Homework Assignment 1
Instructions
This assignment is due to be turned in at the start of class on Monday February 6. You can work on this assignment by yourself or in a team of two. If you choose to work in a team of two, you should turn in only one assignment per team (with both member’s student IDs on the assignment).The assignment consists of two parts. Part A contains discussion questions. These are NOT to be turned in, they are intended to solidify your understanding of the theoretical concepts that we have discussed. I suggest writing down your answers and comparing them with the solutions that I will upload once the assignments have been turned in. Part B contains assignment problems that must be turned in. Remember that these assignments are graded on a √- ,√, √+ system as detailed in the syllabus. You are free to turn in printouts or a clear, legible, handwritten assignment. Where I have drawn problems form the text-book, I have indicated the corresponding problem number in the text.
Part A: Discussion questions (not to be turned in).
1. Problem 1.2. Explain carefully the difference between hedging, speculation, and arbitrage. 2. Problem 1.3. What is the difference between entering into a long forward contract when the forward price is $50 and taking a long position in a call option with a strike price of $50?
3. Problem 1.4.Explain carefully the difference between selling a call option and buying a put option.
4. Problem 1.18. A US company expects to have to pay 1 million Canadian dollars in 6 months. Explainhow the exchange rate risk can be hedged using (a) a forward contract and (b) an option.
5. Why do futures contracts have margins?
6. Problem 2.1. Distinguish between the terms open interest and trading volume. 7. Explain what is meant by basis risk when futures contracts are used for hedging.
8. Problem 3.3.Explain what is meant by a perfect hedge. Does a perfect hedge always lead to a better outcome than an imperfect hedge? Explain your answer.
9. Problem 3.13. “If the minimum-variance hedge ratio is calculated as 1.0, the hedge must be perfect.\
Part B: Homework problems (to be turned in)
1. A trader enters into a one-year short forward contract to sell an asset for $60 when the spot price is $58. The spot price in one year proves to be $63. What is the trader’s gain or loss?
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 also buys a put on the S&P 500 index with a strike price of $2100 and a time to maturity of one 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 delivery is $1400. Suppose an investor can borrow at 3% per year (simple interest). How can the investor 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 in March is $45.5/barrel, and the prices of March call and put options with prices $46/barrel are $2.5 and $3 respectively. Assume that each forward and option contract is for 1000 barrels
a. Should the refinery buy or sell forwards to hedge their exposure? How many contracts 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 in December. The payoff diagram should take into account the premium (but ignore the time value of money)
5. Suppose that you enter into a short futures contract to sell July silver for $17.20 per ounce. The size of the contract is 5,000 ounces. The initial margin is $4,000, and the maintenance margin is $3,000. What change in the futures price will lead to a margin call? 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 futures contracts on the S&P 500 to hedge its risk. The index futures 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?
7. The standard deviation of monthly changes in the spot price of live cattle is (in cents per pound) 1.2. The standard deviation of monthly changes in the forward price of live cattle for the closest contract is 1.4. The correlation between the forward 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 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?
HW 1
