Generalized Benchmarking : Is Blind Index-Tracking Optimal?

I present a generalized benchmarking theory on portfolio selection relative to a market index. Using the bias-variance trade-off of the tracking error, analytical conditions are derived to describe when it is optimal for a portfolio of risky assets to follow the index, or align the portfolio against the index. The intensity and direction of the portfolio's orientation depend on the mean and volatility of the index, asset parameters, and the desired bias for the tracking error. The theory contrasts with the standard index-tracking concept in which a fund is designed to track the index at all times with full intensity regardless of market forecasts, a practice herein referred to as blind indexing, an investment category valued at over $4T. Analytical results show that an optimally-benchmarked portfolio will be following the index only when the underlying assets have sufficiently-strong covariance with the index, relative to the index mean return; otherwise, it is optimal to orient the portfolio opposed to the index. Moreover, the optimal intensity of benchmarking is inversely proportional to the volatility of the index return. The theory also shows that a careful selection of the underlying assets is important for portfolio benchmarking. A case study is presented with out-of-sample performance to highlight the advantages of the approach, which include low trading intensity and better drawdown characteristics, relative to blind index tracking