Futures, Options, Risk Management:
1. On April 6, 2013 a fund manager holds a $28 million stock portfolio that matches the S&P 500 stock index. The manager expects stock prices to be lower by July 2013 when the portfolio will be sold. Assume on April 6, 2013, the S&P 500 spot price is 1400 and the July 2013 futures price is 1425.
a. Design a strategy to hedge the risk of a declining stock market. Indicate whether you would be long or short futures and how many contracts.
b. Now assume that at the delivery date in July 2013 the spot and July futures price is at 1300. Determine the gain or loss in both the spot and futures market and show the effective selling price of the portfolio.
2. Suppose you are a dealer in sugar. It is September 26, and you hold 112,000 pounds of sugar worth $0.0479 per pound. The price of a futures contract expiring in January is $0.0550 per pound. Each contract is for 112,000 pounds.
a) Determine the original basis.
b) Now assume a spot sugar price that is lower than the current spot price of $0.0479. Calculate the profit from a hedge if it is held to expiration and the basis converges to zero.
c) Show how the profit is explained by movements in the basis alone.
d) Now assume the hedge is closed on December 10, when the spot price is $0.0574 and the January futures price is $0.0590. Did the basis strengthen or weaken? Recalculate the profit from the hedge.
3. On July 1, a portfolio manager holds $1 million face value of Treasury bonds, which are the 11.25s maturing in about 29 years. The price is 107 14/32. The bond will need to be sold on August 30. The manager is concerned about rising interest rates and believes a hedge would be appropriate. The September T-bond futures price is 77 15/32. The price sensitivity hedge ratio suggests that the firm
should use 13 contracts.
a. What transaction should the firm make on July 1?
b. On August 30, the bond was selling for 101 12/32 and the futures price was 73 5/32. Determine the outcome of the hedge. Is there an overall gain or loss and how much?
4. You plan to purchase 500 8% 15-year Treasury bonds each with a face value of $1,000 in March 2015. You expect interest rates to fall by March 2015. There are Treasury bond futures contracts on 8% 15-year Treasury bonds with a face value of $100,000. These contracts are priced at $85,600. The contract expires on April 30, 2015. Assume the current spot price on these bonds is $85,000. Also assume that at the end of March 2015 the spot price on the bonds will be $86,100 and the futures price is $86,800
a. Devise a strategy that protects you against falling interest rates. Include whether you are long or short and number of contracts.
b. Does this strategy have basis risk? Why?
c. What did you end up paying for the bonds? Did you have a basis gain or loss? What is the dollar amount of the basis gain or loss?