How Inefficient is the 1/N Asset-Allocation Strategy?
Victor DeMiguel
Decision Sciences
London Business School
Friday, November 11, 2005
1:30 - 2:45 PM
Terman Engineering Center, Room 453
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 value, 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 na¨-Cıve diversification-A
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 mean-variance policy 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.
This is joint work with Lorenzo Garlappi and Raman Uppal.
Operations Research Colloquia: http://or.stanford.edu/oras_seminars.html