Dissertation
zur Erlangung des Grades eines Doktors
der Wirtschafts- und Gesellschaftswissenschaften
durch die
Rechts- und Staatswissenschaftliche Fakultät
der Rheinischen Friedrich-Wilhelms-Universität
Bonn
vorgelegt von
Stefan Koch
aus Bottrop
Bonn 2010
Introduction
What kinds of risk do systematically drive stock returns? This question has prompted vast amounts of research and is still one of the main challenges in finance. It has not only been of interest in the finance literature, but it also concerns investors across the globe. In general, investors aim at avoiding risky stocks but are keen on earning high returns. But which stocks are considered to be risky? Does a premium exist for risky stocks? High returns and low risk - do these two goals conflict with each other? The following dissertation addresses these questions empirically. Studying the German and the US stock market, we investigate the risk-return relationship and evaluate which kind of stocks yield a significant risk premium.
The first model that gave an answer to these questions was the Capital Asset Pricing Model (CAPM). The model was developed by Sharpe (1964), Lintner (1965), and Mossin (1966) in the 1960s and set the foundation for modern asset pricing theory. Its central implication is that every asset’s expected return is a linear increasing function of its market risk or market beta. According to the CAPM, the market excess return is the only systematic risk factor and the market beta, the slope of an asset return on the market excess return, embodies the systematic risk of the asset. Early empirical evidence such as that of Black et al. (1972) and Fama and MacBeth (1973) finds support for the model. However, during the 1980s and 1990s it turned out that market risk is not the only systematic risk. The so-called anomaly literature provides a large amount of evidence that the CAPM does not hold empirically and that other variables also influence stock prices. Banz (1981) documents that small firms have on average higher market risk adjusted returns than large firms in the US. This anomaly is entitled as the size effect.
Further, Rosenberg et al. (1985) and Fama and French (1992) show that stocks with a high book-to-market equity ratio outperform stocks with a low one, which is the so-called book-to-market effect. The CAPM fails to explain the size and book-to-market effect. Fama and French (1993) show that portfolios constructed to mimic risk factors related to size and book-to-market equity add substantially to the variation in stock returns explained by the market factor. For this reason, they argue in favor of a three-factor model. Besides the inclusion of the market excess return as in the CAPM, the Fama-French three-factor model considers the size and book-to-market factor. The size factor is the return of a portfolio of small firms minus the return of a portfolio of big firms. The book-to-market factor is the difference between the return of a portfolio of high book-to-market equity stocks minus the return of a portfolio of low book-to-market equity stocks. Fama and French (1993, 1995) suggest that the size and book-to-market factor mimic combinations of two underlying risk factors or state variables of special hedging concern for investors. Furthermore, Fama and French (1995) argue that the book-to-market beta is a proxy for relative distress. Firms with persistently low earnings have low book-to-market equity and negative slopes on the book-to-market factor. Fama and French (1996) find that the three-factor model absorbs most of the anomalies that have plagued the CAPM. Since its inception, the Fama-French three-factor model has been the standard empirical asset pricing model in the finance literature. For this reason, it is used as a standard of comparison throughout this dissertation.
This dissertation pursues two main goals. The first goal is to examine the relation between risk and return and to develop an appropriate test procedure to evaluate whether significant risk premia prevail. Early tests of the risk-return relation by Lintner1 and Black et al. (1972) use a cross-sectional approach regressing mean returns for each asset on beta estimates. Fama and MacBeth (1973) introduce an alternative for estimating the risk-return relation. Instead of taking sample average returns, they regress asset returns on beta estimates for each month of the sample period. The sample mean of the slope coefficient represents the risk premium. Since its inception, the Fama-MacBeth test has been one of the standard econometric methodologies in the empirical asset pricing literature. In the first chapter of my dissertation, we question the Fama-MacBeth test and evaluate the risk-return relation by applying a conditional approach to the Fama-French model. Subsequently, we develop a procedure to test if the risk is also priced according to the conditional approach. This procedure is compared to the Fama-MacBeth test.
Second, we investigate whether other risk factors, which cannot be captured by the Fama-French factors, also influence stock returns. Although the Fama-French factors are well-established in the literature, there is some evidence that the Fama-French factors cannot explain all asset pricing effects. Jegadeesh and Titman (1993) discover that past winners earn higher returns than past losers, the so-called momentum effect. Fama and French (1996) and Grundy and Martin (2001) find that the momentum effect cannot be captured by the Fama-French factors. As a result of this anomaly, many papers also consider the momentum factor and use a four-factor model. The momentum factor has been first proposed by Carhart (1997) and is the return of a portfolio of past winners minus the return of a portfolio of past losers. There are plenty of other asset pricing variables and risk factors that have been endorsed to be helpful in explaining stock returns in the literature. For example, Chen et al. (1986) propound macroeconomic risk factors as, e.g., interest rates, inflation, and industrial production. Cochrane (1996) suggests a production factor, Jagannathan and Wang (1996) a factor for human capital, Harvey and Siddique (2000) a coskewness factor, Gervais et al. (2001) a trading volume factor, Lamont et al. (2001) a financial constraint factor, Ang et al. (2001) a downside correlation factor, Easley et al. (2002) a measure for information risk, Vassalou and Xing (2004) a measure for default risk, and Ang et al. (2006a) downside beta. This dissertation evaluates the impact of illiquidity (chapter II) and idiosyncratic risk (chapter III) on stock returns. Liquidity measures the ability to trade large quantities quickly at low costs with little price impact. Idiosyncratic or unsystematic risk is the company or industry specific risk that is uncorrelated to the systematic risk. The final goal of chapters II and III is to test whether illiquidity and idiosyncratic risk yield significant risk premia.
Chapter I.2 The first chapter challenges the widely used Fama-MacBeth test. Ac- cording to asset pricing theory, in expectation there is a positive reward for taking risks. Investors are assumed to be risk averse and demand a compensation for holding risky assets. For this reason, riskier assets should yield higher expected returns. For instance, the expected market excess return, the difference between the market return and the risk-free rate, should be positive. To be in line with theory, empirical tests should find a positive relation between risk and expected returns. However, empirical tests are based on realized returns instead of expectations and realized returns are frequently negative. During periods of negative returns, the risk-return relation should be reversed, which is neglected by the standard Fama-MacBeth procedure. In order to take this into account, we make use of a conditional approach differentiating between periods with positive risk factor realizations and negative ones to test the risk-return relation. The conditional approach follows Pettengill et al. (1995). In contrast to the existent literature, we apply the conditional approach to the Fama-French three-factor model. We condition not only on the sign of the market return, but on that of each of the three factors, and test if the book-to-market and size betas retain their explanatory power once the conditional nature of the relation between betas and return is taken into account. As predicted by theory, our results yield strong support for a positive risk-return relation when risk factor realizations are positive and a negative one when risk factor realizations are negative.
However, at this stage results are not comparable to the Fama-MacBeth test as the Fama-MacBeth approach tests if beta risk is priced. Thus, as a further contribution to the literature, we derive a test based on the conditional approach to evaluate if beta risks are priced making the two tests comparable. This test extends the approach by Freeman and Guermat (2006) to multi-factor models. Our results provide evidence that the FG test produces very similar results as the standard Fama-MacBeth test. This finding does not only hold for empirical data from the US stock market, but it is confirmed through simulations based on different return distributions. Therefore, the results of the first chapter justify the application of the Fama-MacBeth test in the next chapters of this dissertation.
In addition, our results stress the importance of the selection of test portfolios in empirical asset pricing. We detect that estimates for risk premia strongly rely on the choice of test portfolios. Results in chapters II and III confirm this finding, emphasizing the lack of robustness of asset pricing models to alternative portfolio formation.
The following two chapters study the German stock market. Although empirical asset pricing is an extensive research field, there are only a few studies dealing with the German stock market. This is mainly due to the fact that a comprehensive set of accounting data and numbers of shares outstanding is not electronically available back to the 1970s, which makes the construction of a long time-series for the book-to-market and size factors impossible. The empirical analyses of chapters II and III are based on a unique data set covering about 1000 German firms. We make use of hand collected data on the number of shares outstanding as well as accounting data from the Hoppenstedt Aktienführer allowing us to construct the size and book-to-market factor for Germany. Daily prices and trading volume are obtained from Deutsche Kapitalmarktdatenbank in Karlsruhe. The sample period runs from January 1974 to December 2006.
Chapter II.3 Numerous episodes of financial market distress have underscored the importance of the smooth functioning of markets for the stability of the financial system. These episodes have been characterized by sudden and drastic reductions in market liquidity, which have led, amongst others, to disorderly adjustments in asset prices and a sharp increase in the costs of executing transactions. For instance, in October 1987, stock markets around the world crashed. Especially, on October 19, denoted as the Black Monday, the S&P 500 plummeted by over 20% creating the greatest loss Wall Street had ever suffered on a single day. Insufficient liquidity had a significant effect on the size of the price drop. Even recent events underline the importance of liquidity in stock markets. The subprime crisis was mainly triggered by the sharp fall in housing prices in the United States. From 2007 to 2009 the crisis rapidly developed and spread into a global economic shock, causing uncertainty across financial institutions. Liquidity dried up, resulting in a number of bank failures, large reductions in the market value of equities and declines in various stock market indices.
These extreme events illustrate that a lack of liquidity in financial markets can cause a decline in asset prices. However, liquidity is not only a concept that is related to the whole market, so-called aggregate market-wide liquidity risk. It can also aim at the risk resulting from a single investment, individual stock liquidity risk. When investors face tight liquidity positions, they may be forced to convert assets into cash. This is relatively more costly and more difficult when liquidity is lower. In order to reduce costs and to avoid the risk that arises from the difficulty of buying or selling an asset, investors should prefer liquid assets. In turn, this implies that investors buying illiquid assets should be compensated by higher expected returns. In the second chapter of this dissertation, we address the question whether illiquidity is a priced risk.
Unfortunately, estimating illiquidity is not straightforward as there is hardly a single measure that captures all of its aspects. Illiquidity is a multi-dimensional concept consisting of four dimensions: trading quantity, trading speed, trading costs, and price impact. In this study, we cover all of them. Our measure for trading quantity is turnover following Datar et al. (1998). Trading speed is measured by the number of days with zero trading volume as suggested by Liu (2006). Trading costs are approximated by the limited dependent variable model as proposed by Lesmond et al. (1999) and price impact by the Amihud (2002) measure.
Although there is evidence for the US market, e.g., Amihud and Mendelson (1986), Pastor and Stambaugh (2003), Acharya and Pedersen (2005), and Liu (2006) that illiquidity is a priced risk, other papers like Mazouz et al. (2009) show that the existence of a liquidity premium outside the US seems to be unclear and requires further analysis. Instead of concentrating on one liquidity measure and one econometric approach as often done so in the literature, this chapter covers all dimensions of liquidity and applies a multitude of different methodologies. Our results reveal that an illiquidity effect prevails. There exists a positive relation between stock returns and illiquidity. Further, we discover a significant risk premium on illiquidity independent of the measure chosen. Yet, the illiquidity premium is not consistent as it strongly relies on the selection of test portfolios. Furthermore, we analyze the link between the size of the firm and the illiquidity of the corresponding stock. Although the two concepts are correlated, we draw the conclusion that the two measures are no substitutes for each other.
Chapter III.4 The third chapter deals with a widely accepted measure of risk, volatility, the standard deviation of returns per time unit. Volatility is often used to identify how risky an investment is or as a measure of the security’s stability. In classical finance theory it is assumed that investors are risk averse and, hence, dislike high volatility. Therefore, they require a compensation for holding volatile stocks. Not only most of the empirical and theoretical asset pricing literature predicts a positive relationship between volatility and expected returns, but also many practitioners believe in the trade-off between volatility and expected returns. They share the view that high volatility must be connived in order to earn higher expected returns.
Volatility consists of two components: systematic and idiosyncratic risk. The largest component is idiosyncratic risk, which represents over 80% of the total volatility on average for single stocks. The last chapter of this dissertation investigates whether idiosyncratic volatility is a priced risk. Our results provide evidence that low idiosyncratic volatility stocks outperform high idiosyncratic volatility stocks. Further, our empirical findings do not support the positive relation between total volatility and expected returns, but show that the trade-off is negative.
Although this finding is in line with papers like Ang et al. (2006b, 2009), it stands in sharp contrast to most of the empirical and theoretical finance literature. Theoretical studies like Merton (1987), Jones and Rhodes-Kropf (2003), and Malkiel and Xu (2006) predict that investors demand a premium for holding stocks with high idiosyncratic risk. A large number of empirical papers confirm this prediction on the US market. Malkiel and Xu (2006), Spiegel and Wang (2005), and Fu (2009) provide unambiguous evidence that portfolios with higher idiosyncratic volatility earn higher average returns. In contrast to estimating idiosyncratic volatility based on daily data over the last month as done by Ang et al. (2006b, 2009), they obtain estimates for idiosyncratic risk based on monthly data. Studying the US market, Huang et al. (2010) find that the negative relation between idiosyncratic risk and returns is driven by monthly stock return reversals and, thus, disappears after controlling for past returns. Bali and Cakici (2008) detect that the negative relation vanishes for equally-weighted portfolios on the US market. In contrast to the existent literature, we construct an idiosyncratic risk factor and explicitly estimate the risk premium on the German stock market controlling for the market, size, book-to-market, and momentum factors. The results reflect the existence of a negative premium for idiosyncratic risk. The estimated factor risk premium is 10% per year after controlling for the other factors. Idiosyncratic risk is negatively significant in almost all specifications not only for the Fama-MacBeth test, but also for the GMM procedure, different test portfolios, different subperiods, and individual returns.
Motivated by the US evidence, we use equally-weighted portfolios and also control for short-term reversal. However, low idiosyncratic risk stocks still outperform high idiosyncratic risk stocks. Given these counterintuitive results, we undertake a multiplicity of new robustness checks. First of all, we evaluate the existence of a monotonic relation between expected returns and idiosyncratic risk applying the Monotonic Relation test proposed by Patton and Timmermann (2010). Further, we differentiate between upside and downside idiosyncratic volatility, apply an (E)GARCH approach, use Dimson Betas as well as different market models to estimate idiosyncratic volatility. We also change the data frequency and use monthly data. However, the puzzle still prevails.
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