3. (Portfolio VaR) Suppose there are two investments A and B. Either investment A or B has a 4% chance of a loss of $10 million, a 5% chance of a loss of $2 million, and a 91% chance of a profit of $4 million. The outcomes of these two investments are independent of each other. (a) What is the 95%VaR of investment A? How about investment B? (b) What is the 95% for a portfolio consisting of both investments A and B? (Hint: write out the probabilities of all possible portfolio outcomes.) (c) Is the summation of the 95%VaRs of the individual investments greater or smaller than the 95%VaR of the portfolio? If we measure the risk of an investment or portfolio using VaR, does this suggest that diversification must decrease risk? (Intuitively, putting A and B in a portfolio is a form of diversification.)