How do non-normal parametric VaR models perform in risk-minimizing portfolios?

This study minimizes the extreme risk of the NASDAQ index by optimizing two six-asset portfolios with developed and emerging Asian stock indices in the pre-crisis and crisis periods. The existing papers in this area usually use the normal VaR model to estimate extreme risk. In the parametric VaR estimation, we try to improve the analysis by using three non-normal distribution functions – logistic, hyper-secant and Laplace, while the normal VaR is a benchmark. CVaR is also used to evaluate its performance relative to heavier-tailed non-normal VaR models. Different VaR models do not affect the multivariate portfolio structure, but the downside risk measures differ. Applying the Kupiec test and visual inspection of probability density functions, it is determined that two fatter tail functions – logistic and hyper-secant, best fit the realized returns in both portfolios and subsamples. From the aspect of hedge effectiveness, the portfolio with emerging Asian indices better mitigates extreme risk because emerging markets are less integrated. In the optimal portfolios, in most cases, NASDAQ is the only asset in the portfolio due to the highest Sharpe ratio in both pre-crisis and crisis periods. The paper points out the need to find the best VaR model because the effectiveness of hedging and the reliability of results depend on it.