Better Betas

Abstract

The authors introduce the data-driven Goldberg, Papanicolaou, and Shkolnik (GPS) adjustment for estimated betas, which leads to material improvements in the accuracy of weights and risk forecasts of minimum variance portfolios. Like the widely used Blume 2/3 rule and Vasicek adjustment developed in the 1970s, the GPS adjustment for estimated betas shrinks raw beta estimates toward one. Unlike its antecedents, the GPS adjustment operates on the dominant factor of a sample covariance matrix, and this adjustment adapts dynamically to varying levels of beta dispersion. The authors illustrate the power of the GPS adjustment in a simulation that is calibrated to calm and stressed market regimes.

TOPICS: Factor-based models, portfolio construction, risk management, simulations

Key Findings

• • Betas play a central role in determining optimized portfolios, and principal component analysis (PCA) is an effective tool to estimate betas.

• • More accurate PCA betas can be achieved with the Goldberg, Papanicolaou, and Shkolnik (GPS) adjustment, which is analogous to standard beta shrinkage adjustments applied to betas obtained from time-series regression.

• • Substantial improvements to the accuracy of minimum variance portfolio weights and risk forecasts may be realized when applying the GPS adjustment, which leads to better betas in any market regime.