Excerpt

## Table of contents

1. Introduction

2. Fundamental theory and previous discoveries

2.1. Different Factor Models

2.2. Returns of different profitable companies

2.3. Profitability anomalies

3. Profitability Anomalies in European stock markets

3.1. Construction of the model

3.2. Summary Statistics

3.3. Factor Spanning Tests

3.4. High minus low quintiles of the Profitability Anomalies

3.5. Quintiles of the Profitability Anomalies

4. Conclusions

References

Appendix

List of profitability anomalies

Correlations of the high minus low Profitability Anomalies

Quintiles of the Profitability Anomalies

## Table of Diagrams and Tables

Diagram 1 Performance of the European stock market

Table 1 Summary Statistics

Table 2 Factor Spanning Tests

Table 3 High minus low quintiles of the Profitability Anomalies

Table 4 Quintiles of the Profitability Anomalies Germany

Table 5 List of profitability anomalies

Table 6 Correlations of the high minus low Profitability Anomalies

Table 7 Quintiles of the Profitability Anomalies France

Table 8 Quintiles of the Profitability Anomalies Italy

## Table of Abbreviations and Symbols

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## Abstract

In this paper, we examine profitability patterns for the German, France and Italian stock markets and compare it to previous research evidence of the European stock market. Most results of our examination are in line with previous investigations. Thus, we can confirm for all three countries, that more profitable firms earn higher risk-adjusted returns on average. Furthermore, Profitability Anomalies are present in the German and France stock market, but astonishingly not identifiable in the Italian stock markets. Five of seven profitability measures are suitable for identifying anomalies.

## 1. Introduction

Latest studies on asset pricing models, like (Fama & French, 2017) or (Bouchaud, et al., 2019) reveal new evidence for anomalies in the stock markets. The investigations of anomalies can be splitted in different categories: *Momentum*, *Value-versus-growth*, *Investment*, *Intangibles*, *Trading frictions* and *Profitability*.^{1}

Most of the investigations assess stock markets on a continental level, like *Europe*, *North America*, *Japan* and *Asia Pacific* for instance. Undoubtedly, these results are very useful for an overall statement, but leaves one question unanswered: Are there any frictions within different European stock markets?

In this paper, we will examine the Profitability Anomalies of the German, France and Italian stock markets. In 2. Fundamental theory and previous discoveries, we will discuss previous research results and discuss suitable *Factor Models* for the upcoming empirical investigations. Next, we will deduce a Four-Factor Model with *Regional Factors* and compare it to the *European Factors* of (French, 2019). Furthermore, we will examine different calculations of the RMW factor, to see if we can improve its predictive power. However, at the end we will investigate the core research questions of this paper: “**Do more profitable firms earn higher risk-adjusted returns on average?**” and “**Is the Profitability Anomaly present within the European stock markets?**”

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Diagram 1 Performance of the European stock market^{2}

Here, we see the performance of comparable German (red), France (green), Italy (orange) and European (blue) stock indices, to get a first impression for the development of the stock markets to scrutinize.

## 2. Fundamental theory and previous discoveries

### 2.1. Different Factor Models

The **Capital Asset Pricing Model** (CAPM), independently introduced by *Jack Treynor * (unpublished manuscript), *William F. Sharpe* (Sharpe, 1964), *John Lintner* (Lintner, 1965) and *Jan Mossin (Mossin, 1966)*, is undoubtedly a major milestone in modern portfolio theory. The well-known CAPM-Equation

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with as the expected return on the capital asset, as the risk-free rate of interest derived from government bonds, as the sensitivity of the expected excess asset returns to the expected excess market returns and as the expected market return, is the basis for many other asset pricing models to follow. The difference between the expected market rate of return and the risk-free rate of return describes the Market Premium (**MKT**).^{3}

Later on, Fama and French (Fama & French, 1993) expanded this model to the **Three-Factor Model**. They added the factors **SMB** (small minus big), as the difference between the returns on diversified portfolios of small stocks and **HML** (high minus low) as the difference between the returns on diversified portfolios of high and low book-to-market stocks.^{4} The Equation

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shows the Three-Factor Model from (Fama & French, 2014, p. 38) with the betas as slopes in the multiple regression of on , and . Despite some controversy criticism about the interpretation of SMB and HML as risk factors, the empirical support for the Fama and French Three-Factor Model is still greater than for the CAPM.^{5} To increase the predictive power of the model, several other academics add factors, e.g. **Momentum** (Carhart, 1997) or restructure the factors e.g. in the **q-Factor Model** (triple 2-by-3-by-3 sort on size, investment-to-assets and return on equity) (Hou, et al., 2015).

The **Five-Factor Model** from (Fama & French, 2015, p. 3) adds two additional factors **RMW**, as the difference between the returns on diversified portfolios of stocks with robust and weak profitability, and **CMA**, as the difference between the returns on diversified portfolios of the stocks of low (conservative) and high (aggressive) investment firms, to the Three-Factor Model. Rewriting the Equation for **Time-Series Regression**

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the exposures to the five factors, , , and capture all variation in expected returns, while the intercept is expected to be zero for all securities and portfolios .^{6} The Five-Factor Model largely absorbs the patterns in average returns.^{7} Finally, all of these models try to describe stock returns in the most significant way. This works quite well for the global version of a factor model, but (Fama & French, 2017, p. 443) realize, that the same global factors do not explain the regional expected returns empirically sufficient enough.

### 2.2. Returns of different profitable companies

The applicability of these models is not only to describe returns for the overall stock market, it can also be used to analyze the returns of different sorts of companies within the market. Many different researchers find empirical significance that more profitable firms earn higher risk-adjusted returns on average than unprofitable firms, like (Fama & French, 2017, p. 446) demonstrate for the North American, European and Asia-Pacific stock markets. Also (Hou, et al., 2015, p. 656) and (Novy-Marx, 2013, p. 3) state, that this argument for profitable firms is true, despite having significantly higher valuation ratios on average. Double sorts on two different characteristics in the data allow inferences that are even more detailed. Thus, (Novy-Marx, 2013, p. 16) finds out, that profitable firms are associated with long run growth in dividends, profits, free cash flows and earnings. They state that profitable firms, also called **growth firms**, mostly have long duration assets, while **value firms** have short duration assets. These results of the analysis seem trustworthy, because of the relatively strong empirical proof, but stand counterfactually to the inferences of (Lettau & Wachter, 2007), who come up with a duration-based explanation of the value premium. The model of Lettau and Wachter predicts that short-duration assets are riskier than long-duration assets and thus that profitable firms should underperform unprofitable firms.^{8} This inference is not in line with the empirical analysis of (Fama & French, 2017) and (Novy-Marx, 2013). Empirically, the value premium is not driven by unprofitable companies.^{9} The fact that returns of growth firms and value firms are negatively correlated leads to the idea of creating a long-short strategy, which reduces the overall portfolio volatility, despite doubling the investor’s exposure to risky assets.^{10} Indeed (Novy-Marx, 2013, p. 14) points out, that controlling for profitability increases the performance of value strategies dramatically, especially for the biggest and most liquid stocks. On the other hand (Fama & French, 2017, p. 444) acknowledge, that the Five-Factor Model fails to fully capture the returns of small stocks which behave like returns of aggressively investing firms with low profitability. This issue could be captured by a liquidity adjustment of the model, as comparatively in (Lee, 2011), because small companies face higher liquidity risks on average.

There are also different ways to calculate the factors for the regression model. For instance RMW was originally calculated with **operating profitability** by (Fama & French, 2015, p. 3). However (Ball, et al., 2016, p. 30) argue, that using **cash-based operating profitability** subsumes accruals in predicting the cross section of average returns and thus outperforms measures of profitability that include accruals. On the other hand (Novy-Marx, 2013, p. 16) concludes, that **gross profits-to-assets** explains most of the earnings related anomalies and a multitude of seemingly unrelated trading strategies.

### 2.3. Profitability anomalies

Before discussing profitability anomalies and trading strategies more deeply, we need to take a closer look at the efficiency of stock markets. The Efficient-Market Hypothesis (**EMH**), developed by (Fama, 1970) claims that asset prices reflect all available information. This leads to the implication, that it is not possible for an Investor to beat the market on a risk-adjusted basis over time.^{11} (Fama, 1970, p. 414) clarifies his Hypothesis to a **strong form**, **semi-strong form** and **weak form** of available information. Researchers like (Alajbeg, et al., 2012, p. 67) manifest that several years later empirical testing cannot reject or confirm the EMH. Also (Gibbons, et al., 1989) develop a test (GRS test) for portfolio efficiency. This test provides empirical evidence for EMH anomalies. Researchers now try to find and explain these anomalies empirically by using different factor models.

In this paper, we will examine different definitions of the **profitability anomaly** in the *European Stock Market*, especially for *Germany*, *France* and *Italy*. (Bouchaud, et al., 2019, p. 640) state, that profitability is one of the stock return anomalies with the largest economic significance. The most discussed definition of profitability anomaly is that stocks with high profitability ratios tend to outperform on a risk-adjusted basis.^{12} Traders can use this evidence to construct a long-short arbitrage strategy^{13} with high *Sharpe Ratios*. On the other hand, (Wang & Yu, 2013, p. 5) examine the role of behavioral bias-induced mispricing in the profitability anomaly, where uninformed demand and a limit on arbitrage are required for mispricing. However (Barinov, 2015, p. 2) argue that unprofitable firms perform abnormally well when expected market volatility increases and highly profitable firms perform unexpectedly poorly in the same periods. He discovers, that high-minus-low profitability strategies do compensate the investor just enough for the propensity of this strategy to perform worse than the prediction of the factor models when aggregate volatility increases.

In the following examination, we will investigate the first, most popular definition of the profitability anomaly for the stock markets of Germany, France and Italy: “*The average returns of more profitable firms tend to outperform, while unprofitable firms tend to underperform the market.*” Profitability can be expressed in many different measures. There is a list of many frequently examined profitability anomalies in the Appendix.^{14}

## 3. Profitability Anomalies in European stock markets

### 3.1. Construction of the model

There are different possible ways of creating a factor model, which is efficient and well applicable for our purpose. Adding additional factors like RMW or CMA to the Three-Factor Model^{15} can increase the validity of the model only if they are able to add descriptive power to explain average returns. In their **Factor Spanning Tests**, using four factors in regressions to explain the average returns on the fifth, (Fama & French, 2017, pp. 446-449) evaluate the factors of the Five-Factor Model^{16} for different markets. They discover that, unlike the other factors, CMA adds very little descriptive power to explain European average returns from 1990 – 2015.^{17} Due to this fact and also by reasoning of a weak data basis to construct the CMA factor, ^{18} we will implement the Five-Factor Model without the CMA factor – a **Four-Factor Model**:

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The following research is based on monthly data from (Thomson Reuters Corporation) for the overall stock markets of *Germany*, *France* and *Italy* from 01.01.1999 to 01.04.2019, without firms of the *financial sector* (Banks, Financial Services, Life Insurances and Non-Life Insurances).^{19} This time span covers at least two business cycles, based on the (Centre for Economic Policy Research, 2019) and take the warning signs not to use TDS Data before 1990 of (Brückner, 2013, p. 26) into consideration. Using already calculated factor data from (French, 2019) would be the easiest way to deal with the model construction, but there exists only factor data for overall European markets, not especially for *Germany*, *France* and *Italy*. The fact that the same global factor models perform poorly in regional portfolios like the European stock market^{20}, suggests that European factor models works probably bad for e.g. the German stock market.^{21} For these reasons, we will calculate the factors by ourselves.^{22}

First, is calculated as the *value weighted market return* of all stocks in this market minus the *risk-free rate* ^{23}. Second, we compute by sorting the stocks above (B = big) or under (S = small) the median of the market value and subtract the equal weighted returns rB from rS. To calculate , we sort the top 30% (H = high) and bottom 30% (L = low) of the BE/ME ratio and subtract the value weighted returns rL from rH. Finally, is calculated equivalently by sorting the top 30% (R = robust) and bottom 30% (W = weak) from the Operating Profits / Book Value ratio and subtract the value weighted returns rW from rR. Furthermore, we will evaluate if Gross Profits instead of Operating Profits in the calculation are more accurate for predicting the cross section average returns, as (Novy-Marx, 2013, p. 16) maintains.

### 3.2. Summary Statistics

We sum up the utilized data by indicating means and standard deviation of the factor returns in panel A of Table 1 Summary Statistics. In this panel, we can identify a data structure, which is very comparable to the summary statistics for Europe of (Fama & French, 2017, p. 445). Thus, we can observe large **Equity Premia** (mean of MKT) and **Profitability Premia** (mean of RMW) near 0.5% for all countries excepting the Profitability Premium of France with only 0.374%. One possible explanation for that fact could be that investors of the French stock market are more sensible to profitability measures, which is reflected in the stock prices and thus leads to a comparatively lower Profitability Premium. On the other hand, the **Size Premia** (mean of SMB) and the **Value Premia** (mean of HML) for all three countries are very low or even negative. The low Size Premia are in line with the European results from (French, 2019) and the examination results of (Fama & French, 2017, p. 445). Apart from that, we can observe that the low Value Premia of the three countries, with means smaller than zero, are contradictory to the Data of (French, 2019) with a mean of 0.461% and the inferences of (Fama & French, 2017, p. 445) with a mean of 0.32%^{24} for Europe. We will come back at this after further investigations to get an explanation for the present contradiction. Furthermore, the examination if we should use the *operating profit margin* or the *gross profit margin* for calculating the RMW factor, we mentioned in Construction of the model, becomes a little clearer. The Profitability Premia for Germany and Italy are much greater for the RMW factor than the RMW (GP) factor, while both factors are nearly the same for Italy.

In panel B of Table 1 Summary Statistics , we see the correlation matrices for the same factor in different regions. The fact that there is a high positive correlation between the different countries, for MKT on average 0.8, for SMB and HML on average 0.4 and for RMW on average 0.7,^{25} supports the *Hypothesis* that there is a comparable trend within the European stock markets. The correlations of the EU factors from (French, 2019), on the other hand, are vanishingly small compared to all three countries. This thwarts the *Hypothesis*, so that stock markets in some countries within the EU do not join this trend. It also underlines the argument from Construction of the model not to use the (French, 2019) factors as a proxy for the three countries to be examined.

**[...]**

^{1} See list in (Hou, et al., 2015, p. 664 f.).

^{2} Diagram from (finanzen.net, 2019).

^{3} See (Fama & French, 2014, p. 36 f.).

^{4} See (Fama & French, 2014, p. 38 f.).

^{5} See (Griffin, 2002, p. 783).

^{6} See (Fama & French, 2015, p. 3) and (Jensen, 1967) for Jensen’s alpha.

^{7} See (Fama & French, 2017, p. 441).

^{8} See (Lettau & Wachter, 2007, p. 88).

^{9} See (Novy-Marx, 2013, p. 16).

^{10} See (Novy-Marx, 2013, p. 15).

^{11} See (Fama, 1970, p. 415).

^{12} See (Bouchaud, et al., 2019, p. 639 f.).

^{13} Buy stocks of high profitability firms and sell stocks of low profitability firms.

^{14} See Table 5 List of profitability anomalies.

^{15} See equation (2).

^{16} See equation (3)a.

^{17} See (Fama & French, 2017, p. 449) with caution, that factor spanning inferences can be sample specific.

^{18} See (Ince & Porter, 2006) for applying screens to Thompson Datastream (TDS) data.

^{19} It is common to leave financial firms out of the examination, because of their special accounting standard. See (Novy-Marx, 2013, p. 9). Their accounting measures could probably distort the sample.

^{20} See (Fama & French, 2017, p. 457).

^{21} This argument is underlined by (Brückner, et al., 2015, p. 20).

^{22} Based on the calculations of (Fama & French, 2015, p. 3).

^{23} We can take the European risk-free rate from (French, 2019) in this case, because there should be no big differences within Europe, derived from AAA rated government bonds.

^{24} The time span of this investigation is from July 1990 – December 2015, 306 months.

^{25} For RMW Data see panel C.

- Quote paper
- Julian Fischer (Author), 2019, Profitability and Asset Prices in European Stock Markets, Munich, GRIN Verlag, https://www.grin.com/document/489732

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