(8 of 18) Ch.21 - Relative purchasing power parity - YouTube

Let's look at what the relative purchasing power parity means.

Just like the absolute purchasing power parity, the relative purchasing power parity connects

exchange rates and prices in two different countries, expect, it doesn't look at the

specific commodity, let's say, Big Mac or a Dell laptop or anything like that, it looks

like at the general overall price level in this country and in some other country.

The idea is the relative purchasing power parity shows that relative prices in two countries

is what determines the change in the exchange rate over time.

So, we are now, kind of, looking at how the exchange rates would be changing in the future,

when we have information on the price levels in two different countries.

Let me explain this topic using the following example, let's say we have Japan and the prices

for everything would typically buy in Japan, kind of the overall price level.

Is expected to increase by 10% over the next one here.

So, if you want to travel to Japan in one year and if you want to be able to buy the

same amount of stuff with your dollars that would be exchanged into Yen, in other words,

to keep your purchasing power unchanged, the dollar should be exchanged into 10% more Yen,

right?

So, if everything is 10% more expensive, but each dollar is exchanged into 2% more Yen,

then you feel like there's no change, no difference to you.

So, the dollar should rise by 10% against Japanese Yen over the next year.

So, the expected exchange rate next year, denoted as E and then in square brackets S1,

should be equal to S0, the current or the spot exchange rate, expressed as how much

Yen per $1, as always, multiplied 1 plus .1, so this little formula increases the exchange

rate by 10% in one year.

So, 10% more Yen per one U.S. dollar that would leave you, you know, in different to

the 10% higher price in Japan.

Now, let's add more information to the story, what else will be happening over the next

year?

Let's say over the next year the prices in the U.S. will also increase, but only by 7%

so we expect a 7% inflation in the U.S. then relative to the U.S. price level in one year,

prices in Japan will increase by more, by about 3% more, right?

And now it changes our conclusion about how the exchange rate should change so that you,

like, feel that your purchasing power isn't changed, you can still by as much stuff your

money that you bring to Japan.

Now do you not need to, you know, hope that the exchange rate will go up by 10% you would

build you know, you'll feel the that your purchasing power is unchanged, if exchange

rate increases only by 3% so the expected exchange rate, in this case, with the inflation

rate with 10% in Japan and 7% in the U.S. the exchange rate should only increase by

3% so that you feel like The high prices in Japan makes no difference to you.

How would we calculate the exchange rate in one year?

We would take the current, or the spot exchange rate, S0, and multiply by 1 plus 3% what is

3% that's the difference between 10% inflation in Japan and 7% inflation in the United States.

Let's apply it to a more specific example; let's say the current spot exchange rate,

S0 equals 120 Yen per one U.S. dollar then with a 10% expected inflation in Japan and

the 7% expected inflation in the U.S.A. which implies a 3% higher prices in Japan, than

in the United States, the next years expected spot exchange rate should equal 120 Japanese

Yen, which is today's spot exchange rate, multiplied by 1 plus the 3% difference in

the -- between the foreign and the domestic inflation rates, which gives 123.6 Japanese

Yen per $1.

So if in one year the exchange rate increases from today's 120 Yen per dollar to 123.6 Yen

per dollar, you wouldn't care about all these, you know, price increases in both countries,

your money, your dollars brought into Japan and exchanged into Japanese Yen, will allow

you to buy the same amount of stuff in one year, as it can buy you today, in other words,

it will keep your purchasing power unchanged.

If we expect the inflation rates in the U.S.A. and in Japan to stay at the same level, so

prices in Japan will keep rising by 10% two years and in three years, and so on, and in

the United States the prices about increase by 7% year after year after year, then we

can calculate the expected spot exchange rate two years in the future, three years in the

future, and so on, by adding the power to two or three to the term 1 plus the 3% difference

in the inflation rates.

So, the expected spot exchange rate in two years denoted at E in square brackets, S,

subscript 2 would equal as 0, which was 120 Yen per dollar, in our example, multiplied

by squared 1, plus.

03, which gives 127.3 Yen per one U.S. dollar, and so on.

In general, the relative purchasing power parity formula says to calculate the expected

spot exchange rate at any point of time, T, in the future, so It could be one, if it's

in one here, it could be two, it could be three, two years in the future, three years

in the future, it would equal, spot exchange rate, S0, which is the amount of foreign currency

per one U.S. dollar, multiplied by open parenthesis, 1 plus the difference between the foreign

inflation rate and the U.S. inflation rate.

Close parenthesis power T. The notations to be used for the two inflation rates are lowercase

h, so h, subscript, FC stands for annual inflation rate in the foreign country.

H subscript U.S.A. Stands for annual inflation rate in the United States.

Let's do an example.

Suppose the Canadian spot exchange rate today is 1.18 Canadian dollars per U.S. dollar,

the U.S. inflation is expected to be 3% per year and the Canadian inflation is expected

to be 2% per year.

The question is, do you expect the U.S. dollar to appreciate or depreciate relative to the

Canadian dollar?

To answer this kind of conceptual question, we need to do some calculations first.

Let's calculate the expected exchange rate or spot exchange rate between the Canadian

dollar and the U.S. dollar in one year.

What do we do for that?

Well, we use the relative purchasing power parity formula, which says take today's exchange

rate, 1.18 Canadian dollars, per one U.S. dollar and multiply it by, you open the parenthesis,

you put 1 plus and then you add the difference between the Canadian and the U.S. inflation

rates, which is .027 minus .03 so it basically gives a negative number, negative 1% difference

in inflation rates.

The answer you get is 1.17 Canadian dollars per U.S. dollar, so the number will drop,

right?

The number's expected to drop.

If the amount of Canadian dollars per U.S. dollars is expected to drop, who would benefit

from that?

Canadians or Americans?

Well, each dollar will buy us fewer Canadian dollars, right?

Each U.S. dollar will buy us fewer Canadian dollars.

So that's a bad thing for the U.S. dollar, and so we say that we expect the U.S. dollar

to depreciate relative to the Canadian dollar, and the other way around for the Canadian

dollar, the Canadian dollar is expected to appreciate or get stronger against the U.S.

dollar because, let's say, Canadians traveling to the United States would be exchanging fewer

Canadian dollars to get each U.S. dollar, which is a good thing for them, but a bad

thing for the U.S. by the way, a problem like this could actually be solved in the financial

calculator.

Let me bring it up.

Let's turn it on, so what is going on in this formula?

We have 1.18 today's exchange rate, we multiply it by and in the parenthesis, we have 1 plus

the difference in the inflation rates, so it may look very similar to the formula to

calculate the future value of some today's amount, the today's amount is today's exchange

rate, 1.18, so let's save it as PV 1.18, let's make it negative and then press the PV button,

which stands for present value.

We are calculating the exchange rate in one year, so let's our number of years or N, in

the calculator.

1N we want to calculate the future exchange rate after one year, so we are going to be

computing FV, computing the future value, and one more thing that we need to enter into

in the calculator is the IY, the interest rate.

Here, the equivalent of the interest rate is the difference between the foreign and

the domestic inflation rates, foreign, minus domestic, Canadian inflation minus U.S. inflation

so 2% minus 3% and negative 1% and so in the calculator, I put 1, plus minus to make it

negative, and then save it as IY, and then I to want compute the future value, compute

FV, 1.17 just like the number I found on my slide.

So, the equivalent of the IY, to compute the future value, is the foreign inflation minus

the domestic inflation