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The predictability of value measures and the hunt for alpha.
Remco Frans Brinkman s1915649
Rijksuniversiteit Groningen ABSTRACT
I investigate the predictability of value measures and their ability to create alpha for investors. I find confirming evidence that both the book-to-market ratio and market value of equity play an important role in explaining European stock returns. However, the ebit-to-enterprise value also plays a significant role in explaining stock returns and the portfolio selection procedure. Moreover, I examine the efficiency of individual and composite value measures and find evidence using Carhart's (1997) four factor model of their ability to create real alpha for investors.
Stock valuation based on fundamental analysis has a long history, dating back to Graham and Dodd (1934). Their value-driven stock selection approach has been successfully applied in different market circumstances and is generally accepted as both a profitable and reliable approach. However, due to the intensive research that is required about the fundamental soundness of companies under consideration, their approach requires a lot of time and is costly. Over the years investors have therefore tried to define a simplified approach to value investing, based on a few easy-to-calculate and reliable indicators. Many investors use such an approach to identify attractive investment opportunities. Extensive academic research has been conducted over the years, relating fundamental variables such as firm size, earnings yield market-to-book ratio to stock returns.
In this paper I will empirically investigate different measures of value based on company fundamentals and their relevance for long-term value investors. The research question I try to answer is as follows: Can long-term investors predict future stock returns and generate alpha using value measures? Answering this question is interesting because it has both practical and academic relevance.
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various measures of value and stock returns. The relevance to investigate whether alpha can be created using measures of value is because, efficient market hypothesis states that markets are efficient and it is therefore not possible to beat the market. In addition, the theory of Campbell and Shiller (1998) states that valuation ratios will converge to their historical means. Based on their findings, among others, I investigate whether stocks with high valuation measures compared to their historical means enhance portfolio performance.
The practical relevance of this study is due to the investigation of the predictive power and efficiency of the different value measures and whether it is possible to create alpha. This is of interest for investors because if value measures are able to predict stock returns and there is a possibility to create alpha, investors are able to beat the market and hence deliver outperformance relative to the market, i.e. higher return for a lower amount of risk.
There are several points on which this paper contributes to the existing literature. First, since most of the existing evidence in the literature is based on U.S. and Japanese stocks, investigating value measures of European stocks may provide additional insights. Examining European stocks may be useful in evaluating the evidence accumulated from studies of U.S. and Japanese stocks. It allows us to compare the results with evidence found for U.S. and Japanese stocks and may result in confirming existing evidence or provide insight on regional differences. Moreover, I do not exclude financial companies and use a more recent period from 1995-2011 to investigate whether older findings still hold.
Second, much existing academic literature relating measures of company value to stock returns show evidence based on relatively short periods of returns, usually on a yearly basis. I will also investigate a longer period of respectively 5 years. This is of importance because Campbell and Shiller (1998), find evidence that extending this period enhances the predictability of value measures on stock returns. Moreover, value investors with a buy and hold strategy usually hold stocks for several years, therefore investigating the predictability of various value measures for longer periods of returns provides additional insight on a possible long-term relationship.
Third, I use relatively more measures of value compared to other academic studies, which allows for more consistent and better comparability between the various measures of value. In addition, much of the existing literature does not explain whether they have tested for stationarity in their data, which may have implications on the results. I will contribute to the literature by providing evidence based on stationary data.
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Montier’s (2007) findings by testing the efficiency and comparing the value measures of the magic formula with the more classical measures of value i.e. earnings yield, return on assets and so forth. In addition, since Greenblatt argues that his formula is able to outperform the market I also examine whether the value measures of the magic formula are able to create real alpha for investors. I formulate several objectives in order to be able to answer the research question of this thesis. First, determine whether there is a significant relationship between the different measures of value and stock returns. Second, investigate whether 5-year normalized valuation measures enhance stock returns' predictability. Third, examine the relative efficiency of individual and composite value measures and investigate whether they can be used to create alpha. Last, investigate the performance of portfolios based on stocks with extreme value measures compared to their historic mean.
To be able to answer these objectives, I use data of companies listed on the Stoxx Europe 600 index. The period covered consists of the years 1995-2012. All the data on stock prices and company fundamentals are retrieved from Thomson Reuters Datastream. Information about inflation rates in the Euro area are retrieved from the database of Eurostat.
I. Literature review
Literature suggest many theories relating stock price movements to measures of company value. First, the efficient market and random walk theory form the base of most academic research. Efficient market theory, first introduced by Fama (1965a), states that all readily-available public information should be reflected in stock prices, which implies that value measures should not be able to predict future stock prices. In accordance with the efficient market theory is the random walk theory, which states that stock prices follow a random walk. This simply implies that stocks take a random and unpredictable path, so past stock performance cannot be used to predict future stock price movements and it is impossible to outperform the market without assuming additional risk (Fama (1965)). Both theories suggest that value measures should not have any predictive power. However, there is contradicting evidence in the literature, which is discussed later on.
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value. Campbell and Shiller’s (1998), results contradict with the efficient market theory, they find evidence that rather stock prices converge than fundamental values. They show that both price-earnings and dividend-price ratios are able to forecast future stock returns, but find no evidence of any predictive power in future growth of the fundamental variable.
Third, the findings of Campbell and Shiller (1998) are in line with the mean-reverting theory, which suggests that stock prices are mean reverting. Poterba and Summers (1988) where one of the first to notice autocorrelation in returns. They find evidence that returns are positively autocorrelated for periods of less than a year and negatively autocorrelated for periods over 3 to 8 years, which as they argue is an indication for transitory components in stock prices. Much research has been conducted to test this theory. Mukherji (2011) reports evidence of the existence of mean reversion in stock returns. His results show significant mean reversion in returns for small and large company stocks for periods of 1 through 5 years. The persistence of mean reversion is most notable for small company stocks.
These theories have important implications because, if measures of company value are able to predict future stock movements, investors could form portfolios that are able to beat the market and hence the efficient market and random walk theory do not hold. Moreover, the existence of price reversion and hence ratios converging to their historical means, would provide investors new investment opportunities. Investors may be able to enhance portfolio performance by forming portfolios of stocks based on valuation measures which are at extreme levels relative to their historical means, allowing investors to receive higher returns for the same amount of risk.
Much research has been conducted relating fundamental variables to the cross-sectional behavior of stock returns. Most of this research was focused on U.S. and Japanese equity markets. This is mostly due to the fact that both equity markets were the two largest in the world, accounting for 67% of the world's stock market capitalization in march 1990. Over the years researchers have studied the relationship between many different fundamental variables and stock returns. The reason for most studies to select such fundamental variables was mostly guided by intuition and their popularity amongst practitioners than by any explicit theoretical model. Many empirical studies have found evidence of a relationship between fundamental variables and stock returns, which is contrary to the predictions of the CAPM model.
Fama (1991) and Fama and French (1988) amongst others, suggest reasons why such variables might be related to stock returns. They argue in particular, that traditional measures of risk such as betas do not account for all the underlying risk in returns and therefore, could any correlation observed between fundamental variables and returns account as proxy for omitted risk factors. This assumption is consistent with inefficiencies in markets.
book-to-5
market (B/M) and market value of equity (MVE) are some of the most extensively studied variables in literature. Basu (1977), investigated the relationship between price-earnings (P/E) ratios (inverse of earnings yield) and U.S. stock returns during the period April 1957-March 1971. His results show abnormal returns for portfolios composed of stocks with low P/E ratios in comparison to random portfolios with equivalent risk. He finds no outperformance for portfolios with high P/E stocks in comparison to randomly selected portfolios. Basu (1997), argues that these findings are a result of exaggerated investor expectations on high P/E stocks and lags in interpreting new information accurately by investors. In addition, he interprets this as evidence of stock returns being a monotone increasing function of their E/P ratios. Research by Chan, Hamao and Lakonishok (1991), shows similar results. They find evidence of a significant positive relationship between returns in the Japanese market and earnings yield. However, when they control for a firm's size and its book-to-market no significant relationship was found. Moreover, the cash flow yield has higher predictive power then earnings yield, which they argue is a result of Japanese firms having distorted earnings due to the allowance of accelerated depreciation. Fama and French (1992), argue that stocks with low P/E ratios earn higher returns because they are fundamentally riskier. However, Lakonishok, Shleifer and Vishny (1994) show that higher average returns on low P/E portfolios cannot be explained by more fundamental risk.
Literature finds earnings based variables to be of limited value in forecasting stock returns. Fama and French (1992), report in their paper no significant relationship between earnings-to-price and stock returns after controlling for a firm's size and its book-to-market. A motivation for papers to explore the relationship of other yield surrogates such as cash flow yield (C/P) and sales-to-price (S/P) ratios amongst others, with stock returns is the shortcomings of accounting earnings. Since, accounting earnings are subject to management/accounting manipulation and volatility due to cyclicality and foreseen or unforeseen circumstances like accelerated depreciation or one time write offs, using other fundamentals may result in greater predictability of stock returns. For example, a reason to use sales-to-price ratios instead of E/P ratios is that a company's annual sales is a more reliable measure of long-term profit potential because it is less affected by temporary occurrences and it may therefore have greater explanatory power for stock returns.
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value, that portfolios with high S/P stocks earn the highest returns. Moreover, low S/P portfolios earn substantially lower returns than high S/P portfolios, which they argue as evidence of a relationship with stock returns. Recent study by Barbee, Jeong and Mukherji (2008) confirms previous findings of a relation between sales-to-price and stock returns. They examine the relationship of multiple fundamentals of U.S. stocks over the period March 1981-99 and find that sales-to-price explains 27% of the stock returns in comparison to 5% for price-cash flow and 6% for both price-earnings and book-to-market. They argue that this high fit is due to a profitability component in the S/P ratio namely the net profit margin. They state that this finding is consistent with evidence provided by other researchers that the value premium reflects market overreaction to both high profitability of growth stocks and depressed profitability of value stocks.
Literature describes growth stocks as firms with low book-to-market (B/M) ratios and having high average returns on capital, whereas value stocks are firms with high B/M values and are less profitable than low B/M stocks. Fama and French (1992) argue that markets judge the prospects of firms with high B/M ratios to be poor relative to firms with low B/M ratios. Moreover, high B/M stocks are typical to firms that are relatively distressed.
Numerous studies have documented a significant relationship of market equity and the book-to-market ratio with stock returns. Early empirical research by Stattman (1980) and Rosenberg, Reid, and Lanstein (1985) shows that a firm's B/M ratio is positively related to average U.S. stock returns. Chan, Hamao and Lakonishok (1991) and Fama and French (1992), report evidence of a strong positive relationship for B/M ratios and strong negative relationship for size with both Japanese and U.S. stock returns. Fama and French (1992), find evidence that most of the cross-section of average stock returns can be explained by market equity and the ratio of book-to-market equity. Banz (1981), reports that small-cap stocks earn substantially higher returns than large-cap stocks. Fama and French (1992) argue that this "size effect" is due to a higher risk factor for small capitalization stocks which is compensated by a higher return. However, when returns are adjusted for market risk, small firms still tend to outperform larger firms.
There is an important debate regarding the practical relevance of the value premium in academic studies. Loughran (1997), argues that the book-to-market premium cannot be captured by most investors because it heavily depends on shorting small-cap growth stocks. However, Dhatt, Kim and Mukherji (1999), show that there is an exploitable value premium for liquid small-cap stocks that does not require shorting growth stocks.
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variables remain arbitrary indicators of risk factors, which are related to returns for unexplained economic reasons.
Fama and French's (1995), research tries to explain this economic void of why those variables are indicators of risk factors. They examine whether the relation of book-to-market equity and size with the behavior of stock prices is consistent with that of earnings. Their findings show that stock prices properly reflect differences in profitability. Book-to-market and size are both related to persistent properties of earnings. Their findings reveal that high B/M values signals sustained low earnings on book value of equity, whereas low B/M are more profitable than high B/M stocks for at least five years after portfolios are formed. In addition, Fama and French (1995) also find evidence that size is related to profitability. After controlling for B/M, large-cap stocks tend to have larger earnings on book value of equity than small-cap stocks. Moreover, their results show that in the years after portfolio formation, growth rates of earnings of high- and low B/M stocks become more similar. Fama and French (1995) suggest that the market understands this convergence in the post-formation period and therefore make unbiased forecasts of earnings growth. The main findings that size and B/M factors in earnings are the same as those in returns suggests that those factors in earnings are the source of the corresponding factors in returns. This is consistent with the argument that book-to-market equity and size proxy for sensitivity to common risk factors in returns.
The aforementioned that size and book-to-market are related to the profitability of a firm, is in accordance with Fama and French's (2006) valuation theory. This theory states that expected stock returns are related to three variables, book-to-market, profitability and investment. The theory suggests that more profitable firms should have higher expected returns. Fama and French's (2006), find confirming evidence for their predictions. Haugen and Baker (1996), also find evidence of profitable firms having higher expected returns. Klement (2011), composes portfolios based on the profitability measure return on asset. The results show for such portfolios an outperformance of 6% per year on average over the benchmark for the period 1996-2010.
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It therefore puts companies on equal footing when comparing earnings yields of companies with different levels of debt and tax rates. Moreover, he argues that ebit-to-tangible capital employed (return on capital) is a better measure of a company's profitability than conventional measures like return on equity, because tangible capital employed is a better indication of what the company needs to conduct the business. The return on capital ratio therefore provides a better indication of a company's ability to generate cash.
Greenblatt (2006) shows that portfolios composed of the highest ranked stocks based on high earnings yield and return on capital are able to outperform the market. He argues that this performance cannot be reasonably attributed to a small-cap effect, since the difference in performance between the top and bottom 10% of stocks based on market capitalization was not significantly different. The results of the magic formula strategy shows that during the 17-year study the 10% best-ranked stocks beat the worst-ranked decile on average by over 14% per year. Montier (2007) tests Greenblatt's method for U.S., U.K., Japanese and European markets for the period 1993-2005. Montier (2007) reports evidence that this method outperforms their respective market benchmark by 3.6% to 10.8% per annum achieved at a portfolio risk typically 10% lower than the volatility of the benchmark. He also tests Greenblatt's method with more classical measures such as return on asset instead of return on capital and finds on average comparable results although Greenblatt's method usually provides the best results in the different regions.
II. Methodology A. Description of the data and criteria.
I use monthly and yearly data of stocks listed on the Stoxx Europe 600 index from the period May 1995 to April 2012. The Stoxx Europe 600 index covers eighteen countries across the European region and represents companies with small, mid and large capitalizations. Data on total monthly returns (including dividends) and company fundamentals come from the Thomson Reuters Datastream database. Data about inflation and risk-free rates are retrieved from the Eurostat database.
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investors as of the end of April. This procedure ensures that my tests are predictive in nature, even if accounting data is not publicly released within four months after fiscal yearend no “look-ahead” bias results. Instead outdated information from the prior fiscal year will be used and hence, results may even be on the conservative side.
In order to be able to conduct both academically consistent and practical relevant research in line with other studies, I use the following criteria for the first part of this paper where I test the relationship between value measures and stock returns. First, I apply a 98% winsorization to the data to reduce the effect of possibly spurious outliers. Conclusions based on winsorized data may understate the actual relationship but it is better to err on the conservative side. Second, all information on company fundamentals and stock prices has to be available to be able to calculate the measures of value. Last, I exclude firms that do not have fiscal years ending in December to ensure that the accounting data are equally fresh for all firms. Although, Fama and French (1992) note that regressing financial data of companies with different fiscal years ending on stock returns does not affect their findings, it may however be reasonably expected that imposing this criterion yields more reliable results.
In order to ensure practical relevance, I apply additional criteria for the second part of this paper where I test the efficiency of individual and composite value measures and form portfolios. The smallest quintile of firms and priced stocks are excluded from the sample. Generally low-priced and small-cap stocks are illiquid and have high percentage transaction costs. Loughran (1997) shows that book-to-market effects are driven by the smallest size quintile. Conrad and Kaul (1993) report that low-priced stocks have an upward bias in monthly returns due to bid-ask spreads.
B. The methodology to test the impact of value measures on stock returns.
I conduct the analysis of the relationship between stock returns and fundamental variables is at the individual security level. Lo and MacKinlay (1990) argue that statistical tests based on data grouped by empirically motivated fundamental attributes such as market value are subject to difficulties. They state that test statistics may be biased when a portfolio grouping approach is used and therefore spuriously exaggerate the relationship between fundamental attributes and portfolios excess returns whereas the use of data from individual securities without grouping them into portfolios results in less severe biases.
The methodology I use for testing the relationship between fundamentals and stock returns is in accordance with that of Chan, Hamao and Lakonishok (1991) who originated it, from Fama and MacBeth (1973). In addition to Chan, Hamao and Lakonishok (1991) who employ a Seemingly Unrelated Regression (SUR) model, I employ the more flexible Full Panel Data approach.
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measures. The dependent variable in the regression equation is the return of stock i, in year t, R , less the risk-free rate for year t, Rf . All returns are calculated as lognormal returns for a yearly and five year period to investigate both short- and long-term relationships.
I use the following explanatory variables to explain excess returns. a , represents the constant term. The (β )it and (β )it represent beta factors or market risks of firm i for year t, based
on the value-weighted and equally weighted indices respectively. Beta factors are estimated from the most recent 36 months of data. After controlling for market risks the remaining explanatory variables represent value measures.
I calculate and analyze the following measures of value for each year t and for every individual firm i. ln(MVE)it, the market value of equity is calculated as the natural logarithm of the
price per share times number of shares outstanding. (E/P)it , the earnings yield is computed as the
fully diluted earnings per share divided by price per share. I calculate the sales-to-price ratio (S/P)it
as net sales per share divided by price per share. The cash flow yield (C/P)it is calculated as cash flow
(net earnings plus depreciation) per share divided by price per share. Greenblatt’s (2006) earnings yield (EBIT/EV)it is calculated as pre-tax operating earnings (EBIT) divided by enterprise value (EV),
consisting of market value of equity plus net interest bearing debt. I calculate the book-to-market ratio ln(B/M)it as the natural logarithm of the book value of equity per share divided by price per
share. Greenblatt's (2006) return on capital (ROC)it is calculated as pre-tax operating earnings (EBIT)
divided by tangible capital employed (net working capital + net fixed assets). (ROA)it , return on
assets is computed as net earnings divided by total assets of the company. (ROE)it, return on equity
is calculated as the net earnings divided by the book value of equity. The ei represents the error
term.
R − Rf = a +b1(β )it +b2(β )it + a ln(MVE)it + a (E/P)it + a (S/P)it + a (C/P)it
+ a (EBIT/EV)it + a ln(B/M)it + a (ROC)it + a (ROA)it + a (ROE)it +eit (1)
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I also investigate the robustness of variables using normalized fundamentals and whether they are able to enhance value measures' predictability. Normalized fundamentals are defined as variables based on average 5 year fundamental values. Formula 2, shows how I calculate these normalized fundamentals.
= ∑ (2)
, is the average fundamental value over a five year period of firm i at time t. This value is calculated by taking the average of the sum of the current value at time t and that of the preceding 4 years. These average fundamental values are then used to calculated normalized value measures. The analogy behind the use of normalized fundamentals is that is smoothes fundamentals and therefore reduces extreme values, which could be a result of a onetime write off, gains on disposal of assets or exceptional high non-recurrent earnings etc. It should therefore provide a more reliable measure of value than measures based solely on one year fundamentals.
The hypothesis I test using regression equation 1 is as follows: H0: Value measures based on fundamentals cannot predict future stock returns. So, there should be no relationship between individual measures of value and stock returns.
C. The methodology to form portfolios and investigate the efficiency of individual and composite value measures.
The analysis of the relative efficiency of individual and composite value measures is conducted at the portfolio level. To form portfolios, I use value measures based on yearly fundamentals which is in line with most of the existing literature. In line with Klement (2011), stocks are ranked annually based on their value measure, where the best value of that measure is ranked 1, e.g. the highest earnings yield is ranked 1. Each year I form two equally weighted portfolios by selecting the 30 stocks which are ranked the highest and lowest based on a measure of value. These portfolios are held for one or five years depending on the horizon investigated. Moreover, I use a combination of the methods of Klement (2011) and Dhatt, Kim and Mukherji (2004) to examine the efficiency of composite value measures. In order to obtain composite value measures, simple averages of different combination of the ranked value measures are computed. I form portfolios in the same why as for individual measures of value however, they are now based on average ranked values of stocks in each year.
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Rpt = n ∑ni = 1rit (3)
I use Carhart's (1997) four factor model to examine the performance of portfolios and value measures' ability to create alpha for investors. His model is based on Fama & French's (1992) three factor model, which is originated from Jensen (1968). Fama & French (199) find evidence of small-cap companies performing better than large-cap companies and that high book-to-market companies perform relatively better than low book-to-market companies. Fama and French (1993) argue that stock returns can be better explained by a three factor model, which extends on the capital asset pricing model by including two new risk factors namely SMB and HML. The SMB factor represents the size premium investors receive from investing in small-cap companies and is calculated as the difference in return between a portfolio of small-cap and large-cap stocks. The HML factor represents the value premium investors receive from investing in high book-to-market companies and is calculated as the difference in return between a portfolio of high and low book-to-market companies.
Carhart (1997), extends the three factor model by adding another factor called momentum (WML). He finds evidence of momentum in stock returns and therefore argues that the three factor model is incomplete. The WML factor represents the premium investors receive from investing in stocks with strong past performance (winners) and is calculated as the difference in return between a portfolio of winners and losers. This momentum factor should be added to Fama-French's three factor model in order to explain the performance of a portfolio and whether true alpha can be created.
Using a four factor model as proposed by Carhart (1997), results in an alpha that is not merely the result of a portfolio's exposure to market beta, size factor by buying small companies, value factor of buying distressed or value stocks and momentum factor by buying stocks that have been increasing recently. As a result, the alpha indicated by the four factor model represents the ability to earn real excess returns. These excess returns are generated by another unknown factor, which may for example represent a fund manager's trading strategy i.e, ability of stock picking. Formula 4, shows the four factor model as proposed by Carhart (1997).
R − Rf = a + a (R − Rf ) + a + a + a + ept (4)
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stocks. The fourth factor measures the portfolio's exposure to momentum stocks. ept, is the
error term. The most important variable of this equation is the a , which represents the alpha. If the coefficient of this variable is positive and statistically significant than the portfolio is able to create alpha. The following hypothesis will be tested using Carhart's four factor model. H0: Portfolios based on value measures are not able to generate alpha. So, there should be no positive relationship between alpha and stock returns.
III. Analysis of the data
I use two datasets to investigate the various research objectives that are formulated. The first and main dataset consists of value measures which are based on yearly fundamental variables. The second set of data is used for robustness check and is composed of value measures based on normalized fundamental variables. Both datasets are composed of 1347 different companies that were listed during the period 1995-2012.
A. Descriptive statistics of value measures based on yearly fundamentals.
Table I shows the descriptive statistics of the main dataset for both dependent and explanatory variables. There are different numbers of observations for each variable indicating an unbalanced set of panel data. This will be taken into account by the full panel data approach that I employ. The amount of observations however, should be sufficient to reliably determine a relationship between variables.
Table I. Descriptive statistics of value measures based on 1 year fundamentals and stock returns.
Mean Median Maximum Minimum Std. Dev. Observations
R 0.0572 0.1014 2.2407 -4.3357 0.4662 12,451 Rf 0.0440 0.0416 0.0663 0.0269 0.0105 13,788 (β )it 1.0234 0.9521 1.1376 -1.2590 0.7142 12,202 (β )it 1.0811 0.9992 1.4150 -2.6472 0.8143 12,202 (MVE)it €6,057,331 €2,151,530 €73,228,810 €21,880 €10,614,330 12,327 (B/M)it 0.6229 0.4928 4.0249 -0.1411 0.5208 12,281 (E/P)it 0.0465 0.0541 0.4136 -1.0239 0.1090 12,244 (C/P)it 0.1106 0.0918 0.7887 -0.7363 0.1254 12,253 (S/P)it 1.5187 0.9690 14.119 0.0236 1.7507 12,168 (EBIT/EV)it 0.0732 0.0733 0.4023 -0.4513 0.0767 11,823 (ROA)it 0.0386 0.0342 0.2896 -0.3658 0.0649 13,156 (ROE)it 0.1178 0.1226 1.3428 -1.5083 0.2113 13,163 (ROC)it 0.2123 0.1709 2.0675 -1.6504 0.2957 9,855
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base with an average beta of 1.0234 for the equally weighted index and 1.0811 for the weighted index. However, when we look at the median values of the betas we can see that the value-weighted beta is close to 1 with a beta of 0.9992 and the equally value-weighted is 0.9521. The market value of equity of the companies in the sample indicates that the dataset consists of small, mid and large companies. All market values of equity are expressed in millions of euro's of 2012 purchasing power (inflation adjusted), which provides reliable comparison between the market values of different years and consistency in the results on their impact on stock returns. We can see that the smallest company is worth merely €21.880,- million euro's whilst the largest firm is worth around €73.228,- billion euro's.
Table II presents five different portfolios of approximately equal size and sorted by yearly average stock returns, where portfolio 1 has the lowest and 5 the highest return. The grouping procedure is repeated every year and averages of the returns and value measures are presented in the table. We can see from Table II that the most apparent relation appears to be between stock returns and the book-to-market ratio. The ebit-to-enterprise value ratio also shows some linear relationship although, the value of portfolio 5 is the same as that of portfolio 4. I find for the sales-to-price ratio some linear relationship with returns. We can see that stocks with low sales-to-sales-to-price ratios have low returns while high ratios provide high returns indicating linearity. The earnings yield and cash flow yield indicate for portfolios 1 through 4 a linear relation with returns however, portfolio 5 shows for both variables lower values in comparison to portfolio 4 indicating a bell-shaped relation. This bell-shaped relation is clearer for the relationship between the market value of equity and stock returns. In addition, Table II shows that portfolio 5 appears to be composed out of small companies, which may provide a size effect and therefore the higher returns. The table indicates for the beta variables a negative or slightly u-shaped relationship with stock returns, which contradicts with the CAPM model. Portfolios with low returns tend to have the highest betas. Furthermore, I find no linear relationship between stock returns and profitability measures, the results indicate an u-shaped relation.
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indicate a negative correlation between betas and ebit-to-enterprise value. In addition, the results from both tables indicate that there could be some correlation between the various variables in itself.
Table II. Summary statistics of portfolios sorted by returns.
Yearly average portfolio returns. standard deviations and fundamental characteristics from the period 1995-2012
Sorted by average returns
1 (low) 2 3 4 5 (high) R -0.5812 -0.1002 0.1015 0.2732 0.6126 Rf 0.0437 0.0436 0.0429 0.0429 0.0426 (β )it 1.2119 0.9928 0.9478 0.9150 1.0712 (β )it 1.2352 1.0265 1.0152 0.9876 1.1310 (MVE)it €6,088,793 €6,504,929 €6,903,292 €6,320,649 €3,518,304 (B/M)it 0.5277 0.5351 0.5369 0.5811 0.6138 (E/P)it 0.0320 0.0498 0.0533 0.0569 0.0488 (C/P)it 0.1019 0.1225 0.1277 0.1375 0.1369 (S/P)it 1.3761 1.3963 1.3837 1.5975 1.8360 (EBIT/EV)it 0.0610 0.0759 0.0831 0.0862 0.0862 (ROA)it 0.0422 0.0487 0.0523 0.0509 0.0480 (ROE)it 0.1061 0.1274 0.1372 0.1370 0.1232 (ROC)it 0.2189 0.2235 0.2381 0.2276 0.2128 N 1,636 1,684 1,582 1,660 1,636
Table III. Summary statistics of portfolios sorted by betas.
Yearly average portfolio returns. standard deviations and fundamental characteristics from the period 1995-2012
Sorted by average Equally Weighted Beta
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B. Testing data for stationarity, unit root processes and multicollinearity.
I test the variables of both datasets for stationarity and the presence of a unit root. Results of the unit root test for the dataset based on yearly fundamentals is left out because, I find no evidence for the presence of an unit root process. Table IV presents the results of the unit root tests for the dataset based on normalized fundamentals. The results reveal the presence of a unit root process in the following variables, market value of equity, cash flow yield and ebit-to-enterprise value however, not in the book-to-market ratio and all of the other variables which are left out. Since, these variables have either a common or individual unit root or both, I also test whether their first difference noted by D() has a unit root. I find no evidence of a unit root for the first differences of these variables. Consequently should the first differences of these variables be used in regression models to reliably investigate the relationship between stock returns and measures of company value, however solely for these variables based on normalized fundamentals.
According to Brooks (2008), stationarity of the data is important since it strongly influences its behaviour and properties and therefore results in regression analysis. Shocks in stationary data will gradually die away while for non-stationary data shocks will persist infinitely, which can lead to spurious regressions. Using non-stationary data in standard regression models may cause t-ratios to become enormously large because, non-stationary data does not follow a t-distribution.
Table IV. Summary of panel unit root test: Testing data based on normalized fundamentals for presence of unit root (probabilities in parentheses).
Levin. Lin & Chu t*
Im. Pesaran and Shin W-stat
ADF - Fisher Chi-square PP - Fisher Chi-square (MVE) -113.47 374.57 2.535.73 1.921.08 (0.00) (1.00) (0.00) (0.93) D(MVE) -938.20 -179.71 2.801.01 2.705.84 (0.00) (0.00) (0.00) (0.00) (C/P) 1.110.46 487.55 2.999.99 2.438.09 (1.00) (1.00) (0.00) (0.00) D(C/P) -577.19 -317.74 3.991.27 4.096.62 (0.00) (0.00) (0.00) (0.00) (B/M) -317.57 -131.69 3.849.44 3.216.48 (0.00) (0.00) (0.00) (0.00) (EBIT/EV) 100.49 -993.97 3.062.59 3.365.43 (1.00) (0.00) (0.00) (0.00) D(EBIT/EV) -826.59 -396.14 4.295.61 4.844.46 (0.00) (0.00) (0.00) (0.00)
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Table V. A. Correlation matrix of value measures based on yearly fundamentals.
Cash flow Yield Ebit/ev Earnings yield Book-to-market Market value Return on assets Return on capital Return on equity Sales-to-price β β
Cash flow yield 1.00 0.52 0.65 0.50 0.01 0.16 0.03 0.21 0.45 -0.07 -0.09
Ebit/ev 0.52 1.00 0.73 0.04 0.03 0.53 0.36 0.47 0.10 -0.16 -0.17 Earnings yield 0.65 0.73 1.00 0.02 0.06 0.56 0.32 0.55 -0.04 -0.17 -0.19 Book-to-market 0.50 0.04 0.02 1.00 -0.12 -0.30 -0.29 -0.27 0.53 0.07 0.08 Market value 0.01 0.03 0.06 -0.12 1.00 0.08 0.07 0.09 -0.13 -0.02 -0.07 Return on assets 0.16 0.53 0.56 -0.30 0.08 1.00 0.64 0.72 -0.28 -0.17 -0.18 Return on capital 0.03 0.36 0.32 -0.29 0.07 0.64 1.00 0.51 -0.19 -0.10 -0.11 Return on equity 0.21 0.47 0.55 -0.27 0.09 0.72 0.51 1.00 -0.19 -0.17 -0.18 Sales-to-price 0.45 0.10 -0.04 0.53 -0.13 -0.28 -0.19 -0.19 1.00 0.06 0.07 β -0.07 -0.16 -0.17 0.07 -0.02 -0.17 -0.10 -0.17 0.06 1.00 0.94 β -0.09 -0.17 -0.19 0.08 -0.07 -0.18 -0.11 -0.18 0.07 0.94 1.00
B. Correlation matrix of normalized value measures.
Cash flow Yield Ebit/ev Earnings yield Book-to-market Market value Return on assets Return on capital Return on equity Sales-to-price β β
Cash flow yield 1.00 0.52 0.69 0.70 0.02 0.07 -0.07 0.13 0.60 -0.11 -0.11
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which correlate with one another. I find the highest correlations between the following variables, ebit-to-enterprise value and earnings yield, earnings yield and cash flow yield and between return on equity and return on assets. These findings are consistently present in both datasets. A possible explanation for these findings may be the fact that some of these variables use a common or highly correlated fundamental variable. For instance, the earnings yield which is calculated using the net income whilst Greenblatt's earnings yield is calculated using income before tax. Both income measures are most likely highly correlated since only the tax and interest expense determine the difference.
Another observation from Table V is a negative correlation between betas and ebit-to-enterprise value ratios, which is as expected and argued in the former part of this section. It is evident that there are several correlations amongst the variables. Therefore, I perform a multivariate analysis to disentangle the impact of the various variables on stock returns.
Investigating the correlations between variables is important since OLS estimation methods implicitly assume that the explanatory variables are not correlated with one another. When explanatory variables are not correlated, coefficients on the variables would not change by adding of removing variables from the regression equation. The most important implication of multicollinearity between variables is that it increases the standard errors of the coefficients which in turn has an impact on the significance of the coefficients. However, according to Brooks (2008), multicollinearity may be ignored if the model is estimated adequate, i.e. statistically and in terms of coefficients having an appropriate sign and being of a plausible magnitude. In addition, the BLUE properties of the OLS estimator are not being affected by the presence of near multicollinearity, meaning estimates will still be consistent, unbiased and efficient. Estimated models can therefore still be used to produce forecasts so long as for the forecasted sample, the relationship between explanatory variables continues to hold.
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Table VI. Descriptive statistics of the value-weighted and equally weighted indices. Value-weighted index Equally weighted index
Monthly average return 0.0039 0.0047
Yearly average return 0.0478 0.0579
Std. Dev. 0.1772 0.1923
Maximum 0.1338 0.1598
Minimum -0.1555 -0.1997
Kurtosis 0.9621 2.2528
D. I test the robustness of the data source.
In order to avoid the survivorship bias which may result in misleading conclusions as described in the methodology section, I also include the companies that ceased to exist. I use constituent lists of the market index to include the firms that were delisted during the study period. Portfolios of equally weighted stocks are formed every month based on the corresponding constituent list for that month and the returns are regressed against returns of the equally weighted market index, the results are presented in Table VII. The results in the table show a fit of 0.9573 for the model and a coefficient of 0.9870 for the portfolio returns. Hence, we can conclude that the data and constituent lists fits the equally weighted market index reasonable well and can therefore be used to conduct the analysis.
Table VII. Testing the robustness of the data by regressing monthly portfolio returns based on constituent lists on the monthly returns of the equally weighted market index.
Portfolio return C Adj. R-squared 0.9870 -0.0021
(36.37) -(1.52) 0.9573 Durbin-Watson stat 1.8264
IV. Analysis of the results
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A. The predictability of European stock returns by different value measures based on yearly fundamentals.
The first analysis I conduct is on the short-term relationship between value measures based on yearly fundamentals and excess stock returns. I perform multiple regressions in order to disentangle the impact of the different measures of value on excess stock returns. This approach is in accordance with prior research which attempts to unravel the separate influences of the explanatory variables on returns.
Table VIII-A presents the main results of the analysis. The first nine models in the table show the impact of every individual explanatory variable on excess stock returns after controlling for market risk. This approach provides insight in a variable’s individual relation with returns and allows us to contrast the results with models existing of multiple variables. It could be that a variable in itself has explanatory power on returns but none in combination with other variables. In addition, the coefficient and sign of a variable may also vary when it is used in combination with other explanatory variables, due to multicollinearity.
The results in Table VIII-A show for both earnings yield (E/P) and cash flow yield (C/P) a positive sign and both have statistically significant coefficients, which indicates that high yields correspond with high returns. These findings are in line with evidence in literature e.g., Chan, Hamao and Lakonishok (1991). The signs of the variables sales-to-price (S/P), ebit-to-enterprise value (EBIT/EV), book-to-market (B/M) and market value of equity (MVE) are all in line with expectations and findings in literature. All the coefficients of these variables are highly significant. These findings indicate that stocks of firms with high sales-to-price, ebit-to-enterprise value and book-to-market ratios earn higher returns in comparison to the stock performance of firms with low values of these ratios. The market value of equity shows a negative sign implying that firms with high market values earn lower returns in comparison to firms with low market capitalizations. This finding is also in accordance with prior research and corroborates on the existence of a size effect because small firms tend to outperform larger firms.
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Table VIII. Panel regression of the short- and long-term relationship between measures of company value and excess stock return for the period 1995-2012
R − Rf = a +b1(β )it +b2(β )it + a ln(MVE)it + a (E/P)it + a (S/P)it + a (C/P)it + a (EBIT/EV)it
+ a ln(B/M)it + a (ROC)it + a (ROA)it + a (ROE)it +eit
A. Relation between yearly stock returns and value measures based on yearly fundamentals (t-statistics in parentheses)
Model β β E/P C/P S/P EBIT/EV ln(B/M) ln(MVE) ROA ROC ROE C Adj. R-squared
(1) -0.0631 0.0322 0.6136 0.0089 -(4.08) -(1.75) (7.39) (0.94) 0.3887 (2) -0.0665 0.0384 0.3475 0.0044 -(4.42) (2.17) (7.34) (0.46) 0.3862 (3) -0.0192 -0.0251 0.0322 0.0087 -(1.27) -(1.44) (10.01) (1.04) 0.3859 (4) -0.0425 0.0138 0.8162 -0.0269 -(2.71) (0.74) (10.53) -(2.62) 0.3976 (5) -0.0244 -0.0175 0.0664 0.1060 -(1.68) -(1.03) (9.68) (1.16) 0.3843 (6) 0.0074 -0.0530 -0.1693 1.3702 (0.53) -(3.26) -(28.21) (29.09) 0.4120 (7) -0.0595 0.0259 0.0378 0.0550 -(3.84) (1.40) (0.34) (5.80) 0.3872 (8) -0.0603 0.0373 -0.0690 0.0685 -(3.56) (1.81) -(2.62) (6.05) 0.3885 (9) -0.0642 0.0302 0.0072 0.0555 -(4.12) (1.63) (0.22) (6.00) 0.3700 (10) -0.0442 0.0272 0.3070 -0.2163 -0.0086 0.8253 -0.0907 -0.2380 0.3641 -0.0324 -0.2480 1.7944 -(2.66) (1.33) (1.37) -(1.70) -(1.25) (5.99) -(5.82) -(21.64) (1.66) -(0.89) -(3.35) (20.87 0.4318 (11) -0.0301 -(1.96) 0.0026 (0.14) 0.6415 (8.29) -0.0635 -(7.41) -0.1923 -(23.95) 1.4495 (23.72) 0.4410
B. Relation between 5 year stock returns and valuation measures based on yearly fundamentals (t-statistics in parentheses)
Model β β E/P C/P S/P EBIT/EV ln(B/M) ln(MVE) ROA ROC ROE C Adj. R-squared
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We can observe from Table VIII-A that the three explanatory variables with the highest t-statistics are ebit-to-enterprise value, book-to-market and market value of equity. This indicates that these variables have the highest predictive ability of stock returns. A combination of these variables may therefore lead to a model with even more predictive power. In addition, we see that the models based on market value of equity and ebit-to-enterprise value have the highest predictive power with an adjusted r-squared of 0.4120 and 0.3976 respectively.
Model 10 in the table represents the full model with all the explanatory variables included. The results from model 10 show that there are only four explanatory variable with the correct signs. Earnings yield shows a positive coefficient but is not statistically significant. The variables ebit-to-enterprise value and market value show highly significant coefficients at the 1% level and have both the correct signs. The signs of the cash flow yield and sales-to-price ratio have changed negatively and the cash flow yield is marginally significant at the 10% level whereas I find no significance of the sales-to-price ratio. The book-to-market ratio in the model has also changed it sign from positive to negative and is clearly significant at the 1% level. The profitability measures return on asset, capital and equity also show changes in comparison to their individual influences on returns. The return on assets still has the correct sign but is now marginally significant at the 10% level whereas return on capital retains its negative sign but is insignificant. The return on equity variable shows for this model a statistically significant but negative impact on returns.
The results from model 10 show clear evidence of a multicollinearity problem amongst the variables, which causes changes in signs and significance of the variables. As a result, this model is both academically en practical not the most optimal and relevant. I therefore perform a sensitivity analysis (Section V) to examine the impact of the various variables on stock returns and investigate which model is both practical and academically most relevant.
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results in a reliable model that does not suffer from implications of multicolliinearity. When we examine the betas in the different models of Table VIII-A, we can see that the value-weighted beta is negatively related to returns and in many of the models statistically significant, which is in line with findings in the data section. I find for the equally weighted beta no significant evidence of its impact on returns. These findings contradict with that of Chan, Hamao and Lakonishok (1991). They report, that an equally weighted beta explains returns substantially better than a value-weighted beta. A possible explanation for this difference could be that my dataset consists of relatively larger companies in comparison to their sample.
In addition to the short-term relationship I also investigate the long-term relationship of value measures with excess stock returns. I apply a White cross-section coefficient covariance method, there was an indication of autocorrelation. The method uses White cross-section standard errors and covariances with degrees of freedom corrected in order to correct for autocorrelation. This method simply implies that more evidence is needed in order to find something significant. I employ the same approach as for the former analysis and the results of this analysis are presented in Table VIII-B.
The results in Table VIII-B are to a large extent in accordance with those of Table VIII-A. We can see that most individual measures of value retain the correct sign and significance in explaining returns. The signs and coefficients of return on assets and equity show for the long-term a clear negative relation with stock returns. The book-to-market and market value of equity are again amongst the variables with the highest individual t-statistic. However, the ebit-to-enterprise value has a lower t-statistics in comparison to Table VIII-A but is still highly significant. The three variables prove again to be very reliable indicators of future stock performance. Moreover, the sensitivity analysis shows that the relation of the book-to-market variable with long-run returns is now always positive and significant. In comparison to the short-term analysis, the book-to-market variable does not lose its positive sign when the market value variable is included in the model.
The results for beta variables show no significant impact on long-run returns. However, there is still an indication of a negative relation between value-weighted betas and returns. Since, I find no significant evidence of a long-term relationship with returns, it may be concluded that betas have no long-term predictability only a short-term negative impact on returns.
At last, when we look in Table VIII-B at the adjusted r-squares of the different models, we can see that value measure's ability of explaining excess returns increases when a longer period is chosen. This finding is consistent with Campbell and Shiller (1998), among others, who argue that extending the period increases value measures' predictability of returns.
long-24
term is 0.2977, which is lower than that of the short-term. This coefficient always lies between zero and one where zero means a perfect fit. The bias proportion indicates that the forecasts made with the model are unbiased. According to Brooks (2008), accurate forecasts are unbiased and have a small variance proportion, most of the forecast error should therefore be attributed to the covariance proportion. We can therefore argue that the model produces more accurate forecasts for the long-term, although the short-term forecast also seems to be adequate.
Table IX. Forecast ability of short- and long-run stock returns.
R − Rf = a +b1(β )it +b2(β )it + a ln(MVE)it + a (EBIT/EV)it+ a ln(B/M)it +eit
Theil Inequality Coefficient Bias Proportion Variance Proportion Covariance Proportion
Short-term 0.4099 0.0000 0.1724 0.8276
Long-term 0.2977 0.0000 0.0893 0.9107
B. The relative efficiency of individual and composite value measures and their ability to create alpha. I use portfolios composed of stocks based on individual or composite value measures to examine the efficiency of these measures and whether they are able to create alpha for investors. Efficient portfolios are defined as portfolios having the highest return for a given risk or lowest risk for a given return. Amongst all the portfolios I create, I will only examine the most efficient portfolios whether they are able to create alpha for investors.
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present in portfolios based on market value or book-to-market ratios and therefore allows investors to capture such premiums.
Table X. Risk-return characteristics of portfolios composed of stocks with high and low measures of company value.
Monthly returns, standard deviations, paired difference test and Sharpe ratios of portfolios based on individual measures of company value for the period 1995-2012 (t-statistics in parentheses).
Portfolio Mean
Standard deviation
Paired
difference test Sharpe ratio Earnings yield
High 0.0081 0.0615
(3.71) 0.1323
Low -0.0072 0.0900 -0.0797
Cash flow yield
High 0.0045 0.0667 (2.71) 0.0679 Low -0.0065 0.0899 -0.0720 Sales-to-price High 0.0043 0.0762 (1.76) 0.0566 Low -0.0018 0.0673 -0.0272 Ebit-to-enterprise value High 0.0083 0.0560 (4.22) 0.1489 Low -0.0097 0.0920 -0.1058
Market value of equity
High 0.0032 0.0628
(1.21) 0.0508
Low 0.0048 0.0665 0.0721
Book-to-market value of equity
High 0.0030 0.0729 (0.71) 0.0416 Low 0.0005 0.0740 0.0062 Return on assets High 0.0053 0.0610 (3.52) 0.0868 Low -0.0076 0.0973 -0.0783 Return on capital High 0.0040 0.0607 (3.49) 0.0662 Low -0.0072 0.0883 -0.0820 Return on equity High 0.0054 0.0587 (4.20) 0.0920 Low -0.0087 0.0887 -0.0978
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The returns and Sharpe ratios of the profitability measures in the table shows some interesting results. All the portfolios composed of stocks with high values of a profitability measure show positive returns and relatively low standard deviations. These findings are in contrast with former analysis of their relationship with returns because I find no positive and significant relationship with returns. However, the results contribute to former presumption of a u-shaped relation with returns, because it seems that high values of these measures are related to moderate stock returns.
Finding positive returns and relatively low standard deviations for portfolios based on high profitability measures is interesting. Since, Table III in the data section indicates a negative relationship between profitability measures and betas, an investors could exploit this by forming portfolios with low beta stocks that have high profitability and achieve high returns for relatively low portfolio risk. A composite value measure based on high values of profitability and low betas could therefore enhance a portfolios performance and result in a more efficient portfolio.
In addition to the efficiency of individual measures based on yearly portfolio rebalancing, I also investigate the efficiency of individual and composite value measures for longer holding periods. Table XI shows the average monthly performance of the portfolios with yearly portfolio rebalancing and a 5-year buy and hold strategy. This table presents besides portfolios based on individual measures of value, only the most efficient portfolios based on composite measures of value and two portfolios based on extreme valuations. The table presents annual average monthly returns, standard deviations and efficiency measures.
We can see in the table that for the strategy with yearly portfolio rebalancing the highest return is achieved by portfolio 6 with an average monthly return of 0.99% respectively. Although, this portfolio receives the highest return it is the second most efficient portfolio based on this strategy. When we look at the 5-year buy and hold strategy we can see that this portfolio still provides robust results but is not the most efficient. The highest average monthly return for a 5-year buy and hold strategy is accomplished by portfolio 13 which is based on solely the ebit-to-enterprise ratio. We can see that the average monthly return is only 0.59% however, this portfolio is not the most efficient to hold. When we look at portfolios' different Sharpe ratios and yearly ranks we see that portfolio 2 is the most efficient portfolio for both a yearly and five-year holding strategy. This portfolio based on stocks with low betas and high values of ebit-to-enterprise value and return on capital does not receive the highest return amongst the portfolios, but has one of the lowest risk resulting in a more efficient portfolio. This finding is consistent with my former assumption on the possible ability of composite value measures based on high profitability and low betas to enhance portfolio performance.
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efficiency seems to be the result of differences in portfolio risk. This difference in portfolio risk is likely a result of including the return on capital variable, which is omitted from the selection procedure for portfolio 1. Although the 1.24 t-statistics of a paired difference test between the two portfolios does not indicate a significant difference between the two portfolios, we could presume that the lower standard deviation of portfolio 2 is the likely result of including the return on capital measure. We can also observe this for portfolios 12 and 13. It looks evident that the return on capital measure reduces portfolio risk and thereby enhances portfolio performance.
Including low beta firms in a portfolio reduces the risk of the entire portfolio. We see in comparison to portfolio 12 that including low beta stocks in the selection procedure for portfolio 2 reduces the risk of this portfolio. In addition, portfolios that include low beta stock receive higher returns in comparison to portfolios without this criteria. An explanation for this observation can be given by the negative relationship between betas and returns that I found.
Another interesting observation from the table is the ability of ebit-to-enterprise value to enhance portfolio performance. When we compare portfolio 5 with 7, we can see that including this variable in the selection procedure enhances the returns and reduces the risk of a portfolio. This is also observable for portfolios 23 and 24. This finding shows again the importance of the ebit-to-enterprise value for investors. It is not only a good predictor of future stock performance it is also a good variable for stock selection.
In addition to the former, I also investigate two portfolios based on stocks with extreme valuations. Extreme valuations are defined as value measures which have extreme values in comparison to their five year average value. Table XI shows two portfolios based on earnings yield and ebit-to-enterprise value which are composed of stocks with extreme value measures. I use these variables because they have the highest Sharpe ratios of portfolios based on individual measures. This makes them the most interesting variables to investigate whether extreme value measure are able to enhance portfolio performance.
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Table XI. Short- and long-term risk-return characteristics of portfolios based on (composite) value measures for the period 1995-2012. Annual means of equally weighted average monthly returns and
standard deviations Annual means of monthly Sharpe ratios and ranks
Portfolio Mean Std. Dev. Sharpe Ratio Ranks
1-year 5-years 1-year 5-years 1-year 5-years 1-year 5-years
(1) + / 0.0065 0.0052 0.0470 0.0495 0.138 0.106 11 2 (2) + / + 0.0078 0.0056 0.0443 0.0477 0.176 0.118 1 1 (3) + 0.0069 0.0041 0.0418 0.0465 0.164 0.088 4 8 (4) / 0.0030 0.0027 0.0729 0.0667 0.042 0.041 24 21 (5) / 0.0045 0.0041 0.0667 0.0649 0.068 0.063 18 15 (6) / + / + / + + 0.0099 0.0058 0.0578 0.0605 0.171 0.096 2 4 (7) / + / 0.0088 0.0055 0.0591 0.0614 0.149 0.089 7 7 (8) / + / + / + 0.0092 0.0054 0.0601 0.0632 0.153 0.085 5 10 (9) / + / + / + 0.0088 0.0053 0.0606 0.0629 0.145 0.083 9 12 (10) / + / + / + + + 0.0078 0.0053 0.0636 0.0635 0.123 0.084 13 1 (11) / + / + / + / + + 0.0086 0.0053 0.0581 0.0587 0.148 0.090 8 6 (12) / + 0.0076 0.0047 0.0541 0.0590 0.141 0.080 10 13 (13) / 0.0083 0.0059 0.0560 0.0602 0.149 0.099 6 3 (14) / 0.0081 0.0036 0.0615 0.0643 0.132 0.055 12 18 (15) / + / + / + + 0.0098 0.0055 0.0582 0.0606 0.168 0.091 3 5 (16) / 0.0035 0.0037 0.0645 0.0638 0.055 0.059 22 16 (17) / 0.0034 0.0028 0.0689 0.0672 0.050 0.041 23 21 (18) -0.0010 0.0017 0.0803 0.0683 -0.012 0.024 25 24 (19) 0.0053 0.0027 0.0610 0.0612 0.087 0.045 17 20 (20) 0.0040 0.0009 0.0607 0.0639 0.066 0.014 19 25 (21) 0.0054 0.0020 0.0587 0.0592 0.092 0.033 16 23 (22) / 0.0043 0.0035 0.0762 0.0685 0.057 0.052 21 19 (23) / + / 0.0051 0.0041 0.0795 0.0708 0.065 0.059 20 16 (24) / + / 0.0075 0.0045 0.0645 0.0637 0.116 0.071 15 14 (25) / + / + / + + 0.0073 0.0054 0.0610 0.0618 0.120 0.087 14 9
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mean reversion for periods over 3 to 8 years. The lack of evidence on extreme value measures' ability to enhance portfolio performance could be a result of the period that I use, which consists of two sub-periods of crises. One could argue that during periods of crisis ratios diverge more than normal form their historic relationship with their mean values and therefore resulting in less evidence.
I perform a robustness check in Section V in order to validate this reasoning and be able to confirm former findings. The period I use consists of the sub-period 1995-2007 and excludes the financial crisis starting late 2007 and currently 2012 ongoing. The results of this robustness check are largely in line with former findings. The main results show an increase in portfolio returns and decrease in portfolio risk, which is mainly due to the exclusion of the financial crisis during 2007-2012. The exclusion of the financial crisis also causes the portfolios based on extreme value measures to become the most efficient portfolios. These portfolios receive the highest returns and have relatively low portfolio risk, which is as expected. There is also a better indication of mean reversion for such portfolios starting at year 3. Moreover, the ebit-to-enterprise value shows again robust results of its importance in the portfolio selection procedure.
In addition to the efficiency of the different portfolios, I also examine their ability to create alpha for investors. Using Carhart's (1997) four factor model to explain portfolio returns provides insight on how returns are obtained by the portfolios. The model disentangles a portfolio's exposure to the four factors and reveals whether a portfolio is able to create real alpha or whether returns are merely obtained due to exposure to the factors market risk, size, value or momentum. In order to obtain practical relevant and concise results, I examine the eight most efficient portfolios and use two control portfolios based on the market value and book-to-market measures. Table XII presents the results of Carhart's model for both a short- and long-term holding period. I use monthly portfolio returns and regress them against the four factors.
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Table XII. Carhart's four factor model - Examine a portfolio's ability to create alpha.
A. Results of a one year buy and hold strategy with portfolios based on individual and composite value measures with yearly portfolio rebalancing for the period 1995-2012 (t-statistics in parentheses). (R − Rf ) (R − Rf ) a Adj. R-squared (1) + / 0.7409 0.4833 0.2383 -0.0635 0.0019 (20.48) (7.09) (3.21) -(1.64) (1.08) 0.7349 (2) + / + 0.7301 0.3036 0.2419 -0.0493 0.0038 (21.31) (4.70) (3.44) -(1.35) (2.29) 0.7333 (3) / 1.2565 0.6343 0.5841 -0.2625 -0.0009 (38.37) (10.28) (8.68) -(7.51) -(0.56) 0.9101 (4) / + / + / + 1.0231 0.4228 0.4672 -0.1756 0.0056 (27.85) (6.11) (6.19) -(4.48) (3.13) 0.8342 (5) / + / + / + + 1.0085 0.2789 0.4528 -0.1612 0.0068 (29.13) (4.28) (6.37) -(4.36) (4.00) 0.8409 (6) / 0.9711 0.4862 0.4381 -0.0905 0.0038 (28.31) (7.52) (6.22) -(2.47) (2.25) 0.8336 (7) / + 0.9577 0.3553 0.4247 -0.0216 0.0030 (26.37) (5.19) (5.69) -(0.56) (1.70) 0.7996 (8) / 1.1038 0.4460 0.4689 -0.2709 0.0049 (26.75) (6.27) (5.56) -(6.53) (2.62) 0.9041 (9) / 1.1117 0.3301 0.5048 -0.1169 0.0048 (24.88) (4.29) (5.52) -(2.60) (2.34) 0.8719 (10) 1.3087 0.0744 1.0507 -0.4131 -0.0013 (24.76) (0.75) (9.68) -(7.33) -(0.49) 0.8075
L = low values of that variable, H = high values of that variable
B. Results of a five year buy and hold strategy with portfolios based on individual and composite value measures with yearly portfolio composition for the period 1995-2012 (t-statistics in parentheses).
(R − Rf ) (R − Rf ) a Adj. R-squared (1) + / 0.8021 0.4608 0.1818 -0.0520 0.0022 (51.68) (16.18) (5.72) -(3.18) (2.83) 0.7981 (2) + / + 0.7964 0.2746 0.1776 -0.0445 0.0032 (51.94) (9.76) (5.65) -(2.76) (4.21) 0.7882 (3) / 1.1370 0.5627 0.4058 -0.1422 0.0001 (70.67) (19.06) (12.31) -(8.40) (0.16) 0.8816 (4) / + / + / + 1.0782 0.4908 0.4507 -0.0900 0.0026 (61.30) (15.21) (12.51) -(4.86) (3.03) 0.8418 (5) / + / + / + + 1.0404 0.3161 0.3899 -0.0748 0.0038 (58.34) (9.66) (10.67) -(3.98) (4.30) 0.8221 (6) / 1.0277 0.4744 0.4165 -0.0920 0.0033 (64.81) (16.30) (12.82) -(5.51) (4.19) 0.8570 (7) / + 1.0236 0.3208 0.3774 -0.0632 0.0026 (61.47) (10.50) (11.06) -(3.60) (3.10) 0.8362 (8) / 1.1320 0.4553 0.3022 -0.1368 0.0031 (56.72) (11.38) (7.26) -(6.81) (3.60) 0.9068 (9) / 1.1151 0.3650 0.3085 -0.0579 0.0038 (54.05) (8.82) (7.17) -(2.79) (4.26) 0.8892 (10) 1.1280 0.3752 0.7402 -0.1840 -0.0002 (50.21) (9.10) (16.08) -(7.78) -(0.17) 0.7859
