Moose Hairies

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Solutions Ch 2
2.26 One orange juice futures contract is on 15,000 pounds of frozen concentrate that in September 2009 a company sells a March 2011 orange juice futures contract 120 cents per pound. In December 2009, the futures price is 140 cents; in December 2010 it is 110 cents and in February 2011 it is closed out at 125 cents. The company has a December year end. What is the company’s profit or loss on the contract? F=140P&L = -20*15000

F=110P&L=+30*15000
F=125P&L=-15*15000
Total P&L =-5*15000=75,000
2.27 A company enters into a short futures contract to sell 5000 bushels of wheat for 450 cents per bushel. The initial margin is $3000 and the maintenance margin is $2000. What price change would lead to a margin call? Under what circumstances could $1500 be withdrawn from the margin account? A drop in the margin account of more than $1000 will cause a margin call. The margin account will drop if the price increases (since this is a short position) by more than $1000/5000=$0.20 or 20 cents. 1500 could be withdrawn if the price drops by $1500/5000=$0.30 or 30 cents. 2.28 Suppose that there are no storage costs for crude oil and the interest rate for both borrowing and lending is 5% per annum. How could you make money on January 8, 2007 by trading June 2007 and December 2007 contracts on Crude oil?

Settle June 2007Settle December 2007
January 8 60.01-0.1=59.91 62.94-0.28=62.66
January 9 60.0162.94

Right now: Long June contract & Short September Contract In June: receive oil, borrow 59.91 at 5%, pay 59.91, store the oil In September: deliver oil and receive 62.66, return loan of 59.91*e^(5%*(6/12))=61.42. 2.25 Explain what is meant by open interest. Why does the open interest usually decline in the month preceding the deliver month? On a particular day, there are 2000 particular futures contracts. Of the 2000 traders on the long side of the market, 1400 closing out position and 600 were entering into new positions. Of the 2000 traders on the short side of the market, 1200 were closing out their positions and 800 were entering in new positions. What is the impact of the day’s trading on the open interest? Open interest measures how many open contracts are in the market. Open interest declines when we are very close to expiration as traders close out their positions. Open interest declined by 600. Here is why:

Long Short Impact on Open Interest
Volume 20002000
Closed positions1400 1200
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New positions 600 800
Contracts closed on both sides 1200 1200 -1200 Contracts changed hands 200 200 0 New contracts initiated on
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both sides 600 600 +600 Total: -1200+600= - 600 -------------------------------------------------

Solutions chapter 3
3.6 Suppose that the standard deviation of quarterly changes in the prices of a commodity is 0.65, the standard deviation of quarterly changes in a futures price on the commodity is 0.81 and the coefficient of correlation between the two changes is 0.8. What is the optimal hedge ratio if the correlation coefficient between the two changes is 0.8. What is the optimal hedge ratio for a three month contract? What does it mean? Hedge ratio = 0.81*0.65/0.8 = 0.642.

This means that the size of the futures position should be 64.2% of the size of the company’s exposure in a month hedge. Hedge ratio = 1.2 * $ 20,000,000/ $1080*250 = 88.89
In order to hedge the company should short 89 futures contracts. This would reduce beta to zero. If instead the company wanted to reduce the beta to 0.6, it should short (1.2-0.6)*20,000,000/1080*250 = 44 contracts 3.24 It is July 16. A company has a...
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