The Strategy Approval Decision: A Sharpe Ratio Indifference Curve Approach

The problem of capital allocation to a set of strategies could be partially avoided or at least greatly simplified with an appropriate strategy approval decision process. This paper proposes such a procedure. We begin by splitting the capital allocation problem into two sequential stages: strategy approval and portfolio optimization. Then we argue that the goal of the second stage is to beat a naive benchmark, and the goal of the first stage is to identify which strategies improve the performance of such a naive benchmark. We believe that this is a sensible approach, as it does not leave all the work to the optimizer, thus adding robustness to the final outcome. We introduce the concept of the Sharpe ratio indifference curve, which represents the space of pairs (candidate strategy's Sharpe ratio, candidate strategy's correlation to the approved set) for which the Sharpe ratio of the expanded approved set remains constant. We show that selecting strategies (or portfolio managers) solely based on past Sharpe ratio will lead to suboptimal outcomes, particularly when we ignore the impact that these decisions will have on the average correlation of the portfolio. Our strategy approval theorem proves that, under certain circumstances, it is entirely possible for firms to improve their overall Sharpe ratio by hiring portfolio managers with negative expected performance. Finally, we show that these results have important practical business implications with respect to the way investment firms hire, layoff and structure payouts.