Does Greater Diversification Really Improve Performance in Portfolio Selection?

One of the fundamental principles in portfolio selection models is minimization of risk through diversification of the investment. This seems to require that in a given working universe, or market, the investment should be spread among all (or almost all) the available assets. Indeed, this is what some classical investment strategies, like Equally-Weighted portfolios, or more recent and refined ones, like Risk Parity, actually recommend. The purpose of this work consists in giving some empirical evidence of the fact that diversifying through the use of larger portfolios is not the best way to achieve an improvement in out-of-sample performance. More precisely, we investigate the role of the restriction on the number of assets in a portfolio (a cardinality constraint) on the in-sample and out-of-sample outcomes of the Equally-Weighted approach and of some well-known portfolio selection models that minimize risk through the use of Variance, Semi-Mean Absolute Deviation, and Conditional Value-at-Risk. Our empirical analysis is based on some new and on some publicly available benchmark data sets often used in the literature