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.     

Testing the CAPM with Time-Varying Risks and Returns

This paper draws on Engle's autoregressive conditionally heteroskedastic modeling strategy to formulate a conditional CAPM with time-varying risk and expected returns. The model is estimated by generalized method of moments. A CAPM that allows mean excess returns to shift in January survives generalized method of moments specification tests for a number of omitted variables. However, a residual dividend yield component is found to remain in the excess returns of smaller firms. We find significant monthly and quarterly components in the risk premia and beta estimates.     

Does the Conditional CAPM Work? Evidence from the Istanbul Stock Exchange

Using a sample of common stocks traded on the Istanbul Stock Exchange from February 1997 to April 2008, we test whether the conditional capital asset pricing model (CAPM) accurately prices assets. In our empirical analysis, we closely follow the methodology introduced in Lewellen and Nagel (2006). Our results show that the conditional CAPM fares no better than the static counterpart in pricing assets. Although market betas do vary significantly over time, the intertemporal variation is not large enough to drive average conditional alphas to zero.     

Testing Conditional Asset Pricing Models Using a Markov Chain Monte Carlo Approach

We use Markov Chain Monte Carlo (MCMC) methods for the parameter estimation and the testing of conditional asset pricing models. In contrast to traditional approaches, it is truly conditional because the assumption that time variation in betas is driven by a set of conditioning variables is not necessary. Moreover, the approach has exact finite sample properties and accounts for errors‐in‐variables. Using S&P 500 panel data, we analyse the empirical performance of the CAPM and the Fama and French (1993) three‐factor model. We find that time‐variation of betas in the CAPM and the time variation of the coefficients for the size factor (SMB) and the distress factor (HML) in the three‐factor model improve the empirical performance. Therefore, our findings are consistent with time variation of firm‐specific exposure to market risk, systematic credit risk and systematic size effects. However, a Bayesian model comparison trading off goodness of fit and model complexity indicates that the conditional CAPM performs best, followed by the conditional three‐factor model, the unconditional CAPM, and the unconditional three‐factor model.     

Learning about beta: Time-varying factor loadings, expected returns, and the conditional CAPM

We amend the conditional CAPM to allow for unobservable long-run changes in risk factor loadings. In this environment, investors rationally “learn” the long-run level of factor loadings from the observation of realized returns. As a consequence of this assumption, we model conditional betas using the Kalman filter. Because of its focus on low-frequency variation in betas, our approach circumvents recent criticisms of the conditional CAPM. When tested on portfolios sorted by size and book-to-market, our learning-augmented conditional CAPM passes the specification tests.     

Cross‐sectional Tests of Conditional Asset Pricing Models: Evidence from the German Stock Market

We study the performance of conditional asset pricing models and multifactor models in explaining the German cross‐section of stock returns. We focus on several variables, which (according to previous research) are associated with market expectations on future market excess returns or business cycle conditions. Our results suggest that the empirical performance of the Capital Asset Pricing Model (CAPM) can be improved when allowing for time‐varying parameters of the stochastic discount factor. A conditional CAPM using the term spread explains the returns on our size and book‐to‐market sorted portfolios about as well as the Fama‐French three‐factor model and performs best in terms of the Hansen‐Jagannathan distance. Structural break tests do not necessarily indicate parameter instability of conditional model specifications. Another major finding of the paper is that the Fama‐French model – despite its generally good cross‐sectional performance – is subject to model instability. Unconditional models, however, do a better job than conditional ones at capturing time‐series predictability of the test portfolio returns.     

Testing conditional factor models

Using nonparametric techniques, we develop a methodology for estimating and testing conditional alphas and betas and long-run alphas and betas, which are the averages of conditional alphas and betas, respectively, across time. The estimators and tests can be implemented for a single asset or jointly across portfolios. The traditional Gibbons, Ross, and Shanken (1989) test arises as a special case of no time variation in the alphas and factor loadings and homoskedasticity. As applications of the methodology, we estimate conditional CAPM and multifactor models on book-to-market and momentum decile portfolios. We reject the null that long-run alphas are equal to zero even though there is substantial variation in the conditional factor loadings of these portfolios.     

Conditional coskewness and asset pricing

We explore the empirical usefulness of conditional coskewness to explain the cross-section of equity returns. We find that coskewness is an important determinant of the returns to equity, and that the pricing relationship varies through time. In particular we find that when the conditional market skewness is positive investors are willing to sacrifice 7.87% annually per unit of gamma (a standardized measure of coskewness risk) while they only demand a premium of 1.80% when the market is negatively skewed. A similar picture emerges from the coskewness factor of Harvey and Siddique (Harvey, C., Siddique, A., 2000a. Conditional skewness in asset pricing models tests. Journal of Finance 65, 1263–1295.) (a portfolio that is long stocks with small coskewness with the market and short high coskewness stocks) which earns 5.00% annually when the market is positively skewed but only 2.81% when the market is negatively skewed. The conditional two-moment CAPM and a conditional Fama and French (Fama, E., French, K., 1992. The cross-section of expected returns. Journal of Finance 47,427465.) three-factor model are rejected, but a model which includes coskewness is not rejected by the data. The model also passes a structural break test which many existing asset pricing models fail.     

An examination of alternative CAPM-based models in UK stock returns

We evaluate the performance of unconditional and conditional versions of seven stochastic discount factor models in UK stock returns between January 1975 and December 2001. We find that the conditional four-moment capital asset pricing model (CAPM) has the best performance among the models we consider in terms of the lowest [Hansen, L.P., Jagannathan, R., 1997. Assessing specification errors in stochastic discount factor models. Journal of Finance 52, 591–607] distance measure and explaining the time-series predictability of industry portfolio excess returns. Conditional models also do a better job than unconditional models. However we find that the superior performance of the conditional four-moment CAPM, and conditional models in general, arises in part due to overfitting the data.     

Examination of Conditional Asset Pricing in UK Stock Returns

I examine the empirical performance of various specifications of the capital asset pricing model (CAPM) in UK stock returns, using the stochastic discount framework. When the proxy for the market portfolio includes a proxy for labor income growth in addition to the stock market index, the performance of the CAPM improves. The improvement in performance shows in the magnitude and significance of the pricing errors and in the reduced impact of asset characteristics and other factors in the pricing of assets. There is further improvement when I use conditional versions of the models.     

On the Efficiency of Conditional Heteroskedasticity Models

This paper discusses how conditional heteroskedasticity models can be estimated efficiently without imposing strong distributional assumptions such as normality. Using the generalized method of moments (GMM) principle, we show that for a class of models with a symmetric conditional distribution, the GMM estimates obtained from the joint estimating equations corresponding to the conditional mean and variance of the model are efficient when the instruments are chosen optimally. A simple ARCH(1) model is used to illustrate the feasibility of the proposed estimation procedure.     

International Asset Pricing and Portfolio Diversification with Time-Varying Risk

We test the conditional capital asset pricing model (CAPM) for the world's eight largest equity markets using a parsimonious generalized autoregressive conditional heteroskedasticity (GARCH) parameterization. Our methodology can be applied simultaneously to many assets and, at the same time, accommodate general dynamics of the conditional moments. The evidence supports most of the pricing restrictions of the model, but some of the variation in risk-adjusted excess returns remains predictable during periods of high interest rates. Our estimates indicate that, although severe market declines are contagious, the expected gains from international diversification for a U.S. investor average 2.11 percent per year and have not significantly declined over the last two decades.     

Currency risk premia and uncovered interest parity in the International CAPM

Zero-investment uncovered interest parity (UIP) portfolio positions provide perfect factor-mimicking portfolios for currency risk in the International CAPM context. Their returns are the currency risk premia. Since the UIP positions on average provide low returns, the currency risk premia must be low so that currency risk appears not to be priced in an unconditional model. However, previous research has shown that UIP returns are predictable and may be quite substantial conditionally. We use this observation to generate a specific conditional version of the International CAPM. A GMM approach shows that the conditional model performs well, while the unconditional International CAPM is (marginally) rejected. The paper thus argues that previous rejections of the International CAPM stem from the fact that currency risk premia are by nature low over extended periods of time and do not provide evidence against the International CAPM.     

Tests of the CAPM with Time-Varying Covariances: A Multivariate GARCH Approach

This paper examines an asset pricing model in which the Sharpe-Lintner CAPM and the zero-beta CAPM are special cases. The model allows the ratio of expected market risk premium to market variance, the conditional expected excess returns, and the risks to change over time. The results are found to be sensitive to the choice of the portfolio formation techniques. Significant time variability is shown in the conditional expected excess asset returns and risks and also in the reward-to-risk ratio.     

The Conditional Relationship Between Beta and Returns: A Reassessment

Abstract:  Several recent empirical tests of the Capital Asset Pricing Model have been based on the conditional relationship between betas and market returns. This paper shows that this method needs reconsideration. An adjusted version of this test is presented. It is then demonstrated that the adjusted technique has similar, or lower, power to the more easily implemented CAPM test of Fama and MacBeth (1973) if returns are normally distributed.     

The conditional CAPM does not explain asset-pricing anomalies

Recent studies suggest that the conditional CAPM holds, period by period, and that time-variation in risk and expected returns can explain why the unconditional CAPM fails. In contrast, we argue that variation in betas and the equity premium would have to be implausibly large to explain important asset-pricing anomalies like momentum and the value premium. We also provide a simple new test of the conditional CAPM using direct estimates of conditional alphas and betas from short-window regressions, avoiding the need to specify conditioning information. The tests show that the conditional CAPM performs nearly as poorly as the unconditional CAPM, consistent with our analytical results.     

Measuring performance in a dynamic world: Conditional mean–variance fundamentals

We develop conditional alpha performance measures that are consistent with conditional mean–variance analysis and the magnitude and sign of the implied true conditional time-varying alphas. The sequence of conditional alphas and betas is estimable from surprisingly simple unconditional regressions. Other common performance measures are derivable from the conditional investment opportunity set based on its conditional asset return moments. Our bootstrap analysis of Morningstar mutual fund returns data demonstrates that the differences between existing conditional alpha measures and our proposed alpha are substantive for typical parameterizations.     

The Conditional Beta and the Cross-Section of Expected Returns

We examine the cross-sectional relation between conditional betas and expected stock returns for a sample period of July 1963 to December 2004. Our portfolio-level analyses and the firm-level cross-sectional regressions indicate a positive, significant relation between conditional betas and the cross-section of expected returns. The average return difference between high- and low-beta portfolios ranges between 0.89% and 1.01% per month, depending on the time-varying specification of conditional beta. After controlling for size, book-to-market, liquidity, and momentum, the positive relation between market beta and expected returns remains economically and statistically significant.     

On market price of risk in Asian capital markets around the Asian flu

This study investigates a contemporaneous relationship between realized market risk premia, and conditional variance and covariance in nine Asian markets and the US. The time period for this study is before, during, and after the Asian financial crisis. A contemporaneous state-dependent capital asset pricing model (CAPM) that allows for negative and positive market prices of variance and covariance risk is investigated. In the light of significant upstate and downstate reward to local and world variance risk for all markets and all periods, we conclude that a market return-generating process is a piecewise function of local and world variance over time. Furthermore, a cross-sectional analysis of upstate and downstate market prices of variance and covariance risk indicates that reward to risk is a mix of reward to local and world variance, depending on the ever-changing correlation with the world market. Our findings are consistent with the one-factor conditional international CAPM.     

The effect of time-varying covariances on asset risk premia

In this article we examine an intertemporal capital asset pricing model (CAPM) that allows for time-varying conditional covariances that are assumed to follow a multivariate integrated generalized autoregressive conditional heteroscedastic (IGARCH) process. The resulting pricing equation includes idiosyncratic risk premia in addition to the usual market beta. Empirical analysis based on ten size and ten industry portfolios reveals significant idiosyncratic premia for most portfolios. Overall, we reject the static CAPM in favor of the intertemporal CAPM.