Reading 47 - Forward Contracts - practice problem 4D.

CFA Level II Derivatives
#1

A security is currently worth $225. An investor plans to purchase this asset in 1 year and is concerned that the price may have risen by then. To hedge this risk, the investor enters into a forward contract to buy the asset in one year. Assume the risk-free rate is 4.75%. D) Supppose that at expiration, the price of the asset is $190. Calculate the value of the forward contract at expiration. Aslo indicate the overall gain or loss to the investor on the whole transaction. Solution:

Value at expiration = 190 - [235.69 / [(1.0475)^0] = - $45.69

Long position suffers a loss of 45.69.

this is where I have trouble…CFA book says GAIN on asset = $35 bc (225 - 190 = 35). Net Loss = - $10.69

I understand how to get to the - $45.69. I am confused as to why this is a gain on the asset and a net loss of $10.69.

My interpretation: 1 year ago the asset was priced at $225. Today (expiration) it’s priced at $190. How is this a gain on the asset? If you’re the long position, then at expiration you’re accepting delivery of an asset that costs $190 but you’re paying the forward contract price of $235.69 to the short position. Seems like a loss to me. How does the $45.69 come into play?

#2

Hi ahungerford,

my perspective about this problem :

because the investor LONG on Forward so it must be SHORT on underlying asset.

So (underlying price at t=0) : 225

St (underlying price at expiration) : 190

price declines so gain for SHORT position = 35

hope this help.

#3

Here’s how they’re looking at it: the investor had two options:

  1. Buy the asset at $225.
  2. Enter into the forward contract and buy the asset one year later at $235.69.

Either way, when the price drops to $190 one year later, he will have lost $35 on the price change. By entering into the forward contract, he lost an additional $10.69.

#4

Thanks. That is so much more clear. I understand their thinking, but why do they call it a gain on the asset?

#5

My pleasure.

#6

Sorry, one quick response. Why do they call it a gain on the asset? Is that a mistake?

#7

I frame it this way, the “gain” on the asset of £35 comes from the fact that the investor chose to buy the future rather than the asset. If he had chosen to buy the asset at the beginning he would have paid £225, however saying as he bought the future instead, at the end of the period he can now buy the asset for £190, i.e. £35 cheaper…so the “gain” is from not buying the asset at the more expensive price.

Its slightly confusing, but I think its just a terminology thing.

#8

I agree: it’s a bizarre way of phrasing it.

Of course, it’s a bizarre problem altogether. Once you take the long position in the futures contract, you have, in effect, already bought the asset: you’ve merely delayed paying for it for a year. (Yes, I know that if there are cash flows you don’t get those, but you also don’t pay for them.) So saying that you would have paid $225 but now you’re paying only $190 simply isn’t true: you’re paying the same $225, plus interest. But you’re correct: they seem to be saying that you’ve saved $35.

Bizarre.

#9

You’re right, he has paid the $225 already when the future was purchased, I was just trying to frame the “gain” element in a way that made intuitive sense, when in fact an overall loss has been made.

Hes made a loss through buying a future at 225 for an asset that is now worth 190, but if you separate that from the fact that he didn’t buy the asset at the higher price, and can now buy it at the cheaper price he has a conceptual “gain” on that side of the trade.