A Directional Multivariate Value at Risk

In economics, insurance and finance, value at risk (VaR) is a widely used measure of the risk of loss on a specific portfolio of financial assets. For a given portfolio, time horizon, and probability $α$, the $100α\%$ VaR is defined as a threshold loss value, such that the probability that the loss on the portfolio over the given time horizon exceeds this value is $α$. That is to say, it is a quantile of the distribution of the losses, which has both good analytic properties and easy interpretat...