A robust framework for risk parity portfolios

Abstract

We propose a robust formulation of the traditional risk parity problem by introducing an uncertainty structure specifically tailored to capture the intricacies of risk parity. Typical minimum variance portfolios attempt to introduce robustness by computing the worst-case estimate of the risk measure, which is not intuitive for risk parity. Instead, our motivation is to shield the risk parity portfolio against noise in the estimated asset risk contributions. Thus, we present a novel robust risk parity model that introduces robustness around both the overall portfolio risk and the assets’ marginal risk contributions. The proposed robust model is highly tractable and is able to retain the same level of complexity as the original problem. We provide a general procedure by which to create an uncertainty structure around the asset covariance matrix. We quantify this uncertainty as a perturbation on the nominal covariance estimate, which allows us to intuitively embed robustness during optimization. We then propose a specific procedure to construct a robust risk parity portfolio through a factor model of asset returns. Computational experiments show that the robust formulation yields a higher risk-adjusted rate of return than the nominal model while maintaining a sufficiently risk-diverse portfolio.