FX spot rate with respect to the Nikkei 225 equity index.
Time-series regression
Source: computation by the author (Data: FRED Economics)

Figure 2. Relationship between the US term structure with respect to the Nikkei 225 equity index.
Time-series regression
Source: computation by the author (Data: FRED Economics)

We conduct a second regression of the Nasdaq US equity index returns on the retained macroeconomic variables. We may emphasize the following: Both factors are not statistically significant at a 10% significance level, indicating that they have a limited ability to predict Nasdaq returns during the past two decades. The model has a low R2 of 4.45%, indicating that only 4.45% of the performance of the Nasdaq can be attributable to the change in the USD/CHY FX spot rate and the US term structure of the yield curve (Table 2).

Table 2. Nasdaq equity index regression output.
Time-series regression
Source: computation by the author (Data: FRED Economics)

Figure 3 and 4 captures the linear relationship between the USD/CHY FX spot rate and the US term structure with respect to the Nasdaq equity index.

Figure 3. Relationship between the USD/CHY FX spot rate with respect to the Nasdaq equity index.
Time-series regression
Source: computation by the author (Data: FRED Economics)

Figure 4. Relationship between the US term structure with respect to the Nasdaq equity index.
Time-series regression
Source: computation by the author (Data: FRED Economics)

Applying APT

We can create a portfolio with similar factor sensitivities as the Arbitrage Portfolio by combining the first two index portfolios (with a Nasdaq Index weight of 40% and a Nikkei Index weight of 60%). This is referred to as the Constructed Index Portfolio. The Arbitrage portfolio will have a full weighting on US equity index (100% Nasdaq equity index). The Constructed Index Portfolio has the same systematic factor betas as the Arbitrage Portfolio, but has a higher expected return (Table 3).

Table 3. Index, constructed and Arbitrage portfolio return and sensitivity table. img_SimTrade_portfolio_sensitivity
Source: computation by the author (Data: FRED Economics)

As a result, the Arbitrage portfolio is overvalued. We will then buy shares of the Constructed Index Portfolio and use the profits to sell shares of the Arbitrage Portfolio. Because every investor would sell an overvalued portfolio and purchase an undervalued portfolio, any arbitrage profit would be wiped out.

Excel file for the APT application

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

Why should I be interested in this post?

In the CAPM, the factor is the market factor representing the global uncertainty of the market. In the late 1970s, the portfolio management industry aimed to capture the market portfolio return, but as financial research advanced and certain significant contributions were made, this gave rise to other factor characteristics to capture some additional performance. Analyzing the historical contributions that underpins factor investing is fundamental in order to have a better understanding of the subject.

Useful resources

Academic research

Lintner, J. (1965) The Valuation of Risk Assets and the Selection of Risky Investments in Stock Portfolios and Capital Budgets. The Review of Economics and Statistics 47(1): 13-37.

Lintner, J. (1965) Security Prices, Risk and Maximal Gains from Diversification. The Journal of Finance 20(4): 587-615.

Roll, Richard & Ross, Stephen. (1995). The Arbitrage Pricing Theory Approach to Strategic Portfolio Planning. Financial Analysts Journal 51, 122-131.

Ross, S. (1976) The arbitrage theory of capital asset pricing Journal of Economic Theory 13(3), 341-360.

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

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

Yu, G., P. Fuller, D. Didia (2013) The Impact of Yield Slope on Stock Performance Southwestern Economic Review 40(1): 1-10.

Business Analysis

Barrons (2022) Apple, Nike, and 6 Other Companies With Big Exposure to China.

The Economist (2019) Japan Inc has thrived in China of late.

Time series

FRED Economics (2022) Chinese Yuan Renminbi to U.S. Dollar Spot Exchange Rate (DEXCHUS).

FRED Economics (2022) 10-Year Treasury Constant Maturity Minus 2-Year Treasury Constant Maturity (T10Y2Y).

FRED Economics (2022) NASDAQ Composite Index (NASDAQCOM).

FRED Economics (2022) Nikkei Stock Average, Nikkei 225 (NIKKEI225).

About the author

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

My personal experience in finance via the yachting industry

January 1, 2023 by Evan CHAISSON

My personal experience in finance via the yachting industry

In this article, Evan CHAISSON (ESSEC Business School, Master in Strategy & Management of International Business (SMIB), 2022-2023) shares his professional experience as in intern in the yachting industry.

About the company

During my first six-month internship I worked for SuperYachtsMonaco. As the name suggests, this company is focused on the yachting industry and is located in Monaco. Founded in 2008, this company has a long history of providing clients with consistent service and top-of-the-line yachts throughout the globe.

Logo of the SuperYachtsMonaco.
Logo of SuperYachtsMonaco
Source: SuperYachtsMonaco.

While interning there, I worked for the Charter department. For those who are not familiar, chartering is when the client wishes to rent a yacht and also have a complete catering service accompanying them on their stay. In other words, chartering a yacht is like renting a hotel on a boat with all the personnel that one might need. Typically, clients will charter a yacht for 1-2 weeks and will set sail on a pre-determined itinerary. An average charter experience involves approximately 10 clients on the same yacht.

My internship

As part of the charter department, my primary mission was to prepare the department’s annual brochure. This is the charter catalogue that new clients will consult before contacting SuperYachtsMonaco and entering more detailed negotiations. Therefore, it was of the utmost importance that the brochure present the yachts in an enticing way and leave potential clients with a good impression of the company. In order to achieve this, I had to create the brochure’s theme and properly organize its layout and photo selection. I also had to write copy for each yacht so as to present the vessel’s most appealing aspects while staying concise.

Additionally, I had to prepare travel itinerary presentations based on itineraries desired by clients. Starting with a simple list of places that were to be visited, this task involved looking up these locations, finding places of interest and then writing copy. One last task I had was to help create the company’s monthly newsletter. This involved writing articles on various yachting-related topics.

Required skills and knowledge

The primary skill that I needed was copy writing. Indeed, I spent a considerable amount of time writing text with a specific target client in mind. This meant that I needed to adapt my writing style every time that the audience changed. Another skill that I needed was the ability to multitask. Aside from my main missions that I previously listed, I also had to accomplish a series of smaller tasks that, in the moment, were just as important as the larger ones. Therefore, it quickly became evident that I would need to find a good balance between the two types of tasks, otherwise I would fall behind on some of them.

What I learned

Overall, I learned the importance of soft skills and, above all, the proper way to interact with colleagues and manage their expectations. Indeed, it was easy to get along with all of my colleagues at the office if the relationship focused on topic external to work. However, it became challenging when I had to interact with these same people in the context of work, especially when these same people were giving me tasks to complete. For instance, my internship mentor initially told me to be open with my colleagues and be direct with them when I did not have the time to help them. Yet when I did this same thing, I was later reprimanded. This is when I learned that I had to read between the lines of what I was being said and communicate accordingly without refusing a task being assigned to me.

Financial concepts related my internship

Given the department that I worked in, I had little to no interaction with anything related to finance. What’s more, this is my work experience during which I came the closest to the world of finance. This is why I can only list one financial concept related to my internship, which is a cost-benefit analysis. One of my missions as an intern was to check an international yachting database for yachts that had recently decreased in price and conduct a cost-benefit analysis to evaluate different options for purchasing or maintaining a yacht. For example. To this end, I had to compare the costs and benefits of buying a new yacht versus a used one and weigh the costs of various maintenance or repair options against the potential benefits of purchasing the yacht in good condition. My findings were then directly reported to the company’s CEO.

Why should I be interested in this post?

A student wishing to enter the world of finance after graduating might find my blog post as useful insight. The first reason is because it provides them with an insight into the yachting industry from the perspective of an intern, which is a position they would likely find themselves in. Even if I had scant experience in finance during my internship.

Aside from this aspect, my hope is that this post will make other students curious to learn more about the yachting industry, as there is immense potential for any student wishing to delve into finance. For instance, I can attest from personal experience that the yachting industry is resplendent with high-net-worth individuals. So, it is easier to find opportunities for students to work with clients who have substantial financial assets and require specialized financial services. It is also a global industry that involves clients from around the world, so, say, a French student wishing to open themselves to the rest of the world might find that the yachting industry to be the perfect opportunity to do so.

Useful resources

SuperYachtsMonaco (SYM)

Super Yacht News

About the author

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

A quick review of the Growth Capital…

March 31, 2024December 31, 2022 by Louis DETALLE

A quick review of the Growth Capital…

In this article, Louis DETALLE (ESSEC Business School, Grande Ecole Program – Master in Management, 2020-2023) explains what is Growth Capital and what it consists in.

What does Growth Capital consist in?

Growth capital refers to the funding that a company receives in order to expand its operations, enter new markets, or develop new products and services. This type of financing is typically sought by companies that are already generating revenue and have a proven track record of success but need additional funds in order to take their business to the next level.

What are the main actors a company can resort to when it comes to Growth Capital?

What is interesting with growth capital is that it is all about companies that are halfway between Venture Capital and Private Equity.

For that matter, there are several sources of growth capital, including venture capital firms and private equity firms that invest at different times in the life of the company. Venture capital firms typically invest in early-stage companies that have high growth potential, but may not yet be profitable. Private equity firms, on the other hand, typically invest in more established companies that are looking to expand through acquisitions (see the notion of “build-up”) or other means. A company will choose its investor according to its stage of development, its sector, its objectives and the network of the investors that it will be able to benefit from.

What does an analyst in Growth Equity work on?

The tasks of a Growth Equity analyst are diverse but similar to those of Private Equity & Venture Capital. They include for example, the producing and challenging a business plan, modelling different scenarios and strategies in Excel. The analyst and the investment teams thoroughly analyze the companies seeking for funding and the environments they are trying to grow into. If a company A well anchored in France is willing to conquer a new market European market, the job will consist in assessing the German market and see if the product developed by company A will work efficiently in the next country or if it is more accurate to try and find a similar company that can be bought there!

In other words, an analyst in Growth Equity will try to determine whether the projections of the seeked investment are reasonable, not overestimated and feasible.

What is the life cycle of a company and where does growth capital intervene?

At the beginning, when the startup is only an idea, the founders talk to Business Angels and VC funds that invest very early (called “seed investors”) and therefore small tickets. However, VC can come at the very beginning, as “seed investors”, of later in core venture with “A-B and C series”. These series mean the different funding rounds of the company that is growing.

Later on, companies can resort to growth capital, which aims at entering the capital of a company that has reached a certain maturity and profitability. The funds collected will then be used for internal and external growth: respectively the development of the company’s offers in order to develop its activities or the acquisition of competitors.

For that matter, Growth Capital will be the bridge between Venture Capital and Private Equity. Indeed, companies will finally reach Private Equity funds interest who will keep investing much more money than the previous actors…

After being bought, the most powerful and resilient companies will reach the IPO which can be considered as the ultimate goal. However, as you may have seen, the IPO arrives very late in the life cycle of a company

Source: https://www.dlacalle.com/en/private-equity-and-cheap-money/

Resources

Youtube Video explaining the different cycles of companies: VC/Growth/Private Equity

The top 10 VC actors in France

About the author

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

A quick review of the Private Debt job…

December 31, 2022 by Louis DETALLE

In this article, Louis DETALLE (ESSEC Business School, Grande Ecole Program – Master in Management, 2020-2023) explains what private debt is and what the working days look like when you work in this sector…

What does the private debt job consist in?

Private debt refers to the money borrowed by private companies from investors, rather than from banks or other financial institutions. Private debt jobs typically involve working for a private debt fund or a private equity firm, where the focus is on providing financing to companies that are seeking capital for expansion, acquisitions, or other business purposes.

What are the missions of the private debt analyst?

Private debt professionals are responsible for sourcing and underwriting investment opportunities, structuring and negotiating debt financing deals, and managing portfolio investments. This often involves conducting thorough due diligence on potential borrowers, evaluating their creditworthiness and financial health, and determining the appropriate terms and conditions for the debt financing.

Private debt professionals must have a strong understanding of the various types of debt financing available, including senior debt, mezzanine debt, and subordinated debt, as well as an in-depth knowledge of credit analysis, financial modeling, and risk management. They must also be adept at building and maintaining relationships with borrowers, investors, and other stakeholders in the private debt market.

Who are the main private debt lenders?

The private debt market is highly dynamic and constantly evolving. However, some of the largest private debt funds and private equity firms that focus on providing debt financing to companies include Apollo Global Management, Blackstone, KKR, Bain Capital, and TPG Capital, among others. These firms typically have significant financial resources and expertise in the private debt market and are well-positioned to provide large-scale financing to companies in need of capital. In France, Eurazeo and Tikehau Capital are very famous actors of this sector.

How to become a private debt analyst?

First, it is important to obtain a solid educational foundation in finance, accounting, and economics. This can be achieved through a bachelor’s or master’s degree program in a relevant field, such as finance, business, or economics. Coursework should focus on topics such as financial analysis, corporate finance, investment management, and risk management.

In addition to formal education, it is also important to gain practical experience in the private debt market. This can be achieved through internships or entry-level positions at private debt funds or private equity firms. These opportunities can provide valuable hands-on experience, as well as the chance to network with industry professionals and learn from more experienced colleagues.

Having gathered these two abilities, you should be able to make a strong application to private debt jobs and get started!

What is especially appealing in Private Debt jobs?

Private debt jobs can be highly rewarding, both financially and personally. In addition to competitive salaries, many private debt professionals also have the opportunity to earn substantial performance-based bonuses and other incentives. Furthermore, private debt young professionals often have the opportunity to work on a wide variety of deals and transactions, providing them with a diverse and challenging workload that can be both intellectually stimulating and professionally fulfilling.

Resources

Amundi Private Debt

Youtube A Webinar on Private Debt

About the author

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

A quick review of the Sovereign Advisory job…

December 31, 2022 by Louis DETALLE

A quick review of the Sovereign Advisory job…

In this article, Louis DETALLE (ESSEC Business School, Grande Ecole Program – Master in Management, 2020-2023) explains what a Sovereign Advisor works on, on a daily basis.

What does the Sovereign Advisory job consist in?

Sovereign advisory is a specialized field of finance that involves providing advice and guidance to governments and sovereign entities on a range of financial matters. This includes things like helping governments to develop and implement economic policies, advising on the issuance of sovereign bonds, and assisting with the management of public debt.

The job of a sovereign advisor is to help governments to make informed financial decisions that are in the best interests of the country and its citizens. This can involve providing expert analysis and guidance on a wide range of issues, including economic growth, public spending, and the management of public debt.

What are the missions of the accountant?

The missions of the Sovereign Advisor consist mainly of three tasks.

About a country’s economic policies

One of the key responsibilities of a sovereign advisor is to help governments to develop and implement economic policies that are effective and sustainable. This can involve providing guidance on the design and implementation of fiscal and monetary policies, as well as helping to identify potential risks and opportunities in the global economy.

About issuing sovereign bonds

Another important aspect of the job is to assist governments with the issuance of sovereign bonds. This can involve providing advice on the structure and terms of the bonds, as well as helping to market the bonds to investors and manage the sale process.

Helping a country master its commercial policy and global regulations

In addition to these core responsibilities, sovereign advisors may also be called upon to provide advice on a range of other financial matters. This can include things like helping governments to manage their public debt, providing guidance on the management of foreign exchange reserves, and assisting with the development of financial sector regulations.

Who are the main Sovereign Advisors?

The main actors of sovereign advisory are typically large financial institutions, such as investment banks and consulting firms. These firms typically have teams of experts with deep knowledge of global economic trends and the ability to provide expert guidance and advice to governments on a range of financial matters. In addition to these large financial institutions, there may also be smaller specialized firms that focus exclusively on providing sovereign advisory services. These firms may have a particular area of expertise, such as public debt management or economic policy development, and may be sought out by governments for their specific knowledge and expertise in these areas.

Examples of banks that provide sovereign advisory services include:
1. Goldman Sachs
2. JPMorgan Chase
3. Citigroup
4. Morgan Stanley
5. Deutsche Bank

How to become a Sovereign Advisor?

A career in sovereign advisory typically requires a strong background in economics, finance, or a related field. Many sovereign advisors hold advanced degrees, such as a Master’s in Business Administration (MBA) or a PhD in Economics. In addition to academic training, many sovereign advisors also have practical experience in the field, such as working in government or in other financial institutions.

In order to work in sovereign advisory, it is important to have a deep understanding of global economic trends and the ability to analyze and interpret complex financial data. This may require studying economics, finance, and related subjects at the undergraduate and graduate levels, as well as gaining practical experience through internships or other job opportunities. Additionally, many sovereign advisors also participate in professional development programs and continuing education courses in order to stay up to date with the latest developments in the field.

Resources

Rothschild & Co Sovereign Advisory

Youtube Interview of a Sovereign Advisor

Lazard Sovereign Advisory

About the author

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

A quick review of an Analyst in Transaction Services’ job…

December 31, 2022 by Louis DETALLE

A quick review of an Analyst in Transaction Services’ job…

In this article, Louis DETALLE (ESSEC Business School, Grande Ecole Program – Master in Management, 2020-2023) explains what does an analyst in Transaction Services work on.

What does Transaction Services consist in?

The Transaction Services consultant assists clients and advises them on their financial transactions. He or she works on disposals, mergers and acquisitions, and restructuring. Clients of a Transaction Services department are generally investment funds, investment banks or very large companies that conduct financial transactions and require the expertise of a Transaction Services team.

What does a Transaction Services analyst work on?

There are two types of missions: buy-side and sell-side due diligence. The approach is different depending on whether you are on the buy side or the sell side. We will review what these missions consist in.

A due diligence is conducted by a specialized audit firm, its objective is to evaluate the risks inherent in the target company when the latter is being sold for instance. All the checks are made possible to understand the company’s strategy, to analyze its strengths and weaknesses, and also to have an overview of its accounting, financial, tax, social and environmental situation.

This analysis is therefore based on the analysis of the historical performance, cash flow and assumptions made in the business plans of the target company.

Calculations of metrics and normative ratios (e.g., EBITDA) or an in-depth analysis of the company’s working capital requirements, sector and business model are also carried out.

In short, the mission of Transaction Services is to carry out all the analyses to ensure that the client and the parties involved do not make any mistakes on the valuation of the company.

What are the biggest Transaction Services firms?

Deloitte, Ernst and Young (EY), PricewaterhouseCoopers (PwC) and KPMG are the four audit and consulting firms that make up the Big Four. They are the most influential consultancies in the world, employing nearly 1,200,000 people worldwide.

What are the main jobs possible after a Transaction Services position?

Some former Transaction Services staff move into areas such as investment banking, private equity (PE), controlling or mergers and acquisitions (M&A). Others use their time in Transaction Services to target departments where they can re-use the skills they have acquired.

To go into M&A or PE, Transaction Services will lack modelling, and this should be kept in mind. Thus, consultants are often found in managerial positions, M&A managers or even in the financial department. Eventually, the excellent command of numbers, operations and the ecosystem allow some to become partners.

Resources

Youtube How to nail TS interviews?

KPMG Careers website

EY Careers website

About the author

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

My experience as an Audit intern at PwC

December 31, 2022 by Louis DETALLE

My experience as an Audit intern at PwC

In this article, Louis DETALLE (ESSEC Business School, Grande Ecole Program – Master in Management, 2020-2023) interviews a former Audit intern at PwC.

First of all, let’s recall what Audit consists in?

The financial auditor expresses an opinion on the financial statements of a company. Their objective is to carry out the work necessary to enable the auditor to give an informed opinion on the true and fair nature of the published accounts.

The financial auditor is therefore the guarantor of the reliability of the company’s financial information and has a great responsibility, in particular to the company’s third-party stakeholders who invest in the company on the basis of the information published by the company.

Where had you applied for and what makes PwC different from other big 4?

It was my first internship in corporate finance, for that matter, I wanted to get into something but I did not really know what was possible. Since, an internship in Audit is a great way to launch one’s career; because you can do whatever you want after; I figured that it would be easier for me to apply there. I quickly got interviews at KPMG and PwC.

The reason why I chose PwC is because I was accepted there first! They offered me the position first and I was very keen to get over my internship hunting!

What does an intern in Audit work on?

An intern in audit at PwC will work on different tasks depending on the specific organization and the needs of the audit team. Some common tasks that an audit intern may be responsible for include:

• Assisting with the preparation of audit plans and procedures
• Conducting research and gathering information to support the audit process
• Analyzing financial statements and other data to identify potential risks and issues
• Participating in meetings with clients to discuss audit findings and recommendations
• Preparing reports and presentations to communicate audit results to clients and internal stakeholders
• Assisting with the development and implementation of internal controls and other risk management processes

Overall, the work of an audit intern typically involves providing support to the audit team in order to ensure that the audit is conducted in a thorough and professional manner. This may involve conducting research, analyzing data, and participating in meetings with clients and other stakeholders.

What do you plan to do next?

Most former Audit intern go for transaction services, investment banking, private equity or M&A internships.

As a consequence, I am not sure, but I think I will try to get into M&A and see if I like it.

Overall, would you recommend this experience to younger students? Why?

I would personally recommend this experience to anyone who is interested in corporate finance. Because it is one of the rare fields of corporate finance that you can have a with no experience before.

For that matter, it is an excellent internship, and anyone would be very lucky to do this internship because it would mean great opportunity to do things after. However, if you are lucky, you will be able to find a more interesting internship in banking perhaps or even in a financial department of a large corporate firm.

Resources

PwC Careers website

Youtube How to succeed in Audit interviews?

About the author

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

A quick review of the Accountant job in France…

December 31, 2022 by Louis DETALLE

A quick review of the Accountant job in France…

In this article, Louis DETALLE (ESSEC Business School, Grande Ecole Program – Master in Management, 2020-2023) explains what an accountant (comptable en français) works on, on a daily basis, in France.

What does the Accountant job consist in?

All businesses and organizations need an accountant whose role is to record the day-to-day expenditure, income, and investments of the business.

The accountant is therefore the internal guarantor of the reliability of the company’s financial information and has a great responsibility, in particular to the company’s auditors & third-party stakeholders, who invest in the company on the basis of the information certified by the Audit firm and the Accountancy Department. The Audit firm will have to certify or to reject the authenticity of the accounts from an external point of view whereas the accountancy department will have this function internally.

What are the missions of the accountant?

The missions of the accountant depend on where he or she works.

In a small company

In a small company, the sole accountant is on all fronts. He or she monitors the company’s payrolls and various tax and social security declarations on a daily basis. On the other hand, the accountant must also anticipate the preparation of the closing of the annual accounts, which will be checked by the chartered accountant and certified by the auditor.

In a large company

In a large company, his or her tasks will in theory be the same, but given the size of the company, a transversality of subjects is not possible. Therefore they will work in a team and will be required to specialise rapidly: in charge of accounts receivable or payable, in charge of payroll. He will be working under the responsibility of the chief accountant.

In an accounting firm

In an accounting firm, the accountant will have various companies whose accounts he or she will have to monitor. He will be in charge of different company files, as an assistant, under the responsibility of the chartered accountant (expert comptable en français). Given the way the accounting firm operates, a great deal of advice and commercial work will be required to maintain and develop the client portfolio. It is a profession that includes busy periods, particularly during the closing of accounts, and is sometimes stressful, but which recruits a lot.

What are the academic diploma required to become an accountant?

In France, although it is possible to become an accountant after 2 years of higher studies, for big accountancy firms, it is often required to obtain specific diploma in accountancy.

The DCG (diploma in accounting and management in French – Diplôme de Comptabilité et de Gestion) is a 3-year training after A level at the end of which the accountant to be will have to take an exam in order to check that the knowledge has been well learnt.

The DSCG (Superior Diploma in accounting and management in French – Diplôme Supérieur de Comptabilité et de Gestion) is a 2-year program that one can take after obtaining the DCG. This will give the accountant a Master’s level, often needed for certain jobs.

The DEC (diploma of certified accountant in French – Diplôme d’Expertise Comptable) …allows you to work as a chartered accountant in an accounting firm. To register for the DEC exams, you must have completed a three-year internship in a public accounting firm and have a baccalaureate +5 years of higher education. The DEC is prepared in 3 years after a Master’s degree, which is often the DSCG mentioned above.

How AI can impact the Accountancy’s job?

Artificial intelligence (AI) can potentially impact the field of accounting especially as regards the automation of tasks. Indeed, AI can be used to automate certain tasks that are currently performed by accountants, such as data entry, reconciliation, and financial reporting. This can potentially save time and reduce the risk of human error. In addition, AI can analyze large amounts of data and identify patterns and trends that might not be immediately apparent to a human accountant. This can help accountants make more informed decisions and provide valuable insights to their clients. AI can also be used to identify unusual patterns or transactions that may indicate fraudulent activity. This can help accountants detect and prevent fraud before it occurs.

Overall, AI has the potential to significantly improve efficiency and effectiveness in the field of accounting, but it’s important to underline that although AI can assist accountants in their work, the final word belongs to humans when it comes to making informed decisions based on their expertise and the help of AI.

Resources

KPMG Careers website

EY Careers website

About the author

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

Interest Rate Swaps

December 29, 2022 by Akshit GUPTA

This article written by Akshit GUPTA (ESSEC Business School, Grande Ecole Program – Master in Management, 2019-2022) presents the derivative contract of interest rate swaps used to hedge interest rate risk in financial markets.

Introduction

In financial markets, interest rate swaps are derivative contracts used by two counterparties to exchange a stream of future interest payments with another for a pre-defined number of years. The interest payments are based on a pre-determined notional principal amount and usually include the exchange of a fixed interest rate for a floating interest rate (or sometimes the exchange of a floating interest rate for another floating interest rate).

While hedging does not necessarily eliminate the entire risk for any investment, it does limit or offset any potential losses that the investor can incur.

Forward rate agreements (FRA)

To understand interest rate swaps, we first need to understand forward rate agreements in financial markets.

In an FRA, two counterparties agree to an exchange of cashflows in the future based on two different interest rates, one of which is a fixed rate and the other is a floating rate. The interest rate payments are based on a pre-determined notional amount and maturity period. This derivative contract has a single settlement date. LIBOR (London Interbank Offered Rate) is frequently used as the floating rate index to determine the floating interest rate in the swap.

The payoff of the contract is as shown in the formula below:

(LIBOR – Fixed Interest Rate) * Notional amount * Number of days / 100

Interest rate swaps (IRS)

An interest rate swap is a hedging mechanism wherein a pre-defined series of forward rate agreements to buy or sell the floating interest rate at the same fixed interest rate.

In an interest rate swap, the position taken by the receiver of the fixed interest rate is called “long receiver swaps” and the position taken by the payer of the fixed interest rate is called “long payer swaps”.

How does an interest rate swap work?

Interest rate swaps can be used in different market situations based on a counterparty’s prediction about future interest rates.

For example, when a firm paying a fixed rate of interest on an existing loan believes that the interest rate will decrease in the future, it may enter an interest rate swap agreement in which it pays a floating rate and receives a fixed rate to benefit from its expectation about the path of future interest rates. Conversely, if the firm paying a floating interest rate on an existing loan believes that the interest rate will increase in the future, it may enter an interest rate swap in which it pays a fixed rate and receives a floating rate to benefit from its expectation about the path of future interest rates.

Example

Let’s consider a 4-year swap between two counterparties A and B on January 1, 2021. In this swap, counterparty A agrees to pay a fixed interest rate of 3.60% per annum to counterparty B every six months on an agreed notional amount of €10 million. Counterparty B agrees to pay a floating interest rate based on the 6-month LIBOR rate, currently at 2.60%, to Counterparty A on the same notional amount. Here, the position taken by Counterparty A is called long payer swap and the position taken by Counterparty B is called the long receiver swap. The projected cashflow receipt to Counterparty A based on the assumed LIBOR rates is shown in the below table:

Table 1. Cash flows for an interest rate swap.

Source: computation by the author

In the above example, a total of eight payments (two per year) are made on the interest rate swap. The fixed rate payment is fixed at €180,000 per observation date whereas the floating payment rate depend on the prevailing LIBOR rate at the observation date. The net receipt for the Counterparty A is equal to €77,500 at the end of 5 years. Note that in an interest rate swap the notional amount of €10 million is not exchanged between the counterparties since it has no financial value to either of the counterparties and that is why it is called the “notional amount”.

Note that when the two counterparties enter the swap, the fixed rate is set such that the swap value is equal to zero.

Excel file for interest rate swaps

You can download below the Excel file for the computation of the cash flows for an interest rate swap.

▶ Jayati WALIA Derivative Markets

▶ Akshit GUPTA Forward Contracts

▶ Akshit GUPTA Options

Useful resources

Hull J.C. (2015) Options, Futures, and Other Derivatives, Ninth Edition, Chapter 7 – Swaps, 180-211.

www.longin.fr Pricer of interest swaps

About the author

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

My apprenticeship experience within client services at BNP Paribas

December 29, 2022 by Akshit GUPTA

In this article Akshit GUPTA (ESSEC Business School, Grande Ecole Program – Master in Management, 2019-2022) shares his apprenticeship experience as a client services analyst at BNP Paribas, which is the leading European banking group.

Introduction

BNP Paribas is a French banking group which was formed as a result of a merger between Banque Nationale de Paris (BNP) and Paribas in the year 2000. The group’s business is divided in 3 major operating divisions including: Commercial, Personal Banking & Services (CPBS), Investment & Protection Services (IPS) and Corporate Institutional Banking (CIB) and the bank has its presence in 65 countries.

BNP Paribas Logo

BNP Paribas is ranked as the largest banking group in Europe and amongst top 10 in the world in terms of total assets which reflects the size of financial institution. BNP Paribas is a publicly listed company on Euronext Paris and is a part of the CAC 40 and Euro Stoxx 50 index.

Table 1. Ranking of banks by total assets

BNP Paribas Ranking

Source: www.advratings.com

My Apprenticeship Experience

I worked as a Client Services Analyst within the Corporate and Institutional Banking (CIB) division of the bank.

Missions

I had the opportunity to undertake two missions during the apprenticeship at BNP Paribas. During my first year, I worked as a Client Services Officer in the Factsheets team wherein I was responsible for creating and producing factsheets on equity and fixed income linked structured products and custom indices for the institutional clients of the bank. The Client Services is a cross functional team within the BNP Paribas Global Markets. They aim to provide the clients with the best possible post-trade service on the global market activity of the bank. The team works in close coordination with various teams operating on the capital markets (Sales, Traders, Business Managers, Middle and Back Office, Compliance, and Lawyers) and on all types of products (equities, fixed income, commodities, foreign exchange, and derivatives).

My work involved analysing the technical term-sheets (documents which present technical information about the products) of different structured products and produce factsheets (documents which mainly present the financial performance of the products) related to these products in conjunction with the Structuring and Sales teams at the bank. The factsheets were automated and produced on different frequencies like daily, weekly, bi-weekly, and monthly to serve the needs of different clients. These reports included products’ performance measures, and commentary on market data and current economic scenarios on these products.

During the second year of my apprenticeship, I worked as an Operational Client Relationship Manager (OCRM) within the same division at BNP Paribas but with a change of business responsibilities and duties to gain more exposure on the client facing side of the business.

In this role, I was responsible for developing and maintaining strong commercial relationships with the top institutional clients of our bank and manage client’s transversal escalations for multi asset classes including Equities, Fixed Income, Foreign Exchange, and Credit Derivatives. I worked on pre and post trade issues in close coordination with cross functional teams like Sales, Trading, Onboarding, Legal, Compliance and Operations to resolve breaks and efficiently serve the clients.

Required skills and knowledge

Strong knowledge of investment banking, equity, and capital markets.
Strong skillset in MS Office pack including MS Excel, MS Word, MS Access, and MS PowerPoint to produce reports and KPI dashboards for internal and external purposes.
Familiarity with programming in VBA and SQL.
Understanding of front-to-back trade lifecycle of different products.
Effective communication skills to interact with clients and internal stakeholders
Strong interpersonal skills.

What I learnt?

With this apprenticeship experience, I gained strong exposure to the different structured products issued by a bank like BNP Paribas in the global markets, understanding of client communication side, and programming skills in VBA and SQL. Along with the technical skillsets, I also learnt the importance of working as a team, understanding each other’s viewpoints, and aiming towards a common goal. It brought into focus the importance of banking sector and has given me a platform to sharpen my financial acumen.

Key concepts

The following are the two concepts that were required in my work at BNP Paribas:

Global markets

Global Markets is a division within an investment bank which handles all the sales and trading services on both the primary and secondary markets for different financial products. It caters to different clients including financial institutions, corporates and large-scale investors. The teams within this division are generally split based on different asset classes. Relevant knowledge of the different functions within this division is important to facilitate and coordinate client escalations and projects.

Structured products

Structured products are pre-packaged product offerings which are designed as per the client’s risk-return profile. The returns on the investments in these products are based on the performance of the underlying assets. These underlying assets can include individual assets or indices in various markets like equities, bonds and commodities, and derivatives on these underlying assets like futures, swaps, and options.
The structured products are highly sophisticated products since they are tailor-made as per the client’s requirements and risk/return profile. These products have pre-defined features like maturity date, early – redemption mechanism, coupon payments (fixed or variable coupons), underlying asset, and the degree of capital protection. They can guarantee full or partial capital protection and a flexible degree of leverage as well.

Why should I be interested in this post

This post is interesting for anyone looking to enter the Global Markets side of an investment bank and looking to kickstart a career in this field by looking for an apprenticeship or an internship contract.

Useful resources

BNP Paribas

BNP Paribas financial reports

BNP Paribas financial report for year 2021

About the author

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

A quick review of the Audit job…

December 28, 2022 by Louis DETALLE

A quick review of the Audit job…

In this article, Louis DETALLE (ESSEC Business School, Grande Ecole Program – Master in Management, 2020-2023) explains what an Audit analyst works on, on a daily basis.

What does the Audit job consist in?

The financial auditor expresses an opinion on the financial statements of a company. Its objective is to carry out the work necessary to give an informed opinion on the true and fair nature of the published accounts.

The financial auditor is therefore the guarantor of the reliability of the company’s financial information and has a great responsibility, in particular to the company’s third party stakeholders who invest in the company on the basis of the information published by the company.

What are the biggest audit firms?

Deloitte, Ernst and Young (EY), PricewaterhouseCoopers (PwC) and KPMG are the four audit and consulting firms that make up the Big Four. They represent the most influential consulting firms in the world. They are the most influential consultancies in the world, employing nearly 1,200,000 people worldwide.

However, some other players are very influential, such as Mazars in France, which is ranked neck and neck with the Anglo-Saxon Big Four. On the other hand, smaller companies do not necessarily need to call on such large firms as their audits are not as labour intensive.

What does an Auditor work on?

In the case of an accounting and financial audit, it is an examination of the company’s financial statements in order to assess the company’s accounts and verify their fairness, compliance and regularity. As the auditor is expected to give an opinion on the fairness of the accounts, the auditor and his team will study the different accounting cycles of the company: income and customers, costs and suppliers, but also equity, cash flow, stocks and fixed assets, etc.

The objective of this review of the major financial masses is to understand the client’s challenges related to its business, its environment, its organisation, and to understand its internal processes in order to see how all this is reflected in the accounts. A meticulous verification of the accounts and invoice amounts is carried out (often subcontracted).

The common objective of all engagements is to provide confidence to both external investors and the client, who may need to make adjustments after the annual audit. The client may have to make adjustments after the annual audit because their internal control systems are more or less effective, and they may present inaccurate accounts unintentionally but more inadvertently.

Other audits may therefore cover the environment, the production system, ethics, safety and many others. The role of a quality audit, for example, is to check whether the client company’s stated quality objectives are being met. The auditors must ensure that the quality management systems comply with the applicable contractual and regulatory requirements.

The use of AI in order to quicken the audit job.

Artificial intelligence (AI) can potentially impact the audit profession in a number of ways. Here are a few examples:

Auditing large amounts of data: AI technologies, such as machine learning algorithms, can help auditors analyze and interpret large amounts of data more efficiently and accurately. For example, an AI system could be used to identify patterns and anomalies in financial data that might indicate fraudulent activity or other problems.

Improving efficiency: AI can automate certain tasks, such as data entry and analysis, allowing auditors to focus on higher-value activities, such as interpreting results and communicating findings. This can help improve the efficiency and effectiveness of the audit process.

Enhancing risk assessment: AI can help auditors better understand and assess the risks associated with a particular business or industry. For example, an AI system could analyze data on economic conditions, market trends, and other factors to help identify potential risks and provide recommendations for how to mitigate them.

Providing real-time monitoring: AI can be used to monitor a company’s financial data in real-time, alerting auditors to any unusual activity or trends that may warrant further investigation. This can help auditors identify potential issues earlier in the process, which can lead to more timely and effective interventions.

Overall, the use of AI in the audit profession has the potential to improve the accuracy and efficiency of the audit process, while also helping auditors to identify and address risks more effectively.

Resources

Youtube The Audit Methodology

KPMG Careers website

EY Careers website

About the author

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

A quick review of the Venture Capitalist’s job…

December 28, 2022 by Louis DETALLE

A quick review of the Venture Capitalist’s job…

In this article, Louis DETALLE (ESSEC Business School, Grande Ecole Program – Master in Management, 2020-2023) explains what a Venture Capitalist works on, on a daily basis.

What does Venture Capital consist in?

Venture Capital (VC) represents fundamental and indispensable early funding-support throughout the life cycle of the company.

VC consists in taking (minority or majority) stakes in the capital of small companies which are generally unlisted on the stock exchange and that have not reached break-even point. It is therefore a method of financing companies in order to support them on the path to growth. Indeed, the objective of a VC fund is obviously to realize a capital gain at the exit, when the start-up has matured and has become a powerful actor.

This is risky because start-ups are less successful in borrowing from banking institutions, so they attract other investors such as business angels and venture capitalists.

What are the main differences among Venture Capitalists?

VC funds can be specialized in sectors such as deep tech, biology, marketplace, telecom and plenty of others. A start-up will therefore have better chances at obtaining funding from them if they target funds that know well the field in which they evolve.

In addition, another aspect of VC is the stage of investment and the size of tickets.

Because VC can come at the very beginning, as “seed investors”, of later in core venture with “A-B and C series”.

For that matter, Growth Capital will be the bridge between Venture Capital and Private Equity.

What are the main VC actors a company can resort to?

Start-ups and small companies can resort to a wide range of financial investors:

Early-stage investment funds (BPI, Axeleo Capital, Alven Capital, etc.
Corporate funds represented by large groups that are interested in the creation of innovative companies.
Business angels, represented mainly by entrepreneurs, who organize themselves into associations or investment companies.
Crowdfunders, who are individuals who invest in start-ups such as Xavier Niel for instance.

A company must choose its investors according to its stage of development, its sector and according to its objectives.

What does an analyst in VC work on?

The tasks of a Venture Capitalist are diverse and include, for example, the producing and challenging a business plan, modelling different scenarios and strategies in Excel. The analyst and the investment teams of the VC teams thoroughly analyze the companies seeking for funding. They try to determine whether the projections of the seeked investment are reasonable and not overestimated.

Indeed, bear in mind that private equity funds intend to fund companies trough equity. And as equity investors (i.e. shareholders) are reimbursed at last in the event of a bankruptcy, their work is to determine if the company will really generate growth with the capital at stake. That’s why deep sector-analysis are also required from a VC analyst.

This is all the truer for Venture Capitalist who will take on huge risks since they are the first financial actors the start-up can turn to.

Why do VC jobs appeal so much to business school students?

First of all, it should be noted that this profession combines corporate finance skills with entrepreneurial thinking, which is rare!

Indeed, the best Venture Capitalist often has previous entrepreneurial background, and this is what enables him to see things that startups cannot: because this person has already made the mistakes the fund-seeking entrepreneur has not.

This entrepreneurial aspect of the job is very well known and argued by VC actors and it attracts young & ambitious students who don’t want to get into large corporate firms and favor more agile structures.

Resources

The top 10 VC actors in France

Youtube How to get a VC internship?

About the author

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

My experience as a Transaction Services intern at EY

December 28, 2022 by Louis DETALLE

My experience as a Transaction Services intern at EY

In this article, Louis DETALLE (ESSEC Business School, Grande Ecole Program – Master in Management, 2020-2023) interviews a former Transaction Services intern at EY.

First of all, let’s recall what Transaction Services consists in?

The Transaction Services (TS) consultant assists clients and advises them on their financial transactions like disposals, mergers and acquisitions and restructuring. Its clients are generally investment funds, investment banks or very large companies that conduct transactions and require the expertise of Transaction Services teams.

In short, the mission of Transaction Services is to carry out all the analyses to ensure that the client and the parties involved do not make any mistakes on the valuation of the company.

Where had you applied for and what makes EY different from other big 4?

It was my second significant internship in corporate finance, for that matter, I wanted to get into M&A or Private Equity, but both are pretty complicated to get into. For that matter, I figured that it would be easier for me to apply for a Transaction Services internship or in M&A corporate. I quickly got interviews at EY, Deloitte and KPMG.

I chose EY because I really got along with my manager-to-be; he insisted that they would make me work on interesting stuff and they offered be the position first.

What does an intern in TS work on?

As you may know, in TS, there are two types of missions: buy-side and sell-side due diligence. The approach is different depending on whether you are on the buy side or the sell side.

As an intern, my job was to help my team assess the risks inherent in the target company while preparing the due diligence. For that matter, all of the checks are made possible to understand the company’s strategy, to analyse its strengths and weaknesses, and also to have an overview of its accounting, financial, tax, social and environmental situation. I could help them on any of the topics above, although the tax aspect of the company was given to a dedicated department.

In the due diligence, I can assist my team in the reading of documents from the major international institutions for all the data relating to global and entire sectors for the specific sections of the due diligence.

Also, a last type of task that I was given was taking notes about Q&A sessions that occur during the M&A process. I would thereafter write a summary for the team.

What do you plan to do next?

Most former Transaction Services intern go for investment banking, private equity, controlling or M&A internships.

As a consequence, I believe that this is what I will do next, I can wait to be on the banking side of the merger! The advantage of my internship is in fact twofold. On the one hand, it allows me to have EY on my CV and on the other hand, I have experience that finance recruiters describe as “significant finance work experience”. So I can do many things afterwards and that is the strength of my internship.

Overall, would you recommend this experience to younger students? Why?

I would personally recommend this experience to anyone who is interested in corporate finance. Because it is one of the rare fields where you gain a lot of knowledge about financial modelling. When you work in TS, you spend most of your time on Excel and this will be a valuable skill for your following internships.

For that matter, it is an excellent internship, and anyone would be very lucky to do this internship because it would mean great exposure and lots of financial analysis.

Resources

EY Careers website

Youtube How to nail TS interviews?

About the author

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

My experience as an Equity Research Intern at Oddo BHF…

December 28, 2022 by Louis DETALLE

My experience as an Equity Research Intern at Oddo BHF…

In this article, Louis DETALLE (ESSEC Business School, Grande Ecole Program – Master in Management, 2020-2023) interviews a former Equity Research Intern at Oddo BHF.

First of all, let’s recall what Equity Research consists in?

The objective of equity research is to make buy or sell recommendations on stocks to advise investors on their asset allocation. In doing so, the Equity Research team will closely monitor certain stocks to see if the stock is outperforming or underperforming. In doing so, they will closely monitor the share price and sell their monitoring as a service to determine whether to buy or sell a share.

This equity research service is therefore sold to investors in the financial markets to provide them with a comprehensive financial analysis, as well as advice on whether to buy or sell particular securities. The analysis report presented by an equity analyst is used by investment banks and private equity firms to evaluate the company for an initial public offering (IPO), a leveraged buy-out (LBO), alliances and others. Therefore, all these investors constitute clients of Equity Research teams.

What banks did you apply for and what makes Oddo BHF different from others?

Most banks have Equity Research teams such as Société Générale, UBS, BNP Paribas, Barclays, Goldman Sachs and Citi for instance. In short, equity research analysts are mainly employed by investment banks but also investment funds (KKR, Blackstone, Bpifrance, etc.) or asset management firms (BlackRock, Vanguard, Amundi, etc.).

For that matter, I had applied virtually everywhere but I only got interviews from UBS, BNP Paribas & Oddo BHF. I was refused at UBS but got the offer at BNP Paribas. However, since I had gotten along very well with the team at Oddo BHF, I chose to go there instead!

Is your equity research team specialised in a specific sector? Which one?

Whereas most equity research teams are specialised in a specific sector such as automotive, aerospace, healthcare, telecoms and biotech, mine isn’t. Some of the team members follow very closely the stock prices and market indicators of certain companies but it is more about personal interest!

That makes the experience super interesting, because I am able to see for myself how the stocks of companies in the luxury sector are impacted by the announcement of the quarter results and how they evolve, relatively to companies from other sectors.

What does an intern in Equity Research work on?

As explained above, an equity research analyst will follow the release of sector or company specific information to write a note for subsequent use by the clients as part of their investment strategy.

As an intern, I have assisted the work of the equity research analyst by doing information research, reading quarterly financial reports, and press releases which may provide information on the company’s performance to date compared to expectations. As the analyst will also look for information on upcoming mergers, I have to keep an eye on financial news as this will impact significantly the prices of stocks.

As for the sectoral notes, I can assist my team in the reading of documents from the major international institutions for all the data relating to global and entire sectors.
Once this research work is completed, equity research analysts proceed to forecast results through financial modelling. I can look at the financial modelling but I must say I am not allowed to work on it since the slightest mistake could cause significant errors.

Also, a last type of task that I was given was taking notes about clients’ questions by telephone during morning meetings. I would thereafter write a summary for the team.

Overall, would you recommend this experience to younger students? Why?

I would personally recommend this experience to anyone who is interested in finance, be it corporate finance or market finance. Because it is one of the rare fields where you enjoy the benefits of each: you analyze financial market products while comparing them to the financial results announced by companies.

For that matter, it is an excellent first internship in this field and anyone would be very lucky to do this internship because it would mean great exposure and lots of financial analysis.

Resources

Finance walk Equity Research Interview Questions with answers

Youtube An analyst in Equity Research’s Youtube Interview

Youtube How to do the Equity Research of a company?

About the author

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

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