INVESTMENTS/Ivkovich Homework 4 Due: 4/26/2016
Instructions: Each student will turn in one solution to the homework. Recall that late submission will not be allowed. Homework must be submitted at the beginning of class on the due date. Make sure to document your work: do not merely give a solution without adequate explanations and intermediate steps necessary to obtain the results. You will be graded not only on the basis of the accuracy of your results, but also on the clarity and completeness of your written solution. The total number of points for this homework is 120 points.
1) (40 points) You are an active portfolio manager. You received the following information regarding the expected market excess returns, market variance, and the risk-free rate:
Market: E(RM) = 0.12, s2M=0.16; rf = 0.02
You also received information regarding four candidate securities for your active portfolio A:
Security ai ßi sie
1 0.04 1.10 0.10
2 0.03 0.90 0.40
3 -0.01 1.20 0.32
4 0.02 0.80 0.25

Your tasks are:
1a) Generate active portfolio A (report weights wA1, wA2, wA3, and wA4)
1b) Generate key parameters of portfolio A (report aA , ßA, s2eA; RA, s2A, cov(RA, RM))
1c) Use the information regarding M, rf, and A to produce the parameters of the improved portfolio P (report wM*, wA*, E(rP), and sP)
1d) Produce a simple graph that outlines the locations of M, A, and P in the E(r)-s plane.
INVESTMENTS/Ivkovich Homework 4 Due: 4/26/2016
2) (20 points) Solve 20.27 from BKM (p. 703).
3) (20 points; 10 points for each problem) Solve 21.11 and 21.12 from BKM (p. 747).
4) (20 points; 10 points for each part) You are holding a $5 million portfolio with a beta of 0.80.
4a) The S&P500 futures beta is 1 and the current level of the index is 1,000. The futures contract is valued at $250 times the index value at the expiration of the contract. Assuming you can hedge with fractional shares of the index, what futures position would you take to hedge yourself as completely as possible?
4b) Suppose you think the market is going to dive, and you want to have the same size portfolio but with a beta of –0.2. What futures position would you take to change your overall market exposure to a beta of –0.2, rather than hedging yourself? You can use fractional shares of the futures.
5) (20 points) You are an importer with a contract to buy 40,000,000 bars of famous Utopian TastesGreat chocolate for a fixed price of 20 Utopian Liras (UTL) each. The current futures price is $0.16/UTL, and the contract specifies delivery of 62,500 UTLs per contact. Assume you can take fractional futures positions if you need to. The exchange rate when you buy the goods will be either $0.18 (with probability 2/3) or $0.15 (with probability 1/3). What position would you take to hedge yourself? Long or short, and how many contracts? Show your resulting total costs (including the futures position) when the exchange rate is $0.18 and when it is $0.15.