BUS333 Derivative Securities
Workshop 4
Problem 3.16.
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?
The beef producer requires a long position in 200000 06 120 000
lbs of cattle.
120, 000
The beef producer should therefore take a long position in 3
40, 000
December contracts closing out the position on November 15th.
1
,Problem 3.18.
On 1 July, an investor holds 50,000 shares of a certain stock. The market price is AUD 30 per share.
The investor is interested in hedging against movements in the market over the next month and
decides to use the September ASX/SPI 200 futures contract. The index is currently 4,000 and one
contract is for delivery of AUD 25 times the index. The beta of the stock is 1.3. What strategy should
the investor follow? Under what circumstances will it be profitable?
S = 50,000 x $30 = $1.5 million (long)
F = 4000 x $25 = $100,000
A short position in
𝑆 1,500,000
𝑁=𝛽 = 1.3 × = 19.5 = 20
𝐹 100,000
September contracts is required.
It will be profitable if the stock outperforms the market in the sense
that its return is greater than that predicted by the capital asset
pricing model.
2
, Problem 3.19.
Suppose that in Table 3.5 the company decides to use a hedge ratio of 1.5. How does the
decision affect the way the hedge is implemented and the result?
If the company uses a hedge ratio of 1.5 in Table 3.5 it would at each
stage short 150 contracts.
Note that the hedge is rolled.
April 11 - Sell 150 Oct 11 contracts
Sept 11 - Close 150 Oct 11, Sell March 12
Feb 12 - Close 150 March 12, Sell 150 July 12
June 12 - Close 150 July 12, Sell 100,000 bbls oil.
The gain from the futures contracts would be
1.50 1.70 $2.55
per barrel and the company would be $0.85 per barrel better off.
3
Workshop 4
Problem 3.16.
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?
The beef producer requires a long position in 200000 06 120 000
lbs of cattle.
120, 000
The beef producer should therefore take a long position in 3
40, 000
December contracts closing out the position on November 15th.
1
,Problem 3.18.
On 1 July, an investor holds 50,000 shares of a certain stock. The market price is AUD 30 per share.
The investor is interested in hedging against movements in the market over the next month and
decides to use the September ASX/SPI 200 futures contract. The index is currently 4,000 and one
contract is for delivery of AUD 25 times the index. The beta of the stock is 1.3. What strategy should
the investor follow? Under what circumstances will it be profitable?
S = 50,000 x $30 = $1.5 million (long)
F = 4000 x $25 = $100,000
A short position in
𝑆 1,500,000
𝑁=𝛽 = 1.3 × = 19.5 = 20
𝐹 100,000
September contracts is required.
It will be profitable if the stock outperforms the market in the sense
that its return is greater than that predicted by the capital asset
pricing model.
2
, Problem 3.19.
Suppose that in Table 3.5 the company decides to use a hedge ratio of 1.5. How does the
decision affect the way the hedge is implemented and the result?
If the company uses a hedge ratio of 1.5 in Table 3.5 it would at each
stage short 150 contracts.
Note that the hedge is rolled.
April 11 - Sell 150 Oct 11 contracts
Sept 11 - Close 150 Oct 11, Sell March 12
Feb 12 - Close 150 March 12, Sell 150 July 12
June 12 - Close 150 July 12, Sell 100,000 bbls oil.
The gain from the futures contracts would be
1.50 1.70 $2.55
per barrel and the company would be $0.85 per barrel better off.
3
