Abstract

We evaluate the out-of-sample performance of the sample-based mean-variance model, and its extensions designed to reduce estimation error, relative to the naive 1/N portfolio. Of the 14 models we evaluate across seven empirical datasets, none is consistently better than the 1/N rule in terms of Sharpe ratio, certainty-equivalent return, or turnover, which indicates that, out of sample, the gain from optimal diversification is more than offset by estimation error. Based on parameters calibrated to the US equity market, our analytical results and simulations show that the estimation window needed for the sample-based mean-variance strategy and its extensions to outperform the 1/N benchmark is around 3000 months for a portfolio with 25 assets and about 6000 months for a portfolio with 50 assets. 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.

Scientific Portfolio AI- Generated Summary

This paper examines the performance of optimal versus naive diversification strategies in the context of mean-variance models. The authors evaluate various models and their ability to outperform the simple 1/N portfolio strategy, which allocates equal weights to all assets in the portfolio. The study finds that, out of sample, the gains from optimal diversification are often offset by estimation error. However, the authors also provide insights on the estimation window needed for these strategies to outperform the benchmark.

The paper begins by discussing the importance of diversification in portfolio management and the challenges associated with constructing optimal portfolios. The authors note that while mean-variance models have been widely used in the literature, they often suffer from estimation error, which can lead to suboptimal portfolio allocations. To address this issue, the authors propose a sample-based mean-variance policy that uses historical data to estimate the expected returns and covariance matrix of the assets in the portfolio.

The authors then evaluate the performance of this policy relative to the 1/N benchmark using data from the US equity market. They find that, on average, the sample-based mean-variance policy does not outperform the benchmark, and that the gains from optimal diversification are often offset by estimation error. However, the authors also show that the estimation window needed for the policy to outperform the benchmark is relatively short, suggesting that investors can benefit from optimal diversification with relatively little historical data.

The paper also examines the performance of other mean-variance models, including the Black-Litterman model and the Bayesian hierarchical model. The authors find that these models generally perform better than the sample-based mean-variance policy, but that their performance is still sensitive to estimation error.

Finally, the authors conduct a series of robustness checks to verify the results of their analysis. They find that their conclusions are generally robust to changes in the estimation window, the choice of asset classes, and the inclusion of transaction costs.

Overall, this paper provides valuable insights into the performance of optimal versus naive diversification strategies in the context of mean-variance models. The authors show that while optimal diversification can lead to improved portfolio performance, investors must be mindful of the estimation error associated with these models. The paper also highlights the importance of choosing an appropriate estimation window and provides guidance on how to implement these strategies in practice.