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.

中文翻译：

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替代风险平价策略的二阶风险

二阶风险的概念将投资组合构建中模型不确定性引起的估计风险操作化。我们研究了它对最近开发的另类风险平价策略的已实现波动率的贡献，这些策略投资于资产领域的不相关分解。对于每种策略，我们为二阶风险推导出封闭形式的解决方案，随后在基于真实市场数据的实证分析中加以说明。我们的结果表明，二阶风险的贡献与投资组合对资产回报协方差矩阵的单个特征向量的敏感性之间存在关系。在考虑的策略中，我们发现主要风险平价策略对方差-协方差矩阵的每个特征向量进行同等投资，以免受二阶风险的影响。对于其他策略，二阶风险可以通过统计方法部分缓解。特别是，我们提供了特征值调整是纠正二阶风险偏差的最有效方法的证据。