Why optimal diversification cannot outperform naive diversification: Evidence from tail risk exposure

Version of January 2013 Abstract This paper examines the outperformance of naive diversification relative to optimal diversification. From out-of-sample analysis using portfolios consisting of individual stocks as well as diversified equity portfolios, we find that optimal diversification fails to consistently outperform naive diversification. Our results show that naive diversification increases tail risk measured by skewness and kurtosis and makes portfolio returns more concave relative to equity benchmarks. In addition, tail risk exposure and concavity increases with the number of stocks in the portfolio. These results imply that the outperformance of naive diversification relative to optimal diversification represents a compensation for the increase in tail risk and the reduced upside potential associated with the concave payoff.