Question

Consider a two-year futures contract on gold. We assume no income and that it costs $2.00 per ounce per year to store gold. The spot price is $1600 per ounce and the risk-free rate is 4% per annum for all maturities. This corresponds to r=0.04, S_0=1600, T=2, and U=2e^(-0.04×2)=1.85. What arbitrage opportunity is possible if the futures price for a contract is $1600 or $1,770?

The equilibrium price is given by F_0^*=(S_0+U)e^rT=(1600+1.85)e^(0.04×2)=$1,683.98
Case 1: F₀=$1600Today: short spot & long forward
At maturity (2-year later):
Case 2: F₀=$1,770>F₀*=$1,683.98
Today: long spot & short forward
At maturity:

Answer 1

The arbitrage opportunity is to short the spot and long the forward when the futures price is $1600. The arbitrage opportunity is to long the spot and short the forward when the futures price is $1770.

Step-by-step explanation:

To determine the arbitrage opportunity, we compare the futures price to the equilibrium price. If the futures price is lower than the equilibrium price, there is an opportunity for arbitrage. In this case, the equilibrium price is $1683.98. Case 1 is when the futures price is $1600, which is lower than the equilibrium price. Therefore, the arbitrage opportunity is to short the spot and long the forward. On the other hand, in Case 2, where the futures price is $1770, which is higher than the equilibrium price, the arbitrage opportunity is to long the spot and short the forward contract.