Estimating Ex-ante Tracking Error from Active Share and Averages of Stocks' Variances and Squared Covariances

Abstract

Ex-ante tracking error is the standard deviation of the potential active return outcomes of an investment portfolio managed relative to a benchmark portfolio. An involved risk model is used for its calculation.

A portfolio's active share metric is often used as a proxy for ex-ante tracking error as it is much simpler to calculate. Only holdings data is required for the portfolio and its benchmark.

We present a stochastic model to describe the relationship between these two statistics. Accordingly, a fund's ex-ante tracking error can be estimated as the product of its Euclidean active share and a function depending on the average volatilities and average squared covariances of its active stock holdings. We evaluate our model empirically using weighted Mincer-Zarnowitz regressions applied to actively managed US equity mutual funds.

The estimator's precision deteriorates with increasing Euclidean active share and increasing average stock volatilities. Conversely, the estimator becomes more accurate as the absolute correlations among the active stocks decrease on average.

Our proposed estimator is considerably better than the active share metric at quantifying a portfolio's active risk.

Keywords: Ex-ante Tracking Error, Active Share, Active Risk, Active Management, Weighted Mincer-Zarnowitz Regression, Risk Model

JEL Classification: C13, C15, C46, C630, G11