Serial correlation and TEV bias in index funds

Abstract

Index or passive fund managers and investors analyse the interim volatility of the difference between their fund’s returns and the index’s returns, i.e. the fund’s tracking error variance** (TEV) in order to monitor the success with which tracker funds mimic their benchmark. The objective of a passive or index fund manager should be to keep TEV as close to zero as possible. Pope and Yadav (1994) show that an index fund that is overweight relative to it’s index in either relatively less or relatively more liquid stocks, is expected to exhibit negative serial correlation in its TE’s. Consequently, estimates of TEV will be upwardly biased, particularly when using high frequency (such as daily or weekly) data.
This article finds evidence of negative serial correlation in the weekly, monthly and quarterly TE’s of domestic index funds. Consequently it is shown that TEV will likely be overestimated. There are two important implications of this upward bias in TEV estimation. Firstly, index funds, which are expected to offer close to zero benchmark-relative or active risk, may appear far more ‘risky’ than they actually are thus damaging their value-proposition to investors. Secondly, when funds appear to have greater TEV than they actually do, the manager may ‘churn’ the fund’s assets more than necessary in order to bring the fund back into alignment with its index thus incurring greater and unnecessary transaction costs.
The analyses in this article therefore suggest that TE measurements should be examined for negative serial correlation before estimates of TEV are made. If serial correlation is detected, estimates of TEV should either be made from lower frequency, uncorrelated TE measurements, if they are available, or an adjustment technique such as the Lo-MacKinlay adjustment should be applied to correct for the bias in TEV estimation.