Solving the "Corner Solution Problem" of Portfolio Optimization

Green & Hollifield derive analytic conditions under which mean-variance-efficient portfolios must be well diversified, and show those conditions fail in practice because equity returns are dominated by a single common factor: hedging factor exposure requires extreme offsetting long-short positions, even though residual risk diversifies away easily.

Crucially, they show this concentration is a structural consequence of the factor structure — unlikely to be attributable to sampling error. Better estimation of means and covariances alone will not fix it.

This model takes the practical route: allow a tiny tolerance around the efficient frontier — say a one-hundredth neighbourhood — and there are thousands of near-efficient portfolios, many of them well diversified. The optimizer searches that neighbourhood for the most diversified one, giving up a sliver of theoretical efficiency for a portfolio an investor will actually hold.