Subset Optimization for Asset Allocation
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 naıvely aggregate many "Subset Portfolios," each optimizing weights over a subset of only Nˆ 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 Nˆ . In ﬁnite samples, the bound on CSPs' expected out-of-sample performance loss due to sampling error generally increases with Nˆ. 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.