Foreign Exchange Parity Theories

• Purchasing Power Parity (PPP)

• International Fisher relation

• Foreign exchange expectations relation

• Interest rate parity relation
  

Purchasing Power Parity (PPP)-
The PPP is the law of one price and argues that every equal product available in two countries should have the same price. Thus should trade flows ensure the one-price rule. However, this strict application of the rule cannot be expected to apply, since between two countries there is only a single exchange rate linking their respective currencies. This suggests that PPP only makes sense when applied to a bundle of goods and services, implying that we should be looking at a price index for each country. Then PPP tells us that there ought to be an exact connection between inflation rates in two countries, and changes in the exchange rate between them. In practice, empirical support for PPP is quite mixed, though on average over fairly long periods it seems to fit the facts fairly well. So why might PPP not fit the facts as well as theory suggests it should?

• First, exchange rates are determined by demand and supply of foreign exchange, which in turn depends on trade flows and international capital movements

• Second, the usual measures of inflation are based on indexes of final goods prices in the domestic and foreign economies. Such indexes rarely include asset prices and rarely focus on the goods and services that participate in trade - for instance, the consumer price index (CPI) is often used.

• Third, many transactions in most economies involve non-traded goods whose prices are not especially relevant to trade or capital flows - yet such prices often form part of published price indexes.

• Hence while there are arguments for PPP, one cannot expect it tohold precisely because we normally don?t have available the?right? price index.
  

International Fisher Relation-
Let the nominal interest rate be r, the real rate be R. Let the expected rate of inflation be E(I). Then for a given economy, Fisher claimed that:

(1 + r) = (1 + R).(1 + E(I))

i.e. the nominal rate of return (or rate of interest) is the real return compounded with the expected rate of inflation. In linear approximation, this is simply: r = R + E(I). (and again, this is only a good approximation for small R and E(I)) According to Fisher, R is likely to be stable over time, hence variations in nominal interest rates are likely to be correlated with movements in inflationary expectations.Fisher went beyond this to suggest that the real returns available in different economies should be essentially equal. In that case, differences in nominal returns depend only on differences in inflationary expectations.

Foreign Exchange Expectations Relation-
All this says is that: F = E(S1), which means that the current value of the forward exchange rate for one period ahead must equal the current expectation of the spot rate that will prevail then. In other words, the forward exchange rate is an unbiased predictor of the future spot rate. However, sometimes it is argued that the relationship, under conditions of risk, needs to be amended by a risk premium. Alternatively, the relationship can be written in the equivalent form involving the forward discount or premium, f: f = E(s).

Interest Rate Parity Relation-

• Various relations between these parity equations can be developed, linking in various ways:
  the interest rate differential

• the inflation differential

• the forward exchange premium (or discount)

• exchange rate movements
  

The empirical evidence is very mixed, especially when we are interested in short term movements and relationships - they perform better on average over longer periods.
- Andrea Pay

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