How Much Error is in the Tracking Error? The Impact of Estimation Risk on Fund Tracking Error
Artemiza Woodgate, Russell Investments
Andrew F. Siegel, University of Washington

The authors explain the poor out-of-sample performance of optimized portfolios (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. Theoretical bias adjustments for this estimation risk are developed by 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 to non-normality. Using these approximation methods it may be possible to assess, before investing, the effect of statistical estimation error on tracking-error-optimized portfolio performance.

Estimation errors in expected asset means and variances lead to poor out-of-sample performance of optimized portfolios. The authors provide theoretical bias adjustments that can permit managers to reduce the costs of rebalancing portfolios. The results should be of interest to quantitative managers who use portfolio optimizers and to investment sponsors who must evaluate the performance of such managers.