We show that the probability of risk parity beating any other portfolio is more than 50 percent. We also prove that if … portfolio performance is measured by Sharpe ratio, risk parity is the only maximin portfolio when (1) all assets' future Sharpe … assets' future Sharpe ratios is greater than some constant. If portfolio performance is measured by expected return, risk …

consumption across countries from the predictions of models with full risk sharing. It is commonly believed that these risk … that the full risk sharing equilibrium may not require much diversification of equity portfolios when there is price …