Portfolio optimization for t and skewed-t returns

Wenbo Hu, Alec N. Kercheval

It is well-established that equity returns are not Normally distributed, but what should the portfolio manager do about this, and is it worth the effort? As we describe, there are now some good choices for multivariate modeling distributions that capture heavy tails and skewness in the data; we argue that among the best are the (Student) t and skewed t distributions. These can be efficiently calibrated to data, and show a much better fit to real data than the Normal distribution. By examining efficient frontiers computed using different distributional assumptions, we show, using for illustration 5 stocks chosen from the Dow index, that the choice of distribution has a significant effect on how much available return can be captured by an optimal portfolio on the efficient frontier.