How Inefficient is the 1/N Asset-Allocation Strategy?

Abstract

In this paper, we compare the out-of-sample performance of the rule allocating 1/N to each of the N available assets to several static and dynamic models of optimal asset-allocation for ten datasets. We devote particular attention to models the literature has proposed to account for estimation and model error. We find that the 1/N asset-allocation rule typically has a higher out-of-sample Sharpe ratio, a higher certainty-equivalent return, and a lower turnover than optimal asset allocation policies. The intuition for the poor performance of the policies from the optimizing models is that the gain from optimal diversification relative to naive diversification under the 1/N rule is typically smaller than the loss arising from having to use as inputs for the optimizing models parameters that are estimated with error rather than known precisely. Simulations show that the performance of optimal strategies relative to the 1/N rule improves with the length of the estimation window, which reduces estimation error. For instance, for the case where wealth can be allocated across four risky assets with an average cross-sectional annual idiosyncratic volatility of 20%, it takes an estimation window of 50 years in order for the classical mean-variance policy implemented using maximum-likelihood estimates of the moments to outperform 1/N. But if the average idiosyncratic volatility drops to 10%, the length of the required estimation window increases to 500 years; and, when the number of assets increases to 100 while average idiosyncratic volatility is 20%, the length of the required estimation window is more than 1,000 years.

Keywords: Portfolio choice, asset allocation, investment management

JEL Classification: G11