A Cross-Sectional Score for the Relative Performance of an Allocation

The aim of this paper is to propose an innovative score measuring the relative performance – in terms of return – of an asset allocation with respect to the alternative allocations offered to the manager. Intuitively, this score is defined as the percentage of alternative allocations outperformed by the manager’s allocation. In particular, considering the case of a manager investing according to the zero-dollar long/short equally weighted strategy, we study in details the computation and the properties of this score and we deal with the related combinatorial issues when the number of assets is large.