Purchasing Power Parity

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theCFAway

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Hi-
i’m confused with question 19 on page 118 on volume 3 of the cfai reading. I would think that if the inflation index is 150 for CHF and 140 for the Fap, we would take 3 fips/1CHF*140/150=2.8 fips/CHF.
I don’t remember doing it the way the solution has it on page 129 or maybe i’ve forgotten since level 2.
 
i had the same error of course , because I tend to simplify things too much. CPI index in each country is measured differently and they’re hardly comparable directly .
The basket on which the CPI is based is uniquely different in each country . So you cannot compare them directly .
When you compare CPI you must measure it in terms of change from a base rate in the sme country and then you can compare it to a change in the same terms in another country. To say that Swiss goods are 150/140 times more expensive than Faps goods is hardly accurate .Both currencies now purchase less of different base baaskets of ggod. One can only claim that the CPI shows that Swiss goods have become 1.5 times more expensive in SFranc than 10 years ago , while Faps goods have become 1.4 times more expensive in Faps terms than 10 years ago.
So now we are comparing a 50% change in Swiss CPI to a 40% change in Faps CPI and the PPP has to adjust rates 10% . So rates have to change from 3 Fips per SF to 2.7 Fips per SF. ( 10% )..
If you think about it currency is only a medium of exchange , so it can be priced only in relative terms . There is no universal amd unchanging base ( e.g. gold ) on which currency is based .
So to do it like you suggest , would imply that SF is a golden standard and never fluctuates in value . The truth is SF only buys different baskets of goods at different points in time and so does Fips. We cannot compare a swiss basket to a Faps basket but we can compare how much more ( or less ) is contained in each basket relative to 10 years ago .
 
On the first go, answer seems to be straight forward . .i.e. 3*1.40/1.5 = 2.8
But then as Jana explained above that inflation index cann not be directly compared unless you know the base of computation of CPIs and basket of goods.
Nevertheless, I think they have approximated the answer by taking the inflation differentials of 10% between the countries over the last 10 years & derived that since swiss inflation is higher by 10% so FIP should appreciate staright away by 10% i.e. 3*0.9 = 2.7.
But I think that if you go PPP formula and derive answer as 2.8 then compare the current spot rate to discern whether currency is over/under valued, it should also be taken as an appropriate asnwer. What you guys say?
 
approximate answer not good enough in this case. CFA may be inducing you to take the wrong approach to penalize you.
If it is an AM q , they may ask you to Show your calculations . In this case the wrong reasoning would not work
. If it is a PM q , there may very well be both 2.7 and 2.8 and you would choose the wrong one without too much effort
 
Using the inflation differential looks like an approximation to me.
 
Janakisri
Ya the ques asks if PPP prevails than what would be the exchange rate
Ok so in text they said, difference between the inflations between the two country will decide the appreciation or depreciation of respective countries.
But if you simply go by the relative PPP formula, you would get the answer as above (i.e. 2.8). Won’t you?
I agree though that sticking to text per se, 2.7 is right answer if PPP prevails in the long run.
 
Inflation is measured as change in CPI within the same country.
Don’t treat the CPI as something you can compare between countries . It is measured as a change within a country between two periods and it is a percent change.
Just for example , let’s say that the problem states that CPI is 150 in 1990 and 165 in 2012 for Switzerland. It is 700 in 1990 and 756 in 2012 for Fap .
Let’s say the exchange rate is 4.0 Fips per SF in 1990
How would you calculate the PPP fair exchange rate in 2012?
 
Isn’t it
4.0*[1+(765-700)/700]/[1+(165-150)/150]=3.97
or approximately
4.0*[1+(765-700)/700-(165-150)/150)]=3.97?
 
By the way, the calculation on 129 is:
(150-100)/100-1.0 = 50%
(140-100)/100-1.0 = 40%
This is incorrect since it ends up with -50% and -60%.-:)
 
Jana,
Ok, as per ur example if we use the formula ans would be
1990 : 4 Fips/ SF
then in 2012
4 * [1+((756-700)/700)] / [1+(165-150) / 150] or
4* (1.08)/(1.10) = 3.927
or as per inflation differential
Swiss had a 10% & FAP had 8%, so FAP should appreciate by 2% which means that 4*0.98 ~ 3.92
approximately both answer r same. So, do you have any point which is missed here?
 
rahuls , in the first example ( 2.8 or 2.7 ) , using your technique of this last post:
3.0* [1+(140-100)/100] / [1+(150-150)/100] =2.8 – Geometric calc
3.0*[ 0.04-0.05 ] = 2.7 – Arithmetic calc
It seems to me the difference is only because of arithmetic vs geometric calculation.
Probably CFA may accept your answer if you wrote of it as such ( i.e. arithmetic versus geometric ) as they do in the IPS sections?
My only concern is if this was a PM question and both answers were in the choice list , what do you do?
 
I looked over my level 2 notes for this and have the answer - the PPP formula is called the Fisher equation, and there’s a precise one, and an approximate one.
Solving with the precise one:
(S1,x/y) / (S0,x/y) = [(1+ Ix)/(1+Iy)]
so let x be fips and y be CHF. The spot rate at time 0, S0,x/y = 3, which is the starting point of the question. Inflation in x, fips, is 40%. Inflation in y, CHF, is 50%. Then you solve for S1, as follows:
(S1) / 3 = [(1.4)/(1.5)], and S1 = 2.8
Solving with the approximate one:
[(S1,x/y) - (S0,x/y)]/ (S0,x/y) = Ix - Iy
[(S1) - 3] / 3 = 0.4 - 0.5
(S1) - 3 = (-.1)*.3
S1 = 2.7
So there you go, if you answered this with 2.8, you are also correct, and I’m sure that on the exam, if they wanted you to give the approximate instead of the precise for some odd reason, they’d say so.
 
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