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


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

Do you have a job opening that you would like to promote on SSRN?

Paper statistics

Abstract Views
PlumX Metrics