Does It Pay to Bet Against Beta? On the Conditional Performance of the Beta Anomaly

Prior studies find that a strategy that buys high‐beta stocks and sells low‐beta stocks has a significantly negative unconditional capital asset pricing model (CAPM) alpha, such that it appears to pay to “bet against beta.” We show, however, that the conditional beta for the high‐minus‐low beta portfolio covaries negatively with the equity premium and positively with market volatility. As a result, the unconditional alpha is a downward‐biased estimate of the true alpha. We model the conditional market risk for beta‐sorted portfolios using instrumental variables methods and find that the conditional CAPM resolves the beta anomaly.     

The Conditional CAPM and the Cross-Section of Expected Returns

Most empirical studies of the static CAPM assume that betas remain constant over time and that the return on the value-weighted portfolio of all stocks is a proxy for the return on aggregate wealth. The general consensus is that the static CAPM is unable to explain satisfactorily the cross-section of average returns on stocks. We assume that the CAPM holds in a conditional sense, i.e., betas and the market risk premium vary over time. We include the return on human capital when measuring the return on aggregate wealth. Our specification performs well in explaining the cross-section of average returns.     

Is value riskier than growth?

We study the relative risk of value and growth stocks. We find that time-varying risk goes in the right direction in explaining the value premium. Value betas tend to covary positively, and growth betas tend to covary negatively with the expected market risk premium. Our inference differs from that of previous studies because we sort betas on the expected market risk premium, instead of on the realized market excess return. However, we also find that this beta-premium covariance is too small to explain the observed magnitude of the value premium within the conditional capital asset pricing model.     

Time-varying state variable risk premia in the ICAPM

We find that the relation between state variables, such as the t-bill rate and term spread, and consumption growth is time-varying. In the cross-section of U.S. stocks, risk premia for exposure to state variables vary over time accordingly. When a state variable predicts consumption strongly relative to its own history, its annualized risk premium increases by 6% (0.4 in Sharpe ratio). This effect implies that risk premia can switch signs and are increasing in the conditional variance of the state variable. These common drivers of time-varying risk premia are consistent with the Intertemporal CAPM. Benchmark factors contain the same conditional expected return effects as state variable risk premia.     

An Analysis of Contrarian Investment Strategies in the UK

The performance of contrarian, or value strategies – those that invest in stocks that have low market value relative to a measure of their fundamentals – continues to attract attention from researchers and practitioners alike. While there is much extant evidence on the profitability of value strategies, however, most of this evidence pertains to the US. In this paper, we provide a detailed characterisation of value strategies using data on UK stocks for the period 1975 to 1998. We first undertake simple one-way and two-way classifications of stocks in which value is defined using both past performance and expected future performance. Using sales growth as a proxy for past performance and book-to-market, earnings yield and cash flow yield as measures of expected future performance, we find that that stocks that have both poor past performance and low expected future performance have significantly higher returns than those that have either good past performance or good expected future performance. Allowing for size effects in returns reduces the value premium but it nevertheless remains significant. We go on to explore whether the profitability of value strategies in the UK can be explained using the three factor model of Fama and French (1996). Broadly consistent with the results for the US, we find that using the one-way classification the excess returns to almost all value strategies can be explained by their loading on the market, book-to-market and size factors. However, in contrast with the US, using the two-way classification there are excess returns to value strategies based on book-to-market and sales growth, even after controlling for their loading on the market, book-to-market and size factors.     

USING BAYESIAN BETAS TO ESTIMATE RISK RETURN PARAMETERS: AN EMPIRICAL INVESTIGATION

Since its original development by Sharpe (1964), the Capital Asset Pricing Model (CAPM) has been the focus of great interest, practical usage, modifications, testing, and controversy. The basic hypothesis of the CAPM is that the minimum expected return required by investors on any asset will equal the risk-free rate plus a premium for the asset's contribution to the variance risk of a diversified portfolio as measured by the asset's beta. The model is often utilized by investors to calculate the relevant risk and required return on an asset, while corporate officers widely employ the theory to compute the appropriate discount rate to use in estimating the net present value of capital budgeting projects when evaluating spending decisions (Gitman and Mercurio, 1982).     

What Cost of Capital Should You Use? The Market Has an Answer

The most widely used means of estimating a company's cost of equity capital is the Capital Asset Pricing Model (CAPM). But as a growing number of academics and practitioners have suggested, use of the CAPM produces estimates that often fail to reflect the risks of the companies as perceived by current and potential investors. The authors' work, together with other research, also suggests that the cost of equity produced by the CAPM is often too high. To the extent this is so, companies are discounting investment projects at rates of return that may be leading them to pass up value‐adding opportunities. The authors advocate the use of a simple and practical alternative to the CAPM that does not use either an assumed market risk premium or a beta. It uses instead an equity premium that is implied by the current market price of a company's stock and, as such, is implicitly derived from investors' assessments of the firm's risk that are reflected in that price. More specifically, the alternative approach solves for the internal rate of return that equates the present value of expected future cash flows to the current market price. In support of this approach, studies have shown that such market‐implied measures are better predictors than CAPM‐based estimates of future stock returns, both at the individual‐firm and aggregate market levels.     

THE STRUCTURE OF SKEWNESS PREFERENCES IN ASSET PRICING MODELS WITH HIGHER MOMENTS: AN EMPIRICAL TEST

In this paper, the authors employ a nonlinear formulation to examine empirically the structural content of the three moment capital asset pricing model (CAPM). Whereas previous research focused on the coefficients of beta and co-skewness, this paper presents empirical results on the market risk premium and elasticity coefficient components of these two coefficients. The results indicate that although the estimated coefficient of coskewness gives important information on the marginal rate of substitution between skewness and expected return, the elasticity coefficient can provide additional (albeit different) information on skewness preference that is independent of the effects of the market risk premium. This research also shows how the non-linear formulation provides a direct linkage between the twomoment and three-moment CAPM versions and thus provides an empirical test of the theoretical conditions under which skewness preference is consistent with the two-moment CAPM empiricial results.     

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.     

Value versus Growth: Time‐Varying Expected Stock Returns

Is the value premium predictable? We study time variations of the expected value premium using a two‐state Markov switching model. We find that when conditional volatilities are high, the expected excess returns of value stocks are more sensitive to aggregate economic conditions than the expected excess returns of growth stocks. As a result, the expected value premium is time varying. It spikes upward in the high volatility state, only to decline more gradually in the subsequent periods. However, out‐of‐sample predictability of the value premium is close to nonexistent.     

Factor beta,overnight and intraday expected returns in China

We study the relationship between common factor betas and the expected overnight versus intraday stock returns. Using data from the Chinese A-share markets, we find that the Fama-French five-factor betas and expected returns exhibit contrasting relationships overnight versus intraday. The market, value, and profitability factors earn positive beta premiums overnight and negative premiums intraday, while the size and investment factors' beta premiums behave oppositely. The night and day factor beta premium differentials are more muted among stocks with higher investor sophistication and vary across macroeconomic conditions. The contrasting day and night beta premiums extend to some other common factors and Chinese B shares, and vary their signs for some factors in the U.S. market.     

The CAPM strikes back? An equilibrium model with disasters

Embedding disasters into a general equilibrium model with heterogeneous firms induces strong nonlinearity in the pricing kernel, helping explain the empirical failure of the (consumption) CAPM. Our single-factor model reproduces the failure of the CAPM in explaining the value premium in finite samples without disasters and its relative success in samples with disasters. Due to beta measurement errors, the estimated beta-return relation is flat, consistent with the beta “anomaly,” even though the true beta-return relation is strongly positive. Finally, the consumption CAPM fails in simulations, even though a nonlinear model with the true pricing kernel holds exactly by construction.     

Did the value premium survive the subprime credit crisis?

We provide evidence that value stocks significantly underperformed growth stocks during the subprime credit crisis, despite a positive value premium before the crisis. The reversal in the value premium concentrates in financially constrained firms, suggesting it was due to the adverse influence of the crisis rather than confounding effects. These findings are robust to alternative financial constraint proxies and asset pricing models. The observation that value stocks are vulnerable to losses during extreme downturns like the crisis is consistent with them being riskier than growth stocks. Our findings have implications for the academic debate on the underlying cause of the value premium and for investors on the profitability of value investing strategies.     

A conditional higher-moment CAPM

This paper investigates whether dynamic and moment extensions to the traditional CAPM can improve its empirical performance and offer some alternative explanation to the cross-section of average returns on portfolios of stocks double sorted on book-to-market ratios and size. We consider three extensions. First, we introduce time-varying factor loadings obtained from a multivariate GARCH and dynamic conditional correlations. Second, we extend the model to a four-moment CAPM, which incorporates coskewness and cokurtosis. Finally, we allow for time-varying risk premia, based on a Markov-switching process. Our results confirm that the higher-moment CAPM does not perform well in its unconditional version, but its performance is significantly improved when we introduce a conditional version that accounts for both time-varying factor loadings and time-varying risk premia. The four-moment CAPM tests lead to a positive total risk premium estimate of 0.67% per month over the period 1926–2021, with all risk premia (beta, coskewness, and cokurtosis) exhibiting the expected theoretical signs.     

Value versus growth stocks in Singapore

This study examines value and growth stocks in Singapore. Specifically, we examine the value premium up to 5 years after the value and growth portfolio formation. We also examine if growth (value) stocks really indicate higher (lower) company profits in the later years, whether analysts’ forecasts are overly optimistic/pessimistic, and if earnings and earnings growth exhibit mean reversion. Our findings are, first, there is a value premium for Singapore stocks, but the premium is concentrated in the first 2 years after the portfolio formation. Second, value (growth) stocks do indicate low (high) earnings growth rates and low (high) return on equity (ROE) in the following years. Third, earnings growth is significantly overestimated for growth stocks but it is not underestimated for value stocks, indicating a one-way over-reaction. Finally, there is some evidence of mean reversion for excess ROE but not for excess earnings growth rates.     

The Effects of Inverted Yield Curves on Asset Returns

Between 1954 and 1991, U.S. stocks, long-term government bonds, and corporate bonds show negative risk premiums during periods preceded by inverted yield curves. Intermediate-term government bonds do not. Going from safer to riskier asset classes, the negative risk premiums increase in absolute value and statistical significance. The consumption CAPM offers a possible explanation for the negative risk premiums. A negative covariance between the growth rate of consumption and the premium on the risky assets will result in a negative risk premium. Empirical tests of the conditional covariance show that the consumption CAPM does not explain the phenomena.     

Can An 'Estimation Factor' Help Explain Cross-Sectional Returns?

Abstract:  We show in a theoretical model that the expected excess return on any asset depends on its covariance not only with the market portfolio, but also with changes in the representative agent's estimate. We test our model using GMM and compare it to the CAPM. The results suggest that adding an 'estimation factor' to the CAPM helps explain cross-sectional returns and that, unconditionally, this estimation factor carries a negative risk premium.     

Conventional and downside CAPM: The case of London stock exchange

Many studies on asset pricing have highlighted the importance of downside risk, in line with the actual losses of investors. In addition, the capital asset pricing model (CAPM), although presented as a universal theory, may provide significantly different rates of return in bull and bear markets. Using the CAPM under different conditions could be regarded as an alternative measurement and valuation approach to downside risk. This paper investigates conventional and downside approaches to risk taking into account different measures of downside beta coefficients. A further contribution of this research is the development of an alternative approach to testing the CAPM relationship. For this purpose, conditional relationships of the CAPM are proposed in which risk premiums are set separately in bull and bear periods. Using equity data and portfolios from the United Kingdom, we obtained positive and statistically significant downside risk premiums. We observed a slight advantage of downside measures over conventional beta measures. Conditional models provide evidence of a positive risk premium in rising markets and a negative risk premium in falling markets. The robustness analysis in subperiods indicates that these findings are largely unchanged for downside beta coefficients, which is not fulfilled by the model in a variance approach.     

The Value Premium and the CAPM

We examine (1) how value premiums vary with firm size, (2) whether the CAPM explains value premiums, and (3) whether, in general, average returns compensate β in the way predicted by the CAPM. Loughran's (1997) evidence for a weak value premium among large firms is special to 1963 to 1995, U.S. stocks, and the book‐to‐market value‐growth indicator. Ang and Chen's (2005) evidence that the CAPM can explain U.S. value premiums is special to 1926 to 1963. The CAPM's more general problem is that variation in β unrelated to size and the value‐growth characteristic goes unrewarded throughout 1926 to 2004.     

Disagreement and return predictability of stock portfolios

This paper provides evidence that portfolio disagreement measured bottom-up from individual-stock analyst forecast dispersions has a number of asset pricing implications. For the market portfolio, market disagreement mean-reverts and is negatively related to ex post expected market return. Contemporaneously, an increase in market disagreement manifests as a drop in discount rate. For book-to-market sorted portfolios, the value premium is stronger among high disagreement stocks. The underperformance by high disagreement stocks is stronger among growth stocks. Growth stocks are more sensitive to variations in disagreement relative to value stocks. These findings are consistent with asset pricing theory incorporating belief dispersion.