Forward and future contracts
1. A bank offers a corporate client a choice between borrowing cash at 11% per annum continuously compounded and borrowing gold at 2% per annum (compounded annually). (If gold is borrowed, interest and principal must be repaid in gold. Thus 100 ounces borrowed today would require 102 ounces to be repaid in 1 year.) The continuously compounded risk-free interest rate is 9,25% per annum and storage costs are 0,5% per annum. Discuss whether the rate of interest on the gold loan is too high or too low in relation to the rate of interest on the cash loan.
2. A trader owns gold as part of a long-term investment portfolio. The trader can buy gold for
$450 per ounce and sell it for $449 per ounce. The trader can borrow funds at 6% per annum and invest at 5,5% per annum (both expressed with annual compounding). For what range of 1-year forward prices of gold does the trader have no arbitrage opportunities? Assume there is no bid-offer spread for forward prices.