Risk Parity and Beyond-From Asset Allocation to Risk Allocation Decisions

In this article, the authors define the number of uncorrelated bets embedded within a given portfolio of N assets as the exponential of the entropy of the portfolio exposure to N uncorrelated factors. They present a set of formal results regarding the existence and uniqueness of portfolios designed to achieve the maximum effective number of bets. They also provide empirical evidence that incorporating constraints or target levels in a portfolio's effective number of bets generates an improvement in out-of-sample risk-adjusted performance with respect to standard mean-variance analysis.