Bayesian Analysis of Stochastic Betas Gergana Jostova

This paper proposes a mean-reverting stochastic process for the market beta. In a simulation study, the proposed model generates significantly more precise beta estimates relative to competing GARCH betas, betas scaled by aggregate or firm-level variables, and betas based on rolling regressions, even when the true betas are generated based on these competing specifications. Applying our model to US industry portfolios, we document significant improvement in out-of-sample hedging effectiveness relative to the traditional OLS beta estimate. In asset-pricing tests, our model provides substantially stronger support for the conditional CAPM relative to competing beta models. It also helps resolve asset-pricing anomalies such as the size, book-to-market, and idiosyncratic volatility effects in the cross-section of stock returns. Beta estimates are essential for many areas of modern finance, such as asset pricing, cash flow valuation, risk management, and performance evaluation. The modeling and measurement of this unobservable parameter can have far reaching implications. For example, Avramov and Chordia (2004) suggest that previously documented anomalies like the book-to-market, size, and firm-characteristics effects in the cross-section of returns may in fact arise from the dynamic behavior of betas. Petkova and Zhang (2002) and Zhang (2004) link the book-to-market effect to different behavior of value and growth betas across the business cycle. Furthermore, Ang and Liu (2004) show that beta variation is also essential for cash flow valuation, especially at longer horizons. From a portfolio management perspective, betas are crucial for effective hedging and underlie important performance measures. The precise measurement of latent betas is therefore an issue of primary importance. This study improves the precision of beta estimates by introducing a new beta model, which describes systematic risk as a general mean-reverting stochastic process. This formulation offers several advantages. First, it includes existing beta models as special cases, which allows testing their imposed restrictions. Indeed, our model combines both time-variation and a stochastic component in the beta process. Early beta models assume that beta has a constant mean and a random component, while a time-varying mean but no separate random component for beta is assumed in later models (i.e. multivariate GARCH models and models conditioning beta on observed instruments). Second, our model accounts for the documented excess kurtosis in security returns. Namely, in previous time-varying beta models randomness in beta is solely driven by return or instrument innovations, constraining beta persistence and return kurtosis by a set of common parameters, thus restricting kurtosis below empirically observed levels. We relax this restriction by allowing both time-variation and randomness in beta. Third, our model captures the theoretically motivated and empirically observed high persistence of beta. Beta persistence, according to Berk, Green, and Naik (1999), accounts for the momentum in returns, while Ang and Chen Early models include Blume (1971), Levy (1971), Vasicek (1973), and Chen and Lee (1982). Bollerslev, Engle, and Wooldridge (1988), Turtle, Buse, and Korkie (1994), Ledoit, Santa-Clara, and Wolf (2003) offer multivariate GARCH models for variances, while Braun, Nelson, and Sunier (1995) introduce a GARCH model for beta. Shanken (1990) and Ferson and Harvey (1993) condition betas on aggregate instruments, while Avramov and Chordia (2004) use firm-level instruments.