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Hi all,
So I have an issue with calculating PPP in that I don’t agree with (or maybe don’t understand) the formula given by the CFAI.
Take the example given in the text (page 99 Book 3). In this case the Canadian dollar is trading at $1.3843 for 1 Euro. Forecast inflation over the next 5 years is 10.41% ($C) and 15.93% (Euro). The answer for PPP in the text takes the view that the expected inflation differential (10.41%15.93%= 5.52%) is the relevant factor, such that to determine the expected exchange rate we simply multiply the current exchange rate by 1+(differential). Of course as Canada is expected to have lower inflation – and thus increase in relative purchasing power – we know that the result will see the $C fall (this is just a sanity check of final results). Anyway, using CFAI’s example, the answer is simply the current exchange rate of C$1.3843 x (15.52%) = C$1.3079. Very simple stuff.
However intuitively this seems (at least to me) to be incorrect. I would have thought that as we are comparing purchasing power, the true exchange rate should be equivalent to 1 unit of $C increased by their rate of inflation (ie., depreciate the actual value of currency), versus 1 unit of euro increased by their rate of inflation. I.e., { C$1.3843 x (1+10.41%)} / {(1.0 x (1+1.1593%)} = C$1.3184.
That’s a difference of about 0.80%, or close to 15% of the interest rate differential, so it seems to be a pretty significant error. I’ve played around with some different numbers and found that the higher the differential generally the higher the error. I.e. if Canada’s inflation was 10% and Euro inflation 50% the error is over 22%, equivalent to approx. 56% of inflation differential.
Could someone point to why I have this so wrong?
Cheers!

I think it’s a matter of what’s the approximate way of doing it (which CFAI sometimes use, confusingly enough) and the ‘true’ way of doing it.
Your way of multiplying/dividing seems to be to be the ‘true’ way of calculating, whereas the use of just the differential of 5.52% is a quick approximate way of doing it.
In the actual exam the multiple choice should be set up in a way that accepts both (slightly different) answers. The options would probably be something like:
“The amount of Canadian dollars trading for 1 Euro at the end of the period is closest to:”
 C$1.38
 C$1.31
 C$1.42

Here’s another example from Investopedia:
Assume that the U.S. is the foreign country and that Japan is the domestic country. The current spot exchange rate is S0 = 115 yen per dollar ($1 per ¥115.00). The expected annual inflation rate for the U.S. is 4.89%, and the annual expected Japanese inflation rate is 6.23%. Compute the approximate expected spot rate and the expected spot rate one year from now.
Answer:
Because Japan is the domestic country we have:S0 = 115 yen per dollar. (1 + Iy) is 1.0489, and (1 + Ix) is equal to 1.0623.
The approximation method would indicate that the yen should decline against the dollar by: (Iy – Ix) =(1.0489 – 1.0623) = 0.0134 = 1.34%
So the value of the yen relative to the dollar would be expected to decline to
(1 – 0.0134) × 115 = ¥113.46 per $
We can calculate the rate more exactly as:
S1 = (1.0489) / (1.0623) × 115 = ¥113.55 per $

Thanks @hairyfairy
Seems strange that the curriculum would use an approximate when simply grossing up each currency’s “price” by their rate of inflation seems (at least to me) to be an easier and more logical approach.
Maybe I’ve overplaying the significance of this (or likelihood of getting this kind of question on the L3 exam) but I’d had to drop 2 or 3 points because I used the wrong method of calculation! 🙂

@hairyfairy is right – the multiple choice would make sure that if you were using a ‘more accurate’ way to calculate, you should never lose points. In the essay, again you should receive full points



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