Can anyone explain this calculation? The textbook just essentially says that if currency A has inflation in excess of currency B then currency A should depreciate relative to B by the inflation differential. However, I’m seeing answers in the back of schweser that are answering questions using what they’re calling the relative PPP formula that essentially looks like the covered interest rate parity formula but inflation rates are switched w/ interest rates.
More specifically schweser refers to the relative PPP formula in an explanation to an answer on their mock as follows:
Where E(S_1) and S_0 are quotes in the form of foreign over domestic (f/d).
They do this on two separate problems (Schweser Mock Book 1, exam 3 problems 13 and 17), but I haven’t seen this definition in the CFA text or Schweser text and it’s driving me nuts right now. Any insights would be greatly appreciated.
They are almost identical you are right in that, but I’m not sure where the issue lies? Imagine if you ignore the currency Xchange portion and just think of it as two different currencies, so you can do it out for for each one. Bare with the notation, too lazy to go crazy lol.
A: Price of a “snack” in USD at t0
E(B): Price of a “snack” in USD at t1
c: USD inflation between t0 and t1.
If the inflation is “c,” and you can buy a “snack0” today for “A/snack0”, you would expect that tomorrow you’ll have to pay (1+c)*A/”snack0″, right? Your dollar is “worth” less, so of course you would, so long as those damn retailers don’t pull any shenanigans and give you less per bag and replace it with air — you know what I’m talking about…
But now imagine that by tomorrow, those bastards took a chip(x% of the snack) out of the bag, which we shall call “snack1”. But remember a snack is a snack, you won’t see Lays version their bag of chips when they change what’s in it. This is the inflation of the other currency fyi. Personally, if I expected to pay (1+c)*A for a “snack” I expect, no, I demand that “snack” I now get have the same weight as it did before. So how must the retailer compensate? By giving me enough “snack1” to replace “snack0” which is approximately (1+x%)*snack1.
So what am I expecting to pay
I expect to pay (1+c)A/(1+x)*snack1 = E(B)
And what am I receiving?
a snack. Remember, a snack is a snack. No versions in real life, sadly.
So…to nicely pair these equations with what you’re seeing:
E(B) = A/snack1 * [(1+c)/(1+x)]
And like I said a snack is a snack, so A/snack1 = A/snack.
And there it is, the final equation:
E(B) = A/snack * [(1+c)/(1+x))]
A/snack is the exchange rate;
c is the inflation on USD;
and x is the (ironically literal) inflation of the snack.
FYI the only flaw I’m seeing in my masterpiece is the how many snack1’s are required to replace snack0. =)
I said 1+x, but technically(if we wanna get reallll deep) the correct amount is 1/(1-x).
Eg. If x was 10%, I would demand 1.111111 snack1’s, not 1.10. Potato, tomato….right?
Also beware of the real bitch on this topic, which I’m not sure is covered…but the formula for Expected Real Exchange Rates. Haven’t read the book in its entirety, but if you have…beware this is the guy that does NOT align with the other formulae.
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