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.     

Unconditional Tests of Linear Asset Pricing Models with Time‐Varying Betas

In conditional affine factor models, estimated risk prices should satisfy certain unconditional constraints. Specifically, a cross‐sectional estimate of the unconditional slope associated with a risk factor should equal the average price of risk of the factor. The estimated slope associated with the product of a risk factor and an instrument should be equal to the covariance of the factor risk premium with the instrument. We show that the constraints only apply to the conditional models with time‐varying betas. We identify an unconditional constraint on unconditional betas for time‐varying beta models and incorporate it into model tests. We show that imposing this unconditional constraint changes estimates of unconditional betas and risk prices significantly.     

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.     

The autumn effect of gold

This paper studies recurring annual events potentially introducing seasonality into gold prices. We analyze gold returns for each month from 1980 to 2010 and find that September and November are the only months with positive and statistically significant gold price changes. This “autumn effect” holds unconditionally and conditional on several risk factors. We argue that the anomaly can be explained with hedging demand by investors in anticipation of the “Halloween effect” in the stock market, wedding season gold jewelery demand in India and negative investor sentiment due to shorter daylight time. The autumn effect can also be characterized by a higher unconditional and conditional volatility than in other seasons.     

Accounting conservatism and voluntary corporate governance mechanisms by Australian firms

This study examines the relationship between voluntary adoption of selected corporate governance mechanisms and accounting conservatism for a sample of firms listed on the Australian Securities Exchange (ASX) over the 11‐year period prior to the promulgation of the ASX Corporate Governance Council Good Governance Principles and Best Practice Recommendations in 2003. Using four accounting and market‐based accounting conservatism measures, our results provide evidence of both conditional and unconditional conservatism in accounting reporting for Australian firms. We find that voluntary audit committee formation, increasing board independence and decreasing board size are positively associated with unconditional accounting conservatism and negatively related to the degree of conditional conservatism. Our results support the contention that firms voluntarily adopting perceived best practice corporate governance mechanisms employ unconditional accounting conservatism as a complimentary agency control device and are consistent with the observed negative association between the unconditional and conditional forms of accounting conservatism practice.     

Conditional beta pricing models: A nonparametric approach

We propose a two-stage procedure to estimate conditional beta pricing models that allows for flexibility in the dynamics of asset betas and market prices of risk (MPR). First, conditional betas are estimated nonparametrically for each asset and period using the time-series of previous data. Then, time-varying MPR are estimated from the cross-section of returns and betas. We prove the consistency and asymptotic normality of the estimators. We also perform Monte Carlo simulations for the conditional version of the three-factor model of Fama and French (1993) and show that nonparametrically estimated betas outperform rolling betas under different specifications of beta dynamics. Using return data on the 25 size and book-to-market sorted portfolios, we find that the nonparametric procedure produces a better fit of the three-factor model to the data, less biased estimates of MPR and lower pricing errors than the Fama–MacBeth procedure with betas estimated under several alternative parametric specifications.     

Testing conditional factor models: A nonparametric approach

Some recent studies of conditional factor models do not specify conditioning information but use data from small windows to estimate the time series of conditional alphas and betas. In this paper, we propose a nonparametric method using an optimal window to estimate time-varying coefficients. In addition, we offer two empirical tests of a conditional factor model. Using our new method, we examine the performance of the conditional CAPM and the conditional Fama-French three-factor model in explaining the return variations of portfolios sorted by size, book-to-market ratios, and past returns, for which recent literature has generated controversial results. We find that, although in general the conditional FF model outperforms the conditional CAPM, both models fail to explain well-known asset-pricing anomalies. Moreover, for both models, the failure is more pronounced for the equally-weighted portfolios than for the value-weighted ones.     

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.     

A Cross-Sectional Empirical Test of a Dual-State Multi-Factor Pricing Model

During empirical testing of the Capital Asset Pricing Model an assumption is typically made that risk is intertemporally constant. However, prior research finds that risk changes over time. We empirically test a conditional dual-state cross-sectional model allowing risk to change through prior identification of different market and economic states. We examine relationships between returns and conditional market and economic-factor betas, size, book-to-market equity, and earnings-price ratios. We find that relationships shift across regimes, suggesting the importance of a conditional, as opposed to unconditional, model. Relationships also change in January.     

The use of domestic and world market indexes in the estimation of time-varying betas

This paper generates time-varying estimates of Australian industry betas relative to an Australian market index and a world market index using the Kalman filter approach. As a means of comparison, these conditional estimated betas are used to forecast each industry’s return in-sample. The forecast error metrics suggest that the estimates of conditional risk relative to the domestic market index are preferred to estimates generated using the world market index, irrespective of the industry concerned. While not to suggest time-varying betas estimated relative to a domestic index are universally superior, these results suggest that they are preferable in certain circumstances.     

Notes on dynamic factor pricing models

These notes discuss three aspects of dynamic factor pricing (i.e., APT) models. First, the diversifiable component of returns is unpredictable in a no-arbitrage world. Second, conditional factor loadings or betas have an unconditional factor structure when returns follow an unconditional factor structure, which provides a link between conditional and unconditional factor pricing models. Third, the estimation of dynamic factor pricing models is easily simplified in large cross sections when returns follow an unconditional factor structure. These results aid in the interpretation of existing applications and identify some of the issues in the formulation and estimation of dynamic factor pricing models.     

CONDITIONAL HETEROSCEDASTICITY IN THE MARKET MODEL AND EFFICIENT ESTIMATES OF BETAS

Previous studies have investigated only unconditional heteroscedasticity in the market model. This paper tests for both conditional and unconditional heteroscedasticities as well as normality. Using the monthly stock rate of return data secured from the Center for Research in Security Prices (CRSP) tape for 1976 through 1983, this paper shows that conditional heteroscedasticity is more widespread than unconditional heteroscedasticity, suggesting the necessity of model refinements that take conditional heteroscedasticity into account. This paper provides an alternative estimation of betas of individual securities and portfolios based on the autoregressive conditional heteroscedastic (ARCH) model introduced by Engle. The efficiency of the market model coefficients is markedly improved across all firms in the sample through the ARCH technique.     

Risk and the January effect

We use a time-series GARCH framework with the conditional variance/covariance as proxies for systematic risk to reexamine the proposition by Rozeff and Kinney (1976) and Rogalski and Tinic (1986) that the January effect may be a phenomenon of risk compensation in the month. We find no clear evidence that either conditional volatility or unconditional volatility in January is predominantly higher across the sampling years. Hence, against the proposition, the January effect is not due to risk per se. Rather, we find strong evidence that the January effect is due to higher compensation for risk in the month. This may be possible if investors have an increasing RRA utility function. Although many studies find that volatility tends to be higher in January, we find it to be period-specific and mostly in value-weighted return series, but not in equal-weighted return series. This is true both for the unconditional and conditional return volatility.     

On Stable Factor Structures in the Pricing of Risk: Do Time-Varying Betas Help or Hurt?

There is now considerable evidence suggesting that estimated betas of unconditional capital asset pricing models (CAPMs) exhibit statistically significant time variation. Therefore, many have advocated the use of conditional CAPMs. If we succeed in capturing the dynamics of beta risk, we are sure to outperform constant beta models. However, if the beta risk is inherently misspecified, there is a real possibility that we commit serious pricing errors, potentially larger than with a constant traditional beta model. In this paper we show that this is indeed the case, namely that pricing errors with constant traditional beta models are smaller than with conditional CAPMs.     

Bias in estimating the systematic risk of extreme performers: Implications for financial analysis, the leverage effect, and long-run reversals

We show how bias can arise systematically in the beta estimates of extreme performers when long-run return reversals are present and partly, or wholly, due to sign changes in unanticipated factor realizations. Our evidence is consistent with this bias being responsible for the large shifts in the beta estimates of extreme performers, more so than the leverage effect, which has been the predominant explanation in prior literature. Bias in these contemporaneous realized betas, estimated with the same returns that are to be risk adjusted, arises due to the general problem of “overconditioning,” where betas are estimated conditional on information that is not yet known. Several methods for conditioning betas on out-of-sample returns are evaluated and found to be lacking, although some offer improvement under certain circumstances. We also show evidence of this bias in the Fama-French Three-factor loadings of extreme performers. Our findings indicate not only that previous studies of long-run reversals understate contrarian profits but that bias is prevalent in the OLS beta estimates of extreme performers, and this has implications for estimating the cost of capital and measuring long-run performance. We offer recommendations for identifying when this bias is likely present, as well as general methods to correct for it.     

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.     

MUTUAL FUND DAILY CONDITIONAL PERFORMANCE

The empirical finance literature reveals that conditional models estimated with monthly data generally improve fund performance. Furthermore, it has been shown that using daily instead of monthly returns in an unconditional framework increases the proportion of abnormal performances relative to timing. In this article, we study conditional performance estimated with daily data in a bivariate generalized autoregressive conditional heteroskedasticity (GARCH) framework. Our daily conditional alphas and global performances with GARCH are significantly better than those estimated with other parametrizations and they persist over time. Finally, the proportion of abnormal timing performances diminishes significantly when conditional parametrizations are used.     

Modelling the asymmetric linkages between spot gold prices and African stocks

We model the asymmetric linkages between returns of spot gold prices and African stock markets using wavelets and quantile regression techniques. The maximal overlap discrete wavelet transform technique was employed to decompose the returns into short-, medium-, and long-term series and the quantile regression was employed to explore the nexus by matching their conditional distributions along 0.05 quantile intervals. We find that the relationship between gold and African stocks is frequency-dependent and asymmetric in nature across the various timescales and quantiles. We find a mixture of negative and positive connections across the various quantiles in the short- and medium-terms. In the long-term, whereas the effect of gold is positive for Ghana, Mauritius, and Nigeria; it is negative for Egypt, Morocco, South Africa, and Tunisia. The results possess important implications for risk management as dependencies are not only studied over the entire conditional distribution at once but based on quantiles and further at different frequencies. Investors can make well-informed decisions to mitigate trade risks as they closely match the time heterogeneity in the markets.     

Modeling Time-Varying Correlations in Volatility Between BRICS and Commodity Markets

This article investigates the asymmetric and long memory volatility properties and dynamic conditional correlations (DCCs) between Brazilian, Russian, Indian, Chinese, and South African (BRICS) stock markets and commodity (gold and oil) futures markets, using the trivariate DCC-fractionally integrated asymmetric power autoregressive conditional heteroskedasticity (FIAPARCH) model. We identify significant asymmetric and long memory volatility properties and DCCs for pairs of BRICS stock and commodity markets, and variability in DCCs and Markov Switching regimes during economic and financial crises. Finally, we analyze optimal portfolio weights and time-varying hedge ratios, demonstrating the importance of overweighting optimal portfolios between BRICS stock and commodity assets.     

A semiparametric conditional capital asset pricing model

This paper proposes using a functional coefficient regression technique to estimate time-varying betas and alpha in the conditional capital asset pricing model (CAPM). Functional coefficient representation relaxes the strict assumptions regarding the structure of betas and alpha by combining the predictors into an index. Appropriate index variables are selected by applying the smoothly clipped absolute deviation penalty. In such a way, estimation and variable selection can be done simultaneously. Based on the empirical studies, the proposed model performs better than the alternatives in explaining asset returns and we find no strong evidence to reject the conditional CAPM.