1) 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, σ2M=0.16; rf = 0.02?You also received information regarding four candidate securities for your active portfolio A:

Your tasks are:

1A) Generate active portfolio A (report weights wA1, wA2, wA3, and wA4)

1B) Generate key parameters of portfolio A (report αA , βA, σ2εA; RA, σ2A, 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 σP)

1D) Produce a simple graph that outlines the locations of M, A, and P in the E(r)-σ plane.

2) You write a call option with X = 50 and buy a call with X = 60. The options are on the same stock and have the same expiration date. One of the calls sells for $3; the other sells for $9.

a. Draw the payoff graph for this strategy at the option expiration date.

b. Draw the profit graph for this strategy.

c. What is the break-even point for this strategy? Is the investor bullish or bearish on the stock?

3) Use the Black-Scholes formula to find the value of a call option on the following stock:

Time to expiration          6 months

Standard deviation        50% per year

Exercise price                $50

Stock price                      $50

Interest rate                    3%

4) You are holding a $5 million portfolio with a beta of 0.80.

4 A) 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?

4 B) 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) 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.