Time Series Momentum in the US Stock Market: Empirical Evidence and Theoretical Implications

Abstract

We start this paper by presenting compelling evidence of short-term momentum in the excess returns on the S&P Composite stock price index. For the first time ever, we assume that the excess returns follow an autoregressive process of order p, AR(p), and evaluate the parameters of this process. Armed with a fairly accurate knowledge of the momentum generating process, we continue this paper by providing a number of important theoretical implications. First, we present analytical results on the profitability of long-only and long-short time-series momentum (TSMOM) strategies. Our results suggest that the long-only TSMOM strategy is profitable, while the long-short one is not. We find that over multiple periods the risk profile of the long-only TSMOM strategy resembles the risk profile of a portfolio insurance strategy. We estimate the power of the statistical test for superiority of the TSMOM strategy and find that the power is much below the acceptable level. Consequently, any empirical study tends not to reject the null hypothesis of no profitability of TSMOM strategy. Finally, we evaluate the precision of identification of the optimal number of lags in the TSMOM rule using a standard back-testing methodology and find that this precision is extremely poor. However, we demonstrate that the performance of the TSMOM rule is robust to the choice of the number of lags.