Question

The spot of gold is currently $1,970 per ounce. The forward price (long or short) for delivery in one year is $1,980. An arbitrageur can borrow or invest money at 4% (semi-annual compounding rate). What should the arbitrageur do? Assume that the cost of storing gold is zero and that gold can be borrowed for a cost based on the spot price of 1% semi-annual, payable in cash when the gold is returned.

Answer 1

Theoretical Forward Price of Gold = Spot Price*[(1+Semi Annual Rate)^2] = 1970*[(1+0.02)^2] = $2049.588

Actual Forward Price is $1980. Therefore, Forward is Undervalued.

Therefore, Buy in Forward Contract and Sell Spot

Steps for Arbitrage:

Now,

1) Borrow Gold @ Spot and Sell it at Spot. Therefore, Inflow of $1970

2) Enter into Forward to Buy Gold after 1 year @ $1980

3) Invest the Inflow of $1970. Therefore, Outflow of $1970

Net Cash Flow = 1970-1970 = 0

After 1 year,

4) Realize Investments with Interest. Therefore, Inflow of 1970*[(1+0.02)^2] = $2049.588

5) Buy Gold under Forward. Therefore, Outflow of $1980

6) Repay Gold with Interest. Therefore, Outflow of 1970*[(1+0.01)^2]-1970 = 2009.597-1970 = $39.597

Arbitrage Gain = Net Cash Flow = 2049.588-1980-39.597 = $29.991