This paper finds statistically and economically significant out‐of‐sample portfolio benefits for an investor who uses models of return predictability when forming optimal portfolios. Investors must account for estimation risk, and incorporate an ensemble of important features, including time‐varying volatility, and time‐varying expected returns driven by payout yield measures that include share repurchase and issuance. Prior research documents a lack of benefits to return predictability, and our results suggest that this is largely due to omitting time‐varying volatility and estimation risk. We also document the sequential process of investors learning about parameters, state variables, and models as new data arrive.

This paper examines continuous‐time stochastic volatility models incorporating jumps in returns and volatility. We develop a likelihood‐based estimation strategy and provide estimates of parameters, spot volatility, jump times, and jump sizes using S&P 500 and Nasdaq 100 index returns. Estimates of jump times, jump sizes, and volatility are particularly useful for identifying the effects of these factors during periods of market stress, such as those in 1987, 1997, and 1998. Using formal and informal diagnostics, we find strong evidence for jumps in volatility and jumps in returns. Finally, we study how these factors and estimation risk impact option pricing.