We cast the construction of long-short portfolios as a statistical decision problem in which the investor seeks to buy the top-performing stocks (the "winners") and sell the worst-performing ones (the "losers") on the basis of stock characteristics. We derive the optimal portfolio selection rule implied by a loss function that accounts for different types of misclassification errors in portfolio construction. This approach leads to a return classification problem and the optimal rule buys or sells stocks based on their probabilities of being winners or losers, conditional on the stock characteristics. When returns are generated by an additive regression model and misclassification costs satisfy a symmetry condition, the optimal rule simplifies to the conventional sorting procedure based on expected returns. An empirical application using U.S. stock data shows that portfolios constructed using the optimal rule achieve higher Sharpe ratios compared to those built using conventional methods. Our results demonstrate that predictive signals in the cross-section of stock returns go beyond expected returns, and that properly optimized portfolio selection rules based on these signals can generate substantial economic value for investors.

We document the existence of sign predictability in equity returns. An investment strategy that buys stocks deemed most likely to have positive returns and sells stocks with the lowest probability of positive returns generates about 1% monthly alpha and is not explained by established asset pricing models. The proposed strategy has higher Sharpe ratios and exhibits fewer crashes than the renowned momentum strategy. We show that profits from exploiting directional information are driven by shifts in retail investors’ expectations after periods of excessive pessimism or optimism, rather than compensation for risk. We provide a simple model to motivate our findings.

This paper introduces composite absolute value and sign (CAVS) forecasts, a nonlinear framework that combines forecasts of the sign and absolute value of a time series into conditional mean forecasts. In contrast to linear models, the proposed framework allows different predictors to impact the sign and absolute value of the target series. Among other results, I show that the conditional mean can be written as a function of mean squared error optimal sign and absolute value forecasts. An empirical application using the FRED-MD dataset shows that CAVS forecasts substantially outperform linear forecasts for series that exhibit persistent volatility dynamics, such as output and interest rates. The empirical application highlights that exploiting nonlinearities in macroeconomic series improves forecast accuracy.

We conduct an out-of-sample backtesting exercise of Growth-at-Risk (GaR) predictions for 24 OECD countries. We consider forecasts constructed from quantile regression and GARCH models. The quantile regression forecasts are based on a set of recently proposed measures of downside risks to GDP, including the national financial condition index. The backtesting results show that quantile regression and GARCH forecasts have a similar performance. If anything, our evidence suggests that standard volatility models such as the GARCH(1,1) are more accurate.

We introduce a framework to evaluate collections of interval forecasts for multiple time series. We propose an evaluation criteria based on the dependence properties of the forecasts. Our criteria assumes that a forecaster prefers, ceteris paribus, the collection that minimizes the probability of simultaneous interval forecast violations for a large number of time series. The evaluation of the collections is carried out by means of a simple loss function and we establish that, under mild assumptions, such loss leads to consistent ranking of the forecasts. We apply our framework to evaluate commonly used Value-at-Risk (VaR) forecasting methods for all S&P 500 stocks. We find that methods that take the factor structure of volatility into account substantially reduce extreme dependence across VaR violations.