Decision trees unearth return sign predictability in the S&P 500

Technical trading rules and linear regression models are often used by practitioners to find trends in asset returns. However, these models typically neglect interaction terms between the lagged daily directional movements. We propose a decision tree forecasting model that has the flexibility to capture arbitrary interaction patterns. To study the importance of interaction terms, we construct a binary Markov process with a deterministic component that cannot be predicted without interaction terms between the lagged directional movements. We show that some tree based strategies achieve trading performance significant at the 99% confidence level on the S&P 500 over the past 20 years, after adjusting for multiple testing. The best strategy breaks even with the buy-and-hold strategy at 21 bps in transaction costs per round trip. A four-factor regression analysis shows significant intercept, and correlation with the market. The directional predictability is strongest during the bursts of the dotcom bubble, financial crisis, and European debt crisis. The return sign predictability during these periods confirms the necessity of interaction terms to model daily returns.