Uncertain Covariance Models and Uncertainty-Penalized Portfolio Optimization

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