FRM Part 1 - Valuing forward contracts

FRM
#1

Hi everyone,

I did learn about valuing a forward contract in CFA L1. However, when crossing these topic in FRM, i found the weird method to calculate the value of the contract (the below content is from GARP materials):
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“We can value the contract by comparing it with a similar contract that could be entered today.
Define K as the forward price at the time the contract was originally entered, F as the current forward price for the contract, and T as the contract’s current time to maturity.

The two different forward contracts we consider are:

  1. A forward contract to buy the asset for price K at time T (the contract we are interested in valuing), and

  2. A forward contract to buy the asset for price F at time T (a contract that could be entered today).

The only difference between these two contracts lies in the price paid at time T. The value of the second contract minus the value of the first contract is the present value of F - K (which can be positive or negative.) However, the second contract is worth zero because it is entered at the current forward price. Therefore, the first contract is worth the present value of F - K.”

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Excuse me?? How can those statements be equivalent? If the value of the second contract = 0, then the first contract should be the PV of K - F (in stead of F - K), and it seems not like the value we know so far.

Could anyone explain this?
Many thanks for your support :sob:

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#2

In the original contract, you have the long position, so you’re short K.

The formula’s correct.

Value = PV\left(what\ you\ will\ receive\right) - PV\left(what\ you\ will\ pay\right)
#3

Isn’t it the same for both the contracts? In the second one, I’m also in the long position and short F? So why do I receive F?
Sorry but still don’t get what you mean :sob:

#4

Nope.

You’ll take the short position in the second contract.

Say that 60 days ago you entered into a 180-day contract to buy oil at USD 81.46/BBL. Today, the spot price on oil is USD 67.32/BBL, and the 120-day forward price is USD 68.21/BBL. To get the value of your existing contract, you’re essentially asking, “If I were to close out my existing contract today, how much will I receive/pay?” How do you close out a long position? By taking a corresponding short position. So, you’ll take the short position in the current (120-day) contract, to receive USD 68.21/BBL. The value is:

Value = PV\left(what\ you\ will\ receive\right) - PV\left(what\ you\ will\ pay\right)
= PV\left(USD\ 68.21\right) - PV\left(USD\ 81.46\right)
= PV\left(USD\ 68.21 - USD\ 81.46\right)

The value of your contract is negative because the price of oil fell: you’ve lost money.

You don’t close out a position to buy oil by buying more oil.

#5

Yeah I got it. Thank you.

I didnt know that I close the position in that case, I just thought I was in long position for both contracts.

Thank you so muchh :smiling_face_with_three_hearts::smiling_face_with_three_hearts:

#6

My pleasure.