Forward quotes and Int Rates

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vir_vict

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Assuming Direct Quotes (DC/FC)

F/S = (1+ rDC)/(1 + rFC)

If the interest rates in domestic country increases (rFC is constant)

How does int rate parity adjust

A) S decreases
B) F increases
C) S decreases and F increases


Ans:
My feeling is because rDC increased -> More foreigners invest -> DC appreciated -> hence S decreases (DC/FC). Is this right ?
 
B) Higher Interest rates will affect the equation as follows:

S * (1.rDC)/1.rFC) = F

As the equation indicates a higher domestic interest rate, with a fixed spot rate, the effect is a higher future rate, an increase in F.

A higher domestic interest rate will cause the domestic currency to depreciate i.e. DC/FC goes up (or put another way you can buy more DC with one FC). This is because if the future rate didn't change then one can arbitrage. Borrow FC convert into DC @ S and then convert back DC * rDC into FC @ F.
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Here is an example:

rDC = 4%
rFC = 2%
S = 2/1
F = 2/1

Now consider rDC going up to 5% (rDC' = 5%), but F stays unchanged. Here are the results of this mismatch:

Borrow 1000 FC @ 2% convert into 2000 DC and invest @ 5% and buy a future at 2/1.

AT T1 you will have 2100 DC or converted at he futures rate 2/1 you will have 1050 FC and paying off the 1000 FC borrowed with 20 FC interest would result in a risk free profit of 30 FC.
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If F had changed as S * (1.rDC)/1.rFC) = F indicates. I.e. F = 2.058824

then you would only only beable to convert your 2100 DC (2100 / 2.058824) at T1 into 1020. Thus the exchange rate / interest rate equilibrium holds.



Edited 2 time(s). Last edit at Friday, April 7, 2006 at 01:10AM by jamespucyk.
 
Hi

Thanks for the elaborate reply. But I feel some of the issues havent been addressed.

1. Int rate parity doesn't hold for current day in your example problem (F=S when rDC not equal to rFC)
2. DC appreciates if real interest rate in DC goes up. (Int Inv ch.2)

Details:

In your example with given rFC and rDC, interest parity doesn't hold. If you plug in S=2/1 into the interest parity equation, we will get 2.0392DC/FC

So we start from here
rDC = 4%
rFC = 2%
S = 2/1
F = 2.0392/1

Now I change the interest rate rDC = 5%, everything else remaining constant

From International Invst ch. 2, it says DC appreciates when the real interest in DC goes up relative to rFC everthing else constant because foreigners will invest -> more demand for DC. (As in this case, everything else remaining constant, rDC increased to 5% so DC has to appreciate instantaneously)

So if you keep F constant at old value 2.039 recalculate S which turns out to be 1.98DC/FC.

By doing this, your DC has appreciated, interest rate parity holds so no arbitrage.

Please feel free to give justifications if something isnt adding up.

Thanks once again
 
I think the answer would be a change in the forward rate (appreciation). Since the interest differential is approximately equal to the forward differential i.e.

F = S * (1 + D) / (1 + F)

D - Dometic Interest Rate
F - Foreign Interest Rate

Solving the above equation will result in:

(F - S)/S = (D - F)/(1+F)

or (F - S)/S approx (D - F)

Which is interest rate differential is equal to forward differential.
 
Yes and this question is about interest rates and IRP and IRP is explicit,the higher the higher relative interest reate will see a depreciation of that currency.

Real interest rates will cause a demand for DC and jack up the direct exhange rate, but this is not what IRP is saying, plus they are talking not about real rates but about nominal rates. The rates that the IRP are concerned about contain an inflation risk premium and a general country specific risk premium, therefore a higher interest rate according to the IRP is not indicative of a higher absolute return but implies an additional risk premium demanded by investors for various risk factors.

I.e. the interest rates in Canda and the US. US treasuries are at a lower rate than GOC (gov't of Canada) rates, but that is based upon the risk of Canada relative the US. Also there is the concept of the relative cost of money and country risk, all in all investors demand a higher interest rate premium in canada and therefore the discrepancy. However all other things constant a higher real rate in Canada will cause an appreciation of C$, everything else constant, adding other factors like inflation, and other risk premiums you can get a higher interest rate and thus the seeming disconnect between IRP and conventional economic logic
 
With all due respect, I strongly believe that you are all wrong.

If the nominal interest rate in the domestic country increases, the forward rate must decrease. Why? According to covered interest parity, arbitrageurs will borrow in their home country (i.e, the foreign country), invest in government bonds in the domestic country to take advantage of the higher interest rate, and *sell forward* the proceeds so that the position is riskless.

This will cause the forward rate to decline until the arbitrage profits are zero. In equilibrium, the forward rate discount will equal the difference in nominal interest rates between the two countries.
 
Dynamic...the mechanics of what you are talking about are spot on if they were using an indirect quote. Meaning the quote would decrease in terms of dollars (dollar depreciates)

The answer is B) F increases...because this is a direct quote

When Domestic Interest Rate increases then domestic currency depreciates, therefore quote increases in terms of the foreign.
 
Yup the initial question was posed upon an indirect rate, DC/FC, not FC/DC, you would be correct otherwise.
 
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