The Bayesian roots of risk balancing

ABSTRACT The authors show that log regularization leads to a fund-separation-type property, where the optimal solution lies between an unconstrained mean-risk-optimized portfolio and a risk-balanced portfolio. They also demonstrate in a Bayesian framework that these log regularizations are actually equivalent to putting prior distributions on the optimal portfolio weights. They provide numerical examples of a typical institutional asset universe and, finally, prove that there are efficient risk-parity portfolios that do not necessarily satisfy equal Sharpe and constant correlation conditions, which have been widely misunderstood to be the only efficiency conditions for risk-parity portfolios in the industry.