Estimation risk and the implicit value of index-tracking
研究了在估计误差下，指数追踪相对于均值方差最优组合的隐含价值，发现机会成本为正且显著，高估计误差时隐含价值提升能带来更高的风险调整收益和更低的换手率。
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.