Derivative Question

[Andy Ho]

A trader owns gold as part of a long-term investment portfolio. The trader can buy gold for $1250 per ounce and sell gold for $1249 per ounce. The trader can borrow funds at 6% per year and invest funds at 5.5% per year. (Both interest rates are expressed with annual compounding. Do not use continuous compounding). For what range of one-year forward prices of gold does the trader have no arbitrage opportunities? Assume there is no bid–offer spread for forward prices.

 

[S2000magician]

Where did you get this question?

 

[Andy Ho]

From my exercise

 

[onlysimon]

you can borrow money, buy gold, store it safely (this is not included), or lend it to a jewler (this is not included).
so, borrow 1250, buy gold sell forward. 12 months later repay 1325, so if forward is 1325 or above you can make a profit.
or, you can sell your gold for 1249, invest for 12 months, and collect 1317.695 if fwd rate is lower than that then you make a profit.
so simple answer is 1317.695-1325.
a quick google told me convenience yield is normally negative for gold, therefore you need to include the cost of the secure storage for the question to be answered properly.