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!

evolsteevol

Guys, I need some help on this topic too, on reading 54 Example 5:
Problem:
The Spot rate for British Pounds is $1.76. The U.S. risk free rate is 5.1%, and the U.K risk-free rate is 6.2%. both are componded annually, one year forward contracts are currently quoted at a rate of $1.75.
Question:
Identify a strategy with which a trade can earn a profit at no risk by engaging in a forward contract, regardless of her view of the pound’s likely movements. Cafully describ the transactions the trader would make . Show the rate of return that would be earned from this transaction. Assume the trader’s domestic currency is US dollars.
Answer:
foward rate= $1.76/1.062*1.051=$1.7418
With the forward contract selling at $1.75, it is slighly overpriced. Thus, the trader should be able to buy the currency and sell a foward contract to earna return in excess of the risk-free rate at no risk. the specific transactions are as follows:
1. take $1.76/1.062=$1.6573. Use it to buy 1/1.062= 0.9416 pounds
2. sell a fowrad contract to deliver 1 pound in one year at the price of &1.75
3. hold the position fo one year, collecting interest at the U.K. risk free rate of 6.2%. The 0.9416 pound will grow to 0.9416*1.062=1 pound
4. at expiration, deliver the pound and receive $1.75. This is a return of 1.75/1.6573 - 1=0.0559
my confusion:
1. what does $1.76/1.062 represent? I understand foward rate= $1.76/1.062*1.051=$1.7418, but what does $1.76/1.062 represent?
2. “Use it to buy 1/1.062= 0.9416 pounds”, what does this represent? use 1 pound devide by rate in UK risk free rate? what does this really mean?
CAN SOME ONE HELP ME PLZZZ?

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.

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.

bkballa

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

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…

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.

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]

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.

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…