Do investors like to diversify? A study of Markowitz preferences

We study rankings of completely and partially diversified portfolios and also of specialized assets when investors follow so-called Markowitz preferences. It turns out that diversification strategies for Markowitz investors are more complex than in the case of risk-averse and risk-inclined investors, whose investment strategies have been extensively investigated in the literature. In particular, we observe that for Markowitz investors, preferences toward risk vary depending on their sensitivities toward gains and losses. For example, it turns out that, unlike in the case of risk-averse and risk-inclined investors, Markowitz investors might prefer investing their entire wealth in just one asset. This finding helps us to better understand some financial anomalies and puzzles, such as the well known diversification puzzle, which notes that some investors tend to concentrate on investing in only a few assets instead of choosing the seemingly more attractive complete diversification.