2. (15 points) Cost-of-Carry Relationship (Futures/Spot Parity). Currently the cash or spot price for
gold is $1,170.00 per ounce and the annualized riskless cost-of-carry is .05. Assume that you have
$1,170,000 in savings earning 5%, that you have 1,000 oz. of gold in your safety deposit box, and that you
can engage in either a cash-and-carry or reverse cash-and-carry arbitrage strategy without incurring
transaction costs.
You notice the following prices are available for gold futures traded on the COMEX: One of the
contracts provides an arbitrage opportunity. Show how you will take advantage of the mispriced futures
contract.
GOLD (CMX)-100 troy oz. $ per troy oz.
Delivery date
Price
5 months
$1,194.00
8 months
$1,198.60
The theoretical cost-of-carry 5-month futures price should be $
Show work for credit
1,190.09682
Future price $_{5month}$ = Spot price \times (1+r_f^{period})^{5/12}
= 1,170 \times (1 + .05 \times (5/12))
= 1,190.09682
The theoretical cost-of-carry 8-month futures price should be $
Show work for credit
1,195.8602
= 1,170 \times (1 + .05 \times (8/12))^{8/12}
\approx 1,195.8602
Today I will (check one and fill out the blanks)
\checkmark Buy 1,000 oz. of gold for $1,170,000 and simultaneously short 10 8-month futures
contract.
OR
Sell 1,000 oz. of gold for $1,170,000 which I will invest at the 5% riskless rate and
simultaneously go long 10 -month futures contract.
In 8 months I will (check one and fill out the blanks)
\checkmark Deliver the gold to satisfy the short contract. I will earn an annualized return of
Show work here
Show work for credit
OR
Take delivery of the 1,000 oz. of gold and pay a net amount of $
Since my $1,170,000 will have grown to $
I will make total dollar profits of $
Show work below for credit
