A Proof of the Optimality of Volatility Weighting Over Time

We provide a proof that volatility weighting over time increases the Sharpe or Information Ratio. The higher the degree of volatility smoothing achieved by volatility weighting, the higher the risk-adjusted performance. Our results apply to risky portfolios managed against a risk free or risky benchmark (so including alpha strategies) and to volatility targeting strategies. We provide an empirical illustration of our results.