Reading 54: Currency forward contract question remember, question, contract

Mechanic

The formula for the price of a currency forward contract is an easy one to remember, but it helps me to fully conceptualize it in order to memorize it easier.
Anyway, the formula is displayed in the CFAI material as:
[Spot/(1+Rf)^T] x (1 + R)^T
It goes on to say: “recall that in pricing equity forwards, we always reduced the stock price by the PV of the dividends and then compounded the resulting value to the expiration date. We can view currencies in the same way [i.e., just think of the interest as dividends].
If that were the case, wouldn’t the equation look like:
[Spot - (1/(1+Rf)^T] x (1+ R)^T
I guess I just can’t figure out why we’re dividing the Spot Rate by (1+Rf)^T ?
Thanks for the help!

Penny-wenny

if S and F are specified as DC/FC
S0 * [(1+rDC) / (1+rFC) ] ^ T = F
Now a little into the future you have a Price St (Spot).
Value of the Future Contract :
ST/(1+RFC)^T-t - F/(1+RDC)^T-t
is just a simple justaposition of the above - and an easy way to remember.
Logic behind: When you buy a currency forward - you sold your domestic currency and bought the foreign currency. So you receive the foreign interest rate rfc and gave them your domestic interest rate.
so to PV those cash flow streams you divide St by (1+rFC) and F by (1+rDC).

kamara5

cpk123 wrote:
Value of the Future Contract :
ST/(1+RFC)^T-t - F/(1+RDC)^T-t
Let’s not get into value yet, I’m still trying to figure out price…
cpk123 wrote:
if S and F are specified as DC/FC
S0 * [(1+rDC) / (1+rFC) ] ^ T = F
Essentially that’s just the equation I wrote, but rearranged….and I’m still confused. I know this is a very easy formula to memorize, and in fact I already have it memorized, but if I don’t have a solid understanding of HOW the formula works, then I know I’m going to miss questions on the exam.
So, I’m still trying to figure out why the CFAI material is seemingly contradicting itself. If we are reducing the spot price by the amount of interest earned, why isn’t it:  {S0 - [1/(1+rFC)^T]} x (1+rDC)^T  ?? In the equation that they actually give for the price, the spot price doesn’t seem to be reduced by the value of the interest at all, even though that is what they say is going on…

hariRaj

did you stop after seeing the formula in my type up?
Logic behind: When you buy a currency forward - you sold your domestic currency and bought the foreign currency. So you receive the foreign interest rate rfc and gave them your domestic interest rate.

kkn006

not the time or place to decipher that. learn it and move on.
in my mind currency and interest are two separate beasts, and each has their own complexity.
you learnt in Level I and also in Econ how to get the forward from spot and vice versa. So just move on.
[And from the look of things - the above must be a Schweeser annotation]

ramzes

Dreary wrote:
What he is saying cpk is why when you calculate the forwrd on an asset, you do it like this:
F = S0 * (1+Rf)^T - Dividen(1+Rf)^T, but when you do it with a currency, you do it like:
F = S0$/Y  * (1+Rf$)^T / (1+RfY)^T, assuming $ yen.
The book says you think of interest same way as dividend, which is not easily seen from above.  They are computed in a different way.
I think they are approximately the same, you can think of it like this:
F = S0$/Y  * (1+Rf$)^T - S0 * RfY
So that the futures price of the currency is the spot rate rising at the DC interest rate minus the interest on the foreign currency…i.e., same as you would do with a forward on an asset.

OmarAdnan

cpk123 wrote:
did you stop after seeing the formula in my type up?
Logic behind: When you buy a currency forward - you sold your domestic currency and bought the foreign currency. So you receive the foreign interest rate rfc and gave them your domestic interest rate.
No, I read it, and the logic makes sense for value:
Discount the spot price at the rFC, and the forward price at the rDC. And you subtract them because the rDC is what you’re giving up. I get it. I’m just having trouble seeing the connection to price…

bkballa

Dreary wrote:
What he is saying cpk..
Yes, exactly.

BC_MBA_student

Dreary wrote:
I think they are approximately the same, you can think of it like this:
F = S0$/Y  * (1+Rf$)^T - S0 * RfY
So that the futures price of the currency is the spot rate rising at the DC interest rate minus the interest on the foreign currency…i.e., same as you would do with a forward on an asset.
But again, in that case, why would we be using S0 twice in the calculation? Aren’t we earning Rf$ on the $ amount and RfY on the yen amount? And isn’t the yen amount 1 (i.e., the spot rate is x units of $ per 1 unit of Yen)? So shouldn’t the amount discounted by the RfY be 1, not S0?
It is very possible that there is something here that I’m completely missing, but again, I’m just trying to get a solid foundation so that my mind will work flexibly on exam questions, especially for the more advanced derivatives concepts.

giorgio10

padniaki wrote:
Dreary wrote:
I think they are approximately the same, you can think of it like this:
F = S0$/Y  * (1+Rf$)^T - S0 * RfY
So that the futures price of the currency is the spot rate rising at the DC interest rate minus the interest on the foreign currency…i.e., same as you would do with a forward on an asset.
But again, in that case, why would we be using S0 twice in the calculation? Aren’t we earning Rf$ on the $ amount and RfY on the yen amount? And isn’t the yen amount 1 (i.e., the spot rate is x units of $ per 1 unit of Yen)? So shouldn’t the amount discounted by the RfY be 1, not S0?
It is very possible that there is something here that I’m completely missing, but again, I’m just trying to get a solid foundation so that my mind will work flexibly on exam questions, especially for the more advanced derivatives concepts.
S0 is not appearing twice, the second one is the interest part only, just like a dividend yield.  That’s the closest I can make it to forwards on an equity…but it’s not perfect.