Hoyle, Edward, and Neil Shephard. Working Paper. “Volatility scaling's impact on the Sharpe ratio”.
Abstract:We study the econometric properties of dynamic risk parity, which volatility scales to equalise risk through time using the precision process, the inverse of the time-varying volatility. A particular focus is on the impact of the Sharpe ratio. We give necessary and suffcient conditions that volatility scaling improves the Sharpe ratio of an investment. We approximate the Sharpe improvement using the sum of two terms: one determined by the convexity of the precision and the other the covariance of the precision and conditional mean. We show that empirically this approximation is very accurate and we document the
relative importance of the two terms.