The modern portfolio theory pioneered by Markowitz (1952) is widely used in practice and extensively taught to MBAs. However, the estimated Markowitz portfolio rule and most of its extensions not only underperform the naive 1/N rule (that invests equally across N assets) in simulations, but also lose money on a risk-adjusted basis in many real data sets. In this paper, we propose an optimal combination of the naive 1/N rule with one of the four sophisticated strategies—the Markowitz rule, the Jorion (1986) rule, the MacKinlay and Pástor (2000) rule, and the Kan and Zhou (2007) rule—as a way to improve performance. We find that the combined rules not only have a significant impact in improving the sophisticated strategies, but also outperform the 1/N rule in most scenarios. Since the combinations are theory-based, our study may be interpreted as reaffirming the usefulness of the Markowitz theory in practice.

As the usual normality assumption is firmly rejected by the data, investors encounter a data-generating process (DGP) uncertainty in making investment decisions. In this paper, we propose a novel way to incorporate uncertainty about the DGP into portfolio analysis. We find that accounting for fat tails leads to nontrivial changes in both parameter estimates and optimal portfolio weights, but the certainty–equivalent losses associated with ignoring fat tails are small. This suggests that the normality assumption works well in evaluating portfolio performance for a mean-variance investor.

In this paper, we point out that the widely used stochastic discount factor (SDF) methodology ignores a fully specified model for asset returns. As a result, it suffers from two potential problems when asset returns follow a linear factor model. The first problem is that the risk premium estimate from the SDF methodology is unreliable. The second problem is that the specification test under the SDF methodology has very low power in detecting misspecified models. Traditional methodologies typically incorporate a fully specified model for asset returns, and they can perform substantially better than the SDF methodology.

We examine the cross-sectional predictability of corporate bond returns using a novel international dataset and a set of machine learning techniques. We find strong predictability in both U.S. and non-U.S. markets, with differing predictive factors. Bonds in developed markets show greater integration with the U.S. market and stronger ties to equity markets. Predictive performance of machine learning models varies over time and is greater before the onset of the COVID-19 pandemic and during periods of deteriorating business conditions, reduced market liquidity, elevated investor sentiment, and heightened risk aversion. The results offer insights into bond pricing and global diversification opportunities.

We investigate lead‐lag relationships among monthly country stock returns and identify a leading role for the United States: lagged U.S. returns significantly predict returns in numerous non‐U.S. industrialized countries, while lagged non‐U.S. returns display limited predictive ability with respect to U.S. returns. We estimate a news‐diffusion model, and the results indicate that return shocks arising in the United States are only fully reflected in equity prices outside of the United States with a lag, consistent with a gradual information diffusion explanation of the predictive power of lagged U.S. returns.

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.

We identify a parsimonious set of factors from a large pool of candidates for explaining hedge fund returns, ranging from equity market, anomaly, and trend-following factors to macroeconomic factors. The resulting 9-factor model, including five anomaly factors, outperforms existing hedge fund models both in sample and out of sample, with a significant reduction in alphas while showing substantial cross sectional performance heterogeneity. Further analysis based on fund holdings confirms the model’s ability to capture returns from arbitrage trading. Overall, the anomaly factors help quantify hedge fund strategies and risk exposures and improve fund performance evaluation.