3. (Portfolio VaR) Suppose there are two investments A and B. Either investment A or B has a 8% chance of a loss of $8 million, a 12% chance of a loss of $1 million, a 30% chance of a profit of $1 million and a 50% chance of a profit of $4 million. The outcomes of these two investments are independent of each other. (a) What is the 90% VaR of the loss of investment A? How about investment B? (b) What is the 90% 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 90% VaRs of the individual investments greater or smaller than the 90% 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.)