Answer: Trader A makes a profit of
S
T
Ӎ
1,000 and Trader B makes a profit of
max(
S
T
Ӎ
1,000, 0) – 100 where
S
T
is the spot price of gold in one year. Trader A does
better if
S
T
is above $900 as indicated in Figure S1.3.
Figure1.3
:
Profit to Trader A and Trader B in Problem 1.24
2.
Assume that the spot price for gold is $1,200 per ounce and the gold futures
contract for one year delivery is trading at $1,270. The risk-free interest rate is 5% per
year. Can you arbitrage? How?
Answer: Theoretical futures price F = 1,200*e
(0.05*1)
= $1,261.53
Since the actual futures price in the market is $1,270 > $1,261.53, it is overpriced so you
can arbitrage
Today:
(1) Borrow $120,000 at 5% for one year to buy 100 ounces of gold at $1,200
(2) Sell a futures contract on gold at $1,270 per ounce (one year delivery)
In one year:
(1) Make the delivery and collect $127,000
(2) Repay the loan (principle plus interest) $126,153 = 120,000*e
(0.05*1)
(3) Take risk-free profit = $847

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