Asset Pricing: Cross-Section Predictability

A fundamental question in finance is the study of why different assets have different expected returns, which is intricately linked to the issue of cross-section prediction in the sense of addressing the question “What explains the cross section of expected returns?” There is vast literature on this topic. There are state-of-the-art methods used to forecast the cross section of stock returns with firm characteristics predictors, and the same methods can be applied to other asset classes, such as corporate bonds and foreign exchange rates, and to managed portfolios such mutual and hedge funds. First, there are the traditional ordinary least squares and weighted least squares methods, as well as the recently developed various machine learning approaches such as neutral networks and genetic programming. These are the main methods used today in applications. There are three measures that assess how the various methods perform. The first is the Sharpe ratio of a long–short portfolio that longs the assets with the highest predicted return and shorts those with the lowest. This measure provides the economic value for one method versus another. The second measure is an out-of-sample R 2 that evaluates how the forecasts perform relative to a natural benchmark that is the cross-section mean. This is important as any method that fails to outperform the benchmark is questionable. The third measure is how well the predicted returns explain the realized ones. This provides an overall error assessment cross all the stocks. Factor models are another tool used to understand cross-section predictability. This sheds light on whether the predictability is due to mispricing or risk exposure. There are three ways to consider these models: First, we can consider how to test traditional factor models and estimate the associated risk premia, where the factors are specified ex ante. Second, we can analyze similar problems for latent factor models. Finally, going beyond the traditional setup, we can consider recent studies on asset-specific risks. This analysis provides the framework to understand the economic driving forces of predictability.