6. Let X be a random variable which denotes the possible monetary loss on a portfolio over a fixed time horizon T (e.g. one day, one week, or one year). Here losses are counted as positive and profits as negative, i.e. X is the negative of the gain on the portfolio over the period [0,T]. The value at risk (VaR) of the portfolio at confidence level a is the minimum value of the loss that we are (1-a)% certain will not be exceeded, i.e. VaRa (X) = min{x : P(X > x) a}. Typical values of a are 5% or 1%. For example, if your portfolio has a 5% one-day VaR of 1 million, then we expect a loss of > 1 million no more than 5% of days. On a given day, we are 95% sure that the loss of the portfolio will be 1 million. (a) Explain why VaR(X) = Fx(1 a).