One of the major advantages of Equity mutual funds is that they allow retail investors to attain a diversified portfolio, which could not be easily obtained buying individual stocks. Our results indicate that mutual funds are not totally diversified; they hold a significant part of idiosyncratic risk and, in general, retail investors do not hold diversified portfolios of funds as it is possible to highly reduce the percentage of the idiosyncratic risk with respect to the total variance of their portfolios. A strategy selecting funds that minimize the idiosyncratic risk of the portfolio (MIR) behaves well in terms of diversification even for those investors worried about the alpha of funds. The benefits of diversification hold even out-of-sample. Finally we use downside risk measures to confirm that mutual funds do not seem to be well diversified and this drawback increases as the investor’s risk aversion increases.