Some Observations on Trend Following: A Binomial Perspective

This paper uses a simple binomial framework to explore trend following. It shows (by counter example) that the existence of positive profits from trend-following strategies, on its own, provides no prima facie evidence on the efficiency or inefficiency of markets. In addition, it explores the most important feature of time series momentum investment strategies: the return shaping impact of trend following through its dynamic positioning. In a stylized efficient market setting (with no transaction costs), the paper shows that the dynamic nature of trend following shapes when profits and losses occur compared to a buy-and-hold strategy. There is, however, a conservation of “mass” in that gains and losses are shuffled across periods such that the unconditional distribution of profits is unaffected. In this sense, trend following, by construction, generates crisis alpha --- for crises where large losses occur over extended periods of time. Due to its ability to shape when profit and losses occur, trend following can provide significant portfolio diversification and hedging potential for those investors with strategic risk-on exposures.