The aim of this paper is to compare the performance of a theoretically optimal portfolio with that of a moving average-based strategy in the presence of parameter misspecification. The setting we consider is that of a stochastic asset price model where the trend follows an unobservable Ornstein–Uhlenbeck process. For both strategies, we provide the asymptotic expectation of the logarithmic return as a function of the model parameters. Then, numerical examples are given, showing that an investment strategy using a moving average crossover rule is more robust than the optimal strategy under parameter misspecification.