Arbitrage Pricing Theory (APT)

Arbitrage Pricing Theory (APT)

Youssef LOURAOUI

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(ri) represents the expected return of asset i
  • rf the risk-free rate
  • βi the measure of the risk of asset i
  • E(rm) the expected return of the market
  • E(rm)- rf the market risk premium.

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

CAPM beta formula

Where:

  • Cov(ri, rm) represents the covariance of the return of asset i with the return of the market
  • σ2(rm) 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(rm)) 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(rp) represents the expected return of portfolio p
  • rf the risk-free rate
  • βk the sensitivity of the return on portfolio p to the kth factor (fk)
  • λk the risk premium for the kth factor (fk)
  • 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(rp) represents the expected return of portfolio p
  • rf the risk-free rate
  • βp, Chinese FX the sensitivity of the return on portfolio p to the USD/CHY FX spot rate
  • βp, US spread the sensitivity of the return on portfolio p to the US term structure
  • λChinese FX the risk premium for the FX risk factor
  • λUS 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.

 Download the Excel file to assess an arbitrage portfolio example

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.

Related posts on the SimTrade blog

   ▶ Jayati WALIA Capital Asset Pricing Model (CAPM)

   ▶ Youssef LOURAOUI Origin of factor investing

   ▶ Youssef LOURAOUI Factor Investing

   ▶ Youssef LOURAOUI Fama-MacBeth regression method: stock and portfolio approach

   ▶ Youssef LOURAOUI Fama-MacBeth regression method: Analysis of the market factor

   ▶ Youssef LOURAOUI Fama-MacBeth regression method: N-factors application

   ▶ Youssef LOURAOUI Portfolio

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.

Investopedia (2022) Arbitrage Pricing Theory: It’s Not Just Fancy Math.

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).

Smart Beta industry main actors

Youssef_Louraoui

In this article, Youssef LOURAOUI (ESSEC Business School, Global Bachelor of Business Administration, 2017-2021) presents the main actors of the smart beta industry, which is estimated to represent a cumulative market value of $1.9 trillion as of 2017 and is projected to grow to $3.4 trillion by 2022 (BlackRock, 2021).

The structure of this post is as follows: we begin by presenting an overview of the smart beta industry actors. We will then discuss the case of BlackRock, the 10 trillion dollar powerhouse of the asset management industry, which is the main actor in the smart beta industry segment.

Overview of the market

The asset management sector, which is worth 100 trillion dollars worldwide, is primarily divided into active and passive management (BCG, 2021). While active management continues to dominate the market, passive management’s proportion of total assets under managed (AUM) increased by 4 percentage points between 2008 and 2019, reaching 15%. This market transition is even more dramatic in the United States, where passive management accounted for more than 40% of the total market share in 2019. A new category has arisen and begun to acquire market share over the last decade. Smart beta exchange-traded funds (ETFs) are receiving fresh inflows and are the industry’s fastest-growing ETF product. Various players are entering the market by developing and releasing new products (Deloitte, 2021).

Active funds have demonstrated divergent returns when compared to passive funds, making the cost difference increasingly difficult to justify (Figure 1). The growing market share of passive funds in both the United States and the European Union is putting further pressure on active managers’ fees. When it comes to meeting the demands of investors, both active and passive management has shown shortcomings. Active management funds often fail to outperform their benchmarks because they lack clear indicators, charge expensive fees, and don’t always have clear indicators. As seen in Figure 1, active funds struggle to deliver consistent returns over a prolonged timeframe, as depicted in the European market. In this sense, the active funds success rate is divided by more than half between year one and year three (Deloitte, 2021). Concentration is a problem for passive funds that are weighted by market capitalization.. These limits have prepared the ground for smart beta funds to emerge (Figure 1).

Figure 1. Active funds success rates (% of funds beating their index over X years)
Active funds success rates
Source: Deloitte (2021).

The smart beta market is dominated by several players who have a strategic position with a large volume of assets under management. Figure 2 compares smart beta actors based on percentage of asset under management (%AUM), one the most important metric in the asset management industry. Some key elements can be drawn for the first figure. BlackRock is the provider with the largest market share, with over 40% of the smart beta industry in the analysis, followed by Vanguard and State Street Global Advisors with 30.66% and 18.44% respectively in this benchmark study underpinning nearly $1 trillion (Figure 2).

Figure 2. % AUM of the biggest Smart Beta ETF providers
Smart_Beta_benchmark_analysis
Source: etf.com (2021).

BlackRock dominance

The main powerhouses of the passive investing industry, BlackRock and Vanguard, are poised to capture the lion’s share of assets in the rapidly rising world of actively managed exchange-traded funds. The conclusion is likely to dissatisfy active fund managers, who have been squeezed by the fast development of passive ETFs in recent years and may have seen the introduction of active ETFs as a chance to fight back and get a piece of the lucrative pie (Financial Times, 2021).

According to a study of 320 institutional investors with a combined $12.9 trillion in assets, institutional investors prefer BlackRock and Vanguard to handle their active ETF investments. The juggernauts were expected to provide the best performance as well as the best value for money. With over a third of the global ETF market capitalization, BlackRock remains the dominant player (The Financial Times, 2021). BlackRock is unquestionably a major force in the ETF business, with an unparalleled market share in both the US and European ETF markets. BlackRock has expanded to become the world’s largest asset manager, managing funds for everyone from pensioners to oligarchs and sovereign wealth funds. It is now one of the largest stockholders in practically every major American corporation — as well as a number of overseas corporations. It is also one among the world’s largest lenders to businesses and governments.

Aladdin, the company’s technological platform, provides critical wiring for large portions of the worldwide investing industry. By the end of June this year, BlackRock was managing a stunning $9.5 trillion in assets, a sum that would be hardly understandable to most of the 35 million Americans whose retirement accounts were managed by the business in 2020. If the current rate of growth continues, BlackRock’s third-quarter reports on October 13 might disclose that the company’s market capitalization has surpassed $10 trillion. It’s expected to have surpassed that mark by the end of the year (FT, 2021). To put this in perspective, it is about equivalent to the worldwide hedge fund, private equity, and venture capital industries combined.

Industry-wide fee cuts had helped BlackRock maintain its dominance in the ETF sector. Its iShares brand is the industry’s largest ETF provider for both passive and actively managed products (CNBC, 2021).

Why should I be interested in this post?

If you are a business school or university undergraduate or graduate student, this content will help you in understanding the various evolutions of asset management throughout the last decades and in broadening your knowledge of finance.

Smart beta funds have become a trending topic among investors in recent years. Smart beta is a game-changing invention that addresses an unmet need among investors: a higher return for lower risk, net of transaction and administrative costs. In a way, these investment strategies create a new market. As a result, smart beta is gaining traction and influencing the asset management industry.

Related posts on the SimTrade blog

Factor investing

   ▶ Youssef LOURAOUI Factor Investing

   ▶ Youssef LOURAOUI Origin of factor investing

   ▶ Youssef LOURAOUI MSCI Factor Indexes

   ▶ Youssef LOURAOUI Smart beta 1.0

   ▶ Youssef LOURAOUI Smart beta 2.0

Factors

   ▶ Youssef LOURAOUI Size Factor

   ▶ Youssef LOURAOUI Value Factor

   ▶ Youssef LOURAOUI Yield Factor

   ▶ Youssef LOURAOUI Momentum Factor

   ▶ Youssef LOURAOUI Quality Factor

   ▶ Youssef LOURAOUI Growth Factor

   ▶ Youssef LOURAOUI Minimum Volatility Factor

Useful resources

Business analysis

BlackRock, 2021.What is factor investing?

BCG, 2021.The 100$ Trillion Machine: Global Asset Management 2021

CNBC, 2021. What Blackrock’s continued dominance means for other ETF issuers.

Deloitte, 2021. Will smart beta ETFs revolutionize the asset management industry? Understanding smart beta ETFs and their impact on active and passive fund managers

Etf.com, 2021.Smart Beta providers

Financial Times (13/09/2020) BlackRock and Vanguard look set to extend dominance to active ETFs

Financial Times (07/10/2021) The ten trillion dollar man: how Larry Fink became king of Wall St

About the author

The article was written in October 2021 by Youssef LOURAOUI (ESSEC Business School, Global Bachelor of Business Administration, 2017-2021).

Origin of factor investing

Origin of factor investing

Youssef_Louraoui

In this article, Youssef LOURAOUI (ESSEC Business School, Global Bachelor of Business Administration, 2017-2021) presents the origin of factor investing. A factor is defined as a persistent driver that helps explain assets’ long-term risk and return properties across asset classes.

This article is structured as follows: we begin by presenting Markowitz’s Modern Portfolio Theory (MPT) as the origin of factor investing (market factor). We then explain the Fama-French three-factor models, which is an extension of the CAPM single factor model (market factor). Furthermore, we explain also the Carhart four-factor model and the Fama-French five-factor model that aimed to capture additional factors to the market factor.

Markowitz’s Modern Portfolio Theory: Origin of the factor investing

Factor investing can be retraced to the work of Harry Markowitz in the early 1950s. The most important aspect of Markowitz’s approach was his fundamental finding that an asset’s risk and return should not be evaluated on its own, but rather on how it contributes to the entire risk and return of a portfolio. His dissertation, titled “Portfolio Selection”, was published in The Journal of Finance (1952). Nearly thirty years later, Markowitz shared the Nobel Prize for economics and corporate finance for his MPT contributions to both disciplines. The holy grail of Markowitz’s work is based on his calculation of the variance of a two-asset portfolio computed as follows:

Markowitz_2_asset_MV

Where:

  • w and (1-w) represents asset weights of assets A and B
  • σ2 represents the variance of the assets and portfolio
  • cov(rA,rB) represents the covariance of assets A and B.

Capital Asset Pricing Model (CAPM)

William Sharpe, John Lintner, and Jan Mossin separately developed another key capital markets theory as a result of Markowitz’s previous works : 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 his derivation of the CAPM, Sharpe, Mossin and Litner made significant contributions to the concepts of the Efficient Frontier and Capital Market Line. Sharpe, Litner and Mossin seminal contributions would later earn him the Nobel Prize in Economics. 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:

CAPM

Where :

  • E(r) represents the expected return of the asset
  • rf the risk-free rate
  • β a measure of the risk of the asset
  • E(rm) the expected return of the market
  • E[rm– rf]represents the market risk premium.

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

Beta

Where:

  • Cov(r, rm) represents the covariance of the asset with the market
  • σ2(rm) is the variance of market return.

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 〖σ(r_m)〗^2) 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.

Additionally, the CAPM makes a distinction between two forms of risk: systematic and specific risk. Systematic risk refers to the risk posed by the market’s basic structure, its participants, and any and all non-diversifiable elements such as monetary policy, political events, and natural disasters. By contrast, specific risk refers to the risk inherent in a particular asset and so is diversifiable. As a result, the CAPM solely captures systematic risk via the beta measure, with the market’s beta equal to one, lower-risk assets having a beta less than one, and higher-risk assets having a beta larger than one.

Finally, the CAPM’s central message is that when investors invest in a particular security/portfolio, they are rewarded twice: once via the time value of money impact (reflected in the risk-free component of the CAPM equation) and once via the effect of taking on more risk. However, the CAPM is not an empirically sound model, owing to an unnecessarily simplified set of assumptions and problems in establishing validating tests at the model’s first introduction (Fama and French, 2004). Thus, throughout time, the CAPM has been revised and modified to address not just its inadequacies but also to keep pace with financial and economic changes. Sharpe (1990), in his evaluation of the CAPM, cites various examples of revisions to his basic model proposed by other economists and financial experts.

The Fama-French three-factor model

Eugene Fama and Kenneth French created the Fama-French Three-Factor model in 1993 in response to the CAPM’s inadequacy. It contends that, in addition to the market risk component introduced by the CAPM, two more factors affect the returns on securities and portfolios: market capitalization (referred to as the “size” factor) and the book-to-market ratio (referred to as the “value” factor). According to Fama and French, the primary rationale for include these characteristics is because both size and book-to-market (BtM) ratios are related to the economic fundamentals of the business issuing the securities (Fama and French, 1993).

They continue by stating that:

  • Earnings and book-to-market ratios are inversely associated, with companies with low book-to-market ratios consistently reporting better earnings than those with high book-to-market ratios
  • Due to a similar risk component, size and average returns are inversely associated. This is based on their observation of the trajectory of small business profits in the 1980s: they suggest that small enterprises experience longer durations of earnings depression than larger enterprises in the event of a recession in the economy in which they operate. Additionally, they noted that smaller enterprises did not contribute to the economic expansion in the mid- and late-1980s following the 1982 recession
  • Profitability is connected to both size and BtM, and is a common risk factor that emphasizes and explains the positive association between BtM ratios and average returns. As thus, the return on a security/portfolio becomes:

FF_3FM

Where :

  • E(𝑟) is the expected return of the asset/portfolio
  • 𝑟𝑓 is the risk-free rate
  • 𝛽 is the measure of the market risk of the asset
  • 𝐸(𝑟𝑀) is the expected return of the market
  • 𝛽𝑆 is the measure of the risk related to the size of the asset
  • 𝛽𝑉 is the measure of the risk related to the value of the security/portfolio
  • 𝑆𝑀𝐵 (which stands for “Small Minus Big”) measures the difference in expected returns between small and big firms (in terms of market capitalization)
  • 𝐻𝑀𝐿 (which stands for “High Minus Low”) measures the difference in expected returns between value stocks and growth stock
  • 𝛼 is a regression intercept
  • 𝜖 is a measure of regression error

Both SMB and HML are derived using historical data as well as a mixture of portfolios focused on size and value. Professor French publishes these values on a regular basis on his personal website. Meanwhile, the betas for both the size and value components are derived using linear regression and might be positive or negative. However, the Fama-French three-factor model is not without flaws. Griffin (2002) highlights a significant flaw in the model when he claims that the Fama-French components of value and size are more accurate at explaining return differences when applied locally rather than internationally. As a result, each of the components should be addressed on a nation-by-country basis (as professor French now does on his website, where he specifies the SMB and HML factors for each nation, such as the United Kingdom, France, and so on). While the Fama-French model has gone further than the CAPM in terms of breaking down security returns, it remains an incomplete model with spatially confined interpretation of its additional variables. Efforts have been made over the years to complete this model, with Fama and French adding two more variables in 2015, profitability and investment strategy, and other scholars, like as Carhart (1997), adding a fourth feature, momentum, to the original Three-Factor model.

The Carhart four-factor model

Carhart (1997) extended the Fama-French three-factor model (1993) by adding a fourth factor: momentum. Momentum is defined as the observable tendency for prices to continue climbing or declining following an initial increase or decline. By definition, momentum is an anomaly, as the Efficient Market Hypothesis (EMH) states that there is no reason for security prices to continue growing or declining after an initial change in their value.

While traditional financial theory is unable to define precisely what causes momentum in certain securities, behavioural finance provides some insight into why momentum exists; indeed, Chan, Jegadeesh and Lakonishok (1996) argue that momentum arises from the inability of the majority of investors to react quickly and immediately to new market information and, thus, integrate that information into securities. This argument demonstrates investors’ irrationality when it comes to appraising the value of certain stocks and making investing decisions. Carhart was motivated to incorporate the momentum component into the Fama-French three-factor model since the model was unable to account for return variance in momentum-sorted portfolios (Fama and French, 1996 – Carhart 1997). Carhart incorporated Jegadeesh and Titman’s (1993) one-year momentum variation into his model as a result.

Carhart_4FM

Where the additional component represents:

  • 𝛽𝑀 is the measure of the risk related to the momentum factor of the security/portfolio
  • 𝑈𝑀𝐷 (which stands for “Up Minus Down”) measures the difference in expected returns between “winning” securities and “losing” securities (in terms of momentum).

As Carhart states in his article, the four-factor model, like the CAPM and the Fama-French Three-Factor, may be used to explain the sources of return on a specific security/portfolio (Carhart, 1997).

The Fama-French five-factor model

Fama and French state in 2014 that the first three-factor model they developed in 1993 does not adequately account for certain observed inconsistencies in predicted returns. As a consequence, Fama and French enhanced the three-factor model by adding two new variables: profitability and investment. The justification for these two factors arises from the theoretical implications of the dividend discount model (DDM), which claims that profitability and investment help to explain the returns achieved from the HML element in the first model (Fama and French, 2015).

Surprisingly, unlike the Carhart model, the new Fama-French model does not incorporate the momentum element. This is mostly because to Fama’s position on momentum. While not denying its existence, Fama thinks that the degree of risk borne by securities in an efficient market cannot fluctuate so dramatically that it justifies the necessity to recognize the momentum factor’s involvement (Fama and French, 2015). According to the Fama-French five-factor model, the return on any security is calculated as follows:

FF_5F

  • 𝛽P is the measure of the risk related to the profitability factor of the security/portfolio
  • 𝑅𝑀𝑊 (which stands for “Robust Minus Weak”) measures the difference in expected returns between securities that exhibit strong profitability levels (thus making them “robust”) and securities that show inconsistent profitability levels (thus making them “weak”)
  • 𝛽𝐼 is the measure of the risk related to the investment factor of the asset
  • 𝐶𝑀𝐴 (which stands for “Conservative Minus Aggressive”) measures the difference in expected returns between securities that engage in limited investment activities (thus making them “conservative”) and securities that show high levels of investment activity (thus making them “aggressive”).

To validate the new model, Fama and French created many portfolios with considerable returns disparities due to size, value, profitability, and investing characteristics. Additionally, they completed two exercises:

  • The first is a regression of portfolio results versus the improved model. This was done to determine the extent to which it explains the observed returns disparities between the selected portfolios
  • The second is to compare the new model’s performance to that of the three-factor model. This was done to determine if the new five-factor model adequately accounts for the observed returns differences in the old three-factor model. The following summarizes Fama and French’s conclusions about the new model.

The HML component becomes superfluous in terms of structure, since any value contribution to a security’s return can already be accounted by market, size, investment, and profitability factors. Thus, Fama and French advise investors and scholars to disregard the HML effect if their primary objective is to explain extraordinary returns (Fama and French, 2015).

They do, however, argue for the inclusion of all five elements when attempting to explain portfolio returns that display size, value, profitability, and investment tilts. Additionally, the model explains between 69% and 93% of the return disparities seen following the usage of the prior three-factor model (Fama and French, 2015). This new model, however, is not without flaws. Blitz, Hanauer, Vidojevic, and van Vliet (henceforth referred to as BHVV) identified five problems with the new Fama-French five-factor model in their 2016 paper “Five difficulties with the Five-Factor model”.

While two of these issues are related to some of the original Fama-French three factor model’s original factors (most notably the continued existence within the model of the CAPM relationship between market risk and return, as well as the new model’s overall acceptance by the academic community while some of the original factors are still contested), several of the other issues are related to other factors. These concerns include the following (Fama and French, 2015) :

  • The lack of motion
  • The new factors introduced lack robustness. The questions here include historical (i.e., will these factors apply to data points before to 1963) and if these aspects also apply to other asset types
  • The absence of adequate empirical support for the implementation of these Fama and French components

Use of the asset pricing models

All the models presented above are mostly employed in asset management to analyze the performance of an actively managed portfolio and the overall performance of a mutual fund.

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

Blitz, D., Hanauer M.X., Vidojevic M., van Vliet, P., 2018. Five Concerns with the Five-Factor Model, The Journal of Portfolio Management, 44(4): 71-78.

Carhart, M.M. (1997), On Persistence in Mutual Fund Performance. The Journal of Finance, 52: 57-82.

Fama, E.F., French, K.R., 1992. The Cross-Section of Expected Stock Returns. The Journal of Finance, 47: 427-465.

Fama, E.F., French, K.R., 2004. The Capital Asset Pricing Model: Theory and Evidence. Journal of Economic Perspectives, 18(3): 25-46.

Fama, E.F., French, K.R., 2015. A five-factor asset pricing model. Journal of Financial Economics, 116(1): 1-22.

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

Mangram, M.E., 2013. A simplified perspective of the Markowitz Portfolio Theory. Global Journal of Business Research, 7(1): 59-70.

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

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

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

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

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About the author

The article was written in September 2021 by Youssef LOURAOUI (ESSEC Business School, Global Bachelor of Business Administration, 2017-2021).

Growth Factor

Growth Factor

Youssef_Louraoui

In this article, Youssef LOURAOUI (ESSEC Business School, Global Bachelor of Business Administration, 2017-2021) presents the growth factor, which is based on a risk factor that aims to get exposure to firms with high growth potential based on a variety of parameters such as historical profits, sales, and expected earnings.

This article is structured as follows: we begin by defining the growth factor and reviewing academic studies. The MSCI Growth Factor Index, which is well used as a benchmark in the asset management industry, is next presented in terms of performance and risk-return trade-off. We showcase the ETF market for investors looking to profit from the growth factor.

Definition

In the world of investing, a factor is any aspect that helps explain an asset’s long-term risk and return performance. In the late 1970s, the portfolio management industry’s objective was to capture the market return on a portfolio. As a result of Markowitz and Tobin’s earlier research, William Sharpe, John Lintner, and Jan Mossin independently developed the Capital Asset Pricing Model (CAPM). Because it enabled investors to properly value assets in terms of systematic risk, the CAPM was a significant evolutionary step forward in the theory of capital market equilibrium (Mangram, 2013).

Eugene Fama and Kenneth French, following the CAPM’s original work, developed the Fama-French Three-Factor model in 1993 to solve the CAPM’s inadequacies. It claims that, in addition to the market risk component of the CAPM, two other factors have an effect on the returns on securities and portfolios: market capitalization (called the “size” factor) and the book-to-market ratio (referred to as the “value” factor). Other factor characteristics were developed to capture some additional performance as financial research advanced and significant contributions were made.

Academic research

The fundamental work of Fama and French may be traced back to the most significant academic works in the factor investing literature. Since the growth factor has a poor academic literature review, we will focus on the work of Fama and French (1993). In response to the CAPM’s limitations, Eugene Fama and Kenneth French developed the Fama-French three-factor model in 1993. It argues that, in addition to the market risk component provided by the CAPM, two additional factors, market capitalization (referred as “size”) and book-to-market ratio (referred as “value”), influence the returns on securities and portfolios. The major rationale for including these attributes, according to Fama and French, is that both size and book-to-market ratios are connected to the economic fundamentals of the firm issuing the securities (Fama and French, 1993).

In 2014, Fama and French claimed that their original three-factor model from 1993 was insufficient to explain certain observed differences in expected returns. As a result, Fama and French expanded their three-factor model to include two more factors: profitability and investment. The theoretical implications of the dividend discount model (DDM), which claim that profitability and investment contribute to the explanation of the returns derived from the High Minus Low premium element in the first model, justify these two aspects (Fama and French, 2015). High Minus Low can be defined as the value premium that accounts for the spread between the return of small capitalization stocks compared to large capitalization stocks.

Active managers have utilized the Growth factor to capture corporate growth possibilities using historical profits, sales, and anticipated earnings, and it has been employed as a possible source of alpha. The impact of unintended exposure, which shows that assets with strong growth can also have high valuations, high volatility, low yield, and bad quality, which can negatively influence portfolio performance, can be a difficulty when using simple selection methods to capture growth (MSCI Factor research, 2021).

Growth investing, often known as capital growth or capital appreciation, has been a prominent investment strategy since the 1950s and is one of active managers’ most intuitive and commonly used investment strategies (MSCI Factor research, 2021). Growth is a well-known investment strategy that, according to risk models, has a strong explanatory power in risk forecasting. In comparison to the MSCI ACWI Index, the pure growth factor has shown an impressive long-term return as well as low or negative correlation with other factors, which may assist diversify a multi-factor portfolio by minimizing short-term cyclicality.

Example of a “growth” stock

Any stock in a firm that is expected to expand at a pace significantly higher than the market average is considered a growth stock. Dividends are seldom paid on these stocks. This is because growth stock issuers are often businesses that seek to reinvest any profits in order to increase growth in the short term. When people buy growth stocks, they expect to profit from capital gains when they sell them later (Investopedia, 2021).

For instance, Amazon Inc. (AMZN) has been regarded as a growth stock for quite some time. It is, and has been for some time, one of the world’s largest companies in 2020. In terms of market value as of July 31, 2021, Amazon is among the top five U.S. stocks.

MSCI Growth Factor Index

MSCI Factor Indexes are rules-based, transparent indexes that target equities with favorable factor qualities, as determined by academic discoveries and empirical outcomes, and are designed for easy implementation, replicability, and usage in both standard indexed and active portfolios.

MSCI Growth Factor Index accounts for unexpected risks and exposures while also extending the notion of growth at a reasonable price (GARP) to include volatility, yield, and quality (MSCI Factor research, 2021). The impact of unintended exposure, which shows that assets with strong growth can also have high valuations, high volatility, low yield, and bad quality, which can negatively influence portfolio performance, can be a difficulty when using simple selection methods to capture growth. MSCI’s growth target index accounts for unexpected risks and exposures while also extending the notion of growth at a reasonable price (GARP) to include volatility, yield, and quality. Growth at a reasonable price (GARP), a long-held notion among growth investors, aims to avoid overpaying for a stock’s prospective growth. The GARP idea may be expanded by limiting value exposure, ensuring that the long-term premium for growth is not reduced by the unintentional and accidental impact of assets with high values, i.e., negative value exposure.

Performance of the MSCI Growth Factor Index

Figure 1 compares the MSCI Growth Factor Index’s performance to those of other factors from May 1999 to May 2020. All indices are rebalanced on a 100-point scale to ensure consistency in performance and to facilitate factor comparisons.

Figure 1. Performance of the MSCI Growth Factor Index from 1999-2020.
Growth factor performance
Source: MSCI Factor research, 2021.

Over the long run, the MSCI World Growth Index has traditionally delivered excess returns, with a yearly return of 1.41 percent over the MSCI World Index since 1999, as seen above. (MSCI Factor research, 2021).

Risk-return profile of MSCI Growth Factor Index

Figure 2 shows the MSCI Growth Factor Index compared to other factors over the period May 1999 – May 2020 in terms of risk/reward. The risk-return trade-off states that the potential return rises with an increase in risk. Individuals connect low levels of uncertainty about future returns with low potential returns, while high levels of uncertainty or risk are associated with large potential returns. According to the risk-return trade-off, an investor’s money can generate higher returns only if the investor is willing to endure a higher risk of loss and return (Figure 2).

Figure 2. Risk-return profile of MSCI Growth Factor Index compared to a peer group.
Growth factor risk return
Source: MSCI Factor research, 2021.

Growth stocks are defined as firms that are projected to expand their sales, profits, or margins faster than the industry or market average. The growth factor may provide value to a multi-factor portfolio by mitigating short-term cyclicality and providing asset managers with diversity and a stable source of premia. MSCI developed the Growth Target Index, based on Barra’s equity index model characteristics, through an optimization process that captures the growth component while limiting unwanted exposures that might erode the growth premium (MSCI Factor research, 2021).

ETFs for the growth factor

Let us recall that an Exchange-Traded Fund (ETF) is an investment vehicle that seeks to mirror the performance of a benchmark like an equity index and is traded on a continuous basis during the day like stocks. By investing in ETFs, an investor gains access to a plethora of diversification options through several asset classes (equity, bonds, currency, commodity, real estate, etc.).

In terms of proportion of assets under management, Figure 3 depicts the total ETF distribution among the leading suppliers of growth factor ETFs. Despite the lack of a real monopoly, the market is more equally distributed.

It’s worth mentioning the ARK Innovation ETF, which accounts for almost a third of the entire growth ETF market that was nominated. This ETF invests on biotech, robotics, artificial intelligence, blockchain, and finance technology, among other areas. It’s a thematically focused fund that invests in a limited number of high-growth companies and makes large swings in them.

The fund’s top 10 holdings make up nearly half of the overall portfolio. The company’s largest investment is Tesla (TSLA), which accounts for about 11% of its assets, followed by Square (SQ), Teladoc Health (TDOC), and Roku (ROKU), which account for 6.5 percent, 6.3 percent, and 5.5 percent, respectively. The top 10 companies include Zillow Group (Z), Zoom Video Communications (ZM), Baidu (BIDU), Shopify (SHOP), Spotify Technology (SPOT), and Exact Sciences (EXAS). The ARK Innovation ETF (ticker: ARKK) had a 153 percent return in 2020 (etf.com, 2021).

Figure 3. Growth factor ETF market.
Growth factor market share
Source: etf.com (2021).

Table 1 gives more detailed information about the biggest growth factor ETF providers: the asset under management (AUM), expense ratio (ER) and the segment for the investments.

Table 1. Ranking of the biggest Growth ETF providers.
Growth factor actors
Source: etf.com (2021).

Why should I be interested in this post?

If you are an undergraduate or graduate student in a business school or at the university, you may have seen in your 101 finance course the CAPM related to the market factor. This post makes aware of the existence of another risk factor priced by the market.

If you are an investor, you may consider adding an exposure to growth factor to enhance the overall portfolio return.

Related posts on the SimTrade blog

   ▶ Youssef LOURAOUI Minimum Volatility

   ▶ Youssef LOURAOUI Value Factor

   ▶ Youssef LOURAOUI Yield Factor

   ▶ Youssef LOURAOUI Momentum Factor

   ▶ Youssef LOURAOUI Size Factor

   ▶ Youssef LOURAOUI Quality Factor

Useful resources

Academic research

Fama, E.F., French, K.R. 1992. The Cross-Section of Expected Stock Returns. The Journal of Finance, 47: 427-465.

Fama, E.F., French, K.R., A five-factor asset pricing model, Journal of Financial Economics, 116(1): 2015, 1-22.

Mangram, M.E., 2013. A simplified perspective of the Markowitz Portfolio Theory. Global Journal of Business Research, 7(1): 59-70.

Business analysis

etf.com, 2021. Biggest Growth ETF providers.

MSCI Investment Research, 2021. Factor Focus: Growth.

Investopedia, 2021. Growth Stock.

About the author

The article was written in September 2021 by Youssef LOURAOUI (ESSEC Business School, Global Bachelor of Business Administration, 2017-2021).

Quality Factor

Quality Factor

Youssef_Louraoui

In this article, Youssef LOURAOUI (ESSEC Business School, Global Bachelor of Business Administration, 2017-2021) presents the quality factor, which is based on a risk factor that aims to get exposure to businesses with long-term business plans and competitive advantages.

This article is structured as follows: we begin by defining the quality factor and reviewing academic studies. The MSCI Quality Factor Index, which is well used as a benchmark in the asset management industry, is next presented in terms of performance and risk-return trade-off. We showcase the ETF market for investors looking to profit from the quality factor.

Definition

In the world of investing, a factor is any characteristic that helps explain an asset’s long-term risk and return performance. In the late 1970s, the portfolio management industry’s objective was to capture the market return on a portfolio. As a result of Markowitz and Tobin’s earlier research, William Sharpe, John Lintner, and Jan Mossin independently developed the Capital Asset Pricing Model (CAPM). Because it enabled investors to properly value assets in terms of systematic risk, the CAPM was a significant evolutionary step forward in the theory of capital market equilibrium (Mangram, 2013).

Eugene Fama and Kenneth French, following the CAPM’s original work, developed the Fama-French Three-Factor model in 1993 to solve the CAPM’s inadequacies. It claims that, in addition to the market risk component of the CAPM, two other factors have an effect on the returns on securities and portfolios: market capitalization (called the “size” factor) and the book-to-market ratio (referred to as the “value” factor). Other factor characteristics were developed to capture some additional performance as financial research advanced and significant contributions were made.

The quality factor is based on a risk factor that aims to get exposure to businesses with long-term business plans and competitive advantages. It can also be defined as the attributes for which investors are prepared to pay a premium (Hsu et al., 2019).

Academic research

The long-term outperformance of the quality factor over the market is well documented in the financial literature. Eugene Fama and Kenneth French added two quality-related components to their distinctive three-factor model (firm size, business value, and market risk): profitability and asset growth. Numerous active strategies have prioritized quality growth in their premium selection and portfolio construction processes. In 2012, Robert Novy-Marx published an essay proving that profitability and stability were just as useful as traditional value measures for assessing returns (MSCI Factor research, 2021).

Asness et al. (2018) propose a valuation model that illustrates how stock prices should increase if qualitative qualities such as profitability, growth, and safety improve. They demonstrate experimentally that high-quality stocks do fetch a premium on average, but not by a huge margin (Asness et al., 2018). Perhaps as a result of this perplexingly little influence of quality on price, high-quality stocks provide appealing risk-adjusted returns. Indeed, in the United States and 24 other countries, a factor that invests in high-quality companies and shorts low-quality companies generates significant risk-adjusted returns. The price of quality fluctuates throughout time, reaching a low point during the internet bubble, and a low price of quality suggests that QMJ will give a high rate of return in the future. Analysts’ price targets and earnings predictions indicate that systemic errors in return and earnings expectations are occurring as a result of quality issues (Asness et al., 2018).

MSCI Quality Factor Index

MSCI Factor Indexes are rule-based, transparent indexes that target equities with favorable factor qualities, as determined by academic discoveries and empirical outcomes, and are designed for easy implementation, replicability, and usage in both standard indexed and active portfolios. The MSCI Quality Factor Index measures the quality factor using three fundamental variables (MSCI Factor research, 2021) :

  • Return on equity – a measure of a company in generating profits
  • Debt to equity – a measure of a company’s leverage
  • Earnings variability – a measure of how smooth earnings growth has been.

Quality is a “defensive” component, which means that it has historically benefited during periods of economic recession (MSCI Factor research, 2021). The quality factor has aided in explaining the performance of equities with low debt, steady profits, and a high profit margin.

Performance of the MSCI Quality Factor Index from

Figure 1 compares the MSCI Quality Factor Index’s performance to those of other factors from May 1999 to May 2020. All indices are rebalanced on a 100-point scale to ensure consistency in performance and to facilitate factor comparisons

Figure 1. Performance of the MSCI Quality Factor Index from 1999-2020.

Quality_factor_performance

Source: MSCI Factor research (2021).

The MSCI Quality Factor Index has traditionally outperformed the MSCI World Index in the long term, with a 1.98 percent annual return over the MSCI World Index since 1999, as seen below (MSCI Factor research, 2021).

Risk-return profile of MSCI Quality Factor Index

Figure 2 shows the MSCI Quality Factor Index compared to other factors over the period May 1999 – May 2020 in terms of risk/reward. The risk-return trade-off states that the potential return rises with an increase in risk. Individuals connect low levels of uncertainty about future returns with low potential returns, while high levels of uncertainty or risk are associated with large potential returns. According to the risk-return trade-off, an investor’s money can generate higher returns only if the investor is willing to endure a higher risk of loss as shown in Figure 2.

Figure 2. Risk-return profile of MSCI Yield Factor Index compared to a peer group.

Quality_factor_riskreturn

Source: MSCI Factor research (2021).

Behavior of the MSCI Quality Factor Index during the Covid-19 crisis

The Covid-19 crisis has not only caused significant social and economic suffering, but it had also an impact on financial markets. To study the behavior of the factors during the Covid-19 crisis, we compute the return of the MSCI Factor indexes during the different stages of the crisis. The MSCI Factor indexes are: value, size, quality, momentum and minimum volatility. Following Pagano et al. (2020) and Hasaj and Sherer (2021), we decompose the Covid-19 crisis into five stages: origin, incubation, outbreak, fever, and treatment. Each stage is described below.

  • Origin (01/11/2019 – 01/01/2020): the first instances are reported in Wuhan, China.
  • Incubation (02/01/2020 – 17/01/2020): during this phase, the number of patients began to rise at a faster rate, raising concerns about the disease’s severity.
  • Outbreak (20/01/2020 – 21/02/2020): the number of cases rose to the point that the World Health Organization (WHO) decided that this illness may pose a major threat to the world’s population, and the pandemic was proclaimed.
  • Fever (24/02/2020 – 20/03/2020): markets are extremely volatile, owing to government restrictions aimed at flattening the infection curve, with the decision to impose a lockdown in numerous nations as the most notable measures, among others.
  • Treatment (23/03/2020 – 15/04/2020): most of this turnaround occurs between March and June 2020, which corresponds with the start of good news about the discovery and widespread use of the vaccine.

Table 1 gives the performance of the MSCI factor indexes during the different stages of the Covid-19 crisis. Performance is measured by the return computed on the time-period of each stage, and then annualized for comparison across the different stages. We use data are from Thomson Reuters.

Table 1. Performance of the MSCI factor indexes during the Covid-19 crisis.

Performance_MSCI_Factor_Indexes_COVID-19_Crisis

Source: computation by the author. Data source: Thomson Reuters.

A conclusive statement can be made based on our analysis. The quality component was the strongest performer throughout the COVID crisis’s inception in late 2020 and during the fever phase, when severe limitations were implemented, resulting in a collapsing market.

ETFs to capture the Quality factor

Let us recall that an Exchange-Traded Fund (ETF) is an investment vehicle that seeks to mirror the performance of a benchmark like an equity index and is traded on a continuous basis during the day like stocks. By investing in ETFs, an investor gains access to a plethora of diversification options through several asset classes (equity, bonds, currency, commodity, real estate, etc.).

Figure 3 illustrates the overall ETF distribution of the major providers of quality factor ETFs in terms of percentage of asset under management. By examining the market overview for quality factor investments, we can observe SPDR dominance in this factor investing market, with 76.07%, representing more than three quarters of the overall quality factor ETF market.

Figure 3. Quality factor ETF market.

Quality_factor_marketshare

Source: etf.com (2021).

Table 2 gives more detailed information about the biggest quality factor ETF providers: the asset under management (AUM), expense ratio (ER) and the segment for the investments.

Table 2. Ranking of the biggest Quality ETF providers.

Quality_factor_actors

Source: etf.com (2021).

Why should I be interested in this post?

If you are an undergraduate or graduate student at a business school or university, you may have encountered the CAPM in your 101 finance course. This post raises awareness of the presence of another market-priced risk factor.

If you are an investor, you may wish to consider increasing your exposure to the quality factor in order to boost your portfolio’s total return.

Related posts on the SimTrade blog

   ▶ Youssef LOURAOUI Minimum Volatility

   ▶ Youssef LOURAOUI Value Factor

   ▶ Youssef LOURAOUI Yield Factor

   ▶ Youssef LOURAOUI Momentum Factor

   ▶ Youssef LOURAOUI Size Factor

   ▶ Youssef LOURAOUI Growth Factor

Useful resources

Academic research

Clifford S. Asness & Andrea Frazzini & Lasse Heje Pedersen, 2019. “Quality minus junk,” Review of Accounting Studies, 24(1): 34-112.

Hasaj, M., Sherer, B., 2021. Covid-19 and Smart-Beta: A Case Study on the Role of Sectors. EDHEC-Risk Institute Working paper, 1-35.

Mangram, M.E., 2013. A simplified perspective of the Markowitz Portfolio Theory. Global Journal of Business Research, 7(1): 59-70.

Pagano, M., Wagner, C., Zechner, J., 2020. Disaster Resilience and Asset Prices, Working paper.

Business analysis

etf.com, 2021. Biggest Quality ETF providers.

MSCI Investment Research, 2021. Factor Focus: Quality.

About the author

The article was written in September 2021 by Youssef LOURAOUI (ESSEC Business School, Global Bachelor of Business Administration, 2017-2021).

Size Factor

Size Factor

Youssef_Louraoui

In this article, Youssef LOURAOUI (ESSEC Business School, Global Bachelor of Business Administration, 2017-2021) presents the size factor, which is based on a risk factor that aims to capture the documented outperformance of small-cap firms compared to larger enterprises.

This article is structured as follows: we begin by defining the size factor and reviewing academic studies. The MSCI Size Factor Index, which is well used as a benchmark in the asset management industry, is next presented in terms of performance, risk-return trade-off, and behavior during the Covid-19 crisis. We showcase the ETF market for investors looking to profit from the size factor.

Definition

In the world of investing, a factor is any aspect that helps explain an asset’s long-term risk and return performance. In the late 1970s, the portfolio management industry’s objective was to capture the market return on a portfolio. As a result of Markowitz and Tobin’s earlier research, William Sharpe, John Lintner, and Jan Mossin independently developed the Capital Asset Pricing Model (CAPM). Because it enabled investors to properly value assets in terms of systematic risk, the CAPM was a significant evolutionary step forward in the theory of capital market equilibrium (Mangram, 2013).

Eugene Fama and Kenneth French, following the CAPM’s original work, developed the Fama-French Three-Factor model in 1993 to solve the CAPM’s inadequacies. It claims that, in addition to the market risk component of the CAPM, two other factors have an effect on the returns on securities and portfolios: market capitalization (called the “size” factor) and the book-to-market ratio (referred to as the “value” factor). Other factor characteristics were developed to capture some additional performance as financial research advanced and significant contributions were made.

The Size factor has captured the long-run proclivity of small-cap firms to outperform larger enterprises. The work of Banz (1981) adds another piece to the growing puzzle. It evaluates the link between a firm’s overall market value and its return on common shares. The findings indicate that, on average, small businesses common stock generated greater risk-adjusted returns than large firms’ common stock throughout the 1936 – 1975 period (Banz, 1981). This impact is referred to as the “size effect”.

Academic research

Rolf Banz, a Ph.D. candidate at the University of Chicago at that time, found the size factor in US stocks in 1981. The size effect’s proponents provide many explanations for it. Banz stated that it is the result of a weakness in the capital asset pricing model (CAPM, the typical approach for forecasting risk and return on stock investments) or a lack of information regarding businesses that receive minimal analyst attention. After economists Eugene Fama and Kenneth French incorporated size as a critical component of their renowned three-factor model, size research exploded (MSCI Factor research, 2021).

Empirical studies

According to academic literature, the single-period capital asset pricing model (henceforth CAPM) postulates a straightforward linear connection between a security’s projected return and market risk. While direct testing has proved inconclusive, emerging evidence supports the possibility of other asset price variables.

For the period 1936-1977, Litzenberger and Ramaswamy (1979) demonstrate a substantial positive association between dividend yield and return on common stocks. Basu (1977) establishes a link between price-earnings ratios and risk-adjusted returns (Banz, 1981). He interprets his findings as evidence of market inefficiency; however, market efficiency tests are frequently conducted in conjunction with tests of the efficient market hypothesis and a particular equilibrium connection. Thus, some of the abnormalities ascribed to a lack of market efficiency may easily be the consequence of model misspecification. However, because the study’s findings are not based on a particular theoretical equilibrium model, it is impossible to clearly establish whether market value matters in and of itself or whether it is only a proxy for undiscovered actual extra elements linked with market value (Banz, 1981).

According to the data given in this paper, the CAPM is misspecified. Over a forty-year period, tiny NYSE businesses have generated considerably higher risk-adjusted returns than large NYSE enterprises (Banz, 1981). This size impact is not linear in market proportion (or market proportion log) but is most evident for the sample’s smallest companies. Additionally, the impact is not very stable over time. A comparison of the ten-year subperiods reveals significant variations in the magnitude of the size factor’s coefficient (Banz, 1981).

Such an impact has no theoretical basis. Banz asserts that we don’t even know if the factor is size itself or if size is only a proxy for one or more genuine but unknown factors that are linked with size (Banz, 1981). However, it is feasible to make certain hypotheses and even debate some aspects for which size is a proxy. Reinganum’s (1980) recent study has ruled out one obvious candidate: the price-earnings (P/E) ratios. He discovers that the P/E effect, as reported by Basu (1977), vanishes when he controls for size for both NYSE and AMEX stocks, but that there is a significant size effect even when he controls for the P/E ratio, implying that the P/E ratio effect is a proxy for the size effect and not the other way around (Banz, 1981).

Naturally, there are still a vast number of potential elements to evaluate. Thus, a lack of knowledge about small businesses results in less diversification and thus greater returns on ‘undesirable’ small business stocks (Banz, 1981). It may be tempting to use the size effect as the basis for a theory of mergers – big businesses may pay a premium for small firms’ shares because they can discount the same cash flows at a lower discount rate. Naturally, this may turn out to be total nonsense if it is demonstrated that size is only a proxy. While this informal model fits the empirical data, it is only speculation. The size effect occurs, but its cause is unknown. It should be regarded with caution until an answer is found (Banz, 1981).

MSCI Size Factor Index

MSCI Factor Indexes are rules-based, transparent indexes that target equities with favorable factor qualities, as determined by academic discoveries and empirical outcomes, and are designed for easy implementation, replicability, and usage in both standard indexed and active portfolios. The MSCI Equal Weighted Indexes tend to favor smaller cap firms. At each rebalance date, index components are weighted equally, thereby eliminating the influence of that constituent’s price (high or low) from the index. Size is a “pro-cyclical” element, which means it has historically benefited from periods of economic boom.

For decades, institutional investing has included a size premium. It has been a key component of several factor-based indexes during the last few years. MSCI Equal Weighted Indexes tend to favor smaller sized firms in comparison to the benchmark parent index (MSCI Factor research, 2021). At each rebalancing date, index components are weighted equally, thereby eliminating the influence of a constituent’s price (high or low) on the index.

Performance of the MSCI Size Factor Index

Figure 1 compares MSCI World Equal Weighted Index (Size factor) performance to those of other factors from May 1999 to May 2020. All indices are rebalanced on a 100-point scale to ensure consistency in performance and to facilitate factor comparisons.

Figure 1. Performance of the MSCI Size Factor Index from 1999-2020.
Size_factor_performance
Source: MSCI Factor research (2021).

Over the long term, the MSCI World Equal Weighted Index (Size factor) has traditionally provided excess returns, with an annual return of 1.54 percent over the MSCI World Index since 1999 (MSCI Factor research, 2021).

Risk-return profile of MSCI Size Factor

Figure 2 shows the MSCI World Equal Weighted Index (Size factor) compared to other factors over the period May 1999 – May 2020 in terms of risk/reward. The risk-return trade-off states that the potential return rises with an increase in risk. Individuals connect low levels of uncertainty about future returns with low potential returns, while high levels of uncertainty or risk are associated with large potential returns. According to the risk-return trade-off, an investor’s money can generate higher returns only if the investor is willing to endure a higher risk (Figure 2).

Figure 2. Risk-return profile of MSCI Size Factor Index compared to a peer group.
Size_factor_riskreturn
Source: MSCI Factor research (2021).

Behavior of the MSCI Size Factor Index during the Covid-19 crisis

The Covid-19 crisis has not only caused significant social and economic suffering, but it had also an impact on financial markets. To study the behavior of the factors during the Covid-19 crisis, we compute the return of the MSCI Factor indexes during the different stages of the crisis. The MSCI Factor indexes are: value, size, quality, momentum and minimum volatility. Following Pagano et al. (2020) and Hasaj and Sherer (2021), we decompose the Covid-19 crisis into five stages: origin, incubation, outbreak, fever, and treatment. Each stage is described below.

  • Origin (01/11/2019 – 01/01/2020): the first instances are reported in Wuhan, China.
  • Incubation (02/01/2020 – 17/01/2020): during this phase, the number of patients began to rise at a faster rate, raising concerns about the disease’s severity.
  • Outbreak (20/01/2020 – 21/02/2020): the number of cases rose to the point that the World Health Organization (WHO) decided that this illness may pose a major threat to the world’s population, and the pandemic was proclaimed.
  • Fever (24/02/2020 – 20/03/2020): markets are extremely volatile, owing to government restrictions aimed at flattening the infection curve, with the decision to impose a lockdown in numerous nations as the most notable measures, among others.
  • Treatment (23/03/2020 – 15/04/2020): most of this turnaround occurs between March and June 2020, which corresponds with the start of good news about the discovery and widespread use of the vaccine.

Table 1 gives the performance of the MSCI factor indexes during the different stages of the Covid-19 crisis. Performance is measured by the return computed on the time-period of each stage, and then annualized for comparison across the different stages. We use data are from Thomson Reuters.

Table 1. Performance of the MSCI factor indexes during the Covid-19 crisis.
Performance of the MSCI factor indexes during the Covid-19 crisis
Source: computation by the author. Data source: Thomson Reuters.

According to an examination of more than one year worth of market data, the size factor underperformed throughout the study period, most notably during the period of economic stress in the financial markets caused by the Covid-19 crisis. Given the crisis’s unprecedented severity, lockdown essentially shut down small and medium-sized firms, which finally suffered a period of catastrophic financial hardship, culminating in a non-negligible number of chain bankruptcies in the hardest-hit industries. This may help to explain why the Fever phase is the lowest-returning for the size factor. As the crisis progressed and governments spent billions on an accommodating monetary strategy to stimulate demand and re-establish healthy growth, size outperformed in the time after the pandemic’s fever phase (Figure 3).

ETFs to capture the Size factor

Let us recall that an Exchange-Traded Fund (ETF) is an investment vehicle that seeks to mirror the performance of a benchmark like an equity index and is traded on a continuous basis during the day like stocks. By investing in ETFs, an investor gains access to a plethora of diversification options through several asset classes (equity, bonds, currency, commodity, real estate, etc.).

Figure 3 illustrates the overall ETF distribution of the major providers of size factor ETFs in terms of percentage of asset under management. By examining the market overview for size factor investments, we can observe Blackrock and Vanguard dominance in this factor investing market, with 53.40% and 37.27% respectively, representing 90.67% of the overall size factor ETF market.

Figure 3. Size factor ETF market.
Size_factor_marketshare
Source: etf.com (2021).

Table 2 gives more detailed information about the biggest size factor ETF providers: the asset under management (AUM), expense ratio (ER) and the segment for the investments.

Table 2. Ranking of the biggest Size ETF providers.
Size_factor_actors
Source: etf.com (2021).

Why should I be interested in this post?

If you are an undergraduate or graduate student in a business school or at the university, you may have seen in your 101 finance course the CAPM related to the market factor. This post makes aware of the existence of another risk factor priced by the market.

If you are an investor, you may consider adding an exposure to size factor to enhance the overall portfolio return.

Related posts on the SimTrade blog

▶ Youssef LOURAOUI Minimum Volatility

▶ Youssef LOURAOUI Value Factor

▶ Youssef LOURAOUI Yield Factor

▶ Youssef LOURAOUI Momentum Factor

▶ Youssef LOURAOUI Quality Factor

▶ Youssef LOURAOUI Growth Factor

Useful resources

Academic research

Banz, R.W., 1981. The relationship between return and market value of common stocks. Journal of Financial Economics, 9: 3-18.

Basu, S., 1977. Investment performance of common stocks in relation to their price-earnings ratios: A test of Efficient Market Hypothesis. The Journal of Finance, 32: 663-682.

Fama, E.F., French, K.R. 1992. The Cross-Section of Expected Stock Returns. The Journal of Finance, 47: 427-465.

Fama, E.F., French, K.R., 2015. A five-factor asset pricing model. Journal of Financial Economics, 116(1): 1-22.

Hasaj, M., Sherer, B., 2021. Covid-19 and Smart-Beta: A Case Study on the Role of Sectors. EDHEC-Risk Institute Working paper.

Litzenberger, R., Ramaswamy, K., 1982. The Effects of Dividends on Common Stock Prices Tax Effects or Information Effects? The Journal of Finance, 37(2): 429-443.

Mangram, M.E., 2013. A simplified perspective of the Markowitz Portfolio Theory. Global Journal of Business Research, 7(1): 59-70.

Pagano, M., Wagner, C., Zechner, J., 2020. Disaster Resilience and Asset Prices, Working paper.

Reinganum, M., 1981. The Arbitrage Pricing Theory: Some Empirical Results. The Journal of Finance, 36(2): 313-321.

Business analysis

etf.com, 2021. Biggest Size Factor ETF providers.

MSCI Investment Research, 2021. Factor Focus: Size.

About the author

The article was written in September 2021 by Youssef LOURAOUI (ESSEC Business School, Global Bachelor of Business Administration, 2017-2021).

Momentum Factor

Momentum Factor

Youssef_Louraoui

In this article, Youssef LOURAOUI (ESSEC Business School, Global Bachelor of Business Administration, 2017-2021) presents the momentum factor, which is based on a risk factor that aims to get exposure to stocks that have a winning tendency in the upside and downside assuming that they will continue to do well in the short term.

Another similar concept related to momentum is trend following. It is a trading strategy that seeks to profit on an asset’s momentum in a certain direction. A trend occurs when the price moves in a consistent direction (upward or downward). Momentum investing and trading are based on the premise that prices respond to the strength of their supply and demand sources (at least in part) (Investopedia, 2021). It’s considered as a forward-looking strategy. Momentum manifests itself in a variety of different ways. It might be based on publicly traded firms’ earnings reports, the connection between buyers and sellers in the market, or even the usual pace of price rises and decreases in the past.

This article is structured as follows: we begin by defining the momentum factor and reviewing academic studies. The MSCI Momentum Factor Index, which is well used as a benchmark in the asset management industry, is next presented in terms of performance, risk-return trade-off, and behavior during the Covid-19 crisis. We showcase the ETF market for investors looking to profit from the momentum factor.

Definition

In the world of investing, a factor is any attribute that helps explain an asset’s long-term risk and return performance. In the late 1970s, the portfolio management industry’s objective was to capture the market return on a portfolio. As a result of Markowitz and Tobin’s earlier research, William Sharpe, John Lintner, and Jan Mossin independently developed the Capital Asset Pricing Model (CAPM). Because it enabled investors to properly value assets in terms of systematic risk, the CAPM was a significant evolutionary step forward in the theory of capital market equilibrium (Mangram, 2013).

Eugene Fama and Kenneth French, following the CAPM’s original work, developed the Fama-French three-factor model in 1993 to solve the CAPM’s inadequacies. It claims that, in addition to the market risk component of the CAPM, two other factors have an effect on the returns on securities and portfolios: market capitalization (called the “size” factor) and the book-to-market ratio (referred to as the “value” factor).
Other factor characteristics were developed to capture some additional performance as financial research advanced and significant contributions were made.

The Momentum factor refers to a winning stock’s tendency to continue doing well in the short term (Jegandeesh and Titman, 1993).

Academic research

The momentum premium was originally found by academics in 1993, when UCLA researchers Narasimhan Jegadeesh and Sheridan Titman proved that buying well-performing equities and selling underperforming ones provided large positive returns over three to twelve-month holding periods. The study finds that these techniques are profitable not because of their systematic risk or delayed stock price responsiveness to common causes. However, a portion of the anomalous returns achieved in the first year following portfolio creation fade away during the next two years. A similar pattern of returns is often observed around the earnings releases of previous winners and losers (Jegandeesh and Titman, 1993).

Empirical studies

Numerous subsequent research have established that the momentum factor exists across stock sectors, nations, and, more broadly, asset classes. Momentum is not as well understood as other variables, even though several theories seek to explain it. Some feel it is remuneration for taking on a high degree of risk, while others believe it is a result of market inefficiencies caused by delayed pricing reactions to firm-specific information.

While contrarian strategies have garnered much attention in recent academic research, the early work on market efficiency concentrated on relative strength strategies that invest in previous winners and sell past losers. Notably, Levy (1967) asserts that a trading method that purchases equities at prices significantly higher than their average price over the previous 27 weeks generates considerable anomalous profits. Jensen and Bennington (1970), on the other hand, note that Levy developed his trading rule after evaluating 68 alternative trading rules in his dissertation and express reservations about his results as a result (Jegandeesh and Titman, 1993). Jensen and Rennington examine the profitability of Levy’s trading rule over a lengthy period that falls mostly outside of Levy’s initial sample period. They discover that Levy’s trading rule does not outperform a buy and hold strategy throughout their sample period, and so ascribe Levy’s outcome to selection bias (Jegandeesh and Titman, 1993).

Economical interpretation

While the scholarly discussion has shifted away from relative strength trading rules, a lot of practitioners continue to utilize relative strength as a stock selection criterion. For example, Grinblatt and Titman (1989, 1991) found that most mutual funds purchased equities that had grown in price over the preceding quarter (Jegandeesh & Titman, 1993).

MSCI Momentum Factor Index

MSCI Factor Indexes are rules-based, transparent indexes that target equities with favorable factor qualities, as determined by academic discoveries and empirical outcomes, and are designed for easy implementation, replicability, and usage in both standard indexed and active portfolios. Momentum is classified as a “persistence” component, which means that it benefits from long-term market (MSCI Factor research, 2021). The MSCI Momentum Index measures:

  • Risk-adjusted excess return – that is, return that surpasses the benchmark – during a 6-month period
  • Risk-adjusted excess return that outperforms the benchmark over a 12-month period

These findings conclude in the research paper of Moskowitz et all (1999) hold up to a variety of criteria and treatments and provide critical practical insights into the profitability of momentum investing (Moskowitz, 1999). For example, these findings suggest that momentum strategies are not very well diversified, as both winners and losers typically come from the same industry. Additionally, if trading on momentum is desired, industry-based techniques tend to be more profitable and implementable. Unlike individual stock momentum techniques, which appear to be primarily driven by the sell side, industry momentum generates as much or more profit on the purchase side as on the sell side. Additionally, unlike individual stock momentum, sector momentum earnings continue to be robust among the largest, most liquid companies (Moskowitz, 1999).

Performance of the MSCI Momentum Factor Index

Figure 1 compares MSCI Momentum Factor Index performance to those of other factors from May 1999 to May 2020. All indices are rebalanced on a 100-point scale to ensure consistency in performance and to facilitate factor comparisons.

Figure 1. Performance of the MSCI Momentum Factor Index from 1999-2020.
Performance of the MSCI Momentum Factor Index from 1999-2020.
Source: MSCI Factor research (2021).

According to MSCI research, the momentum component has historically been one of the most effective generators of excess returns, consistently excelling in macro conditions characterized by a prolonged cycle in underlying market trends. As per the figure below, the MSCI World Momentum Index has historically generated excess returns over the long run, outperforming the MSCI World Index by 3.17 percent year since 1999 (MSCI Factor study, 2021).

Risk-return profile of MSCI Momentum Factor Index

Figure 2 shows the MSCI Momentum Factor Index compared to other factors over the period May 1999 – May 2020 in terms of risk/reward. The risk-return tradeoff states that the potential return rises with an increase in risk. Individuals connect low levels of uncertainty about future returns with low potential returns, while high levels of uncertainty or risk are associated with large potential returns. According to the risk-tradeoff trade-off, an investor’s money can generate higher returns only if the investor is willing to endure a higher risk of loss (Figure 2).

Figure 2. Risk-return profile of MSCI Momentum Factor Index compared to a peer group.
Risk-return profile of MSCI Momentum Factor Index compared to a peer group
Source: MSCI Factor research (2021).

Behavior of the MSCI Momentum Factor Index during the Covid-19 crisis

The Covid-19 crisis has not only caused significant social and economic suffering, but it had also an impact on financial markets. To study the behavior of the factors during the Covid-19 crisis, we compute the return of the MSCI Factor indexes during the different stages of the crisis. The MSCI Factor indexes are: value, size, quality, momentum and minimum volatility. Following Pagano et al. (2020) and Hasaj and Sherer (2021), we decompose the Covid-19 crisis into five stages: origin, incubation, outbreak, fever, and treatment. Each stage is described below.

  • Origin (01/11/2019 – 01/01/2020): the first instances are reported in Wuhan, China.
  • Incubation (02/01/2020 – 17/01/2020): during this phase, the number of patients began to rise at a faster rate, raising concerns about the disease’s severity.
  • Outbreak (20/01/2020 – 21/02/2020): the number of cases rose to the point that the World Health Organization (WHO) decided that this illness may pose a major threat to the world’s population, and the pandemic was proclaimed.
  • Fever (24/02/2020 – 20/03/2020): markets are extremely volatile, owing to government restrictions aimed at flattening the infection curve, with the decision to impose a lockdown in numerous nations as the most notable measures, among others.
  • Treatment (23/03/2020 – 15/04/2020): most of this turnaround occurs between March and June 2020, which corresponds with the start of good news about the discovery and widespread use of the vaccine.

Table 1 gives the performance of the MSCI factor indexes during the different stages of the Covid-19 crisis. Performance is measured by the return computed on the time-period of each stage, and then annualized for comparison across the different stages. We use data are from Thomson Reuters.

Table 1. Performance of the MSCI factor indexes during the Covid-19 crisis.
Performance of the MSCI factor indexes during the Covid-19 crisis
Source: computation by the author (data source: Thomson Reuters).

Both during the pre-lockdown phase (January 2nd to January 17th 2020) and during the post-lockdown phase (23 March 2020 – 15 April 2021), the momentum component performed well, attaining the second best risk/reward tradeoff (Table 1).

ETFs to capture the Momentum factor

Let us recall that an Exchange-Traded Fund (ETF) is an investment vehicle that seeks to mirror the performance of a benchmark like an equity index and is traded on a continuous basis during the day like stocks. By investing in ETFs, an investor gains access to a plethora of diversification options through several asset classes (equity, bonds, currency, commodity, real estate, etc.).

Figure 3 illustrates the overall ETF distribution of the major providers of momentum factor ETFs in terms of percentage of asset under management. By examining the market overview for momentum factor investments, we can observe Blackrock’s dominance (iShares), with assets under management underpinning $27 billion of the overall market value, holding 55% of the overall percentage of the benchmark retained.

Figure 3. Momentum factor ETF market.
 Momentum factor ETF market
Source: etf.com (2021).

Table 2 gives more detailed information about the biggest momentum factor ETF providers: the asset under management (AUM), expense ratio (ER) and the segment for the investments.

Table 2. Ranking of the biggest Momentum ETF providers.
Ranking of the biggest Momentum ETF providers
Source: etf.com (2021).

Why should I be interested in this post?

If you are an undergraduate or graduate student in a business school or at the university, you may have seen in your 101 finance course the CAPM related to the market factor. This post makes aware of the existence of an other risk factor priced by the market.

If you are an investor, you may consider adding an exposure to momentum factor to enhance the overall portfolio return.

Related posts on the SimTrade blog

   ▶ Youssef LOURAOUI Minimum Volatility

   ▶ Youssef LOURAOUI Value Factor

   ▶ Youssef LOURAOUI Yield Factor

   ▶ Youssef LOURAOUI Size Factor

   ▶ Youssef LOURAOUI Quality Factor

   ▶ Youssef LOURAOUI Growth Factor

Useful resources

Academic research

Fama, E.F. and French, K.R. (1992), The Cross-Section of Expected Stock Returns. The Journal of Finance , 47: 427-465.

Jegandeesh, N., Titman, S., 1993. Returns to buying winners and selling losers: Implication for stock market efficiency. The Journal of Finance , 48(1), 1-34.

Jensen, M. C., Benington, G. A. 1970. Random walks and technical theories: Some additional evidence. The Journal of Finance , 25: 469-482

Levy, R. A. 1967. Relative strength as a criterion for investment selection. The Journal of Finance , 22: 595-610.

Mangram, M. E., 2013. A simplified perspective of the Markowitz Portfolio Theory. Global Journal of Business Research , 7(1): 59-70.

Hasaj, M., Sherer, B., 2021. Covid-19 and Smart-Beta: A Case Study on the Role of Sectors. EDHEC-Risk Institute Working Paper, 1-35.

Pagano, M., Wagner, C., Zechner, J. 2020. Disaster Resilience and Asset Prices, Working paper.

Business analysis

etf.com, 2021. Biggest Momentum ETF providers.

MSCI Investment Research, 2021. Factor Focus: Momentum

Investopedia, 2021. The difference between Trends and Momentums

About the author

The article was written in September 2021 by Youssef LOURAOUI (ESSEC Business School, Global Bachelor of Business Administration, 2017-2021).

Is smart beta really smart?

Is smart beta really smart?

Youssef LOURAOUI

In this article, Youssef LOURAOUI (ESSEC Business School, Global Bachelor of Business Administration, 2017-2021) presents the concept of smart beta used in the asset management industry.

Mutual funds and Exchange traded funds (ETF) based on the smart beta approach have increased in size during the recent years. As Burton Malkiel (2014), we also wonder if the smart beta approach is really smart.

The smart beta industry

Smart beta funds have experienced a significant growth with total assets under management approaching market 620 billion dollar in the U.S. as shown in Figure 1 (Morningstar Reseach, 2017).

Figure 1. Smart Beta Exchange Traded Products growth in the US market (2000-2017).
Smart Beta Exchange Traded Products growth
Source: Morningstar Research (2017).

Traditional approach in portfolio management

The traditional approach to build asset portfolio is to define asset weights based on the market capitalization. The framework of this traditional approach is based on the Capital Asset Pricing Model (CAPM) introduced by the work of Henry Markowitz and William Sharpe in 1964. The CAPM is based on a set of hypotheses about the market structure and investors:

  • No intermediaries
  • No constraints (possibility of short selling)
  • Supply and demand equilibrium
  • Inexistence of transaction cost
  • Investors seeks to maximise its portfolio value by optimizing the mean associated with expected returns while minimizing variance associated with risk
  • Investors are considered as “rational” with a risk averse profile
  • Investors have access to the information simultaneously in order to execute their investment ideas

Under this framework, Markowitz developed a model relating the expected return of a given asset and its risk:

Relation between expected return and risk

where E(r) represents the expected return of the asset, rf the risk-free rate, β a measure of the risk of the asset and E(rm) the expected return of the market.

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

Beta

where Cov(r,rm) represents the covariance of the asset with the overall market, and σ(rm)2 is the variance of market return.

The beta represents the sensibility of the asset to the fluctuations of the market. This risk measure helps investors to predict the movements of their asset according to the movement of the market overall. It measures the asset volatility in comparison with the systematic risk inherent to the market. Statistically, the beta represents the slope of the line through a regression of data points between the stock returns in comparison to the market returns. It helps investors to explain how the asset moves compared to the market.

More specifically, we can consider the following cases for beta values:

  • β = 1 indicates a fluctuation between the asset and its benchmark, thus the asset tends to move in a similar rate than the market fluctuations. A passive ETF replicating an index will present a beta close to 1 with its associated index.
  • 0 < β < 1 indicates that the asset moves in a slower rate than market fluctuations. Defensive stocks, stocks that deliver consistent returns without regarding the market state like P&G or Coca Cola in the US, tend to have a beta with the market lower than 1.
  • β > 1 indicates a more aggressive effect of amplification between the asset price movements with the market movements. Call options tend to have higher betas than their underlying asset.
  • β = 0 indicates that the asset or portfolio is uncorrelated to the market. Govies, or sovereign debt bonds, tend to have a beta-neutral exposure to the market.
  • β < 0 indicates an inverse effect of market fluctuation impact in the asset volatility. In this sense, the asset would behave inversely in terms of volatility compared to the market movements. Put options and Gold typically tend to have negative betas.

In order to better monitor the performance of an actively managed fund, active fund managers seek to improve the performance of their fund compared to the market. This additional performance is measured by the “alpha” (Jensen, 1968) defined by:

Alpha Jensen

where E(r) is the average return of the fund over the period studied, rf the risk-free rate, E(rm) the expected return of the market, and β×(E(rm)-rf) represents the systematic risk of the fund.

Jensen’s alpha (α) represents the abnormal returns of the fund.

The Smart beta approach

The smart beta approach is based on the construction of a portfolio of assets using several different yield enhancement “factors”. BlackRock Investment Solutions (2021) lists the following factors mainly used in the smart beta approach:

  • Quality, which aims to study the financial environment of the underlying asset.
  • Volatility which aims to filter assets according to their risk.
  • Momentum, which aims to identify trends in the selection of assets to be retained by focusing on stocks that have performed strongly in the short term.
  • Growth is the approach that aims to select securities that have strong return expectations in the medium to long term.
  • Size which aims to classify according to the size of the assets.
  • Value that seeks to denote undervalued assets that are close to their fundamental values.

The smart beta approach is opposed to the traditional portfolio approach where a portfolio is constructed using the weights defined by the market capitalization of its assets. The smart beta approach aims to position the portfolio sensitivity or “beta” according to the market environment expectation of the asset manager. For a bull market, the fund manager will select a set of factors to achieve a pronounced exposure of his portfolio. Symmetrically, for a bear market, the fund manager will select another set of factors opting for a beta neutral approach to protect the sensitivity of his portfolio against bear market fluctuations.

Performance and impact factor

S&P Group (2016) studied the performance of different factors (volatility, momentum, quality, value, dividend yield, growth and size) on the S&P500 index for 1994-2014 broken down into sub-sectors (see Table 1). This study finds that each sector is impacted differently by choosing one factor over another. For example, in the energy sector, the strategies of value and growth has led to a positive performance with respectively 1.22% and 2.56%, while in the industrial sector, the strategies of size were the only factor with a positive performance of 1.66%. In practice, there are two approaches: focusing on a single factor or finding a combination of factors that offers the most interesting risk-adjusted return to the investor in view of his/her investment strategy.

Table 1. Sector exposures to smart beta factors (1994-2014).
Sector exposures to smart beta factors
Source: S&P Research (2014).

S&P Group (2016) also studies the performance of the factors according to the market cycles (bull, bear or recovery markets), business cycles (expansion or contraction) and investor sentiment (neutral, bullish and bearish). The study shows how each factor has been mostly effective for every market condition.

Table 2. Performance of factors according to different market cycles, business cycles and investor sentiment.
Performance of factors
Source: S&P Research (2014).

In summary, the following characteristics of the different approaches discussed in this article can be identified:

  • The CAPM approach aims to give a practical configuration of the relationship between the return of an asset with the market return as well as the return considered as risk-free.
  • Alpha is an essential metric in the calculation of the portfolio manager’s return in an actively managed fund. In this sense, alpha and CAPM are linked in the fund given the nature of the formulas used.
  • Smart beta or factor investing follows an approach that straddles the line between active and passive management where the manager of this type of fund will use factors to filter its source of return generation which differs from the common approach based on CAPM reasoning (Fidelity, 2021).
  • The conductive link of these three reasoning is closely related to the fact that historically the CAPM model has been a pillar in financial theory, the smart beta being a more recent approach that tries to disrupt the codes of the so-called market capitalization based investment by integrating factors to increase the sources of return. Alpha is related to smart beta in the sense that the manager of this type of fund will want to outperform a benchmark and therefore, alpha allows to know the nature of this out-performance of the manager compared to a benchmark.

Is smart beta really smart?

Nevertheless, the vision of this smart beta approach has raised criticisms regarding the relevance of the financial results that this strategy brings to a portfolio’s return. Malkiel (2014) questioned the smartness of smart beta and found that the performance of this new strategy is only the result of chance in the sense that the persistence of performance is dependent in large part on the market configuration.

In his analysis of the performance of the smart ETF fund called FTSE RAFI over the period 2009-2014, he attributed the out-performance to luck. The portfolio allocation was highly exposed to two financial stocks, Citigroup and Bank of America, which accounted for 15% of the portfolio allocation. Note that Citigroup and Bank of America were prosecuted by the American courts for post-crisis financial events and interest rate manipulation operations related to the LIBOR scandal. This smart beta fund outperformed the passive managed US large cap ETF (SPY). Malkiel associated the asset selection of the FTSE RAFI fund with a bet on Bank of America that with another market configuration it could have ended in a sadder way.

Figure 2. FTSE RAFI ETF (orange) compared with its benchmark (FTSE RAFI US 1000) and with SPY ETF (green).
FTSE RAFI ETF
Source: Thomson Reuters Datastream.

We can conclude that the smart beta strategy can allow, as outlined in Blackrock’s research (BlackRock Investment Solutions, 2021), an opportunity to improve portfolio performance while seeking to manage variables such as portfolio out-performance, minimizing its volatility compared to the market or seeking diversification to reduce the risk of the investor’s portfolio. It is an instrument that must be taken judiciously in order to be able to affirm in fine if it is smart in the end, as Malkiel would say.

Related posts on the SimTrade blog

   ▶ Jayati WALIA Capital Asset Pricing Model (CAPM)

   ▶ Youssef LOURAOUI Beta

   ▶ Youssef LOURAOUI MSCI Factor Indexes

   ▶ Youssef LOURAOUI Factor Investing

   ▶ Youssef LOURAOUI Origin of factor investing

Useful resources

Academic articles

Malkiel, B. (2014). Is Smart Beta smart? The Journal of Portfolio Management 40, 5: 127-134

El Lamti N. (2017) Are smart beta strategies really smart? HEC Paris.

Business resources

BlackRock Investment Solutions (2021) What is Factor Investing

Fidelity (2021) Smart beta

S&P Global Research (2016) What Is in Your Smart Beta Portfolio? A Fundamental and Macroeconomic Analysis

Morningstar Research (2017) A Global Guide to Strategic-Beta Exchange-Traded Products

Fidelity (2021) Smart beta

About the author

The article in April 2021 was written by Youssef LOURAOUI (ESSEC Business School, Global Bachelor of Business Administration, 2017-2021).

ETFs in a changing asset management industry

ETFs in a changing asset management industry

Youssef LOURAOUI

In this article, Youssef LOURAOUI (ESSEC Business School, Global Bachelor of Business Administration, 2016-2020) talks about his research conducted in the field of investing.

As a way of introduction, ETFs have been captivating investors’ attention in the last 20 years since their creation. This financial innovation has shaped how investors place their capital.

Definition

An ETF can be defined as a financial product that is based on a basket of different assets, to replicate the actual performance of each selected investment. An ETF has more or less the same proportion of the underlying components of the basket, depending on the style of management of the asset manager. ETFs represent nearly 90% of the asset under management of the global Exchange Traded Products (ETP).

History

The first ETF was the Standard and Poor’s Depository Receipts (SPDR) introduced in 1993. It appears to be an optimized product that enables investors to trade it like a stock, with a price that fluctuates during the day (not like mutual funds whose value is known at the end of the day only). The main advantage of ETFs for investors is to diversify their investment with lower fees than buying each underlying asset separately. The most important ETFs in the market are the ones with the lowest expense ratio as it is a crucial point to attract money from investors in the fund.

Types of ETF

ETFs can be segmented in different types according to the asset class, geography, sector, investment style among other criteria. According to Blackrock’s classification (2021), the overall ETF market can be divided into the following classes:

  • Stock ETFs track a certain stock market index, such as the S&P 500 or NASDAQ.
  • Bond ETFs offer exposure to a wide selection of fixed income instruments.
  • Sector and industry ETFs invest in a particular industry such as technology, healthcare, or financials.
  • Commodity ETFs track the price of a commodity such as oil, gold, or wheat.
  • Style ETFs are devoted to an investment style or market capitalization focus such as large-cap value or small-cap growth.
  • Alternative ETFs offer exposure to the alternative asset classes and invest in strategies such as real estate, hedge funds and private equity.
  • Foreign market ETFs follow non-U.S. markets such as the United Kingdom’s FTSE 100 index or Japan’s Nikkei index.
  • Actively managed ETFs aim to provide a certain outcome to maximize income or outperform an index, while most ETFs are designed to track an index.

Figure 1. Volume of the ETF market worldwide 2003-2019.
Volume of the ETF market worldwide 2003-2019
Source: Statista (2021).

Figure 1 represents the volume of the ETF market worldwide over the period 2003-2019. With over 6,970 ETFs globally as of 2019 (Statista, 2021), the ETF industry is growing at an increasing pace, recording a thirty-fold increase in terms of market capitalization in the 17-year timeframe of the analysis. It reflects the growing appetite of investors towards this kind of financial instruments as they offer the opportunity for investors to invest virtually in every asset class, geographical region, sector, theme, and investment style (BlackRock, 2021).

iShares (BlackRock), Xtrackers (DWS) and Lyxor (Société Générale) can also be highlighted as key players of the ETF industry in Europe. As shown in Figure 2, Lyxor (a French player) is ranked 3rd most important player with nearly 9% of the overall European ETF market (Refinitiv insights, 2019). iShares represents nearly eight times the weight of Lyxor, which is slightly above the average of the overall European ETF volume in dollars.

Figure 2. Market share at the promoter level by Assets Under Management (March 31, 2019)
Market share at the promoter level by Assets Under Management (March 31, 2019)
Source: Refinitiv insights (2019).

It goes without saying that the key player worldwide remains BlackRock with nearly 1/3 of the global ETF market capitalization. According to Arte documentary, BlackRock is without a doubt a serious actor of the ETF industry as shown in Figure 2 with an unrivaled market share in the European and global ETF market. With more than 7 trillion of asset under management, BlackRock is the leading powerhouse of the asset management industry.

Benefits of ETF

The main benefits of investing in ETFs is the ability to invest in a diversified and straightforward manner in financial markets by owning a chunk of an index with a single investment. It allows investors to position their wealth in a reference portfolio based on equities, bonds or commodities. It also helps them to create a portfolio that suits their needs or preferences in terms of expected return and risk and also liquidity as ETFs can be bought and sold at any moment of the day. Finally, ETFs also allow investors to implement long/short strategies among others.

Risks

Market risk is an essential component to fully understand the risk of owning an ETF. According to the foundations of the modern portfolio theory (Markowitz, 1952), an asset can be deconstructed into two risk factors: an idiosyncratic risk inherent to the asset and a systematic risk inherent to the market. As an ETF are composed of a basket of different assets, the idiosyncratic risk can be neutralized by the effect of diversification, but the systematic risk, also called the market risk is not neutralized and is still present in the ETF.

In terms of risk, we can mention the volatility risk arising from the underlying assets or index that the ETF tries to replicate. In this sense, when an ETF tries to emulate the performance of the underlying asset, it will also replicate its inherent risk (the systematic and non-systematic risk of the underlying asset). This will have a direct impact on the overall risk-return characteristic of investors’ portfolio.

The second risk, common to all funds and that can have a significant impact on the overall performance, concerns the currency risk when the ETF owned doesn’t use the same currency as the underlying asset. In this sense, when owning an ETF that tracks another asset that is quoted in another currency is inherently, investors bears some currency risk as the fluctuations of the pair of currencies can have a significant impact on the overall performance of the position of the investor.

Liquidity risk arises from the difficulty to buy and sell a security in the market. The more illiquid the market, the wider the spreads to compensate the market maker for the task of connecting buyers and sellers. Liquidity is an important concern when picking an ETF as it can impact the performance of the portfolio overall.

Another risk particular to this instrument, is what is called the tracking error between the ETF value and its benchmark (the index that the ETF tries to replicate). This has a significant impact as, depending on the overall dispersion, the mismatch in terms of valuation between the ETF and the benchmark can impact the returns of investors’ portfolio overall.

Passive management and the concept of efficient market

Most ETFs corresponds to “passive” management as the objective is just to replicate the performance of the underlying assets or the index. Passive management is related to the Efficient Market Hypothesis (EMH), assuming that the market is efficient. Passive fund managers aim to replicate a given benchmark believing that in efficient markets active fund management cannot beat the benchmark on the long term.

Passive fund managers invest their funds by:

  • Pure replication of the benchmark by investing in each component of the basket (vanilla ETF)
  • Synthetic reproduction of the benchmark by replicating the basket with derivatives products (like futures contracts).

An important concept is market efficiency (also known as the informational efficiency), which is defined as the ability of the market to incorporate all the available information. Efficient market is a state of the market where information is rationally processed and quickly incorporated in the market price.

It is in the heart of the preoccupations of fund managers and analysts to unfold any efficiency in the market because the degree of efficiency impacts their returns directly (CFA Institute, 2011). Fama (1970) proposed a framework analyzing the degree of efficiency in a market. He distinguishes three forms of market efficiency (weak, semi-strong and strong) which correspond to the degree in which information is incorporated in the prices. Earning consistently abnormal returns based on trading with information is the opposite view of what an efficient market is.

  • The weak form of market efficiency refers to information composed of past market data (past transaction prices and volumes). In a weakly efficient market, past market information is already included in the current market price, and investors will not be able to distinguish any pattern or prediction of future prices based on past data.
  • The semi-strong of market efficiency refers to publicly available information. This includes market data (as in the week form) and financial disclosed data (financial accounts published by firms, press articles, reports by financial analysts, etc.). If a market is considered in the semi-strong sense, then it must be in a weak sense as well. In this context, there is no additional gain in determining under or overvalued security as all the public data is already incorporated in the asset price.
  • The strong of market efficiency refers to all information (both public and private). Markets are strongly efficient when they reflect all the available information at any time in the asset prices.

Related posts on the SimTrade blog

   ▶ Micha FISCHER Exchange-traded funds and Tracking Error

   ▶ Youssef LOURAOUI Passive Investing

Useful resources

Academic resources

Fama, E. (1970) “Efficient Capital Markets: A Review of Theory and Empirical Work” Journal of Finance 25(2), 383–417.

Business

Arte documentary (2014) “Ces financiers qui dirigent le monde: BlackRock”.

BlackRock (January 2021) ETF overview.

Refinitiv insights (2019) Concentration of the major players in the European ETF market.

About the author

The article was written in February 2021 by Youssef LOURAOUI (ESSEC Business School, Global Bachelor of Business Administration, 2016-2020).