1/N

Abstract

In this paper, we evaluate the out-of-sample performance of the portfolio policy from the sample-based mean-variance portfolio model and the various extensions of this model, designed to reduce the impact of estimation error relative to the benchmark strategy of investing a fraction 1/N of wealth in each of the N assets available. Of the fourteen models of optimal portfolio choice that we evaluate across seven empirical datasets, we find that none is consistently better than the 1/N rule in terms of Sharpe ratio, certainty-equivalent return, or turnover. This finding indicates that, out of sample, the gain from optimal diversification is more than offset by estimation error. To gauge the severity of estimation error, we derive analytically the length of the estimation window needed for the sample-based mean-variance strategy to outperform the 1/N benchmark; for parameters calibrated to U.S. stock market data, we find that, for a portfolio with only 25 assets, the estimation window needed is more than 3,000 months, and for a portfolio with 50 assets, it is more than 6,000 months, although in practice these parameters are estimated using 120 months of data. Using simulated data, we further document that even the various extensions to the sample-based mean-variance model designed to deal with estimation error reduce only moderately the estimation window needed to outperform the naive 1/N benchmark. This suggests that there are still many "miles to go" before the gains promised by optimal portfolio choice can actually be realized out of sample.