Improved Tracking-Error Management for Active and Passive Investing

ADIA Lab Research Paper Series, No. 13.

Gianluca De Nard, Olivier Ledoit, Michael Wolf (2025)

Tracking-error management is largely absent from the academic literature but ubiquitous in real life: Most portfolio managers are tied to a benchmark. Some of them aim to track a benchmark (such as the S&P 500), which is not necessarily a trivial task because the benchmark often contains assets that are difficult or expensive to trade. In this case, the objective is to minimize tracking error. Other managers aim to take on an active tilt without deviating too much from a benchmark. In this case, the objective is to control tracking error. In both cases, managers need an estimator of the covariance matrix of many (excess) returns for their objective. This article demonstrates the benefit of sophisticated shrinkage estimators (in conjunction with multivariate GARCH models) to this end, relative to the commonly used sample covariance matrix.