On the power of cross-sectional and multivariate tests of the CAPM

This paper examines the power of the cross-sectional and multivariate tests of the CAPM under ideal conditions. When the CAPM is true the positively weighted market portfolio is MV-efficient and securities plot on the security market line. When the CAPM is false an alternative asset pricing model determines prices. An examination of the population intercepts, slopes and R² from cross-sectional regressions of expected returns on betas indicates that all three are unreliable indicators of whether the CAPM holds. Simulation analysis of the power of the cross-sectional tests expands on and reinforces the analysis based on the population values. The Gibbons et al. (1989) multivariate test fares much better.     

Estimation of expected return: CAPM vs. Fama and French

Most practitioners favour a one-factor model (CAPM) when estimating expected return for an individual stock. For estimation of portfolio returns, academics recommend the Fama and French three-factor model. The main objective of this paper is to compare the performance of these two models for individual stocks. First, estimates for individual stock returns based on CAPM are obtained using different time frames, data frequencies, and indexes. It is found that 5 years of monthly data and an equal-weighted index, as opposed to the commonly recommended value-weighted index, provide the best estimate. However, performance of the model is very poor; it explains on average 3% of differences in returns. Then, estimates for individual stock returns are obtained based on the Fama and French model using 5 years of monthly data. This model, however, does not do much better; independent of the index used, it explains on average 5% of differences in returns. These results therefore bring into question the use of either model for estimation of individual expected stock returns.     

CAPM and APT-like models with risk measures

The paper deals with optimal portfolio choice problems when risk levels are given by coherent risk measures, expectation bounded risk measures or general deviations. Both static and dynamic pricing models may be involved. Unbounded problems are characterized by new notions such as (strong) compatibility between prices and risks. Surprisingly, the lack of bounded optimal risk and/or return levels arises for important pricing models (Black and Scholes) and risk measures (VaR, CVaR, absolute deviation, etc.). Bounded problems present a Market Price of Risk and generate a pair of benchmarks. From these benchmarks we introduce APT and CAPM-like analyses, in the sense that the level of correlation between every available security and some economic factors explains the security expected return. The risk level non correlated with these factors has no influence on any return, despite the fact that we are dealing with risk functions beyond the standard deviation.     

Consumption-based CAPM models: International evidence

We examine the performance of several types of the consumption-based CAPM (C-CAPM) models to explore if consumption factors matter for determining excess returns across 17 MSCI country indexes. While the classic world C-CAPM does exhibit some power in explaining cross-sectional variations of expected excess returns, the model seems to require an implausibly large coefficient of risk aversion. The more sophisticated models including the heterogeneous C-CAPM, the world surplus consumption and the habit-formation models provide more reasonable estimates and add substantial explanatory power for the variation in the cross section of excess stock returns. Our results suggest that country-specific consumption risk is not fully diversified thus implying that stock returns are related to idiosyncratic consumption risk.     

Using the credit spread as an option-risk factor: Size and value effects in CAPM

This paper takes an option-theoretic approach to explain why pricing anomalies are observed when traditional CAPM is used. By extending CAPM to incorporate the option-risk factor of stocks, we show that stockholders’ limited liability can explain Fama and French’s size and value effects. We use bonds’ excess credit spread as a proxy for stocks’ default risk to control for the changing non-diversifiable option-risk characteristic of stocks. Because sensitivity to the excess credit spread becomes smaller as size increases and as value decreases, excess credit spread explains the CAPM anomalies in a fashion similar to the Fama–French factors. While the excess credit spread is significant in explaining Fama and French’s size and value effects, adding the Fama–French factors does not improve the performance of our model. Our revised model resembles conditional CAPM, but it offers a more intuitive explanation for the size and value effects.     

The performance of cross-sectional regression tests of the CAPM with non-zero pricing errors

We show that in the presence of non-zero pricing errors, the Fama–MacBeth (FM) cross-sectional regression test is very likely to either reject the Capital Asset Pricing Model (CAPM) when it (almost) holds or accept the model when it grossly fails. We investigate the case when pricing errors are correlated with betas and demonstrate that the test performance depends crucially on the correlation, cross-sectional distribution of betas, and several other parameter values. Even when the CAPM holds exactly (pricing errors are zero) the FM test is equally likely to either reject or accept the model when typical sample sizes are used.     

LIQUIDITY AND ASSET PRICING UNDER THE THREE‐MOMENT CAPM PARADIGM

We examine whether the use of the three‐moment capital asset pricing model can account for liquidity risk. We also make a comparative analysis of a four‐factor model based on Fama–French and Pástor–Stambaugh factors versus a model based solely on stock characteristics. Our findings suggest that neither of the models captures the liquidity premium nor do stock characteristics serve as proxies for liquidity. We also find that sensitivities of stock return to fluctuations in market liquidity do not subsume the effect of characteristic liquidity. Furthermore, our empirical findings are robust to differences in market microstructure or trading protocols between NYSE/AMEX and NASDAQ.     

Downside risk aversion,fixed-income exposure,and the value premium puzzle

The value premium is relatively small for investors with a material fixed-income exposure, such as insurance companies and pension funds, especially when they are downside-risk-averse. Value stocks are less attractive to these investors because they offer a relatively poor hedge against poor bond returns. This result arises for plausible, medium-term evaluation horizons of around one year. Our findings cast doubt on the practical relevance of the value premium for these investors and reiterate the importance of the choice of the relevant test portfolio, risk measure and investment horizon in empirical tests of market portfolio efficiency.     

Cashflow risk,systematic earnings revisions,and the cross-section of stock returns

The returns of stocks are partially driven by changes in their expected cashflow. Using revisions in analyst earnings forecasts, we construct an analyst earnings beta that measures the covariance between the cashflow innovations of an asset and those of the market. A higher analyst earnings beta implies greater sensitivity to marketwide revisions in expected cashflow, and therefore higher systematic risk. Our analyst earnings beta captures exposure to macroeconomic fluctuations and has a positive risk premium that provides a partial explanation for the value premium, size premium, and long-term return reversals. From 1984 to 2005, 55.1% of the return variation across book-to-market, size, and long-term return reversal portfolios is captured by their analyst earnings betas.     

Stock return volatility,operating performance and stock returns: International evidence on drivers of the ‘low volatility’ anomaly

This study highlights the link between stock return volatility, operating performance, and stock returns. Prior studies suggest that there is a ‘low volatility’ anomaly, where firms with a low stock return volatility out-perform firms with a high stock return volatility. This paper confirms that low volatility stocks earn higher returns than high volatility stocks in emerging markets and developed markets outside of North America. We also show that low volatility stocks have higher operating returns and this might explain why low volatility stocks earn higher stock returns. These results provide a partial explanation for the ‘low volatility effect’ that is independent from the existence of market anomalies or per se inefficiencies that might otherwise drive a low volatility effect. We emphasize the importance of controlling for stock return volatility when analyzing operating performance and stock performance.     

CAPM option pricing

This paper extends the option pricing equations of [Black and Scholes, 1973] , [Jarrow and Madan, 1997] and [Husmann and Stephan, 2007] . In particular, we show that the length of the individual planning horizon is a determinant of an option’s value. The derived pricing equations can be presented in terms of the Black and Scholes [1973. Journal of Political Economy 81, 637–654] option values which ensures an easy application in practice.     

A conditional asset-pricing model with the optimal orthogonal portfolio

This paper employs a conditional asset-pricing model based on the optimal orthogonal portfolio approach to construct a factor portfolio that embodies all the latent factors important for pricing a given set of test assets. The advantage of this portfolio to the anomaly related mimicking portfolios is its ability to separate out the components of average return that are not related to the return covariation. The performance of this portfolio is evaluated against several conventional factors, using both cross-sectional and time-series regression approaches, as well as the Hansen and Jagannathan (1997) distance measure. Its strong out-of-sample results indicate that our suggested methodology may have important applications in risk management, portfolio selection and performance evaluation.     

Risk aversion and skewness preference

Empirically, co-skewness of asset returns seems to explain a substantial part of the cross-sectional variation of mean return not explained by beta. This finding is typically interpreted in terms of a risk averse representative investor with a cubic utility function. This paper questions this interpretation. We show that the empirical tests fail to impose risk aversion and the implied utility function takes an inverse S-shape. Unfortunately, the first-order conditions are not sufficient to guarantee that the market portfolio is the global maximum for this utility function, and our results suggest that the market portfolio is more likely to represent the global minimum. In addition, if we do impose risk aversion, then co-skewness has minimal explanatory power.     

Consumer expectations and short-horizon return predictability

Lettau and Ludvigson [Lettau, M., Ludvigson, S, 2001. Consumption, aggregate wealth and expected stock returns. Journal of Finance 56, 815–849] argue that fluctuations from the equilibrium ratio of consumption to wealth (cây) reflect changing expectations of asset returns and document significant short-horizon predictability based on cây. This paper further explores the role of consumer expectations in modeling time variation of expected equity returns by considering two measures of consumer expectations: (i) consumer behavior as reflected in cây, and (ii) a more-direct measure of expectations captured by the Index of Consumer Sentiment (ICS). We report strong regression-based evidence of return predictability based on cây, which remains evident even after accounting for various sources of estimation risk. However, the regression-based evidence of predictability does not necessarily imply that shifts in aggregate consumption and the components of aggregate wealth give rise to economically significant investment signals. The survey-based measure of expectations (ICS) is shown to complement the behavioral measure (cây) but has no apparent stand-alone predictive value in forecasting equity returns.     

Asset pricing with heterogeneous beliefs and relative performance

We propose an equilibrium asset pricing model in which agents with heterogeneous beliefs care about relative performance. We find that the concern with relative performance leads agents to trade more similarly, a development that has two effects. First, similar trading directly decreases volatility. Second, similar trading decreases the impact of dominant agents. The second effect dominates the first when agents expect large differences between their final performances, and vice versa when agents expect small differences between their final performances. Compared with the case in which agents are unconcerned about relative performance, the stock return volatility is higher when the second effect dominates, and lower when the first effect dominates. This paper also demonstrates that the concern about relative performance influences investors’ holdings, stock prices and risk premia.     

Dividend distributions and closed-end fund discounts

Empirical support for the hypothesis that closed-end fund discounts are related to overhanging tax liabilities has been mixed. We introduce a new approach to testing this hypothesis by examining changes in discount levels following distributions of dividends and capital gains. Since distributions reduce future shareholder tax liabilities, the tax liability hypothesis implies that closed-end fund discounts should decline following distributions. Focusing on changes in discounts isolates this tax effect by eliminating the impact of other fund-specific factors on discount levels. Our results support the tax liability hypothesis, showing that short-run fluctuations in discounts are directly affected by taxable distributions.     

The world price of jump and volatility risk

We study international integration of markets for jump and volatility risk, using index option data for the main global markets. To explain the cross-section of expected option returns we focus on return-based multi-factor models. For each market separately, we provide evidence that volatility and jump risk are priced risk factors. There is little evidence, however, of global unconditional pricing of these risks. We show that UK and US option markets have become increasingly interrelated, and using conditional pricing models generates some evidence of international pricing. Finally, the benefits of diversifying jump and volatility risk internationally are substantial, but declining.     

Preference heterogeneity and asset prices: An exact solution

We introduce a general equilibrium model of a multi-agent, pure-exchange economy and find a set of conditions that enable us to obtain explicit closed-form solutions to the equilibrium interest rate, stock price, risk premium and stock market volatility when investors have heterogenous risk aversions. Because the market is dynamically complete, full risk sharing obtains and a representative agent can be constructed, though the risk aversion of this agent fluctuates over time with the state of the economy, as the relative wealth distribution of the individual investors changes. We show that preference heterogeneity can cause asset prices to be significantly more volatile than the underlying dividends and that it can lead to leverage-like effects in volatility, in the sense that volatility increases after stock-market declines.     

Disagreement,tastes, and asset prices

Standard asset pricing models assume that: (i) there is complete agreement among investors about probability distributions of future payoffs on assets; and (ii) investors choose asset holdings based solely on anticipated payoffs; that is, investment assets are not also consumption goods. Both assumptions are unrealistic. We provide a simple framework for studying how disagreement and tastes for assets as consumption goods can affect asset prices.     

A note on capital asset pricing and heterogeneous taxes

In this paper, we present a stylized model where we show how asset prices, i.e., required expected rates of returns, may be characterized in a world with heterogeneous asset taxes. Within a simple CAPM-like framework, we derive an after-tax beta equal to the pre-tax beta multiplied by a (non-obvious) asset specific tax adjustment. We further show in what sense the Security Market Line here can be replaced by a Security Market Fan. Well-known CAPM relations are obtained as special cases, and policy implications are analyzed.