Uncertain Covariance Models and Uncertainty-Penalized Portfolio Optimization
20 Pages Posted: 9 Jun 2015 Last revised: 4 Apr 2023
Date Written: June 9, 2015
Abstract
Covariance appears throughout investment management, e.g., risk reporting, portfolio optimization, risk parity, smart beta, algorithmic trading, and hedging. It is often represented via multi-factor model. The imposed structure - comovement through sensitivity to common factors, diagonal residuals - offers advantages such as less data for estimation, easy proxying, and removing transient behavior and low eigenvalue directions. Nevertheless, parameter values are inferred and imperfect. Though it's common to ignore the error and proceed from point estimates, the spread of possible values is considered in Bayesian techniques and robust optimization. The research in this paper connects to both: Forecasts of mean and variance of the factor model parameters propagate to forecast the mean and variance of the covariance matrix. Using the result, optimization is performed to maximize portfolio utility a given number of standard deviations below the mean.
Keywords: Covariance, Estimation error, Multi-factor models, Portfolio optimization, Regularization, Uncertainty
JEL Classification: C00, C11, C53, G19
Suggested Citation: Suggested Citation