Problem 22.2 Suppose that the daily change in the value of a portfolio is, to a good approximation, linearly dependent on three factors, calculated from a principal components analysis. The delta of a portfolio with respect to the first factor is 6 , the delta with respect to the second factor is 4, and the delta with respect to the third factor is 5. The standard deviations of the factors are 8, 20, and 3 respectively. a) What is the 5-day 95\% VaR? b) If you could only choose two of the three factors in the PCA, which would you choose and why? c) Recalculate your answer to part a) given your choice in b)