Finance 100 Problem Set Futures

Transcription

1 Finance 100 Problem Set Futures 1. A wheat farmer expects to harvest 60,000 bushels of wheat in September. In order to pay for the seed and equipment, the farmer had to draw $150,000 from his savings account on January 1 this year. He earns 4.8% p. a. on the savings account, and interest on the account accrues monthly in arrears. The farmer is worried about fluctuations in the wheat price and wishes to hedge the position. Wheat futures are currently quoted as: September December cent/bu cent/bu Prices are in cents per bushel, and wheat futures contracts are per 5,000 bushels. 1.a Construct the perfect hedge for the farmer, using futures contracts. How many contracts should he buy or sell? 1.b Demonstrate that your hedge is indeed perfect by comparing different developments of the wheat price between January and September to 325, 335 and 345 cents per bushel of wheat. 1.c What is the break even exchange rate the farmer must obtain, if the farmer could work for a salary instead of growing wheat from January to September 1

2 for $3,500 per month (paid in arrears) and lease the land for a total of $5,000 during this period, payable in September. In this case he would leave the capital in his savings account. 1.d Suppose the farmer could actually store the wheat at a cost of $1,200 per month from September to January. Assume all the wheat is harvested at the end of September, and storage costs are paid at the end of the months October to December. Should the farmer still sell the wheat forward in September, or store it until December and sell it forward in December? 1.e Suppose the farmer could store up to 100,000 bushels of wheat at the same price as we used in 4), i. e. the marginal costs of storage are zero. Is there an opportunity for making money in this case? 1.f Harvests are usually not that predictable. The total amount harvested depends on the weather. Unfortunately, whenever the weather is good for one farmer, it is typically good for many and the price of wheat is accordingly lower. Suppose harvests are of only two types: they are either good or bad with the following outcomes: Good Harvest Bad Harvest Quantity 70,000 bu 50,000 bu Price (spot, Sept.) 320 cents/bu 360 cents/bu Is the hedge you constructed under 1. still optimal? As personal financial advisor to the farmer, what other strategy might you recommend? 2. Suppose you observe that the S&P 500 index, S, is at a level of and the S&P 500 futures contract expiring in exactly three months is at a level of If the riskless rate of interest is 6.5% p.a., what is the implied dividend yield on the S&P 500 stock portfolio if no costless arbitrage opportunities exist in the marketplace? 2

3 3. Now suppose that the dividend yield on the S&P 500 stock portfolio is actually 4% p.a. How can you earn a costless arbitrage profit by transacting in the securities in question 3? Assume that any transactions can be executed at the prices reported above. 4. A portfolio manager holds a portfolio that mimics the S&P 500 index. The S&P 500 index started the year at 800 and is currently at The December S&P 500 futures price is currently The manger s fund was valued at $10 million at the beginning of the year. Since then the fund has already generated a handsome return for the year, the manger wishes to lock in its current value. That is, the manger is willing to give up potential increases in order to ensure that the value of the fund does not decrease. How can you lock in the value of the fund implied by the December futures contract (each S&P500 Futures contract trades for 250 times the indext)? Show that the hedge does work by considering the value of your net hedged position when the S&P 500 index finishes the year at and 1, Your company makes a sale of machines to a Swiss customer. The sale price is 8 million Swiss Francs payable at the end of the year. The forward rate for the December payment is 0.8 SFR/$. You are worried that the Swiss Franc will move between now and the end of the year. How can you hedge the exchange rate risk? Show what will happen if the Swiss Franc turns out to be 1.6 or 0.4 in December. 6. Your accountants have done a cash flow analysis and have determined that you will have a cash shortage of $2 million in the second quarter of next year. To finance this cash shortage, the firm will borrow at the LIBOR. You are concerned that interest rates will rise between now and the end of the year. The March Eurodollar futures contract is currently trading at 92. How does the firm protect itself from increases in the interest rate implied by this futures contract? Show that the firm s net hedged position will result in it receiving the same total amount of funds whether LIBOR turns out to be 10% p.a. or 6% p.a. in March. 3

4 7. The S&P 500 Stock Index is at and the S&P futures contract on the index is at The current futures contract expires in exactly one month. The current S&P 500 dividend yield is 2.0% annually. The 3 month Treasury bill rate is 5.0% annually (this rate can be used in the natural exponential). 7.a Is the futures price over, under or correctly priced in relation to the cash index? 7.b Support your answer in part (a) by demonstrating a set of transactions that result in either a zero or a positive profit. Be sure to illustrate the timing of each cash flow. Assume that you can lend or borrow at 5.0%. Assume that you receive all proceeds of any short sales of stock. 7.c In words, briefly explain the logic underlying the transactions listed in part (b). 7.d Immediately after you initiate the arbitrage (i.e., the time 0 transactions) a large blue chip company unexpectedly announces that they are cutting their dividend payment by 50%. As a result, market expectations of the S&P 500 s yield drop to 1.9% annually. How will this unexpected change affect the value of your terminal positions one-month from now? Is this good news or bad news? 8. Sofas Express, Inc. (SEI) is a Malaysian firm with a U.S. customer base. Production facilities are located in Kuala Lumpur. The firm is going to raise 5 million dollars of capital in the U.S. in two months in order to develop distribution facilities. SEI s primary investors are Japanese and SEI is concerned with consistent profitability in yen terms. SEI does not want exposure to yen/dollar exchange rate volatility over the two months preceding issuance of US dollar denominated debt. 4

5 The current Japanese yen futures price is ($/yen) and two months remain to expiration. The notional amount underlying the futures contract is 12,500,000yen. Round to the nearest number of whole contracts to set up your hedge. Construct a hedge to stabilize the value of the capital raised in Yen terms. 9. Consider the following price range for LIBOR futures, given in the Wall Street Journal for February : Year Month Futures Price 1997 March June September December March June September December March June September December Suppose a company has a somewhat cyclical cash flow pattern. Cash outflows in September 1997 are expected to be $12 million. Cash inflows are due in December 1997 and are estimated to be $16 million. The company pays an annual dividend in March Assume all cash flows are always at the end of the month. The company can borrow at a floating interest rate of LIBOR+150 basis points, and can lend money at LIBOR-100 basis points. 9.a What are the implied LIBOR rates for the above futures? Plot these rates against the maturity of the futures contract. How are these rates related to the term structure of interest rates? 5

6 9.b In order to meet the cash outflow in September the company needs to borrow against its cash inflow in December. If the company wishes to lock in the currently available interest rate, then how many Eurodollar futures contracts do they have to buy or sell? 9.c Demonstrate that this hedge is perfect by showing that the net result from investing in September and trading in Eurodollar futures is independent of movements in the interest rate. Consider movements of 1% in LIBOR in either direction. Which borrowing rate have they managed to lock in? 9.d The company also wishes to invest the remaining $3million between December and March. What is the perfect hedge for this investment? 9.e Demonstrate that the hedge is perfect using the same procedure as in 9.c Which lending rate did they manage to lock in? 6