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BAFI 430

Mid Term Exam

Practice Exam 2

1. [10] A company has a $20 million portfolio with a beta of 1.2.  It would like to use futures contracts on the S&P 500 to hedge its risk.  The index is currently standing at 1080, and each contract is for delivery of $250 times the index.  What is the hedge that minimizes risk?  What should the company do if it wants to reduce the beta of the portfolio to 0.6?

2. A one-year long forward contract on a non-dividend-paying stock is entered into when the stock price is $40 and the risk-free rate of interest is 10% per annum with continuous compounding.

[5] a) What are the forward price and the initial value of the forward contract?

[5] b) Six months later, the price of the stock is $45 and the risk-free interest rate is still 10%.  What are the forward price and the value of the forward contract?

3. [10] The standard deviation of monthly changes in the spot price of live cattle is 1.2 (in cents per pound).  The standard deviation of monthly changes in the futures price of live cattle for the closest contract is 1.4.  The correlation between the futures price changes and the spot price changes is 0.7.  It is now October 15.  A beef producer is committed to purchasing 200,000 pounds of live cattle on November 15.  The producer wants to use the December live-cattle futures contracts to hedge its risk.  Each contract is for the delivery of 40,000 pounds of cattle.  What strategy should the beef producer follow?

4.[5] a) What is a lower bound for the price of a four-month call option on a non-dividend-paying stock when the stock price is $28, the strike price is $25, and the risk-free interest rate is 8% per annum?

[5] b) What is a lower bound for the price of a one-month European put option on a non-dividend-paying stock when the stock price is $12, the strike price is $15, and the risk-free interest rate is 6% per annum?

[5] c) The price of a European call that expires in six months and has a strike price of $30 is $2.  The underlying stock price is $29, and a dividend of $0.50 is expected in two months and again in five months.  The term structure is flat, with all risk-free interest rates being 10%.  What is the price of a European put option that expires in six months and has a strike price of $30?

5. [5] Three put options on a stock have the same expiration date and strike prices of $55, $60, and $65.  The market prices are $3, $5, and $8, respectively.  An investor buys 1 55 and 1 65 and sells 2 of the 60s.  Construct a table showing the profit from the strategy.  For what range of stock prices would the butterfly spread lead to a loss?

6. A firm decides to issue the following contract, to raise funds.  The contract promises to pay 1,000 times the price of oil in 5 years time, or $40,000, whichever is higher.  However, a cap of $60,000 is placed on the payout.

[5] a) Plot the payout of the contract offered as a function of the price of oil in 5 years.

[5] b) Show how the value of this contract can be represented by positions in oil and in options.  Clearly define the terms of each of these options.