Question

The current spot price of Copper is $2.7445 per pound. The storage costs are $0.05 per pound per year payable monthly. Physical holding of copper now can yield $0.13 per pound per year which is achievable monthly. The price of a 9-month futures contract of copper is currently listed as 2.7685. Assume that interest rates are 10% per annum and monthly compounded.

a) If the cost-of carry relationship is held under no-arbitrage conditions, what should the 9-month futures price be (4 d.p.)?

b) Is the listed 9-month futures price provide arbitrage opportunity (assume transaction costs are negligible)? Justify.

c) If the listed futures price is correct, what would be the underlying annual yield.

show all steps ,formula ,and calculations

Answer 1

Answer (A) The future pricing of a commodity is done using the below formula,

i.e. F = Se ^ ((r + s - c) x t)

Where:

• F = the future price of the commodity
• S = the spot price of the commodity
• e = the base of natural log
• r = the risk-free interest rate
• s = the storage cost
• c = the convenience yield
• t = time to delivery of the contract, expressed as a fraction of one year

here we have S= $2.7445 per pound

s =  $0.05 per pound per year

c = $0.13 per pound per year

t = 9/12 = 0.75

r =10% p.a

therefore by putting the values in formula we will get F= 2.7445 * e^((10% + 0.05 - 0.13) * 0.75)

F = $2.7859

Answer (B) The current market price of 9 month future contract of copper is $2.7685 and the price according to us is $2.7859 .

Thus our current price in market is trading in discount (contango) thus according to the equation price will reach towards it original value at the time of expiry of contract. Thus we can get an arbitrage opportunity by taking long position in the current market price .