8) The current spot price of gold is $1,020 per ounce. The risk free rate is 3%

Question

8) The current spot price of gold is $1,020 per ounce. The risk free rate is 3% per year. A gold futures contract has a contract size of 100 oz. Assume that anyone can borrow at the risk-free rate. (10 pts) a. What should the futures price be for a contract with a time period of exactly one year? b. Say that you observe that the contract for gold with a time period of exactly one year is actually selling for $1,060. Describe a strategy that you could use to make a profit that would exceed the risk free rate, and what profit you could earn.

Explanation / Answer

Suppose that F0 is the one-year future price of gold. If F0 is relatively high, the trader can borrow $1020 at 3%, buy one ounce of gold and enter into a future price to sell gold in one year for F0. The profit made in one year is

=F0 - $1020*1.03 = F0 - $1050.6

This is profitable if F0 >1050.6 If F0 is relatively high, the trader can sell one ounce of gold for $1060, invest the proceeds at 10%, and enter into a future price to buy the gold back for F0. The profit (relative to the position the trader would be in if the gold were held in the portfolio during the year) is

=$1060*1.01 - F0 =$1070.6 - F0

This shows that there is $20.6 earn profit if the future price is between $1070.6 and $1050.6 per ounce.

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