Question

Consider a forward contract on gold. Each contract covers 100 ounces of gold and matures one year from now. Suppose it costs $2 per ounce per year to store gold with the payment being made at the end of the year. Assume that the spot price of gold is $1300 per ounce, the continuously compounded risk-free interest rate is 4% per annum for all maturities.

a) In the absence of arbitrage, find the current forward price. Show your calculations.

b) Assume you immediately sell one contract. What is the value of your position in 3 months’ time if the gold spot price has fallen to $1200 per ounce and interest rates have not changed? Show your calculations.

Answer 1

a)

Theoretical Forward Value at beginning = [Spot Price+PV of Cost of Carry]*Future Value Factor

where,

Spot Price = $1300

PV of Cost of Carry = 200*(PV Factor) = 200*[e^(-0.04)] = 200*[0.9608](from table) = $192.16

Future Value Factor = e^(0.04) = 1.0408 (from table)

Therefore, Theoretical Forward Value (No arbitrage value) = [1300+192.16]*1.0408 = $1553.04

b)

Value of Forward Contract, 3 months from now = Spot Price*e^(Risk Free Rate-Storage Cost)

where,

Spot Price = $1200

PV of Cost of Carry = 200*(PV Factor) = 200*[e^(-0.04)] = 200*[0.9608](from table) = $192.16

Future Value Factor = e^(0.04*9/12) = 1.0305(from table)

Therefore, Value of Contract, 3 months from now = [1200+192.16]*1.0305 = $1434.62