Conditional CAPM Research Articles

Learning about Beta: Time-Varying Factor Loadings, Expected Returns, and the Conditional CAPM

This paper explores the theoretical and empirical implications of time-varying and unobservable beta. Investors infer factor loadings from the history of returns via the Kalman filter. Due to learning, the history of beta matters. Even though the conditional CAPM holds, standard OLS tests can reject the model if the evolution of investor's expectations is not properly modelled. We use our methodology to explain returns on the twenty-five size and book-to-market sorted portfolios. Our learning version of the conditional CAPM produces pricing errors that are significantly smaller than standard conditional or unconditional CAPM and the model is not rejected by the data.

Country and Industry Equity Risk Premia in the Euro Area: An Intertemporal Approach

This paper provides new evidence on the dynamics of equity risk premia in euro area stock markets across country and industry portfolios. We develop and estimate a conditional intertemporal CAPM where returns on aggregate euro area, country and industry portfolios depend on the market risk as well as on the risk that the investment opportunity set changes over time. Prices of risks are time-varying, according to a Kalman filter approach. We find that both market and intertemporal risks are significantly priced. When we include country and industry-specific risk factors they turn out to be not significantly priced for most industries, suggesting that euro area equity markets are well integrated. Overall, the analysis indicates that omitting the intertemporal factor leads to mispricing and misleading conclusions regarding the degree of financial integration across sectors and countries.

Intertemporal CAPM with Conditioning Variables

This paper derives and tests an ICAPM based on a conditional version of the two-beta ICAPM (bad beta, good beta, BBGB) from Campbell and Vuolteenaho (2004). The novel factor is a scaled cash flow factor that results from the interaction between cash flow news and a lagged state variable. The cross-sectional tests over 10 portfolios sorted on size, 10 portfolios sorted on book-to-market and 10 portfolios sorted on momentum show that the scaled ICAPM explains relatively well the dispersion in excess returns on the 30 portfolios. The results for an alternative set of equity portfolios (25 portfolios sorted on size and momentum) show that the scaled ICAPM prices particularly well the momentum portfolios. Moreover, the scaled ICAPM compares favorably with alternative asset pricing models in pricing both sets of equity portfolios -- the BBGB model, the unconditional CAPM, the conditional CAPM, the Fama and French (1993) three-factor model, and the Carhart (1997) four-factor model. The scaled factor is decisive to account for the dispersion in average excess returns between past winner and past loser stocks. More specifically, past winners are riskier than past losers in times of high price of risk. Therefore, a time-varying cash flow beta/price of risk provides a rational explanation for momentum.

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

Abstract 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.

The Progeny of CAPM

This paper reviews the recent literature on CAPM and APT, and reaches a surprising conclusion. While APT died a silent death, CAPM's progeny is alive and well! We provide a short review of the recent literature on the conditional CAPMs, intertemporal CAPMs, and higher-order Co-Moments-based CAPMs. Some of these multifactor extensions of CAPM not only have higher explanatory power than the three-factor Fama and French (FF) model, but also are not rejected in the empirical tests, while the FF model is rejected.

Firm Size and Volatility Analysis in the Spanish Stock Market

In this article, three strongly related questions are studied. First, volatility spillovers between large and small firms in the Spanish stock market are analyzed by using a conditional CAPM with an asymmetric multivariate GARCH-M covariance structure. Results show that there exist bidirectional volatility spillovers between both types of firms, especially after bad news. Second, the volatility feedback hypothesis explaining the volatility asymmetry feature is investigated. Results show significant evidence for this hypothesis. Finally, the study uncovers that conditional beta coefficient estimates within the used model are insensitive to sign and size asymmetries in the unexpected shock returns but the unconditional beta estimate has a significant error specification. These results are relevant for asset valuation, portfolio management and dynamic hedging strategies design.

Testando o CAPM condicional nos mercados brasileiro e norte-americano

Nas ultimas décadas o modelo CAPM tem despertado grande interesse por parte da comunidade científica. Apesar das críticas, o aprimoramento do CAPM estático, dando origem a novos modelos dinâmicos, traz maior segurança para o investidor ao longo do ciclo de negócios. O CAPM e suas versões estáticas foram e são de grande importância em finanças. Nos dias de hoje, encontramos adaptações mais complexas do modelo CAPM, as quais nos permitem ter respostas sobre questões em finanças que, por muito tempo, permaneceram não solucionadas. Diante deste panorama e considerando toda essa grande discussão acerca da validade do CAPM, este trabalho procura apresentar as vantagens dos modelos condicionais em relação ao modelo estático. Para constatar tais fatos estudar-se-ão os testes dos modelos condicionais (beta variando ao longo do tempo), que não são comumente estudados na literatura. Esses testes são convenientes para incorporar variâncias e covariâncias que se alteram ao longo do tempo. Dentre os testes dos modelos condicionais destacamos o de Jagannathan e Wang (1996). Conclui-se que esse modelo explica satisfatoriamente a variação cross-sectional dos retornos do mercado brasileiro e norte-americano.

The Cross-Section of Commodity Futures Returns

In this paper we study consumption risk pricing in commodity futures markets. We find that, like stock returns, the conditional Consumption CAPM explains up to 60% of the cross sectional variation in mean futures returns. However, unlike stock returns, using contemporaneous plus future consumption growth reduces the performance of the model. We attribute this result to the fact that for commodities supply changes impact prices and therefore consumption. Consistent with this notion we find that production- and inventory-based factors are significant determinants of the long run risk in commodities markets, which may explain the poor performance of ultimate consumption risk model.

Resurrecting the (C)CAPM: A Cross-Sectional Test when Risk Premia wre Time-Varying

This paper explores the ability of theoretically based asset pricing models such as the CAPM and the consumption CAPM-referred to jointly as the (C)CAPM-to explain the cross-section of average stock returns. Unlike many previous empirical tests of the (C)CAPM, we specify the pricing kernel as a conditional linear factor model, as would be expected if risk premia vary over time. Central to our approach is the use of a conditioning variable which proxies for fluctuations in the log consumption-aggregate wealth ratio and is likely to be important for summarizing conditional expectations of excess returns. We demonstrate that such conditional factor models are able to explain a substantial fraction of the cross-sectional variation in portfolio returns. These models perform much better than unconditional (C)CAPM specifications, and about as well as the three-factor Fama-French model on portfolios sorted by size and book-to-market ratios. This specification of the linear conditional consumption CAPM, using aggregate consumption data, is able to account for the difference in returns between low book-to-market and high book-to-market firms and exhibits little evidence of residual size or book-to-market effects.

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.

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.

La prime de risque dans un cadre international : le risque de change est-il apprécié ?

Résumé L’objet de cet article est d’étudier les déterminants et la dynamique de la prime de risque des actions dans un cadre international. Pour ce faire, nous utilisons un modèle GARCH multivarié et testons une version conditionnelle du MEDAF international avec déviations de la PPA. Le modèle est estimé sous l’hypothèse d’intégration financière parfaite puis sous l’hypothèse de segmentation partielle conjointement pour cinq marchés : deux marchés développés, deux marchés émergents et le marché mondial. Nos résultats soutiennent le MEDAFI et indiquent que le risque des taux de change est rémunéré internationalement. Cependant, nous trouvons que la prime de change varie considérablement dans le temps et d’un marché à l’autre.

Is the Ex Ante Risk Premium Always Positive? Further Evidence

An implicit assumption of the conditional CAPM is that the ex ante equity risk premium is positive in all states of the world. Studies on US portfolios by Boudoukh, Richardson and Smith (1993) and on world portfolios by Ostdiek (1998) find violations of this assumption. This paper seeks to test the sign of the equity risk premium in the Australian market using two parallel tests. First, the series is examined for the presence of two regimes using a test developed in Bayesian inference. Truncated normal priors are applied to the means in this test to specifically detect means of opposite sign. Once a negative regime is identified in the risk premium, we try to identify it ex ante using the test developed by Boudoukh, Richardson and Smith (1993). This test allows the moments implied by the model to be conditioned on observable information. We were able to reject the null of a single regime in favour of the two-regime model using the regime-switching test. In addition the inequality tests on contemporaneous data rejected the restriction of a positive risk premium.

CAPM over the long run: 1926–2001

Abstract A conditional one-factor model can account for the spread in the average returns of portfolios sorted by book-to-market ratios over the long run from 1926 to 2001. In contrast, earlier studies document strong evidence of a book-to-market effect using OLS regressions over post-1963 data. However, the betas of portfolios sorted by book-to-market ratios vary over time and in the presence of time-varying factor loadings, OLS inference produces inconsistent estimates of conditional alphas and betas. We show that under a conditional CAPM with time-varying betas, predictable market risk premia, and stochastic systematic volatility, there is little evidence that the conditional alpha for a book-to-market trading strategy is different from zero.

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 (1999) (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 (1993) 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.

The Conditional CAPM and Time Varying Risk Premium for Equity REITs

Executive Summary.Given the recent interest in Real Estate Investment Trusts (REITs), this study investigates whether REITs provide investors with a superior risk-return trade off. Utilizing a conditional CAPM, the findings reveal that equity REITs have outperformed the stock market with an average abnormal annual return of 2.25% with a low time-varying beta of around .24 during the June 1995 to December 2003 period. Utilizing time-varying risk premium models for equity REITs with GARCH specifications, the findings reveal that both the ARCH and GARCH effects are significant in the estimated models. In addition, the volatility shocks are quite persistent. The results show that the market returns and the first-order autocorrelation help explain the excess returns of equity REITs. However, the movement of interest rates contributes to equity REIT returns only when the market return is not present in the models.

Bayesian Analysis of Stochastic Betas

AbstractWe propose a mean-reverting stochastic process for the market beta. In a simulation study, the proposed model generates significantly more precise beta estimates than GARCH betas, betas conditioned on aggregate or firm-level variables, and rolling regression betas, even when the true betas are generated based on these competing specifications. Our model significantly improves out-of-sample hedging effectiveness. In asset pricing tests, our model provides substantially stronger support for the conditional CAPM relative to competing beta models and helps resolve asset pricing anomalies such as the size, book-to-market, and idiosyncratic volatility effects in the cross section of stock returns.

Conditional Beta Estimation and Forecasting with Panel Data Methods

Standard approaches to the estimation and testing of conditional CAPM models with time-varying or random beta have ignored the potential panel nature of …nancial data. We test for whether or not homogeneity restrictions on the time-variation component of multifactor betas and on the slope parameters for the conditioning variables can be rejected. We …nd that such homogeneity restrictions are not rejected, and show that there are resultant bene…ts for testing conditional CAPM and forecasting expected returns and beta. Further, this panel approach yields more precise parameter estimates, and a greater understanding of the signi…cance of

Asset Pricing with Estimation-risk and Uncertain Information Quality

We derive a conditional CAPM in a general equilibrium model where investors face estimation-risk on mean returns, and learn from information of uncertain quality or precision. In equilibrium, the loading on market risk augments the standard beta with the random or information-dependent conditional covariance matrix of the unknown mean returns. Therefore, announcement effects on equilibrium asset prices can occur because of changes in the required rate of return due to event-induced variations in estimation-risk, rather than revisions in estimated cash flows. In support of this prediction, we find that firms initiating cash payouts through repurchases during 1988-2000 show significant reduction in the post-event betas and their standard errors. The model is consistent with post-earnings-announcement drifts, and generates refutable predictions on the deviation of cross-sectional expected returns from the unconditional CAPM. Quantitatively, numerical simulations with an appropriately calibrated version of the model indicate that information quality risk has a substantial effect on equilibrium asset prices.

On the Kurz Model Of Asset Prices with Rational Beliefs

Kurz (1997) proposes an appealing model of asset pricing that appears to be an interesting example of a conditional CAPM. In the Kurz model, agents develop a diversity of inaccurate but rational beliefs through a Bayesian process. Kurz avoids the problematic issue of unobservable conditioning information by developing a general equilibrium model based upon rational beliefs, which means that agents do not know the demand functions of other agents, and therefore cannot compute equilibrium prices. They can, however, develop diverse beliefs that cannot be rejected by historical economic data. Such unrejectable beliefs are defined by Kurz to be rational, and lead to a continuum of Rational Belief Equilibria. Kurz uses the concept of endogenous uncertainty (EU), which measures the sum of agents' forecasting mistakes. To the extent asset price variance differs from variance in the exogenous fundamental economic variables, Kurz' approach attributes the difference to EU, or aggregate forecasting mistakes which are consistent with rational beliefs. To the extent that the Arrow-Debreau (1954) model is based exclusively on exogenous uncertainty, Kurz views this as fundamentally flawed and offers a new and interesting way to distinguish between exogenous and endogenous uncertainty. The most interesting aspect of such delineation is it supports the prior theory of Treynor and Black (1973) and Cvitanic et al (2002) on the existence and estimation of appraisal premia for capital assets, in a conditional CAPM framework.