What is the proper relation between the VaR in a portfolio and the amount of capital that should be held against it?
There are many considerations, if capital is to be based on VaR. VaR doesn’t tell you how big your losses could be on a bad day, it only defines what distingishes a bad day from other days. If you have two portfolios with exposures to risks of different markets, but the portfolios nevertheless have the same VaR, then it may be wrong to keep the same capital against each portfolio, because one may have much worse performance given a VaR exceedance day. Also, since VaR looks at only a particular forecast horizon, and a bad economic environment may extend beyond that horizon, the relationship between VaR and a business-continuity-threatening type of market event is murky at best. Finally, the relationship between the amount of risk taken and the amount of capital to be held may come down to the nature of the trading and the risk appetite of the “owners” of the capital. If the portfolio has significant nonlinear risks, then the relation between the capital and VaR is even more difficult to
