Unconditional CAPM Research Articles

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.

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.

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.

Investment and Returns

A general equilibrium production economy with heterogeneous firms and irreversible investment generates the value premium. Investment irreversibility prevents unprofitable value firms from optimally scaling down their capital stock. In contrast, profitable and fast growing - growth - firms can optimally use investment to provide consumption insurance. Value firms are riskier and have higher expected returns than growth firms, especially in bad times when consumption volatility is high. The value premium is larger for small stocks as small value firms are more severely affected by irreversibility. Firms’ investment and capital predict the cross-section of stock returns much like book-to-market and market equity both in the model and data. The model can replicate the failure of the unconditional CAPM. Multifactor models, including the Fama and French (1993) factor model, and to a lesser extent, conditional versions of the CAPM, outperform the unconditional CAPM.

Conditional Asset Pricing - Predicting Time Varying Beta-Factors with Group Method of Data Handling Methods

Allowing for time-varying risk premia yields sophisticated asset pricing models, but the search for adequate model specifications is more challenging. We introduce, to our knowledge, previously in conditional asset pricing not used Group Method of Data Handling (GMDH) that rests on sorting out requiring statsitical models for complex problems of unknown structure but does not require a model to predict conditional variation in betas. We find that lagged instruments used to proxy for expected returns in conditional asset pricing provide a challenge not only for the unconditional CAPM but also the Fama-French-model. Thereby non-linear GMDH-algorithms challenge traditional models of conditional asset pricing as we find a highly non-linear influence of lagged instruments on both conditional alphas and betas. Therefore, predetermining a structure for functional relationships between conditional alphas as well as betas and lagged instruments may lead to a significant misspecification of asset pricing models.

The Conditional CAPM Does Not Explain Asset-Pricing Anomalies

Recent studies suggest that the conditional CAPM might hold, period-by-period, and that time-varying betas can explain the failures of the simple, unconditional CAPM. We argue, however, that significant departures from the unconditional CAPM would require implausibly large time-variation in betas and expected returns. Thus, the conditional CAPM is unlikely to explain asset-pricing anomalies like book-to-market and momentum. We test this conjecture empirically by directly estimating conditional alphas and betas from short-window regressions (avoiding the need to specify conditioning information). The tests show, consistent with our analytical results, that the conditional CAPM performs nearly as poorly as the unconditional CAP

The Conditional CAPM Does Not Explain Asset-pricing Anomalies

Recent studies suggest that the conditional CAPM might hold, period-by-period, and that time-varying betas can explain the failures of the simple, unconditional CAPM. We argue, however, that significant departures from the unconditional CAPM would require implausibly large time-variation in betas and expected returns. Thus, the conditional CAPM is unlikely to explain asset-pricing anomalies like book-to-market and momentum. We test this conjecture empirically by directly estimating conditional alphas and betas from short-window regressions (avoiding the need to specify conditioning information). The tests show, consistent with our analytical results, that the conditional CAPM performs nearly as poorly as the unconditional CAPM.

An Evaluation of International Asset Pricing Models

This paper assesses the ability of international asset pricing models to explain the cross-sectional variation in expected returns. All the models considered seem to capture national market returns fairly well. However, global portfolios, sorted on earnings-price ratio and market value, pose a special challenge. We find that an unconditional international CAPM cannot explain the cross-sectional variation in these portfolio returns. Interestingly, a conditional international asset pricing model that includes foreign exchange risk factors is able to explain a large part of the variation in average returns. Our empirical work suggests that this model has the same explanatory ability as an international three-factor model, where zero-cost portfolios based on earnings-price ratios and market values are used in addition to the world market portfolio. Importantly, the loadings associated with the zero-cost portfolios are driven out by the characteristics themselves, indicating a misspecification.

Resurrecting the (C)CAPM: A Cross-Sectional Test When Risk Premia are 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.

Testing Asset Pricing Models: The Case of Athens Stock Exchange

This article applies a conditionally heteroskedastic asset pricing model to describe the time variation in the first and second moments of asset returns in an interdependent way in the emerging capital market of Greece. Depending on the observability of the factors and under the chosen parameterization it is possible to derive tests to address economically important questions that the models impose on the risk-return relationship. We apply the derived tests on the nine sectorial portfolios and the value weighted index of the Athens Stock Exchange, over the period 1985-1997. The evidence from the unconditional and conditional CAPM, with the Value Weighted Index as a benchmark portfolio, suggests the inefficiency of the Index. On the other hand, the dynamic latent factor model, considered here, describes sectorial returns in a much better way. However, there is still a shadow of doubt on the hypothesis that the price of risk is common across assets.

Performance Attribution Using a Multivariate Intertemporal Asset Pricing Model with One State Variable

AbstractThe stock‐picking and market‐timing abilities of Canadian mutual fund managers were tested using the Jensen (1968) and Lehmann and Modest (1987) tests. The benchmark was Chamberlain's (1988) conditional intertemporal APM with one state variable. Compared to previous tests of the CAPM for Canadian equities, this intertemporal APM explained the conditional expected returns of size‐sorted portfolios of Canadian equities well. Significantly negative stock‐picking and market‐timing abilities were identified. Like Lehmann and Modest (1987), an invariancy problem was identified. The performance inferences are sensitive to the choice of the timevarying risk premia estimates.RésuméCette étude présente une évaluation de la capacitédes gestionnaires de fonds mutuels à identifier les firmes suret/ou sous‐évaluées et à anticiper les mouvements du marchéà partir des tests de Jensen (1968) et Lehmann et Modest (1987). Ces tests s'appuient sur le modèle intertemporel de Chamberlain (1988) fondésur une variable d'état. Comparativement aux études précédentes du modèle CAPM en contexte canadien, le modèle intertemporel explique relativement bien le rendement espéréde portefeuilles construits à partir de la valeur de capitalisation des firmes canadiennes sous‐jacentes. Les résultats, statistiquement significatifs, indiquent que les gestionnaires possèdent des habilités négatives à identifier les firmes sur‐ et/ou sous‐évaluées et à anticiper les mouvements du marché. Comme pour Lehmann et Modest (1987), un problème de robustesse existe puisque différentes estimations d'une prime de risque variable dans le temps amènent différentes conclusions.