Example of traditional Value at Risk

Question

Illustrates an example of traditional Value at Risk by Artzner et al?

Answer 1

Artzner et al. (1997) provide a simple example of traditional VaR that violates this, and exemplifies perfectly the problems of measures which are not coherent. Portfolio X contains only a far out-of-the-money put along with one day to expiry. Portfolio Y contains only a far out-of-the-money call with one day to expiry. Let us assume that every option has a probability of 4 percent of ending up in the money. For all options individually, at the 95 percent confidence level the one-day traditional VaR is efficiently zero. At this instant put the two portfolios together and there is a 92 percent chance of not losing anything, 100 percent less two lots of 4 percent. Therefore at the 95 percent confidence level there will be an important VaR. Putting the two portfolios together has in this illustration increased the risk.