Second-Order Risk of Alternative Risk Parity Strategies

Abstract

The concept of second-order risk operationalizes the estimation risk in portfolio construction induced by model uncertainty. We study its contribution to the realized volatility of recently developed alternative risk parity strategies that invest in an uncorrelated decomposition of the asset universe. For each strategy, we derive closed-form solutions for the second-order risk, subsequently illustrated in empirical analysis based on real market data. The results suggest a relation between the contribution of second-order risk and the sensitivity of a portfolio to single eigenvectors of the covariance matrix of assets' returns. Among the strategies considered, we find the principal risk parity strategy, that invests equally in each eigenvector underlying the variance-covariance matrix, to be immune to second-order risk. For the other strategies, second-order risk can be partially mitigated by means of statistical methods. In particular, we provide evidence for the eigenvalue adjustment being the most effective method for correcting the the SOR bias.

Keywords: Estimation Risk, Second-Order Risk, Portfolio Construction, Risk Parity, Diversification

JEL Classification: G11, D81