Optimal portfolio selection based on parametric and non-parametric multi-horizon expected shortfall

Expected shortfall measures the loss of a portfolio in mathematical expectation when the amount of loss exceeds a threshold for a certain level of confidence and in a certain time horizon. Multi-horizon expected shortfall extends the concept of expected shortfall for an investment with a set of maturity horizons. In the present study, two stock portfolio models are designed based on the multi-horizon expected shortfall, the first is based on historical simulation and the second is parametric and based on the distribution of normal-Laplace mixture for proper fitting of tail data. Also, expectile is used to compute the expected shortfall in parametric form. The result of the experimental study of stock portfolio models designed on a stock portfolio with eight indices of the Tehran Stock Exchange by coding in the MATLAB software in the period 1390 to 1399 shows that the parametric approach in the test data in average return and Sharpe ratio criterions has a better performance than the historical scenario. Also, the relative error between the period expected shortfall predicted by the stock portfolio and its estimate in the test data in the parametric approach is less.