The relative performance of several portfolio selection strategies is assessed empirically. These strategies vary in sophistication from a ‘naive’ strategy of maintaining equal dollar investments in each stock available to a strategy that periodically uses updated parameter estimates to calculate new optimal proportions of portfolio value to be invested in the stocks available. Although it is to be expected a priori that relatively sophisticated strategies will perform at least as well as the more naive strategies, implementation costs will clearly differ across strategies and across investor-specific parameters such as total portfolio value. Thus estimation of the various strategies' performance gross of these costs is a necessary consideration in rational strategy selection by any given investor.