Covariance matrix estimation for robust portfolio allocation

Ahmad W. Bitar (1, 2) , Nathan de Carvalho (3, 2, 4) , Valentin Gatignol (5, 2)

1 UTT - Université de Technologie de Troyes
2 CentraleSupélec
3 UPCité - Université Paris Cité
4 Engie Global Markets
5 Qube Research and Technologies

In this technical report , we aim to combine different protfolio allocation techniques with covariance matrix estimators to meet two types of clients' requirements: client A who wants to invest money wisely, not taking too much risk, and not willing to pay too much in rebalancing fees; and client B who wants to make money quickly, benefit from market's short-term volatility, and ready to pay rebalancing fees. Four portfolio techniques are considered (mean-variance, robust portfolio, minimum-variance, and equi-risk budgeting), and four covariance estimators are applied (sample covariance, ordinary least squares (OLS) covariance, cross-validated eigenvalue shrinkage covariance, and eigenvalue clipping). Some comparisons between the covariance estimators in terms of eigenvalue stability and four metrics (i.e. expected risk, gross leverage, Sharpe ratio and effective diversification) exhibit the superiority of the eigenvalue clipping covariance estimator. The experiments on the Russel1000 dataset show that the minimum-variance with eigenvalue clipping is the model suitable for client A, whereas robust portfolio with eigenvalue clipping is the one suitable for client B.

Keywords: Robust portfolio; minimum-variance; eigenvalue clipping; OLS covariance

Domains: Quantitative Finance [q-fin]

Ahmad W. Bitar, Nathan de Carvalho, Valentin Gatignol. Covariance matrix estimation for robust portfolio allocation. CentraleSupélec; Université de Technologie de Troyes; Université Paris Cité. 2023. ⟨hal-04046454⟩