# Second-order risk of alternative risk parity strategies

## Simone Bernardi, Markus Leippold and Harald Lohre

#### Need to know

• The authors analyze the bias in the realized volatility of alternative risk parity strategies.
• The paper derives analytical and empirical estimations of the volatility bias across different strategies.
• The most efficient way to mitigate the bias is through the weighting of the principal portfolios.
• The principal risk parity strategy is most successful in minimizing the volatility bias.

#### Abstract

The concept of second-order risk operationalizes the estimation risk induced by model uncertainty in portfolio construction. 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. Our 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 second-order risk bias.
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