Optimal granularity for portfolio choice

Many optimization-based portfolio rules fail to beat the simple 1/N rule out-of-sample because of parameter uncertainty. In this paper we suggest a grouping strategy in which we first form groups of equally weighted stocks and then optimize over the resulting groups only. This strategy aims at balancing the trade-off between the benefits from optimization and the losses from estimation risk. We rely on Monte-Carlo simulations to illustrate the performance of the strategy, and we derive the optimal group size for a simplified setup. Furthermore, we show that estimation risk also has an impact via the criterion by which the assets are sorted into groups (like the expected excess returns or betas), but does not negate the grouping approach. We relate our work to linear asset pricing models, and we conduct out of sample back-tests in order to confirm the validity of our grouping strategy empirically.