How Much Error Is in the Tracking Error? The Impact of Estimation Risk on Fund Tracking Error

Abstract

The authors explain optimized portfolios’ poor out-of-sample performance (to minimize tracking error relative to a given benchmark, while achieving a specified expected excess return) in the presence of estimation error in the underlying asset means and covariances. The theoretical bias adjustments for this estimation risk developed by the authors involves taking mathematical expectations of asymptotically expanded future returns of portfolios formed with estimated weights. They provide closed-form adjustments for estimates of the expectation and standard deviation of the portfolio’s excess returns. The adjustments significantly reduce bias in global equity portfolios, reduce the costs of rebalancing portfolios, and are robust to sample size and non-normality. By using these approximation methods before investing, it may be possible to assess the effect of statistical estimation error on tracking-error-optimized portfolio performance.