You are examining the gold market on February 1 and notice a potential discrepancy between spot...

You are examining the gold market on February 1 and notice a potential discrepancy between spot and futures prices. The spot price is $1,325 per ounce and the May futures price is $1,310 per ounce. Delivery on the May futures contract begins on May 1. The three-month LIBOR rate is 2.75% (continuously compounding, expressed as annual rate). Is there an arbitrage opportunity? What are the cash flows generated by the arbitrage strategy?

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Expert Solution

Cash flows today:

Short sell an ounce of gold today which leaves you with a positive cash flow of $1,325. Invest this $1,325 at the three month LIBOR of 2.75%.
At the same time, enter into the future contract to buy an ounce of gold at a price of $1,310 three months from now.

The value of $1,325 invested can be calculated using the future value formula, given continuous compounding, which is:

Where

FV is the future value
PV is the present value
e is constant (2.718)
r is the periodic interest rate
T is the number of periods

So, $1,325 invested at a 2.75% interest rate become

Cash flow three months from now:

Cash inflow of $1,361.94 (calculated above). You use $1,310 out this money to buy an ounce of gold as per the future contract and use that to cover your short position.
So, net you pocket $51.94 per ounce ($1,361.94- $1,310).

jeff jeffy answered 1 year ago

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