1) Purchasing Power Parity (PPP)

Logic dictates that as the currency loses purchasing power at home, it will eventually lose it overseas as well - that is, the currency should eventually depreciate. This same logic, by the way, is the underlying assumption of the PPP equation. Another way of looking at PPP, is it assumes that the real exchange rate does not change over time That is, if one Mercedes cost the same as one Cadillac last year, they will cost the same this year.

Now, there is a tougher version of PPP called the Law of One Price but this version applies only to tradable goods. The PPP equation does not assume everything must cost the same in each country.  Instead, relative PPP assumes that any differences between two country's price level we see today, we will also see tomorrow.   If  Switzerland is twice as expensive as Mexico today, it will be twice as expensive three years from now.    This persistence is due to fact that many goods or inputs for goods are nontradable (the price of a Big Mac, for one, incorporates the cost of rent, labor costs etc. - see the discussion on the purchasing power parity button).

The PPP equation uses relative inflation rates to predict future spot rates.

e₁ = e₀ (1+infl_$)/(1+infl_for)

Infl stands for inflation either in $s or in a foreign currency. "e" stands for the spot exchange rate and is always a direct quote.   The exchange rate at time period zero is known, the rate at time period one (and in italics) is what you are predicting.

A simple example would where the $1.20 buys a Euro today. What is the Euro likely to cost next year if the U.S. has 10% inflation and "Euroland" has none? The formula predicts the Euro will cost 10% more or $1.32. If Euroland has five percent inflation, the change will be less ($1.257).

2) Interest Rate Parity (IRP)

There are several ways to look at why IRP works, and the chapter notes go into an example or two. Consider an importer who owes Euros in six months (and thus is short Euros) and wishes to hedge the currency exposure (thus he wishes to arrange to buy some Euros, either now or for future delivery in six months). One can buy Euros on the forward market delivery in six months, or one can buy them now and leave them in a Euro bank account, collecting the prevailing Euro interest rate. This last choice, called a money-market hedge(or a spot hedge) also means giving up the opportunity to earn U.S. interest rates on the funds. Since, at the moment, the Euro interest rate is about 2% less than the U.S. rate, most folks would rather not use a spot hedge here, and buy on the forward market. Logic (and Markets) would dictate, however, that the forward hedge choice would be equally disadvantageous.

The IRP equation uses relative interest rates to predict (actually set) the current forward rates.

f₁ = e₀ (1+r_$)/(1+r_for)

"r" stands for interest rates in each currency. "f" stands for the forward rate that is currently available for delivery in the next time period.

A simple example would where $1.20 buys a Euro today (spot). What is the three-month Euro likely to cost on the forward market? If the U.S. rate is 6% and the Euro rate is 4% and dividing all rates by four to reflect that contract is for one quarter of a year, we get

f₁ = $1.20 (1+.015)/(1+.01) = $1.2059

Thus the forward rate is more expensive than the spot rate, reflecting opportunity costs associated with the interest rates in the spot markets. What are the main Assumptions of IRP? Mostly that that there is free flow of capital, transactions costs are not too high, and taxes don't distort the decision.

3) International Fisher Effect (IFE)

Most of you are familiar with the "ordinary" Fisher Effect: Interest Rates are a combination of a "real" rate (the text uses the letter "a") and an inflation premium

r = a +infl or more accurately

(1+r) = (1+a)_*(1+infl)

In this model, real rates are supposed to be fairly stable and the major source of interest rate volatility comes from changes in inflation (or more accurately, changes in inflationary expectations).

The International Fisher Effect (1) extends the Fisher Effect to all nations and (2) also assumes that real rates the are the same in most countries.   Solving for the inflation factor, we get

(1+infl) = (1+r)/(1+a)

and substituting for the (1+infl) into the PPP equation (one for each currency), we get

e₁ = e₀ [(1+r_$)/(1+a_$)]/[(1+r_for)/(1+a_for)]

Since IFE assumes real rates are the same in the two countries we get
 

e₁ = e₀ (1+r_$)/(1+r_for).

The IFE equation which uses relative interest rates to predict the future spot rates.

4) How these three relations fit together.
 
First, realize that they don't really have to fit together.  IRP is a result of market arbitrage and can stand on its own.   PPP is a theoretical way of predicting the future spot rate, based on relative rates of inflation (but you have to predict inflation).    IFE is really a simpler version of PPP, where interest rates supposedly reflect investor expectations of relative inflation (and thus r substitutes for infl).

However, there is a belief among some that forward (or future) rates are supposed to "predict" a spot rate in the future: the spot rate that one will observe at the time the forward contract matures.  However, I think the best we can say about the forward rate is that it is an unbiased estimate of the future spot rate.  Now, before you assume my statement constitutes a ringing endorsement of the forward rate as predictor, think again.  An unbiased predictor simply means that if we add up the predictor's track record, that is the amount it has overestimated and underestimated the future spot, we find no tendency to be high or low.  This is not necessarily a good thing, as it can be analogous to the world's worst archer, who shoots arrows all over (and around) the target, never hitting the bull's eye, but also never consistently pulling high or low and thus unbiased .  Actually, a bias might not be a bad thing, as an archery coach could help the archer correct for it.

Let's see how the forward rate is supposed to work:  First f₁ and the two country's interest rates must link through IRP.  usually, this is not a bad assumption - if governments do not interfere with the two nations ' currency market.   Next, we assume that interest rates reflect future relative rates of inflation (IFEs main assumption -than the one that comes with PPP).  That's at best, a long-term linkage.  Real rates do differ from country to country, at least in the short run.    Real rates are function of a number of things, especially monetary policy; a monetary policy designed to slow down a booming economy is likely produce higher real rates (temporarily) than a policy that is designed to "jump start" an economy in recession.  Finally, to get from relative inflation to the future spot rate, we use PPP - where the "real" exchange rate does not change from year to year.  Well, sorry, the real exchange does change from year to year - sometime a whole lot!  Simply look at the high international purchasing power of the dollar in the mid 1980s to the low levels of the late 1970s.  Compare the Brazilian Real, before and after devaluation.

In a nutshell,
(1)  IRP is a good assumption, in the long and short term.
(2) PPP and IFE, however, are strictly long-term relationships.  And remember, J.M. Keynes said that "in the long-run we are all ..."

Here's the Big Equation:     (~ and italics indicates a prediction)
_~   
e₁ = e₀ (1+infl_$)/(1+infl_for) =  e₀ (1+r_$)/(1+r_for) = f₁
   PPP                                    IFE                                               IRP