Understanding the outperformance of the minimum variance portfolio

Minimum variance portfolio (MVP) seems to outperform the mean-variance optimized portfolio on a risk-adjusted basis. Scherer (2011) conjectures that the MVP tilts toward low beta and low idiosyncratic risk assets. Consequently, the MVP capitalizes on both the beta anomaly and the idiosyncratic risk anomaly. By providing a counter-example, Yanushevsky and Yanushevsky (2015) show that the proof of the conjecture is incomplete. In this article, we provide conditions under which Scherer (2011) conjecture remains valid. Specifically, we show that the counter-example in Yanushevsky and Yanushevsky (2015) represents a knife-edge case. We also analytically identify the MVP weight sign.