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Parities Made Easy (Connecting IRP and International Assets Pricing)
I believe many exam taker were or have been confused with the relationships between the interet rate parities and how they are related to the Int'l Asset Pricing topic in Portfolio management. I hope the summary below will help.
First of all, ALL THE EXCHANGE RATE BELOW ARE DENOTED IN THE BASE OF FC, i.e DC per FC. If you get the notation screwed up, none of the following will work.
Second, the magic starts with the rearrangement of maths formulas.
The Precise measure formulas are:
For Covered IRP (Foward rate, Spot rate and Nominal Interest Rate)
F/So = (1 + rDC )/( 1 + rFC )
For uncovered IRP (Expected spot exchange rate S1, Spot rate So and Nominal Interest Rate), you REPLACE F with E(S1)
E(S1)/So = (1 + rDC )/( 1 + rFC )
International Fisher:
(1+ Inflation DC)/(1+ Inflation FC) = (1 + rDC )/( 1 + rFC )
Please note, for the three formulas above, the Right Hand Side (RHS) are exactly the same. All with Domestic Interest Rate in the numerator, and the Foreign Interest Rate in the denominator. And please recall that ALL EXCHANGE RATE DENOTED HERE ARE BASED IN FOREIGN CORRENCY. DC/FC. This will help you remember the formulas.
And now, let's look at the linear approximation. There's nothing mysterious about the linear approximation.
If you minus 1 at both sides of the equations, you will get:
F/So - 1 = (1 + rDC )/( 1 + rFC ) - 1
==> (F-So)/So = [(1 + rDC )-( 1 + rFC )]/( 1 + rFC )
==> (F-So)/So = (rDC - rFC )/( 1 + rFC )
and if you omit the value of rFC, that is to make rFC = 0, you get your linear approximation
(F-So)/So ~= rDC - rFC
For uncovered IPR, you replace F with E(S1);
[E(S1)-So]/So ~= rDC - rFC
For Internationaol Fisher, you do the same, minus 1 at both sides of the equations, you get:
(1+ Inflation DC)-(1+ Inflation FC)/(1+ Inflation FC) = (1 + rDC )-( 1 + rFC )/( 1 + rFC )
Inflation DC- Inflation FC ~= rDC - rFC
you make both the denominators be 1
For Questions asking you to calculate domestic return, you use the linear approximation equations to solve for rDC (domestic return)
There are three forms:
[E(S1)-So]/So ~= rDC - rFC ===> rDC =rFC + [E(S1)-So]/So
Inflation DC- Inflation FC ~= rDC - rFC ===> rDC =rFC + Inf DC- InfFC?
(F-So)/So ~= rDC - rFC ===> rDC =rFC + [F-So]/So
For FCRP, you simply rearrange the linear approximation form of the uncovered IRP, use the LHS - RHS.
[E(S1)-So]/So ~= rDC - rFC
FCRP = [E(S1)-So]/So - (rDC - rFC); and if (F-So)/So ~= rDC - rFC holds, you replace (rDC - rFC) with (F-So)/So, which gives you the other form of FCRP
FCRP = (E(S1) - F)/So
AND, let me reiterate: ALL EXCHANGE RATES MUST BE EXPRESSED IN DC/FC FORMAT TO MAKE THE ABOVE EQUATIONS WORK.
Edited 1 time(s). Last edit at Saturday, May 29, 2010 at 07:13AM by watleeds. |
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发表于 2011-7-13 15:24
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