Risk Adjustment and Trading Strategies

Abstract

In this paper, we assess the profitability of momentum trading strategies using a stochastic discount factor approach. We estimate the stochastic discount factor from a set of basis assets, assuming that the law of one price (or, alternatively, no-arbitrage) holds, and simultaneously assess the risk-adjusted performance of the trading strategies. Our method has the advantages that we need not specify (and therefore perhaps misspecify) a particular parametric model to assess performance, and the method can easily encompass conditional or time-varying moments. In unconditional tests, some profitability of the trading strategies remains relative to the basis asset benchmark, although the level of momentum profits declines substantially after risk adjustment. When expectations are allowed to vary conditional on a limited set of public information, no abnormal profits remain. This result contrasts sharply with those observed when a CAPM benchmark is used. To understand this difference, we investigate the relation between the risk of momentum strategies and the magnitude of the risk premium. We show analytically that the risk of a momentum strategy should be increasing with respect to the market risk premium. Empirically, while the risk measures of the strategies, estimated relative to the stochastic discount factor, behave as predicted, market betas do not. This suggests that the use of CAPM benchmarks to assess the risk-adjusted performance of momentum strategies may lead to incorrect inferences.