SAINT MARY’S UNIVERSITY
FINANCE, INFORMATION SYSTEMS, & MANAGEMENT SCIENCE
FINANCE 4468
ASSIGNMENT #1
DUE: Sunday, February 09 by 11:59 PM
TOTAL VALUE 30 MARKS
Please show all your calculations
Problem 1 (16 pts):
It is February 2. The spot price of Gold is $2,835 per ounce and the March Futures price is $2,810 per
ounce. Each futures contract is on 100 Oz. Lana-Jewelry and Talia- Jewelry are two high-end luxury jewelry
houses. Both Lana-Jewelry and Talia -Jewelry know that they will need 1,500 Oz of Gold on March 27
(Both Lana-Jewelry and Talia-Jewelry need to buy gold in March). Talia-Jewelry decided to hedge its
position using March futures contracts. Lana-Jewelry decided not to hedge its position.
A. How can Talia-Jewelry hedge its position? (2pts)
Talia-Jewelry will be buying gold in the future. It can hedge its position by being long corn futures contract.
The number of futures contracts to short is equal to:
𝑄
1,500
=
= 15
𝑄
100
Talia-Jewelry should go long 15 gold futures contracts in order to hedge its position.
𝑙𝑜𝑛𝑔 =
B. At what price will Lana-Jewelry buy the 1,500 Oz of gold if the spot gold price is $2,235 on March
27? (2pts)
Lana-Jewelry will buy its gold directly in the market for $2,235 per Oz:
Lana-Jewelry will buy all its gold for: 1,500 x $2,235 = $3,352,500
C. At what price will Talia-Jewelry buy the 1,500 Oz of gold if the spot gold price is $2,235 on March
27? (2pts)
Talia -Jewelry will buy its gold through the futures contract for $2,810 per Oz:
Talia -Jewelry will buy all its gold for: 15 x 100 x $2,810 = $4,215,000
D. What will Talia-Jewelry realize (gain/loss amount) on the futures contracts if the spot gold price is
$2,235 on March 27 (2pts)
Talia -Jewelry will buy its gold through the futures contract for $2,810 per Oz instead of buying it in the
market for $2,235 per Oz:
Gain (loss) = 15 x 100 x ($2,235 - $2,810) = 15 x 100 x -$575 = -$862,500 (A Loss of $862,500)
E. At what price will Lana-Jewelry buy the 1,500 Oz of gold if the spot gold price is $2,975 on March
27? (2pts)
Lana-Jewelry will buy its gold directly in the market for $2,975 per Oz:
Lana-Jewelry will buy all its gold for: 1,500 x $2,975 = $4,462,500
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F. At what price will Talia-Jewelry buy the 1,500 Oz of gold if the spot gold price is $2,975 on March
27? (2pts)
Talia -Jewelry will buy its gold through the futures contract for $2,810 per Oz:
Talia -Jewelry will buy all its gold for: 15 x 100 x $2,810 = $4,215,000
G. What will Talia-Jewelry realize (gain/loss amount) on the futures contracts if the spot gold price is
$2,975 on March 27 (2pts)
Talia -Jewelry will buy its gold through the futures contract for $2,810 per Oz instead of buying it in the
market for $2,975 per Oz:
Gain (loss) = 15 x 100 x ($2,975 - $2,810) = 15 x 100 x $165 = $247,500 (A Gain of $247,500)
H. Why would Talia-Jewelry hedge its position using futures contracts? (1 pt)
Talia -Jewelry might have decided not to hedge for multiple reasons:
-
They expected gold price to increase….
To eliminate the effect of price fluctuations ….
I. Why would Lana-Jewelry choose not to hedge its position using futures contracts? (1pt)
Talia -Jewelry might have decided not to hedge for multiple reasons:
-
They expected gold price to decrease….
They expected that their investors wanted to be exposed to gold price fluctuations as part
of their investment strategy….
They expected that none of their competitors will hedge, so hedging might make their
cashflows sensitivity to gold prices different from their competitors….
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Problem 2 (4 pts):
Company ABC-Agriculture enters into a short futures contract to sell 15,000 bushels of corn for 494 cents
per bushel in May. The initial margin is $8,000 and the maintenance margin is $5,600.
a) What price change would lead to a margin call? (2pts)
To have a margin call, the company should suffer a loss of $2,400 ($8,000 - $5,600) on the position. Since
this is a short futures position, a loss will occur if there is an increase in the price!
15,000 × [$4.94 − 𝐾] = −$2,400 ⟹ $4.94 − 𝐾 = −
$ ,
,
⟹ 𝐾 = $4.94 + 0.16 = $5.1 =
510 𝑐𝑒𝑛𝑡𝑠
$2,400
15,000
⟹ 𝑡ℎ𝑒 𝑛𝑒𝑤 𝑐𝑜𝑟𝑛 𝑝𝑟𝑖𝑐𝑒 𝑤𝑜𝑢𝑙𝑑 𝑏𝑒: 𝐾 = $5.10 𝑝𝑒𝑟 𝑏𝑢𝑠ℎ𝑒𝑙
⟹ 𝒕𝒉𝒆 𝒑𝒓𝒊𝒄𝒆 𝒔𝒉𝒐𝒖𝒍𝒅 𝒅𝒆𝒄𝒓𝒆𝒂𝒔𝒆 𝒃𝒚 $𝟎. 𝟏𝟔 $0.16 =
b) Under what circumstances could $3,300 be withdrawn from the margin account? (2pts)
To be able to withdraw $3,300 from the account, the company should earn a gain of $3,300 on the current
position. Since this is a short position, a gain will occur if there is a decrease in the price!
15,000 × [$4.94 − 𝐾] = $3,300 ⟹ $4.94 − 𝐾 =
$3,300
⟹ 𝐾 = $4.94 − 0.22 = $4.72
15,000
= 472 𝑐𝑒𝑛𝑡𝑠
$3,300
15,000
⟹ 𝑡ℎ𝑒 𝑛𝑒𝑤 𝑐𝑜𝑟𝑛 𝑝𝑟𝑖𝑐𝑒 𝑤𝑜𝑢𝑙𝑑 𝑏𝑒: 𝐾 = $4.72 𝑝𝑒𝑟 𝑏𝑢𝑠ℎ𝑒𝑙
⟹ 𝒕𝒉𝒆 𝒑𝒓𝒊𝒄𝒆 𝒔𝒉𝒐𝒖𝒍𝒅 𝒅𝒆𝒄𝒓𝒆𝒂𝒔𝒆 𝒃𝒚 $𝟎. 𝟐𝟐 $0.22 =
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Problem 3 (10 pts):
Trader A enters into a forward contract to sell an asset for $930 in one year. Trader B buys a put option to
sell the asset for $930 in one year. The cost of the option is $32.
A. What is the difference between the positions of the two traders? (2pts)
Trader B has the choice but not the obligation to sell the asset for $930 in one year. Trader B will choose
to sell the asset for $930 through the option contract if the market conditions are good and if such transaction
is for her benefit. Trader A has the obligation to sell the asset for $930 in one year independent of market
conditions.
B. If after one year, the asset price is $1000.
i.
What is the profit/loss achieved by trader A? (2pts)
Trader A has the obligation to sell the asset for $930 using the forward contract. She will sell the asset for
$930 through the forward contracts instead of selling it in the market for $1000.
𝐻𝑒𝑟 𝑝𝑟𝑜𝑓𝑖𝑡 (𝑙𝑜𝑠𝑠) 𝑜𝑛 𝑡ℎ𝑒 𝑝𝑜𝑠𝑖𝑡𝑖𝑜𝑛 = $930 − $1,000 = −$70 (loss of $70)
ii.
What is the profit/loss achieved by trader B? (2pts)
Trader B has the choice but not the obligation to sell the asset for $930 using the option contract. She will
sell the asset for $1,000 in the market because it is a higher price. Remember that she has already paid
$32 to purchase the option contract and she did not use the option contract. Consequently, she has only
lost the $32 price of the option she has paid (loss of $32)
C. If after one year, the asset price is $870.
i.
What is the profit/loss achieved by trader A? (2pts)
Trader A has the obligation to sell the asset for $930 using the forward contract. She will sell the asset for
$930 through the forward contracts instead of selling it in the market for $870.
𝐻𝑒𝑟 𝑝𝑟𝑜𝑓𝑖𝑡 (𝑙𝑜𝑠𝑠) 𝑜𝑛 𝑡ℎ𝑒 𝑝𝑜𝑠𝑖𝑡𝑖𝑜𝑛 = $930 − $870 = $60 (gain of $60)
ii.
What is the profit/loss achieved by trader B? (2pts)
Trader B has the choice but not the obligation to sell the asset for $930 using the option contract. She will
sell the asset for $930 through the option contracts instead of selling it in the market for $870. Remember
that she has already paid $5 to purchase the option contract.
𝐻𝑒𝑟 𝑝𝑟𝑜𝑓𝑖𝑡 (𝑙𝑜𝑠𝑠) 𝑜𝑛 𝑡ℎ𝑒 𝑝𝑜𝑠𝑖𝑡𝑖𝑜𝑛 = $930 − $870 − 32 = $28 (gain of $28)
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