Data-driven distributionally robust risk parity portfolio optimization

TL;DR

This paper introduces a distributionally robust approach to risk parity portfolio optimization, accounting for uncertainty in data probabilities to enhance portfolio robustness and performance.

Contribution

It formulates a novel convex-concave minimax problem incorporating ambiguity sets for probabilities and proposes an efficient algorithm to solve it.

Findings

Robust portfolios outperform nominal ones in risk-adjusted returns.

The method is flexible with different statistical distance measures.

Algorithm is scalable and adaptable to various data scenarios.

Abstract

We propose a distributionally robust formulation of the traditional risk parity portfolio optimization problem. Distributional robustness is introduced by targeting the discrete probabilities attached to each observation used during parameter estimation. Instead of assuming that all observations are equally likely, we consider an ambiguity set that provides us with the flexibility to find the most adversarial probability distribution based on the investor's desired degree of robustness. This allows us to derive robust estimates to parametrize the distribution of asset returns without having to impose any particular structure on the data. The resulting distributionally robust optimization problem is a constrained convex-concave minimax problem. Our approach is financially meaningful and attempts to attain full risk diversification with respect to the worst-case instance of the portfolio risk measure. We propose a novel algorithmic approach to solve this minimax problem, which blends projected gradient ascent with sequential convex programming. By design, this algorithm is highly flexible and allows the user to choose among alternative statistical distance measures to define the ambiguity set. Moreover, the algorithm is highly tractable and scalable. Our numerical experiments suggest that a distributionally robust risk parity portfolio can yield a higher risk-adjusted rate of return when compared against the nominal portfolio.