Value of a Forward Contract - Example

Could somebody pls help me to understand the value of the short position of the following example:

Basically, the spot price of wheat is $330 per ton. The forward contract is for $315 and expires in 5 month. The risk free rate is 4%.

Value of the long position: 330 - 315*e^-0.04*5/12 = $20.2605

The logic behind this (if I understand it correctly) is that the person having the long position gets interest for 5 months for 315 and the difference of 330-315. This makes partially sense to me. Why can I assume that the price of wheat will still be 330 in 5 months?

However, what I don't understand at all is why the short position is just the negative number of the long position (-$20.2605). The short position does not have to pay the interest for the long position but could rather gain interest for 330. So the short position should exhibit a negative amount of less than $15, or?

Thanks in advance!

2 Comments
 

Doesn't seem to me you understand correctly, tbh. Why don't you look at bionic turtle or hull's book for this kind of stuff?

> Why can I assume that the price of wheat will still be 330 in 5 months? You do not assume that, you short 5mo forward at 335.546, guaranted pay-off 335.54-315=20.55 in 5 months, PV of 20.21.

> However, what I don't understand at all is why the short position is just the negative number of the long position Forwards are a zero-sum game.

 

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