When computing Minimum Variance Hedge Ratios as explained f.e. in Hull (2012) the goal is to select a hedge ratio such that the variance of the portfolio is minimized. My question is now what are the implications on the tails f.e. the VaR. In my understanding these are not considered in the optimizations. Hence, a portfolio, which has the lowest variance does not necesserily also have the lowest VaR i.e. lowest tail risk. Is that correct?