Subset Optimization for Asset Allocation

Abstract

Subset optimization provides a new algorithm for asset allocation that's particularly useful in settings with many securities and short return histories. Rather than optimizing weights for all N securities jointly, subset optimization constructs Complete Subset Portfolios (CSPs) that naively aggregate many "Subset Portfolios," each optimizing weights over a subset of only ^N randomly selected securities. With known means and variances, the complete subset efficient frontier for different subset sizes characterizes CSPs' utility loss due to satisficing, which generally decreases with ^N . In finite samples, the bound on CSPs' expected out-of-sample performance loss due to sampling error generally increases with ^N . By balancing this tradeoff, CSPs' expected out-of-sample performance dominates both the 1=N rule and sample-based optimization. Simulation and backtest experiments illustrate CSPs' robust performance against existing asset allocation strategies.

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