Uncertain Covariance Models and Uncertainty-Penalized Portfolio Optimization

23 Pages Posted: 9 Jun 2015 Last revised: 24 May 2021

See all articles by Anish Shah

Anish Shah

Investment Grade Modeling; Brown University - Division of Applied Mathematics

Date Written: June 9, 2015

Abstract

Covariance appears throughout investment management, e.g., in risk reporting and control, portfolio construction, risk parity, smart beta, algorithmic trading, and hedging. It is usually represented via multi-factor model. The form’s fewer parameters and structure—comovement through sensitivity to common factors, a residual component for uncorrelated variance—soften insufficient and non-stationary data issues. Nevertheless, parameter values remain inferred and not perfectly accurate. Common practice ignores the error and proceeds from point-estimates. This paper retains the error and propagates estimates of parameters’ mean and covariance to their effect at the investment portfolio level. Forecasted portfolio variance changes from a number to a mean and standard deviation, the latter representing uncertainty. Applications include more informative portfolio risk assessment, uncertainty-penalized optimization to counter estimation error and improve realized utility, and uncertainty indifference bands to lower trading costs.

Keywords: Covariance, Estimation error, Multi-factor models, Portfolio optimization, Regularization, Uncertainty

JEL Classification: C00, C11, C53, G19

Suggested Citation

Shah, Anish, Uncertain Covariance Models and Uncertainty-Penalized Portfolio Optimization (June 9, 2015). Available at SSRN: https://ssrn.com/abstract=2616109 or http://dx.doi.org/10.2139/ssrn.2616109

Anish Shah (Contact Author)

Investment Grade Modeling ( email )

Cambridge, MA 02139
United States

HOME PAGE: http://www.linkedin.com/in/anishrshah

Brown University - Division of Applied Mathematics

182 George St
Providence, RI 02912
United States

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