1. A trader enters into a one-year short forward contract to sell an asset for $60 when thespot price is $58. The spot price in one year proves to be $63. What is the trader's gain orloss?
a. Show a dollar amount and indicate whether it is a gain or a loss.
b. When is this money actually received or paid?
c. How would your answers change if the trader bought a future instead of a forward?
2. A trader buys a 1 year forward contract on the S&P 500 index at a price of 2100 and alsobuys a put on the S&P 500 index with a strike price of $2100 and a time to maturity ofone year.
a. Draw the payoff diagram for this combined position
b. What does this remind you of?
c. What if the put cost $80. Ignoring the time value of money repeat part (a) above,taking into account the premium ($80)
3. The current spot price of gold is $1280 per ounce. The forward price for 1 year deliveryis $1400. Suppose an investor can borrow at 3% per year (simple interest). How can theinvestor make a riskless profit (assuming there is no cost or benefit to storing gold)
4. A refinery will buy 10,000 barrels of oil in March. The forward price for delivery inMarch is $45.5/barrel, and the prices of March call and put options with prices $46/barrelare $2.5 and $3 respectively. Assume that each forward and option contract is for 1000barrelsa. Should the refinery buy or sell forwards to hedge their exposure? How manycontracts should the firm trade? Draw a payoff diagram showing how the firm's payoff change with the spot price in March for their underlying position, the forward contract, and their net position.
b. Suppose the refinery trades half as many contracts as you assumed in part
(a).Redraw the payoff diagrams and explain the intuition
c. If the refinery hedges using options, should it trade calls or puts? Buy or sell?How many contracts? Draw a payoff diagram showing how the firm's purchase price (with and without hedging) varies with the spot price of oil inDecember. The payoff diagram should take into account the premium (butignore the time value of money)
5. Suppose that you enter into a short futures contract to sell July silver for $17.20 perounce. The size of the contract is 5,000 ounces. The initial margin is $4,000, and themaintenance margin is $3,000. What change in the futures price will lead to a margincall? What happens if you do not meet the margin call?
6. A company has a $20 million portfolio with a beta of 1.2. It would like to use futurescontracts on the S&P 500 to hedge its risk. The index futures is currently standing at1080, and each contract is for delivery of $250 times the index. What is the hedge thatminimizes risk? What should the company do if it wants to reduce the beta of theportfolio to 0.6?
7. The standard deviation of monthly changes in the spot price of live cattle is (in centsper pound) 1.2. The standard deviation of monthly changes in the forward price oflive cattle for the closest contract is 1.4. The correlation between the forward pricechanges and the spot price changes is 0.7. It is now October 15. A beef producer iscommitted to purchasing 200,000 pounds of live cattle on November 15. Theproducer wants to use the December live-cattle forward contracts to hedge its risk. Each contract is for the delivery of 40,000 pounds of cattle. What strategy should the beef producer follow (long or short, how many contracts)?
8. On July 1, an investor holds 50,000 shares of a certain stock. The market price is $30 per share. The investor is interested in hedging against movements in the market over the next month and decides to use the September Mini S&P 500 futures contract. The index is currently 1,500 and one contract is for delivery of $50 times the index. The beta of the stock is 1.3. What strategy should the investor follow? Under what circumstances will it be profitable?