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Master Thesis Finance
Using historical accounting information in
European value-growth strategies
Abstract
This thesis uses the book-to-market ratio combined with Piotroski’s (2000) accounting-based F Score to investigate the value premium in European equity markets. A value-growth strategy that uses contrarian historical information to take advantage of mispricing generates positive returns, providing evidence for a behavioral explanation for the European value premium. A test on the factors of the Fama and French (2015) five factor model results in a positive and significant alpha, indicating that the factors in this model are not fully able to explain the returns on this strategy. Robustness tests across time periods and firm size categories show that, except for the largest firms, the strategy performs consistently well.
Author: Johannes Cijsouw Student number: S2340631
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Acknowledgements
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Table of contents
1. Introduction ... 4
2. Literature ... 6
2.1 The value premium ... 6
2.2 F Score ... 6
2.3 The Fama-French five factor model ... 7
3. Methodology and hypotheses ... 10
4. Data and portfolio construction ... 11
4.1 Data sources and construction of BM and F Score portfolios ... 11
4.2 Construction of the F Score ... 11
4.3 Construction of the Fama French factors ... 14
4.4 Descriptive statistics ... 15
5. Results ... 19
5.1 Univariate portfolio sorts ... 19
5.2 Bivariate portfolio sorts and investment strategies ... 20
5.3 Investment strategy returns and the Fama French factors ... 23
6. Conclusion... 26
References ... 28
Appendix ... 31
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1. Introduction
Where does the value premium come from? This question has occupied finance professionals and scholars for a long time, and a definitive answer does not yet exist. The value premium refers to the return difference between value stocks and growth stocks. Value stocks are stocks that trade at a low price relative to some measure of fundamental value, while growth stocks are stocks that trade at a relatively high price. As fundamental value is subjective and not directly observable, there are several ways to measure ‘value’ and ‘growth’. One of the first and most prominent measures is the book-to-market (BM) ratio. The ability of this ratio to predict stock returns was first proved by Fama and French (1992).
Although there is abundant international evidence for the existence of the value premium (e.g. Rosenberg, Reid, and Lanstein, 1985; Fama and French, 1998) there is a long going debate about its cause. There are two main explanations; proponents of the efficient market hypothesis argue that the value premium is compensation for risk, as value firms are riskier than growth firms (Chan and Chen, 1991; Fama and French, 1996). On the other hand, a behavioral perspective states that the return difference between value and growth stocks is caused by mispricing of securities by the market (Lakonishok, Shleifer and Vishny 1994; La Porta, 1996), leading to undervaluation of value firms and overvaluation of growth firms. The return difference between value and growth stocks is a result of price corrections that follow when the prices of the undervalued and overvalued stocks adjust towards their ‘true’ values. Despite the great number of studies that have investigated the question, there still exists no definitive answer.
Using data from 30 European countries covering the period from July 1998 to June 2020, this paper attempts to answer the following research question:
Is the value premium for European firms a result of mispricing or compensation for exposure to risk factors?
From a mispricing point of view, if the market is too pessimistic about certain stocks, this is reflected by too high BM ratios. On the other hand, if there is excessive optimism, this is reflected by too low BM ratios. But as the ‘true’ value of a stock is not directly observable, how does one know which stocks are undervalued and which stocks are overvalued? By comparing recent changes in financial performance to expectations about future performance, Piotroski and So (2012) attempt to identify ex ante stocks for which contrarian historical accounting information is not yet reflected in the stock’s prices. They do so by interacting the BM ratio with an accounting based measure of recent financial performance, Piotroski’s (2000) F Score. The BM ratio reflects the market’s expectations about future financial performance, while the F Score indicates whether firms have shown improvement or deterioration in recent financial performance. Within the value and growth classifications, the F Score attempts to discriminate between ‘strong’ firms that have shown improvement recently and ‘weak’ firms that have shown deterioration.
5 performance. For firms included in this strategy, both positive and negative performance surprises1 are expected when the recent historical information has not been incorporated in the stock prices yet. The second strategy invests in portfolios where recent performance and expectations about future performance point in the same direction. For the portfolios in this strategy, no positive or negative financial performance surprises are expected. If markets are efficient, a value-growth investment strategy based on historical accounting information should not be able to generate abnormal returns. If the value-growth difference is an artifact of mispricing, however, an investment strategy that uses contrarian information to select under- and overvalued stocks will be able to earn positive returns. Therefore, positive abnormal returns on the first strategy will be considered evidence in favor of the mispricing explanation of the value premium.
In order to assess whether the value premium in Europe may be compensation for risk, the returns on the two strategies described above are regressed against the factors of a well-established asset pricing model, the Fama and French (2015) five factor model. If the risk factors of this model are able to explain the returns on the strategy that takes advantage of mispricing, this will be evidence in favor of a risk-based explanation.
Understanding the source of the value premium will benefit academics as well as practitioners in finance. There has been extensive research into the value-growth return difference, but the results remain rather inconclusive. This paper contributes to the literature by shedding additional light on value-growth return characteristics across countries and different time periods. Although Walkhäusl (2017) tests the interactions between the BM ratio and F Score for Europe as well, this paper covers a sample of more recent data and allows for an investigation into a larger number of post-great recession years. Furthermore, this paper considers a broader sample of European countries to test the robustness of Piotroski and So’s (2012) findings.
The results of this paper are in line with Piotroski and So (2012) and Walkhäusl (2017) and provide evidence for a mispricing-based explanation for the value premium. The strategy that takes advantage of mispricing generates a statistically significant raw return of 1.34% per month, while the return on the strategy that does not take advantage of mispricing is economically and statistically insignificant. The significant alpha’s of the regressions on the factors of the five factor model indicate that this model is not able to explain the abnormal returns earned on both strategies.
The paper is organized as follows: section 2 will explore the literature on the value premium, the F Score, and the Fama French five factor model. Section 3 presents the methodology used in this study. Section 4 presents the data. Section 5 shows the results of the portfolio sorts, value-growth investment strategies, and the regressions of the strategy returns on the five factor model. Section 6 concludes.
1 The term ‘performance surprise’ may be a bit vague but knowing the exact form in which such a surprise
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2. Literature
2.1 The value premium
Fama and French (1996) argue that the higher returns on value stocks are compensation for risk that has not been captured by the basic CAPM, and attribute this to a higher exposure to financial distress risk due to negative events or unfavorable prospects, in line with the findings of Chan and Chen (1991). Chen and Zhang (1998) agree and dive further into the determinants of this additional risk. They find that besides firm distress, also financial leverage and uncertainty in future earnings can explain the return differences between value stocks and growth stocks. Other sources of risk that are related to the value premium stem from the ability of a firm to change its investment in reaction to exogenous shocks. According to Zhang (2005), value firms suffer more from investment irreversibility than growth firms. This causes them to be stuck with more unproductive capital in downturns, increasing their riskiness. If the economy recovers, however, growth firms have to increase their investment, while the value firms are able to utilize their previously unproductive assets more efficiently. This causes the risk spread between value and growth firms to increase during downturns and decrease during recovery. Carlson et al. (2004) show that as equity prices decrease due to external events, and fixed operating costs are proportionate to the capital stock (proxied by the book value of equity) which does not change, the riskiness of the firm increases due to an increase in operating leverage.
An alternative explanation for the higher returns on value stocks lies within behavioral finance. De Bondt and Thaler (1985) and Lakonishok et al. (1994) argue that investors tend to assume that past performance trends will continue in the future. They fail to incorporate mean-reversion in their expectations, assuming that recently observed growth will persist. This leads to expectations about future performance that are too optimistic for growth stocks and too pessimistic for value stocks, which is reflected in the market prices of these stocks. The expectation errors stem from underreaction to changes in fundamental strength of firms. As value (growth) firms perform better (worse) than expected, these expectations are reconsidered, leading to price increases (decreases) for value (growth) firms, resulting in the value return effect. La Porta et al. (1997) also find evidence for these expectation errors, as earnings announcement returns for value stocks are considerably higher than those for growth firms. This suggests that investors are on average more pessimistic about the performance of value firms than for growth firms.
2.2 F Score
7 condition. By sorting portfolios based on F Score, he finds that the mean return on a value portfolio can be increased by at least 7.5% if only value firms with a high F Score are included, and that a strategy that goes long in high F Score value firms and short in low F Score value firms earns a positive annual return difference of 23%. The returns on the traditional value strategy disappear in environments where information is spread more easily (e.g. large firms with high analyst coverage), and the ability of the F Score to identify strong and weak value firms is most prominent in environments where information spreads slowly.
Piotroski and So (2012) use the F Score to investigate the returns of value and growth strategies for US firms through what they call an expectation errors approach. They view the BM ratio as a measure of the market’s expectations about future performance, while the F Score measures ‘fundamental strength’ of the firms. They argue that part of the value-growth return effect is due to expectations that are overly optimistic for growth firms and overly pessimistic for value firms. They use the F Score to identify firms that are potentially overvalued or undervalued. The ‘expectation errors’ exist for value firms with a high F Score and growth firms with a low F Score, as the expectations about future performance implied by the BM ratio are opposite to the increase or decrease in fundamental strength implied by the F Score for these firms. Based on a mispricing explanation for the value premium, they argue that a strategy that takes advantage of these expectation errors will generate returns superior to the returns of traditional value-growth strategies, as investors can profit from the price corrections that arise if the market’s expectations are revised. Their results support their argument, since the investment strategy that takes advantage of the expectation errors by going long in strong value firms and short in weak growth firms earns a statistically significant average annual return of 22%. In contrast, the ‘opposite’ strategy with low expectation errors generates economically and statistically insignificant returns. Tests with explicit forecasting data and the four factor model of Fama and French (1993) and Carhart (1997) support the view that the return patterns are an artifact of mispricing instead of risk compensation.
Various follow-up papers have proven the robustness of the findings of Piotroski (2000) and Piotroski and So (2012) across regions and time periods. Walkhäusl (2017) uses data from European countries represented in the MSCI Europe Index to test the interaction between the BM ratio and F Score, while Ng and Shen (2016) do so for seven Asia-Pacific markets. Tikkanen and Äijö (2018) interact F Score with several valuation ratios in order to improve returns on long only strategies for European value firms. Ahmed and Safdar (2018) and Walkhäusl (2019) use F Scores to increase the performance of traditional momentum strategies for the US and Europe, respectively. Lastly, Hyde (2018) and Ng and Shen (2019) investigate the performance of portfolios where F Score is used as a quality measure for the Australian market and five Asian markets, respectively. All papers mentioned in this paragraph find a significant positive F Score premium, where monthly return premiums vary from 0.71% to 1.31%, and annual premiums range from 6.73% to 17.33%.
2.3 The Fama-French five factor model
8 Sharpe (1964), Lintner (1965), and Black (1972). For a long time, the CAPM has been the main model used for explaining the cross section of stock returns and pricing assets. According to this model, a stock’s exposure to market risk (often denoted by β) is the only factor that investors need to be compensated for, since non-systematic risk can be eliminated through diversification. The CAPM relates the excess return of a stock or portfolio to the excess market return. The CAPM can be represented by equation (1).
𝑅𝑖𝑡 − 𝑅𝐹𝑡 = 𝛼𝑖 + 𝛽1𝑖(𝑅𝑀𝑡− 𝑅𝐹𝑡) + 𝑒𝑖𝑡 (1)
Where Rit is the return of the stock over period t, RFt is the risk free rate, and RMt is the
market return.
However, the CAPM fails to explain certain anomalies related to firm size and the BM ratio. Banz (1981) finds that, given their betas, small firms have too high returns and large firms have too low returns. Because small firms tend to be less diversified and are less able to deal with negative shocks, they are riskier, so investors require higher returns for holding these stocks. This leads to the size effect. The other anomaly not captured by the CAPM is the positive return difference between high BM ‘value’ stocks and low BM ‘growth’ stocks, (Rosenberg, Reid and Lanstein, 1985), the value premium. Fama and French (1992) investigate the size and BM factors and find that these are better able to explain the variation in stock returns than the market factor, which becomes insignificant for their sample after controlling for size. As a consequence, Fama and French (1996) develop the three factor model to supplement the basic CAPM., and is described in equation (2).
𝑅𝑖𝑡− 𝑅𝐹𝑡= 𝛼𝑖 + 𝛽1𝑖(𝑅𝑀𝑡− 𝑅𝐹𝑡) + 𝛽2𝑖𝑆𝑀𝐵𝑡+ 𝛽3𝑖𝐻𝑀𝐿𝑡+ 𝑒𝑖𝑡 (2)
Where SMBt represents small-minus-big, the difference between the returns on small cap
stocks and large cap stocks, and HMLt is high-minus-low, the difference between the return
on high BM stocks and low BM stocks. Both factors turn out to perform well in explaining stock returns, both in the US and internationally (Fama and French, 1998).
Fama and French (2015) add two factors, investment and profitability, to the three factor model described above. The theoretical justification for the two new factors comes from the dividend discount model. This model links the price of a stock to its expected dividends. The model states that two stocks with the same expected dividends but different prices must have different expected returns. If the stocks are rationally priced, the return difference must be a consequence of different levels of risk. Some modifications to the dividend discount model lead to equation (3), which describes the relation between expected returns, the BM ratio, investment, and profitability.
𝑀𝑡
𝐵𝑡
=
∑∞𝜏=1𝐸(𝑌𝑡+𝜏−𝑑𝐵𝑡+𝜏)/(1+𝑟)𝜏
𝐵𝑡
(3)
Where Mt is the stock price at time t, Bt is the book value of equity at time t, E(Yt+τ) refers
to expected total earnings for period t+τ, E(dBt+τ) is the expected change in book value in
9 Holding everything in (1) constant except r and Mt, a decrease in the stock price implies a
higher expected return. Since a lower stock price with a constant value of book equity is equivalent to a higher BM ratio, equation (1) shows the positive relation between BM and expected return. Next, all variables except r and Yt+τ are held constant. An increase in expected
total earnings, i.e. an increase in profitability, must be accompanied by an increase in expected return to keep the right hand side of equation (1) constant. Lastly, fixing everything besides r and dBt+τ, a higher expected increase in the book value of equity (i.e. higher investment)
implies a lower expected return. Summarized, this mechanism shows how the size, value, investment, and profitability factors of the five factor model are linked to stock prices, and how higher excess returns can be explained by higher profitability and lower investment. Equation (4) represents the five factor model.
𝑅𝑖𝑡− 𝑅𝐹𝑡= 𝑎𝑖+ 𝑏𝑖(𝑅𝑀𝑡− 𝑅𝐹𝑡) + 𝑠𝑖𝑆𝑀𝐵𝑡+ ℎ𝑖𝐻𝑀𝐿𝑡+ 𝑐𝑖𝐶𝑀𝐴𝑡+ 𝑟𝑖𝑅𝑀𝑊𝑡+ 𝑒𝑖𝑡, (4) where all variables have the same meaning as for the three factor model, CMAt is
conservative minus aggressive or the investment factor, and RMWt is robust minus weak or
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3. Methodology and hypotheses
In order to provide an answer to the research question, this paper uses portfolio sorts on BM ratio and F Score to investigate the return behavior of value and growth stocks. Firms with a high BM ratio are classified as value firms while firms with a low BM ratio are classified as growth firms. Firms are considered weak if they have a low F Score and strong if they have a high F Score.
Firstly, the returns for univariate sorts on the BM ratio and F Score will be examined to assess the characteristics and return behavior of these portfolios. After that, the portfolio returns resulting from the interaction of the BM ratio and F Score will be reviewed.
To investigate whether the mispricing explanation for the value premium holds, two long-short investment strategies are created. The strong value minus weak growth (SV-WG) strategy takes a long position in strong value firms and shorts weak growth firms. For strong value firms, positive performance surprises are expected, while for weak growth firms, negative performance surprises are expected. The weak value minus strong growth (WV-SG) strategy takes a long position in weak value firms and shorts strong growth firms. For these firms, no positive or negative surprises in financial performance are expected, since the recent financial performance of these firms points in the same direction as the performance expectations implied by the BM ratio. If the value-growth returns are due to mispricing, the SV-WG strategy will generate positive returns, since the positive performance surprises for strong value firms translate into price increases while the negative performance surprises for weak growth firms translate into price decreases. Simultaneously, the WV-SG strategy should not generate significant returns. Therefore, the first hypothesis is as follows:
H1: A strategy that goes long in strong value firms and shorts weak growth firms generates positive returns, while a strategy that goes long in weak value firms and shorts strong growth firms does not.
If hypothesis H1 is not rejected, this is considered evidence for the mispricing explanation of the value premium.
The returns of the two strategies will then be regressed on the factors of the five factor model to assess whether these factors are able to explain the strategy returns. If the returns on both strategies can be attributed to the risk factors in the five factor model, one would expect a small and insignificant intercept. A significant intercept would indicate that the model is not able to explain all of the variation in the strategies’ returns. This leads to the second hypothesis:
H2: The five factor model is able to explain the variation in returns on the strong value minus weak growth investment strategy.
11 will be the difference in alpha’s between the two strategies, and the resulting t-statistic reflects the significance of the difference in alpha’s.
In order to find out whether the results hold across time periods, the sample will be split at June 2008, when the great recession started in Europe. This will be an interesting check for the consistency of both measures to predict stock returns. Furthermore, the sample will be divided into small, middle, and large firms based on their market capitalization2 in order to better understand the return behavior of the portfolio sorts.
4. Data and portfolio construction
4.1 Data sources and construction of BM and F Score portfolios
The sample consists of listed firms from 26 European Union member countries3 plus Iceland, Norway, Switzerland, and the United Kingdom, covering the period 1998-2019. To avoid the survivorship bias, the sample consists of all firms that have been active during this period, including delisted firms. The data used in this paper is obtained from the Refinitiv database. Following Fama and French (1992) and Piotroski & So (2012), financial firms with Standard Industrial Codes (SIC) between 6000 and 6999 are excluded from the sample, as well as firm-years with insufficient data to calculate the F Score. Table 1 shows that of the initial sample of 112,389 firm-year observations, 46,622 observations are lost due to missing data for the F Score. This may result in bias. The final sample consists of 58,320 firm-year observations.
To make sure that the accounting information used to create the F Score is available before the portfolios are formed to calculate the returns, the portfolios are formed on the last trading day of June of year t using accounting information for the fiscal year ending in year t-1. The portfolios are rebalanced annually. The BM ratio is calculated as the ratio of book equity to market equity at the fiscal year ending in t-1. Market equity is calculated as the stock price times the number of common shares outstanding.
Following Piotroski and So (2012), portfolios are formed using univariate and bivariate sorts on BM ratio and F Score. If the BM ratio is above the 70th percentile, a firm is considered a value firm, if the BM ratio is below the 30th percentile, the firm is considered a growth firm, and if the BM ratio lies within the 30th and 70th percentile, the firm is considered neutral. Firms with an F Score of 0-3 are considered weak, firms with an F Score of 4-6 are middle, and strong firms have an F Score of 7-9.
4.2 Construction of the F Score
The F Score consists of the sum of nine binary signals that measure changes in the firm’s financial condition. The signals indicate whether the firm is performing well, and whether
2 Following Asness, Moskowitz, and Pedersen (2013), firms are ranked on market capitalization in a
descending order. The firms that form 90% of total market capitalization are categorized as large, the firms that take this number up to 98% are categorized as middle, and the firms that constitute the remaining 2% of total market capitalization are categorized as small. This results in 33,049 firm-year observations for small firms, 12,312 for middle firms, and 8,459 for large firms.
12 Table 1 – Sample selection and loss of observations
This table shows the number of firm-years of the original dataset and the loss in observations due to missing data.
Criterion Number of firm-years
Total number of firm-years retrieved from Refinitiv database for the sample countries between 1997-2019, excluding financial firms with SIC between 6000-6999 and firms with negative book value of equity.
112,389
Minus firm-year observations with insufficient data to calculate the F Score.
-46,622
Minus loss in firm-year observations due to missing return data or market capitalization data.
-7,447
Final sample 58,320
improvement has occurred over the past year along the dimensions of profitability, leverage, liquidity, and operational efficiency. In summary, a firm with a high F Score is a profitable firm that is not likely to experience financial distress. The nine signals below are equal to one if the condition holds, zero otherwise.
The first four signals are related to profitability. Piotroski (2000) states that profitability and cash flow realizations are a sign that a firm is able to generate funds internally and take advantage of profitable opportunities when they occur. An increase in profitability is considered a sign that the firm will be able to increase future cash flow. Indeed, Novy-Marx (2013) finds a positive relationship between profitability and returns.
1. ROA: The firm’s return on assets (ROA) should be positive. The ROA is defined as net income before extraordinary items (NI) divided by the beginning of year total assets.
2. ∆ROA: The growth in ROA should be positive, where the growth in ROA is calculated as the ROA in year t minus the ROA in year t-1.
3. CFO: The firm’s cash flow from operations (CFO) should be positive, where CFO is scaled by total assets at the beginning of the year. Foerster, Tsagarelis, and Wang (2017) show that a positive relationship exists between operating cash flows and stock returns. They argue that cash flows are more reliable predictors of stock returns than earnings, as they represent the ‘real’ inflows while earnings can be manipulated through, for example, accruals.
13 Signal five and six are related to operating efficiency. Piotroski (2000) argues that both ratios are key in calculating return on assets. Improvement in these ratios means that a firm is able to use its assets more efficiently, thereby increasing profitability.
5. ∆MARGIN: The growth in gross margin ratio should be positive, where the gross margin ratio is defined as gross margin divided by beginning of year total assets. This signals an improvement in operating efficiency, which may stem from cost reductions or price increases. In both cases it is considered a positive sign for future performance.
6. ∆TURNOVER: The growth in the asset turnover ratio should be positive, where the asset turnover ratio is defined as total sales divided by beginning of year total assets. This signal indicates that the assets in place have been employed more efficiently.
The last three signals concern leverage, liquidity, and sources of funds. The F Score originally has been developed for firms with high BM ratios that trade at a relatively low price and are more likely encounter financial distress. An increase in equity financing or debt financing is considered a bad signal, as it indicates that the firm is not able to internally generate sufficient funds and it may further decrease the firm’s financial flexibility. On the other hand, external financing may be beneficial for the firm in case of profitable investment opportunities. Piotroski & So (2012) argue that without further details on the specific circumstances for each firm, the three signals can be assumed to be bad news. This is in line with the findings of Sloan and Richardson (2003), who find a negative relationship between net external financing and future stock returns, and Penman, Richardson, and Tuna (2007), who find a negative relationship between leverage and stock returns.
7. ∆LEVERAGE: The leverage ratio should decrease compared to the previous year, where the leverage ratio is defined as total long term debt divided by average total assets.
8. ∆CURRENT: The current ratio should improve compared to the previous year. The current ratio is defined as current assets divided by current liabilities. An increase in the current ratio is a signal that the firm will be better able to fulfill its current debt and cash flow obligations.
9. ISSUANCE: The company did not issue new shares in the previous year.
14 deteriorating current ratios. In conclusion, all averages point in the desired direction and the average binary outcome for each variable and F Score category is as expected.
Table 2 – Descriptive statistics for the variables underlying the F Score
This table shows the mean and standard deviation of all variables used to calculate the F Score per F Score category for the total sample of 53,820 firm-years for the period 1998-2019. The last column presents the average outcome in terms of the binary variable. A firm with a F Score of 0-3 is considered weak, 4-6 is medium, and 7-9 is strong. The ROA is return on assets, ∆ROA is the change in return on assets, CFO is cash flow from operations scaled by total assets,
ACCRUAL is the difference between CFO and net income scaled by total assets, ∆MARGIN is the
change in the gross margin ratio, ∆TURNOVER is the change in the asset turnover ratio,
∆LEVERAGE is the change in the leverage ratio, ∆CURRENT is the change in the current ratio,
and ISSUANCE is the number of common shares issued measured in millions.
Variable F Score Mean Std. Dev. Average binary outcome
ROA Weak -0.106 0.258 0.285 Medium 0.019 0.232 0.741 Strong 0.066 0.076 0.960 ∆ROA Weak -0.059 1.268 0.124 Medium -0.011 0.790 0.378 Strong 0.039 0.090 0.892 CFO Weak -0.069 0.705 0.344 Medium 0.064 0.222 0.852 Strong 0.119 0.110 0.993 ACCRUAL Weak 0.037 0.686 0.588 Medium 0.045 0.284 0.764 Strong 0.054 0.103 0.910 ∆MARGIN Weak -0.721 25.137 0.179 Medium -0.055 21.464 0.439 Strong -0.004 5.927 0.763 ∆TURNOVER Weak -1.608 105.967 0.182 Medium -0.317 19.327 0.401 Strong 0.090 0.654 0.773 ∆LEVERAGE Weak 0.024 0.096 0.319 Medium 0.002 0.085 0.544 Strong -0.017 0.068 0.775 ∆CURRENT Weak -0.353 1.962 0.239 Medium 0.025 3.700 0.445 Strong 0.143 1.716 0.670 ISSUANCE Weak 13.935 116 0.323 Medium 7.585 168 0.537 Strong 2.227 74.9 0.753
4.3 Construction of the Fama French factors
The returns of the WV-SG and SV-WG strategies will be regressed on the market factor, size factor, value factor, investment factor and profitability factor of the five factor model. The following time-series regression will be estimated:
15 where Rit is the strategy returnfor period t, RMt is the market return, RFt represents the
risk-free rate, SMBt is small minus big, or the size factor, HMLt is high minus low or the value factor,
CMAt is conservative minus aggressive or the investment factor and RMWt is robust minus
weak or the profitability factor. The market return is calculated as the market capitalization-weighted return on all stocks used in the sample, as this best reflects the true market return. The 1-month LIBOR rate is used as a proxy for the risk free rate. For SMBt and HMLt, each year
at portfolio formation, the firms are sorted into six portfolios using a 2x3 sort on size and BM ratio. SMBt is the average of the returns on the three small stock portfolios minus that of the
three large stock portfolios. HMLt is the average of the returns on the two highest BM
portfolios minus that of the two lowest BM portfolios. Similar procedures are used to construct the investment and profitability factors. For portfolios formed in June of year t, investment is calculated as the growth in total assets for the fiscal year ending in year t-1 divided by total assets at the end of year t-2. The profitability factor is calculated as annual revenues minus cost of goods sold, interest expense and general, selling, and administrative costs, divided by book equity. For the size sorts, the median is used as a breakpoint, while the 30th and 70th percentiles are used as breakpoints for the value, investment and profitability factors.
4.4 Descriptive statistics
Table 3 panel A shows the number of observations, mean firm size, mean BM ratio and mean F Score per country and the means for these variables over the complete sample. France, Germany and the United Kingdom are represented by the highest number of firm-year observations. The mean BM ratios range from 0.68 in Sweden to 3.38 in Cyprus, while the F Scores range from 5.21 in Ireland to 6.27 in the Czech Republic. With regard to firm size and the BM ratio, it seems to be the case that Western European firms are, on average, larger and have lower BM ratios than firms from Eastern Europe. Finally, there is little variation in the F Score across countries.
The average BM ratio across the entire sample of 0.98 is higher than the average found by Piotroski and So (2012) and Walkhäusl (2017), who find average BM ratios of 0.81 for the US and 0.77 for Europe, respectively. Although both papers do not report the BM ratios and F Scores per country, one possible explanation for this difference with the European sample of Walkhäusl (2017) could be that firms from the additional countries included in this paper have, on average, high BM ratios. The mean F Score of 5.49 is similar to the mean F Scores found by bothpapers.
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Table 3 – Observations and firm characteristics per country and industry
Panel A shows the number of firm-year observations, the mean size, the mean BM, and the mean F Score per country and for the full sample. Panel B shows the number of firm-year observations, the mean size, the mean BM, and the mean F Score per industry as classified by SIC. The sample period covers 1998-2019. Size is measured in million euros.
Panel A: Characteristics per country
Country Number of Size BM Ratio F Score
Firm-years Mean Mean Mean
Austria 775 1,129 1.01 5.89 Belgium 1,234 2,240 0.85 5.70 Croatia 457 286 1.67 5.66 Cyprus 433 119 3.38 5.52 Czech Republic 115 3,196 2.31 6.27 Denmark 1,393 1,565 0.89 5.79 Estonia 178 173 0.97 5.93 Finland 1,856 1,727 0.75 5.53 France 7,734 3,059 0.88 5.42 Germany 6,116 3,163 0.86 5.66 Greece 1,871 281 2.16 5.32 Hungary 263 1,005 1.16 5.63 Iceland 128 403 0.71 5.95 Ireland 544 2,015 0.78 5.21 Italy 3,219 1,889 0.91 5.46 Latvia 177 60 2.90 5.83 Lithuania 298 116 1.44 5.90 Luxembourg 358 3,762 1.68 5.72 Malta 82 250 0.69 5.96 Netherlands 1,813 5,225 0.71 5.42 Norway 1,565 1,658 0.98 5.25 Poland 3,343 272 1.21 5.52 Portugal 630 1,443 1.30 5.79 Romania 486 228 2.20 5.83 Slovakia 63 300 1.89 5.86 Slovenia 261 339 2.26 5.94 Spain 1,446 4,322 0.77 5.69 Sweden 3,812 1,323 0.68 5.35 Switzerland 2,584 5,677 0.76 5.78 United Kingdom 10,586 2,892 0.85 5.25 Full sample 53,820 2,469 0.98 5.49
Panel B: Characteristics per industry
Industry Number of Size BM Ratio F Score
Firm-years Mean Mean Mean
Agriculture, Forestry and Fishing 423 269 1.22 5.47
Mining 1,617 2,592 1.29 5.12
Construction 2,120 1,247 1.19 5.26
Manufacturing 26,876 3,004 0.98 5.53
Transportation, communications &
electric, gas and sanitary service 6,177 4,167 0.97 5.69
17
Resale trade 3,138 2,199 0.86 5.68
Services 10,612 727 0.84 5.31
Nonclassifiable 480 6,587 1.02 5.33
Table 4 presents descriptive statistics for the variables used in this study to construct the BM and F Score portfolios and Fama French factors. There is wide variation market
capitalization. The mean for the small cap portfolio is 55 million euros with a standard
deviation of 96 while the mean for the large cap portfolio is 4,854 million euros with a standard deviation of 14,987. The total range of market cap is from 0.067 million euros for the smallest firm included in the sample to 271,067 for the largest firm. The average BM ratio for growth firms in this sample is 0.28 while the average BM ratio for value firms of 2.07 is higher, as expected. The high BM portfolio shows the greatest variation in BM ratios with a standard deviation of 2.74. The average F Score increases from 2.58 for the weak F Score portfolio to 7.49 for the strong F Score portfolio. The medium F Score portfolio has an average of 5.10. For the investment portfolios, the average growth in total assets is negative for the conservative portfolio with a value of -0.13 while it is 0.55 for the aggressive investment portfolio, which also has the highest variation with a standard deviation of 3.89. Average profitability is negative for the weak portfolio and positive with a value of 1.15 for the robust portfolio. The robust portfolio shows substantial variation in profitability ratios, as shown by the standard deviation of 6.58. The large extreme values for profitability are mainly due to low book values of equity for these observations.
Table 5 shows descriptive statistics for the monthly average returns on the Fama and French (2015) factor portfolios. Except for the size factor, the t-statistics indicate that all factors show significant and positive factor returns at a 5% significance level. The market factor shows the highest return. The return of 0.57% is comparable in size to the one found by Fama and French (2015) for the US who find an excess market return of 0.50% for the period 1963-2013. The market factor also shows the highest variation in returns with a standard deviation of 4.38%, and returns ranging from a lowest value of -13.81% to a maximum of 16.47%. The positive and significant returns for the value, investment, and profitability factors indicate that value firms with a conservative investment policy and strong profitability earn, on average, higher returns than growth firms with low profitability that invest a lot. The higher returns on small cap stocks relative to large cap stocks do not seem to hold for this sample.4
4 This could be due to the use of the median to separate small and large stocks, causing too much small
18
Table 4 – Descriptive statistics for the variables used to create portfolios and factors
This table shows the number of firm-year observations, mean, standard deviation, minimum value, and maximum value for the different portfolios categorized by market capitalization in millions of euros, the book-to-market (BM) ratio, the F Score, profitability, and investment for the total sample of 53,820 firm-years for the period 1998-2019. The breakpoint for the market capitalization portfolios is the median. The breakpoints for the portfolios of the other variables are the top and bottom 30th percentiles.
Variable Portfolio Obs Mean Std. Dev. Min Max
Market cap Small 26,928 55.089 95.615 0.067 1,557.151
Large 26,892 4,853.819 14,987.47 68.049 271,067.400 BM ratio Growth 16,121 0.276 0.126 0.000 0.630 Neutral 21,563 0.691 0.228 0.276 1.536 Value 16,136 2.067 2.737 0.600 201.143 F Score Weak 6,670 2.584 0.637 0 3 Medium 31,531 5.101 0.789 4 6 Strong 15,619 7.488 0.642 7 9 Investment Conservative 16,081 -0.134 0.137 -0.991 0.086 Neutral 21,573 0.043 0.062 -0.103 0.296 Aggressive 16,166 0.551 3.891 0.025 396.977 Profitability Weak 16,109 -0.240 2.508 -147.732 0.231 Middle 21,578 0.254 0.091 0.081 0.594 Robust 16,133 1.152 6.578 0.339 531.409
Table 5 – Descriptive statistics for the returns of the Fama French factors
This table presents the mean, standard deviation, minimum and maximum value, and the t-statistic for the returns on the Fama and French (2015) for the total of 264 monthly observations covering the period 1998-2019. RM-RF is the market
return in excess of the risk-free rate, SMB is the size factor, HML is the value factor,
RMW is the profitability factor, and CMA is the investment factor.
Variable Mean Std. Dev. Min Max T-statistic
Rm – RF 0.566 4.381 -13.810 16.472 2.099
SMB 0.042 1.788 -4.718 6.403 0.382
HML 0.485 2.170 -8.629 8.464 3.630
CMA 0.366 1.655 -7.772 6.617 3.440
19
5. Results
5.1 Univariate portfolio sorts
Table 6 shows the monthly raw portfolio returns for univariate sorts on the BM ratio and F Score and the average characteristics of the firms in these portfolios. Starting with the characteristics of the BM portfolios, table 6 shows that firm size, measured by market capitalization, decreases as the BM ratio increases, so value firms are on average smaller than growth firms, consistent with the evidence of Fama and French (1992). No clear relationship emerges between the F Score and the BM ratio, as average F Scores are similar across BM portfolios. For the portfolios formed on F Score, there seems to be a positive relationship between F Score and firm size. This implies that large firms are on average financially healthier than small firms, in the sense that they more frequently show improvements in financial ratios and are less likely to encounter financial distress.
Table 6 shows that the portfolio returns increase from the low BM to the high BM portfolios. The return difference between the value portfolio and the growth portfolio of 0.55% per month is both economically and statistically significant for the period 1998-2019, as shown by the t-statistic of 3.93, implying significance at the 1% level. This finding is similar to Walkhäusl (2017), who finds a monthly value-growth return difference of 0.54%. As for the F Score, the high F Score portfolio outperforms the low F Score portfolio with a return difference of 0.75% per month for the full sample period, the difference is also significant at the 1% level. This is in line with the findings of Novy-Marx (2014), who considers the F Score (among other measures) as a stand-alone tool for stock-selection and proves its ability to do so.
If the sample is split at June 2008, there is a substantial change in the returns on the value and growth portfolios. Pre-2008, the value minus growth return is highly significant and almost 1% per month, while for the post-2008 subsample the return difference drops to 0.17% and is no longer significant at the 1% level but still significant at the 5% level. Compared to the pre-crisis period, the returns to the high BM and neutral BM portfolios have decreased. In contrast, the returns to the growth portfolio actually increased and are higher than the returns on firms with a neutral BM ratio. This increase in returns on growth firms might be a hint that growth could serve as an insurance against recessions.
The returns on the F Score portfolios decrease substantially for the post-crisis period. The return spread between strong and weak firms, however, is similar for the two sub-periods, so the F Score is consistent in separating winners from losers.
Moving from small to large firms, the returns on the growth portfolio increase, the returns on the neutral portfolio remain roughly the same, while the returns on the value portfolio decrease for middle and large firms. For small firms, there is a return difference between the value and growth portfolios of 0.70% per month, significant at the 1% level. For middle and large firms, the value minus growth return difference loses its significance. The value effect seems to disappear as firm size increases.
20 a significant return difference. For the weak portfolio, returns increase from small to large firms, while for the middle and strong portfolios the returns decrease from small to large. For univariate sorts on BM ratio and F Score, the return differences thus seem to disappear when we move from small to large firms.
Table 6 – Monthly raw returns and characteristics for univariate sorts on BM and F Score
This table presents the average monthly raw returns in percent for univariate portfolio sorts on BM ratio and F Score, and the characteristics of these portfolios with regard to size, BM ratio and F Score for the total sample of 53,820 firm-years covering the period 1998-2019. The pre- and post-2008 columns show the returns for two sub-periods split at June 2008. The small, middle, and large firm columns show the returns Size is measured in million euros. A BM ratio below the 30th percentile is considered growth,
between the 30th and 70th is neutral, and above the 70th percentile is value. Firms with an F Score of 0-3
are considered weak, 4-6 is medium, and 7-9 is strong. V-G represents the return difference between the value and growth portfolios. S-W represents the return difference between strong and weak firm portfolios. The numbers in parentheses are t-statistics.
Returns Characteristics (full sample) Full Sample Pre 2008 Post 2008 Small Firms Middle Firms Large Firms Size BM F Score BM Growth 0.601 0.520 0.667 0.535 0.695 0.662 4,499 0.28 5.51 Neutral 0.809 1.112 0.557 0.821 0.832 0.836 2267 0.69 5.53 Value 1.149 1.520 0.839 1.239 0.985 0.737 691 2.07 5.40 V-G 0.548 0.999 0.173 0.704 0.290 0.075 (t-stat) (3.929) (4.052) (1.181) (4.590) (1.647) (0.386) F Score Weak 0.314 0.506 0.154 0.301 0.533 0.527 907 1.13 2.58 Medium 0.848 1.077 0.656 0.958 0.741 0.741 2553 0.98 5.10 Strong 1.068 1.258 0.909 1.180 1.054 0.772 2959 0.91 7.49 S-W 0.754 0.753 0.755 0.879 0.520 0.246 (t-stat) (4.538) (2.619) (3.991) (4.345) (2.499) (0.984)
5.2 Bivariate portfolio sorts and investment strategies
21 the F Score has been developed by Piotroski (2000) for separating winners from losers among value firms only. This indicates that the performance measures of the F Score can be applied to a broader set of firms to separate winners from losers.
The average return to the SV-WG strategy of 1.34% per month is both economically and statistically significant at the 1% level, indicating that value firms that performed well over the past year and growth firms that performed poorly over the past year have indeed experienced the expected performance surprises. In contrast, the WV-SG strategy has not been able to generate statistically significant returns.
For the sub-period preceding June 2008, table 7 panel B shows that within each F Score portfolio, the returns increase as the BM ratio increases. Within each BM portfolio, returns increase as we move from the weak to the strong portfolios. Returns vary from -0.09% for weak growth firms to 1.70% for strong value firms. Panel C shows that the BM ratio seems to lose its power in explaining returns for the sub-period following June 2008. The SV-WG strategy generates positive and statistically significant average returns of 1.79% and 0.97% per month for the pre- and post-2008 periods, respectively. The average returns to the WV-SG strategy are again small and statistically insignificant. The return difference between the two periods can be explained by the BM ratio. Where the value minus growth return differences are larger and statistically significant for the pre-2008 period compared to the full sample period, the post-2008 value minus growth differences are small and insignificant. The F Score is more consistent in separating winners from losers across the two sub-periods.
Panel D, E, and F of table 7 present the returns on sub-samples of small, middle, and large firms based on market capitalization, respectively. For small and middle firms, the bivariate BM ratio and F Score portfolios display similar return behavior as for the entire sample. Most of the value minus growth and strong minus weak return spreads become insignificant for the middle-sized firms, however. The WV-SG strategy is not able to earn significant returns for the small and middle firms, while the strong value minus weak growth strategy for small firms earns a positive return of 1.48% and for middle-sized firms 1.06% per month. For the large firm sub-sample, the BM ratio and F Score are no longer able to explain returns, as the value minus growth and strong minus weak differences are not significantly different from zero. Both investment strategies are unable to generate statistically significant returns.
22
Table 7 – Monthly raw returns for bivariate sorts on BM and F Score and strategy returns
Panel A presents average monthly raw returns in percent for bivariate portfolio sorts on BM ratio and F Score for the period 1998-2019, Panel B and C for two sub-periods split at June 2008, and panel C, D, and E for small, middle, and large firms. Firms are considered growth, neutral, or value if their BM ratios are below the 30th, between 30th and 70th, or above the 70th percentile. Firms with an F Score of 0-3 are placed in the
weak portfolio, 4-6 is medium, and 7-9 is strong. V-G represents the return difference between value and growth. S-W represents the return difference between strong and weak. Panel B shows the returns in percent for two investment strategies. The weak value minus strong growth (WV-SG) strategy goes long in weak value firms and shorts strong growth firms. The strong value minus weak growth (SV-WG) strategy goes long in strong value firms and shorts weak growth firms. The numbers in parentheses are t-statistics.
23 5.3 Investment strategy returns and the Fama French factors
Table 8 presents the regression results for the SV-WG and WV-SG strategy returns in excess of the risk-free rate on the factors of the Fama and French (2015) five factor model.5 If the risk factors of this model are able to explain the returns of the strategies, the alpha’s for both strategies would be insignificant and the adjusted R2 would be high. A positive or negative alpha indicates that there are abnormal returns that the model cannot explain while a low adjusted R2 means that a large proportion of the variation in strategy returns remains unexplained by the factors.
Table 8 panel A shows that for the complete sample, the alphas for both regressions are significant. The five factors are able to explain 41.2% of the variation in returns for the SV-WG strategy and 59.4% of the variation in the returns for the WV-SG strategy. The SV-WG strategy has a significant positive alpha of 0.87%, suggesting that there are abnormal positive returns on this strategy that the five factor model cannot explain. The WV-SG strategy has a significant negative alpha of -0.66% per month. The low loadings on the market factor for both strategies suggest that they are not very sensitive to systematic risk, as can be expected for long-short strategies. The SV-WG portfolio has a negative coefficient of -0.37 for the size factor, which implies that strong value firms are on average larger than weak growth firms, while the positive coefficient of 0.79 for the WV-SG strategy shows that weak value firms are on average smaller than strong growth firms. Both strategies have large loadings on the value factor, indicating that they are true value strategies. With regard to the investment factor, the negative coefficient of -0.43 for SV-WG indicates that on average, strong value firms invest more than weak growth firms, while weak value firms are more conservative in their investment policies than strong growth firms. The profitability factor is insignificant for both strategies. This is an unexpected result, as profitability is an important aspect of the composition of the F Score.
Panels B and C of table 8 show the regression results for the two sub-periods split at June 2008. The significance of the factors and R2 shows that the model is better able to explain the returns on both strategies for the post-2008 period, but the significant positive alpha of 0.79% for the SV-WG strategy for that period shows that the model is still not able to explain all of its return behavior. The profitability factor is positive for SV-WG and negative for WV-SG, indicating that, on average, strong value firms and strong growth firms are more profitable than weak value firms and weak growth firms. For the pre-2008 period, the alpha of the SV-WG strategy is significant and positive.
Panel D, E, and F of table 8 present the regression results for the sub-samples of small, middle, and large firms, respectively. The alpha’s for the SV-WG strategy are positive and significant for the small and middle firms, while the strategy’s alpha among large firms is insignificant. This is consistent with the raw portfolio returns where the return predicting ability of the sorts on BM ratio and F Score were not present among large firms. The only factor consistent in explaining returns across size segments is the value factor. The size factor is mostly insignificant.
5 A White test for heteroscedasticity points out that the variance of the residuals from this regression is not
24
Table 8 – Regression results
This table shows the results from regressions of the WV-SG and SV-WG monthly strategy returns in excess of the risk-free rate on the factors of the Fama French (2015) five factor model. The WV-SG goes long in weak value firms and shorts strong growth firms, the SV-WG strategy goes long in strong value firms and shorts weak growth firms. The table reports the monthly alpha in percent and shows the factor sensitivities to the market factor (Rm-RF), size factor (SMB), value factor (HML),
investment factor (CMA), and profitability factor (RMW). Panel A shows the results for the full sample covering the period 1998-2019, panel B for the sub-period preceding June 2008, panel C for the sub-period following June 2008, panel D for small firms, panel E for middle firms and panel F for large firms based on market capitalization. The table also reports the adjusted R2 and the
number of observations for the regression. The numbers in parentheses are Newey-West standard errors and *, **, *** represent significance levels of 10%, 5% and 1%, respectively.
Sample Panel A: Full sample Panel B: Pre 2008 Panel C: Post 2008
SV-WG WV-SG SV-WG WV-SG SV-WG WV-SG α 0.870*** -0.655*** 0.647** -0.617 0.791*** -0.461** (0.192) (0.245) (0.302) (0.497) (0.217) (0.219) (Rm – RF) -0.334*** 0.277*** -0.237** 0.309** -0.389*** 0.234*** (0.069) (0.077) (0.114) (0.150) (0.064) (0.054) SMB -0.370** 0.787*** -0.265 0.675* -0.468*** 0.850*** (0.152) (0.203) (0.254) (0.367) (0.117) (0.122) HML 1.291*** 0.703*** 1.513*** 0.591** 1.182*** 0.820*** (0.127) (0.156) (0.184) (0.251) (0.134) (0.138) CMA -0.427*** 0.530*** -0.399** 0.539** -0.601*** 0.552*** (0.136) (0.196) (0.183) (0.268) (0.162) (0.170) RMW 0.529* -0.442 0.296 -0.161 0.888*** -0.826*** (0.275) (0.321) (0.360) (0.428) (0.188) (0.165) Adjusted R2 0.412 0.594 0.253 0.662 0.643 0.510 Observations 264 264 120 120 144 144
Sample Panel D: Small firms Panel E: Middle firms Panel F: Large firms
25 As the alpha for the SV-WG strategy is positive and significant, hypothesis H2 is rejected. Although some of the variation in returns on the SV-WG strategy can be explained by the risk factors, a significant abnormal return of 0.87% remains unexplained. Interestingly, the WV-SG strategy shows a significant risk-adjusted return of -0.66% per month, while the raw returns on this strategy are close to zero and insignificant. Table 9 shows the results of a formal test that the difference in alpha’s between the two strategies is significant and amounts to 1.52% per month.
Table 9 – Test of significance of difference in alpha’s
This table shows the results for a test of the significance of the difference in alpha’s between the regressions of the strong value minus weak growth and weak values minus strong growth strategies. The difference in alpha’s is reported, along with the standard deviation, t-statistic and p-value.
Sample α diff. Std. Dev. T-stat P
26
6. Conclusion
The aim of this thesis is to answer the following research question:
Is the value premium for European firms a result of mispricing or compensation for exposure to risk factors?
In order to answer this question, data of firms from 30 European countries covering the period July 1998 to June 2019 is used. Based on portfolios sorted on BM ratio and F Score, a value-growth strategy is constructed that is designed to take advantage of temporarily mispriced stocks. By comparing recent financial performance trends to expectations about future performance, portfolios are formed with stocks where performance surprises are likely to occur. In an efficient market that reflects all historical available information in prices, such a strategy should not earn positive returns. As this strategy is able to generate positive and statistically significant returns, and outperforms traditional value strategies, this is evidence in favor of a mispricing explanation for the value premium. This finding is in accordance with the evidence found by Piotroski and So (2012) and Walkhäusl (2017).
To assess whether risk factors can explain the value premium, the returns of the value-growth strategies are regressed on the market factor, size factor, value factor, investment factor, and profitability factor of the Fama and French (2015) five factor model. This results in a significant positive alpha for the strategy that takes advantage of mispricing, indicating that the risk factors are not fully able to explain the strategy’s returns.
The robustness checks for sample periods and firm size categories in this thesis show that, although there are substantial differences between the returns and effectiveness of BM ratios and F Score in predicting returns across sub-samples, the SV-WG strategy consistently produces significant positive returns, even when adjusted for risk factors. The exception is the large firm sub-sample. However, since large firms’ stocks tend to be more liquid and more information is available about them, this would also decrease the probability of performance surprises as information is spread more rapidly, narrowing the window of opportunity for taking advantage of mispricing.
As both the strategy returns and results from the Fama French regression point in the same direction, and the findings are robust across several sub-samples, it can be concluded that for this sample, the mispricing explanation is a more plausible explanation for the value premium than risk compensation.
For academics, this thesis contributes to the literature by providing a robustness check of Piotroski and So’s (2012) findings for a new sample of firms and more recent years, and adjusts the returns for the risk factors of a new asset pricing model.
27 implies that using the method employed here for stock selection enables a portfolio manager to increase returns relative to risk.
28
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31
Appendix
Appendix A
Appendix table A1 – Results of White and Breusch-Godfrey tests
Panel A of this table shows the results of a White test for heteroscedasticity and panel B shows the results of a Breusch-Godfrey test for autocorrelation up to three lags concerning the regression of the strong value minus weak growth and weak value minus strong growth strategy returns on the Fama and French (2015) five factor model. The table reports the Chi2 statistic along with its p-value.
Panel A – White test for heteroscedasticity
Strategy Chi2 P
SV-WG 128.31 0.000
WV-SG 103.41 0.000
Panel B – Breusch-Godfrey test for autocorrelation
Strategy Lag Chi2 P
