Estimation risk and the implicit value of index-tracking

We study [Roll, R., A mean/variance analysis of tracking error. J. Portfolio Manage., 1992, 18, 13–22.] conjecture that there exists an implicit value in index-tracking (IVIT) relative to forming mean-variance (MV) optimal portfolios under estimation error. We derive an analytical definition for the opportunity cost facing the MV investor who does not index-track. Our findings indicate that the opportunity cost is positive and statistically significant. The existence of an IVIT (positive opportunity cost) is strongly associated with a reduction in the portfolio's induced estimation risk under index-tracking relative to an MV-efficient portfolio of equal target mean return. Under high estimation error cases, increased IVIT translates to higher risk-adjusted returns, lower volatility, higher Sharpe-ratio, lower turnover, and larger certainty equivalent returns. Empirically, a one standard deviation increase in IVIT translates to an annual increase of 4%–5% in the out-of-sample Sharpe-ratio and a 6%–15% decrease in the monthly turnover.