Currency Translation Risk - Example of p. 116 Schweser Book 4

CFA Level III Derivatives
#1

Hi,

So I have spent the last 30 minutes trying to figure this out and I feel that I may be missing something simple.

Schweser Book 4, p.116 - Currency Translation Risk Example

When we calculate the return on the futures contract, we use:

Rfut = 1MM euros x (-Ft +Fo) = 12.8M USD

I simply don’t understand why we are not using the spot rate, rather than Ft. I am assuming here that she sells a 90-day futures contract to protect herself against a variation in the spot rate at day 90 (when she will have to sell the 1MM euros). Why do we care about Ft which I am assuming is for another 90 days (so 180 days since the beginning).

Thanks for your help.

#2

Usually F0 = S0 … Spot = Futures price at initiation. And nothing is paid up front.

When the contract expires - that is Ft - F0 is the gain or loss on the contract.

If you sold the contract up front -> -NP ( Ft - F0) = Return on the contract…

#3

You say that:

“When the contract expires - that is Ft - F0 is the gain or loss on the contract.”

But shouldn’t it be St - F0 at expiration of the contract? I am forced to sell at F0 at expiration vs. selling at spot had I not decided to sell the futures contract.

Why are we even considering Ft which refers to a future date after our contract expires (90 days from start)?

Comparing Ft to F0 makes sense to me only if we have not reached the contract’s maturity (say 30 days from the start).

Then Ft would be the forward exchange rate in 60 days which allows to compare apples with apples.

#4

you will usually find St=Ft and S0=F0.

Since you are taking F0 -> Ft-F0

If you took S0 as the starting point St-S0 would make sense.

#5

and if you thought about it, even St is at the future date.

#6

In that specific example, St is not equal to Ft because Ft is the futures exchange rate at time t (an exchange rate at some time after t). To me it still makes sense to compare Fo (the futures exchange rate that was determined at time = 0 but applicable after 90 days) to the spot rate at that day = 90. Why would I compare F0 which applied to day = 90 to Ft which is determined on day = 90 but which would apply later on (I would assume 180 days).

Had she sold the contract with a maturity of 1 year (for example), then the example makes sense to me because Ft would be determined at day = 90 but applicable in 270 days and that rate could be compared to F0.

I am still confused and I think that this example would have been much clearer if they had included the maturities of the contract she sold (I assumed it was 90 days but it may not be) and the maturity of Ft.

#7

THis statement is erroneous.

F0 = Futures Price on Day 90 determined at Day 0.

FT = Futures Price on Day 90 determined when the Hedge is lifted (at Day 90).

#8

You mean FT is the Futures exchange rate on day 90 which is applicable ON day 90? (on not applicable on a future date like on day 180?)

Please say yes so I can move on hahaha. But how can you have a Futures exchange rate applicable on the same date? Wouldn’t just that be the spot price?

#9

definition as in the text

Ft is the futures exchange rate: domestic currency value of one unit of foreign currency quoted at time t (e.g., $1.95/£)

#10

Still not clear to me.

I am talking about the Schweser example, not the CFAI example which is one week after initiation (and not at maturity).

The Schweser example seems to compare F0 to Ft at 90 days, and I still don`t understand what Ft is (when was it established and when is the rate applicable - today or in 90 days).

I’ll just pray that it doesn’t appear on the exam.

Edit: I just checked the CFAI example and that is clear to me. Initiation is in September and maturity is in December.

A few weeks later (so before maturity), the return on the futures contract is evaluated by comparing F0 and FT and BOTH maturities coincide (in December).

In the Schweser example, it seems that maturity has already been reached so I don`t know what Ft is referring to (hence my initial question: why F0 is not compared to the spot rate since we are already at maturity).

You can`t establish a Futures contract on day 90 for delivery on day 90 can you? It would just be the spot rate.

#11

they have not defined the varibles. nor have they indicated what they are supposed to mean. The CFAI text does clearly state what they are.

I believe though I could be wrong - that on Day 90 there is a possible end of day price for contracts of that day. and it might just be the spot rate.

#12

Thanks for your help.

I will follow the rationale of the CFAI curriculum (maturity has not been reached).

#13

Futures contract delivers on a set date . Your statement “Why do we care about Ft which I am assuming is for another 90 days (so 180 days since the beginning).” is incorrect.

Ft converges to St as the time converges to expiration , so the window of time for Ft continuously shrinks , down to zero on expiration day

#14

And that’s the issue with the Schweser example…

From that example, you can only assume that you are at expiration (on day 90) when the calculations take place. Ft is NOT equal to St on that specific day; which prompted my initial question.

#15

You cannot mix spot ( which is a deliverable such as physical oil or a financial bond ) with the futures instrument which is a derivative.

You cannot use Spot and pretend it is a future price

If you want to mark to market a futures contract , your P&L gain per contract is Ft-F0 , not St-S0

#16

can tell what example in the CFAI text corresponds to this example in Schweser?

#17

in CFAI p.271 Volume 3.

In my head, this issue is now pretty clear (and even if I’m wrong it shall be one question on the exam - got to move on!).

Scenario 1: you have not reached maturity of the futures contract (this is the example in the CFAI curriculum)

You should indeed compare Fo to Ft (which is established today and to be applied at maturity). Ft is a function of St. The rates compared need to be on the same day, which is why St in this case is not valid.

Somebody mentioned MTM and this implies you are talking about this scenario.

Scenario 2: you have reached maturity of the futures contract

You should compare Fo to St (the spot rate at maturity). If my futures contract expires today, I need to compare Fo to the spot rate I can get on the market today. I don’t think that you can set a futures exchange rate on the same date the rate should be applied (it would be the spot rate anyways).

What remains less clear to me is whether the Schweser example details Scenario 1 or Scenario 2. It sounds like it’s scenario 2, but seems to only make sense if it’s Scenario 1 since they are comparing Fo to Ft.