Forward Arbitrage solution seems incorrect?

[ebb]

A commodity forward contract for delivery in four months is written with a forward price of $38. The underlying asset's spot price is $40. The continuously compounded interest rate is 5 percent. In present value terms, how much is the potential arbitrage profit assuming there are no .transaction or storage costs and the commodity pays no dividends?

V (forward conrract) = arbitrage profit = $40 - ($38*e^[-0.05x(4/12l] = $2.63

This solution seems wrong.

Shouldn't it be 40*e^(0.05*4/12) - 38 = 2.68?

 

[David Harper CFA FRM]

Hi bunnyblaster,

This isn't our question, right? Because I don't see the arbitrage profit given the assumptions. By the answer, it looks like the question means that $38 is the delivery price (K) such that it is solving for the present value (f) of the futures contract; i don't see how that is an arbitrage profit since no futures price (F0) is given.

But, please notice that your answer is consistent with the answer given, only yours is the future value of the same: if we multiply both of your terms by exp(-5%*4/12), which discounts to current, we get the answer given.

Thanks, David

 

[ebb]

That makes sense. It seems like a silly oversight by me. Thank you!