Distribution assumptions and risk constraints in portfolio optimization

Empirical distributions are often claimed to be superior to parametric distributions, yet to also increase the computational complexity and are therefore hard to apply in portfolio optimization. In this paper, we approach the portfolio optimization problem under constraints on the portfolio's Value at Risk and Expected Tail Loss, respectively, under empirical distributions for the Standard and Poor's 100 stocks. We apply a heuristic optimization method which has been found to overcome the restrictions of traditional optimization techniques. Our results indicate that empirical distributions might turn into a Pandora's Box: Though highly reliable for predicting the assets' risks, employing these distributions in the optimization process might result in severe mis-estimations of the resulting portfolios' actual risk. It is found that even a simple mean-variance approach can be superior despite its known specification errors.