Question

If the current gold price is $1300 per oz. A 1-yr gold forward is priced at $1345. Suppose one year interest rate is 1.5%. How can you profit from these instruments?

A. There is no arbitrage opportunity

B. Buy 1oz of gold; short the forward contract; borrow 1300 now.

C. Short 1oz of gold; long the forward contract; invest 1300 now.

D. Short the forward contract; buy 1oz of gold 1 year later and deliver the gold

Answer 1

B. Buy 1 oz of gold; short the forward contract; borrow 1300 now

Fair price of forward can be computed as below:

$F = S*(1+r)^t$

where,

F = Forward price

S = Current price of asset

r = risk free rate

t = maturity time

putting the values:

$F = 1300*(1+0.015)^1$

$F = \$1,319.5$

Thus, Fair Forward price of 1 oz gold is $1,319.5 but in the market it selling at $1,345 which means it is over priced in the market.

Arbitrager can make risk free profit by following strategy

Short forward contract as it is over priced in the market at $1,345

Borrow $1,300 at 1.5% pa

Buy gold at $1,300 now at spot market

After a year.

repay the borrowed amount with interest i.e $1,319.5

and sale the gold at forward contract price i.e $1,345

your arbitrage profit would be $1,345 - $1,319.5 = $25.5

Hope this will help, please do comment if you need any further explanation. Your feedback would be highly appreciated.