Current exchange rate if PPP prevails

[johntavv]

The question in reading 16, practice problem 19A says:
10 yrs ago the exchange rate was 3 Fips per 1 CHF and inflation indices in Switzerland and Fap were both 100. Now the exchange rate is 2 Fips per 1 CHF, Swiss inflation index is at 150 and Fap inflation index is at 140. Determine exchange rate.
In level 2, we had the formula:
expected spot exchange rate after t periods = spot exchange rate today x [(1+inflation A) / (1+inflation B)]^t
Why can’t we apply this level 2 formula to answering this question? The answer uses 0.9 x (3 Fips per 1 CHF) = 2.7

 

[S2000magician]

I’m not sure where they’re getting the 0.9; it should be 140/150, and the answer should, therefore, be 2.80.

 

[cpk123]

100 - 150 => 50% inflation
100 - 140 => 40% inflation
so all things equal - an inflation differential of 10% (or 90% of the original would be seen).

Quote:
The Swiss price index has increased by (150 − 100)/100 − 1.0 = 50%. The Fap price index has increased by (140 − 100)/100 − 1.0 = 40%. The inflation differential is therefore 10 percent. According to PPP, to offset higher Swiss inflation, the fip should appreciate against the Swiss franc by approximately the same percentage to 0.90 × (3.0 fips per 1 CHF) = 2.70 fips per 1 CHF

 

[S2000magician]

cpk123 wrote:100 - 150 => 50% inflation
100 - 140 => 40% inflation
so all things equal - an inflation differential of 10% (or 90% of the original would be seen).

Quote:The Swiss price index has increased by (150 − 100)/100 − 1.0 = 50%. The Fap price index has increased by (140 − 100)/100 − 1.0 = 40%. The inflation differential is therefore 10 percent. According to PPP, to offset higher Swiss inflation, the fip should appreciate against the Swiss franc by approximately the same percentage to 0.90 × (3.0 fips per 1 CHF) = 2.70 fips per 1 CHF

It sure is stupid that they use the approximation when they could have, as easily, used the proper calculation.

 

[johntavv]

Why can’t we use the level 2 formula below?
expected spot after t periods = spot exchange rate today x [(1+inflationA) / (1+inflationB)]^t
expected spot after t periods = 3 x (1.4/1.5)^10
= 1.5

 

[cpk123]

you would not need to do the ^10 part - since they gave you the indexed inflation in time period 10 already.
So you would either do 3 * 1.4/1.5 = 2.8 or do what is done in the text book.

 

[johntavv]

Got it, instead of giving annual inflation, to which we would have done ^10, they gave the index level in 10 years.
Thanks.

 

[S2000magician]

johntavv wrote:Got it, instead of giving annual inflation, to which we would have done ^10, they gave the index level in 10 years.
Thanks.

Bingo!
(Personally, I’d be very concerned if two economies had 40% and 50% annual inflation.)