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Commodity Futures Hedging Guide

The optimal hedge ratio for a three-month commodity futures contract is the coefficient of correlation (0.8) divided by the ratio of the standard deviations of the futures price changes (0.81) to the standard deviations of the spot price changes (0.65). For a minimum variance hedge, the trader should take a long position in the number of futures contracts equal to the ratio of the standard deviations (0.40/0.43) times the amount owned (55,000 units) divided by the contract size (5,000 units). For hedging future copper purchases, the company should buy futures contracts according to the hedge ratio (80%) for each delivery month up to 13 months in

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391 views2 pages

Commodity Futures Hedging Guide

The optimal hedge ratio for a three-month commodity futures contract is the coefficient of correlation (0.8) divided by the ratio of the standard deviations of the futures price changes (0.81) to the standard deviations of the spot price changes (0.65). For a minimum variance hedge, the trader should take a long position in the number of futures contracts equal to the ratio of the standard deviations (0.40/0.43) times the amount owned (55,000 units) divided by the contract size (5,000 units). For hedging future copper purchases, the company should buy futures contracts according to the hedge ratio (80%) for each delivery month up to 13 months in

Uploaded by

keshav
Copyright
© © All Rights Reserved
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Practice Questions

1.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 for a
three-month contract? What does it mean?

2. A trader owns 55,000 units of a particular asset and decides to hedge the value of her position
with futures contracts on another related asset. Each futures contract is on 5,000 units. The spot
price of the asset that is owned is $28 and the standard deviation of the change in this price over
the life of the hedge is estimated to be $0.43. The futures price of the related asset is $27 and the
standard deviation of the change in this over the life of the hedge is $0.40. The coefficient of
correlation between the spot price change and futures price change is 0.95.

(a) What is the minimum variance hedge ratio?


(b) Should the hedger take a long or short futures position?
(c) What is the optimal number of futures contracts when adjustments for daily settlement are
not considered?
(d) How can daily settlement be taken into account?

3. The spot price of silver is $25 per ounce. The storage costs are $0.24 per ounce per year
payable quarterly in advance. Assuming that interest rates are 5% per annum for all maturities
and continuous compounding, calculate the forward price of silver for delivery in nine
months.

4. 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 futures price of live cattle for
the closest contract is 1.4. The correlation between the futures 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
futures contracts to hedge its risk. Each contract is for the delivery of 40,000 pounds of cattle.
What strategy should the beef producer follow?

5. Sixty futures contracts are used to hedge an exposure to the price of silver. Each futures
contract is on 5,000 ounces of silver. At the time the hedge is closed out, the basis is $0.20per
ounce. What is the effect of the basis on the hedger’s financial position if (a) the trader is
hedging the purchase of silver and (b) the trader is hedging the sale of silver?
6. It is now October 2017. A company anticipates that it will purchase 1 million pounds of
copper in each of February 2018, August 2018, February 2019, and August 2019. The
company has decided to use the futures contracts traded by the CME Group to hedge its risk.
One contract is for the delivery of 25,000 pounds of copper. The initial margin is $2,000 per
contract and the maintenance margin is $1,500 per contract. The company’s policy is to hedge
80% of its exposure. Contracts with maturities up to 13 months into the future are considered
to have sufficient liquidity to meet the company’s needs. Devise a hedging strategy for the
company. (Do not make the adjustment for daily settlement.)

Assume the market prices (in cents per pound) today and at future dates are as follows. What
is the impact of the strategy you propose on the price the company pays for copper? What is
the initial margin requirement in October 2017? Is the company subject to any margin calls?
Date Oct 2017 Feb 2018 Aug Feb 2019 Aug 2019
2018
Spot Price 372.00 369.00 365.00 377.00 388.00
Mar 2018 Futures 372.30 369.10
Price
Sep 2018 Futures 372.80 370.20 364.80
Price
Mar 2019 Futures 370.70 364.30 376.70
Price
Sep 2019 Futures 364.20 376.50 388.20
Price

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