Portfolio selection: from under-diversification to concentration.

The two opposing investment strategies, diversification and concentration, have often been directly compared. While there is much less dispute regarding Markowitz's approach as the benchmark for diversification, the precise meaning of concentration in portfolio selection remains unclear. This paper offers a novel definition of concentration, along with an extreme value theory-based estimator for its implementation. When overlaying the performances derived from diversification (in Markowitz's sense) and concentration (in our definition), we find an implied risk threshold, at which the two polar investment strategies reconcile—diversification has a higher expected return in situations where risk is below the threshold, while concentration becomes the preferred strategy when the risk exceeds the threshold. Different from the conventional concave shape, the estimated frontier resembles the shape of a seagull, which is piecewise concave. Further, taking the equity premium puzzle as an example, we demonstrate how the family of frontiers nested inbetween the estimated curves can provide new perspectives for research involving market portfolios. [ABSTRACT FROM AUTHOR]