We study an investor’s asset allocation problem with a recursive utility and with tradable volatility that follows a 2-factor stochastic volatility model. Consistent with previous findings under the additive utility, we show that the investor can benefit substantially from volatility trading due to hedging demand. Unlike existing studies, we find that the impact of elasticity of intertemporal substitution (EIS) on investment decisions is of 1st-order importance. Moreover, the investor can incur significant economic losses due to model and/or parameter misspecifications where the EIS better captures the investor’s attitude toward risk than the risk aversion parameter.

We show theoretically that the usual estimated investment strategies will not achieve the optimal Sharpe ratio when the dimensionality is high relative to sample size, and the $ 1/N $ rule is optimal in a 1-factor model with diversifiable risks as dimensionality increases, which explains why it is difficult to beat the $ 1/N $ rule in practice. We also explore conditions under which it can be beaten, and find that we can outperform it by combining it with the estimated rules when $ N $ is small, and by combining it with anomalies or machine learning portfolios, conditional on the profitability of the latter, when $ N $ is large.

Can the degree of predictability found in data be explained by existing asset pricing models? We provide two theoretical upper bounds on the R 2 of predictive regressions. Using data on the market portfolio and component portfolios, we find that the empirical R 2 s are significantly greater than the theoretical upper bounds. Our results suggest that the most promising direction for future research should aim to identify new state variables that are highly correlated with stock returns instead of seeking more elaborate stochastic discount factors.

This paper proposes a way to allow Bayesian priors to reflect the objectives of an economic problem. That is, we impose priors on the solution to the problem rather than on the primitive parameters whose implied priors can be backed out from the Euler equation. Using monthly returns on the Fama-French 25 size and book-to-market portfolios and their 3 factors from January 1965 to December 2004, we find that investment performances under the objective-based priors can be significantly different from those under alternative priors, with differences in terms of annual certainty-equivalent returns greater than 10% in many cases. In terms of an out-of-sample loss function measure, portfolio strategies based on the objective-based priors can substantially outperform both strategies under alternative priors and some of the best strategies developed in the classical framework.

In this paper, we analytically derive the expected loss function associated with using sample means and the covariance matrix of returns to estimate the optimal portfolio. Our analytical results show that the standard plug-in approach that replaces the population parameters by their sample estimates can lead to very poor out-of-sample performance. We further show that with parameter uncertainty, holding the sample tangency portfolio and the riskless asset is never optimal. An investor can benefit by holding some other risky portfolios that help reduce the estimation risk. In particular, we show that a portfolio that optimally combines the riskless asset, the sample tangency portfolio, and the sample global minimum-variance portfolio dominates a portfolio with just the riskless asset and the sample tangency portfolio, suggesting that the presence of estimation risk completely alters the theoretical recommendation of a two-fund portfolio.

We provide an entropy approach for measuring the asymmetric comovement between the return on a single asset and the market return. This approach yields a model-free test for stock return asymmetry, generalizing the correlation-based test proposed by Hong, Tu, and Zhou (2007). Based on this test, we find that asymmetry is much more pervasive than previously thought. Moreover, our approach also provides an entropy-based measure of downside asymmetric comovement. In the cross section of stock returns, we find an asymmetry premium: Higher downside asymmetric comovement with the market indicates higher expected returns.

In this paper, we document that an application of a moving average timing strategy of technical analysis to portfolios sorted by volatility generates investment timing portfolios that substantially outperform the buy-and-hold strategy. For high-volatility portfolios, the abnormal returns, relative to the capital asset pricing model (CAPM) and the Fama-French 3-factor models, are of great economic significance, and are greater than those from the well-known momentum strategy. Moreover, they cannot be explained by market timing ability, investor sentiment, default, and liquidity risks. Similar results also hold if the portfolios are sorted based on other proxies of information uncertainty.

We propose an investor attention index based on proxies in the literature and find that it predicts the stock market risk premium significantly, both in sample and out of sample, whereas every proxy individually has little predictive power. The index is extracted using partial least squares, but the results are similar by the scaled principal component analysis. Moreover, the index can deliver sizable economic gains for mean-variance investors in asset allocation. The predictive power of the investor attention index stems primarily from the reversal of temporary price pressure and from the stronger forecasting ability for high-variance stocks.

In this article, we propose two asymmetry measures for stock returns. Unlike the popular skewness measure, our measures are based on the distribution function of the data rather than just the third central moment. We present empirical evidence that the greater upside asymmetries calculated using our new measures imply lower average returns in the cross section of stocks. In contrast, when using the skewness measure, the relationship between asymmetry and returns is inconclusive.

We study how equity option trading affects the market risk premium. We find that a measure of aggregate call order imbalance (ACIB), defined as the cross-sectional average of the difference between open-buy and open-sell volume, negatively forecasts future stock market returns significantly from days to months. Moreover, ACIB represents an option-based investor sentiment measure that accounts for excess option buying or selling, and is highly correlated with the stock investor sentiment. Our findings shed new insights on the distinctions for call and put option trading, index and equity option trading, and cross-sectional and time-series predictions.