When Do Stop-Loss Rules Stop Losses?

Stop-loss rules-predetermined policies that reduce a portfolio's exposure after reaching a certain threshold of cumulative losses-are commonly used by retail and institutional in- vestors to manage the risks of their investments, but have also been viewed with some skep- ticism by critics who question their e±cacy. In this paper, we develop a simple framework for measuring the impact of stop-loss rules on the expected return and volatility of an arbitrary portfolio strategy, and derive conditions under which stop-loss rules add or subtract value to that portfolio strategy. We show that under the Random Walk Hypothesis, simple 0/1 stop-loss rules always decrease a strategy's expected return, but in the presence of momen- tum, stop-loss rules can add value. To illustrate the practical relevance of our framework, we provide an empirical analysis of a stop-loss policy applied to a buy-and-hold strategy in U.S. equities, where the stop-loss asset is U.S. long-term government bonds. Using monthly returns data from January 1950 to December 2004, we find that certain stop-loss rules add 50 to 100 basis points per month to the buy-and-hold portfolio during stop-out periods. By computing performance measures for several price processes, including a new regime- switching model that implies periodic "flights-to-quality", we provide a possible explanation for our empirical results and connections to the behavioral finance literature.