Optimal risk trade-off in relative performance evaluation

In this study, I consider a company’s optimal use of relative performance evaluation (RPE) in principal/ agent relations to filter out common risk. I construct a risk-parity aggregate of the company’s peer group to be the sum of the ratios of the common-and idiosyncratic-risk components of the group of peers’ outputs, scaled by the variance of the common risk. I demonstrate that this aggregate embodies the peer group’s informativeness about the common risk, so it captures precisely the group’s innate capability to trade off optimally between the common-and idiosyncratic-risk components of those peers’ outputs. The optimal use of RPE therefore entails a partial substitution of the common risk with the peers’ idiosyncratic risks. Moreover, the risk-parity aggregate enables us to identify a boundary condition, which helps us rule out ineffective uses of RPE that completely eliminate the common risk, thereby improving the statistical power of a strong-form RPE test.