Optimality conditions for a trend-following strategy

Based on trend-following trading strategies that are widely used in the investment world, this work provides a set of sufficient conditions that determines the optimality of the traditional trend-following strategies when the trends are completely observable. A dynamic programming approach is used to verify the optimality under these conditions. The value functions are characterized by the associated HJB equations, and are shown to be either linear functions or infinity depending on the parameter values. The results reveal two counter-intuitive facts: (a) trend following may not lead to optimal reward in some cases even when/if the investor knows exactly when a trend change occurs; (b) stock volatility is not relevant in trend following when trends are observable.