Base currency Vs foreign currency

[jyothi1965]

David

Always had this confusion on interpreting the BC and FC.

The current exchange rate between Japanese yen and US dollar is 134 yen/dollar. The one-year
interest rate in USA is 1.95 percent and the one-year interest rate in Japan is 0.65 percent.
According to interest rate parity the one-year forward yen/dollar exchange rate should be
CLOSEST to:

A. 130.59.
B. 131.73.
C. 132.29.
D. 133.50.

The question is simple; the answer being Spot * (1+ domestic)/(1+foreign)

The question is how do you interpret which is domestic and which is foreign? Also is there is a rough cut way of double checking with respect to interest rates. (if domestic interest rates < foreign interest rates) then ..... and vice versa

Grateful for a quick reply... as I am not able to get a fix on this

Thanks as always

J

PS: while you have pointed out that Interest rate parity is not included in the LOs, the sample FRM questions 2007 has a similar question as above, and in any case these kind of questions is an appln of the forward price determination.

 

[David Harper CFA FRM]

Jyothi,

I am not myself quick with these problems, rote formulas confuse me; e.g., the question could have instead used a dollar/yen rate. I can only keep them straight by using old fashioned ratio canceling.

If it helps, I think about these based on Hull Ch 5: to visualize that two paths must be equivalent (no arbitrage). I myself don't think about domestic/foreign labels (I am influenced by CFA CIPM/GIPS here, where they avoid this semantic confusion by referring to local versus base currency returns - foreign/domestic are relative terms).

So, you can either invest at the spot [local] and exchange in 1 (n) years, or you can exchange today and grow at the foreign [base] rate. Either way, at period's end, your (expected) foreign units must be the same. So I always start with this formula:

"Yens in future, if i exchange end of period" = "Yens in future, if i exchange today:"
(1 + dollar rate)(Yen/dollar forward) = (Yen/dollar spot)(1 + Yen rate)

So, of course:
Yen/dollar forward = (Yen/dollar spot)(1 + Yen rate)/(1 + dollar rate)

If i had time, i'd check it with "134 yen grows at 0.65%. Okay, that's 134.87. On the other hand, $1 dollar grows to 1.195 and converts at [$133.29, my answer] = $134.87. Okay, I am good, both paths give me same yen at the end."

Of course you know the following Jyothi, but for others: the key "skill" is just "ratio canceling". That is, $1 dollar x [yen/dollar] = yen. Or if you have a future yen, then yen x dollar/yen = dollar. If a new student were confused by all of this, I would ask them to practice this ratio canceling without numbers.

I hadn't thought about the double-check (I prefer the above). I suppose you could look at it and say "my US rate is higher, so the no arbitrage means I will be forward converting fewer than 134 yen"

BTW, per a previous thread, Hull implements IRP with continuous compounding, so here that looks like (continuous compounding, so elegant!)

(spot)exp[yen rate]/exp[dollar rate] = (spot)exp[yen - US] = 134[exp(0.65%-1.95%)].

PS: Agreed, the IRP is my list, that i sent to GARP back in April, of twenty or so "rogue items" that are not assigned readings but seem to be implied by the sample questions (e.g., GARCH to project volatility is like IRR, on 2007 but unassigned). IRP was on the curriculum last year/2 years ago before but fell off.

 

[jyothi1965]

David Thanks as ever for your prompt and detailed replies.

My generic way of doing this is (given the numerous ways Prof Voldemort ("You Know Who"!!!) can confuse us):

The no arbitrage can be stated as:

1. Borrow in currency A and convert into currency B at spot

2. Invest in currency B

3. Sell the principal and Int (maturing in currency B) back into A

Basically the market will adjust the forward rate such that there is no arbitrage interest in 1 and 2.

The logic is that one will always borrow in the lower interest rate and invest in the higher interest rate to earn the arbitrage profit.

So one way of generalizing your above eqn is Forward = spot (1+lower Int rate)/(1+higher int rate) in case of yearly rates or in case of CC rates forward = Spot *exp (lower Int rate - higher Int rate)

This I think works!!!

We need to have short cuts to these FX questions. This is the easier part. What happens when there are cross currency pairs.... calculations are even more voldemortish!!!

Jyothi

 

[kgolf20]

I was having a related confusion with this question:

The 1 year USD interest rate is 3 % and the 1 year CAD interest rate is 4.5%. The current USD/CAD spot exchange rate is 1.5. Calculate the 1 year forward. (assume annual comp.)

A. 1.5225
B. 1.5218
C. 1.5207
D. 1.5199

I would think that the answer would be F = 1.5 * (1.03) / (1.045) = 1.48...

but the answer given is actually B, which is obtained through F = 1.5 * (1.045) / (1.03)

Am i misinterpreting the phrase "current USD/CAD spot exchange rate is 1.5" by assuming it means that there are 1.5 USD for every 1 CAD ?

Thanks

 

[David Harper CFA FRM]

Hi kgolf20,

I get the same answer as you.

But the sanity check eliminates all doubt:

Start with a 1.0 investment in CAD:
1 CAD becomes $1.045 CAD (1 * 1.045) in one year

Compare to the "round-trip" no-arbitrage equivalent:
1.5 USD (i.e., 1 CAD converted at spot 1.5 USD/CAD = 1.5 USD) becomes $1.545 USD in one year.

Now if the forward is 1.5218 USD/CAD then:
1.545 USD / (1.5218 USD/CAD) = $1.0152 USD in one year. Which is not equal to the $1.045, so this is not the forward rate, it creates arbitrage opportunity.

But if forward is 1.048, then
1.545 USD / (1.048 USD/CAD) = $1.045 in one year. Which is the required result to avoid arbitrage. So, this is indeed the forward price.

Re: am i misinterpreting the phrase “current USD/CAD spot exchange rate is 1.5 by assuming it means that there are 1.5 USD for every 1 CAD ? You are correct.

David