Comparison of Markowitz and Hellinger-Normal Portfolios

In this paper we compare the performances of Markowitz portfolio and the portfolio closest to normal in distribution. The latter is obtained by fixing the same desired level of expected returns and optimizing the Hellinger distance to Gaussian distribution with parameters obtained from Markowitz portfolio optimization for the same expected return. We confine ourselves to long-position portfolio only. We found that in contrast to the expectations, the Hellinger-Normal portfolio does not smooth enough the extreme loses, but do not worse in that regard than Markowitz portfolio. We also found that overall in non-long run passively managed portfolios, the Hellinger-Normal portfolio had better overall realized Sharpe and Kelly ratios.