Question

The price of gold is currently $1,400 per ounce. The forward price for delivery in one year is$1,500. An arbitrageur can borrow money at 4% per annum. What should the arbitrageur do? Assume that the cost of storing gold is zero and that gold provides no income.

Answer 1

Answer:

The arbitrageur should borrow money at 4% per annum since it is cheaper than paying the forward price for delivery

Explanation:

Current price of gold=$1,400 per ounce

Forward price=$1,500

The arbitrageur can either pay the forward price or borrow $1400 and pay the interest of 4% in a year. Consider option 1 paying the forward price of 1500

Option 1

Since there are no additional costs, the total cost for buying the gold=forward price=$1,500

Option 2

If the arbitrageur borrows the 1400 to pay for the gold now, then pay the interest in 1 year;

The total cost=Amount borrowed+interest accrued in 1 year

Total cost=1400+(4%×1400)

1400+((4/100)×1400)

1400+56=$1456

Since there are no additional costs, option 2=$1456

If we compare option 1 to option 2, we notice that option 2 is slightly cheaper than option 1 by $44

(Option 1-Option 2)=(1500-1456)=$44

The arbitrageur should borrow money at 4% per annum since it is cheaper than paying the forward price for delivery