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

Abstract: Technical trading rules and linear regressive models are often used by practitioners to find trends in financial data. However, these models are unsuited to find non-linearly separable patterns. We propose a decision tree forecasting model that has the flexibility to capture arbitrary patterns. To illustrate, we construct a binary Markov process with a deterministic component that cannot be predicted with an autoregressive process. A simulation study confirms the robustness of the trees and limitation of the autoregressive model. Finally, adjusting for multiple testing, 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. 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 return anomalies are strongest during the bursts of the dotcom bubble, financial crisis, and European debt crisis. The correlation of the return signs during these periods confirms the theoretical model.