Nonparametric Dynamic Conditional Beta*

This article derives a dynamic beta representation using a Bayesian semiparametric multivariate generalized autoregressive conditional heteroskedasticity (GARCH) model. The conditional joint distribution of excess stock returns and market excess returns is modeled as a countably infinite mixture of normals. This allows for deviations from the elliptic family of distributions. Empirically, we find the time-varying beta of a stock nonlinearly depends on the expected value of excess market returns. The nonlinear dependence is robust to different GARCH specifications as well as more factors in the model. In highly volatile markets, beta is almost constant, while in stable markets, the beta coefficient can depend asymmetrically on the expected market excess return. We extend the model to several factors and find empirical support for a three-factor model with nonlinear factor sensitives.

FAST METHODS FOR LARGE-SCALE NON-ELLIPTICAL PORTFOLIO OPTIMIZATION

Simple, fast methods for modeling the portfolio distribution corresponding to a non-elliptical, leptokurtic, asymmetric, and conditionally heteroskedastic set of asset returns are entertained. Portfolio optimization via simulation is demonstrated, and its benefits are discussed. An augmented mixture of normals model is shown to be superior to both standard (no short selling) Markowitz and the equally weighted portfolio in terms of out of sample returns and Sharpe ratio performance.