Question

Gold currently sells at $1,000 per troy ounces. An off market forward contract, signed several months ago expires in 1 year with a forward price of $1,095. The annual risk-free rate is 2.5%.

a) What is the fair value of the contract.

b) If the contract is traded at it's fair value, indicate if the payment is made by the long to the short, or vice-versa.

Answer 1

a)

Theoretical Futures Price = Spot Price*e^[risk free rate*t]

Where e = constant (2.71828), t = years to expiry

Applying the above formula,

Spot Price = 1000, Risk Free Rate = 0.025, t = 1

Therefore, Fair Value = Theoretical Futures Price = 1000*e^0.025 = 1000*1.0253(from table) = $1025.3

b)

As the Traded Value i.e. Fair Value is LOWER than Forward Price, person holding long(buyer) is in loss and person holdig short(seller) is in profit. Therefore, Payment will be made BY LONG TO SHORT