Menu simplification for portfolio selection under short-sales constraints

We introduce a risk-reduction-based procedure to identify a subset of funds with a resulting opportunity set that is at least as good as the original menu when short-sales are imposed. Relying on Wald tests for mean-variance spanning, we show that the better results for the subset can be explained by a higher concentration of covariance entries between its assets, ultimately leading to smaller Frobenius norms of the associated matrices. With data on US-defined contribution plans, where participants have limited financial literacy, tend to be overwhelmed and prefer to make decisions among fewer choices, we obtain a 75% average reduction.