1. Purchasing Power Parity Interest Rate Parity
International Corporate Finance
P.V. Viswanath

2. Learning Objectives Law of One Price
How arbitrage links good prices and asset returns
Relations between spot and forward exchange rates, inflation rates and interest rates
Difference between real and nominal exchange rates
P.V. Viswanath

3. Arbitrage
Law of One Price – in competitive markets with many buyers and sellers with low-cost access to information, exchange-adjusted prices of identical tradable goods and financial assets must be within transaction costs worldwide.
Risk-adjusted expected returns on financial assets in different markets should be equal.
P.V. Viswanath

4. Law of One Price
In the absence of frictions, the same good will sell for the same price in two different locations.
Either because of two-way arbitrage or
Because buyers will simply go to the lower cost seller
If goods are sold in different locations using different currencies, then
The law of one price says: after conversion into a common currency, a given good will sell for the same price in each country.
If $1=£0.8 (£1=$1.25), and a bushel of wheat sells for $15, it must sell for (15)(0.8) or £12 in the UK.
P.V. Viswanath

5. Static PPP
If e is the $/£ exchange rate (i.e. the number of $ needed to buy £1, then
P$ = e.P£
Hence, e = P$/P£
The static PPP is difficult to test because different baskets of goods are consumed in different countries; indexes reflect different consumptions.
P.V. Viswanath

6. Dynamic PPP
The dynamic PPP simply states that the absolute PPP relationship will hold in terms of changes; if  refers to the inflation rate, then:
(et+1-et)/et = ($- £)/(1+£)
Thus, if a unit of consumption costs $15 in the US and £12 in the UK, we have seen static PPP holds.
If inflation is 10% in the UK and 20% in the US, then, prices will be $18 in the US and £13.2 in the UK. Then, static PPP will require that e = 18/13.2 or 1.36.
The percentage change in e is ( )/1.125 = 9.09%
The RHS is also ( )/1.1 = 9.09%
P.V. Viswanath

7. Static vs. Dynamic PPP
In the above example, both static and dynamic PPP holds.
But, suppose the original exchange rate were not $1.25, but $1.3/£, due to some friction.
Then dynamic PPP would assert that the exchange rate would increase by 9.09% or rise to 1.3(1.0909) or $1.4182/£.
If price changes are not too large, then approx.,
(et+1-et)/et = ($- £)
If we take the expectation of both sides, we find
E(et+1-et)/et = E($- £)
The expected change in interest rates will be equal to the expected differential in inflation rates.
P.V. Viswanath

8. Causes for deviation from PPP
PPP is reinforced by two-way arbitrage
If transportation of goods is costly, static PPP is violated.
Import tariffs and quotas can cause static PPP violations.
Many items cannot be traded such as on-site services (haircuts), perishable goods, etc. Hence PPP measured with standard price indexes can be violated.
Movement of buyers can compensate for movement of goods, sometimes. For example, vacations.
Movement of producers can also compensate. Producers will move to places where the goods price is high.
In the long run, PPP should hold even if there are non-traded goods.
P.V. Viswanath

9. Covered Interest Rate Parity
Investing $1 for 1 year will generate $(1+r$), where r$ is the rate quoted on dollar-denominated investments.
Investing $1 for 1 year in pound-denominated investments will generate £(1/e0)(1+r£). If e1 is the future exchange rate, this will equal $(e1/e0)(1+r£). However, the value of this expression depends on e1 and is unknown at t=0.
If f1 is the forward exchange rate for delivery at t=1, then the pound value, which is known in advance can be converted to $(f1/e0)(1+r£). Hence, we find
1+r$ = (f1/e0)(1+r£) or equivalently, (1+r$)/(1+r£) = f1/e0
Or approx. the forward premium, (f1- e0)/e0 = r$ - r£
P.V. Viswanath

10. Uncovered Interest Rate Parity
The Unbiased Expectations Hypothesis says that the forward rate is equal to the expected future spot rate.
If the forward rate is greater than the expected future spot rate, then speculators will sell the foreign currency forward. If the forward rate is lower than the expected future spot rate, then they will buy forward contracts on the foreign currency.
Putting this together with the covered interest rate parity condition, we derive the uncovered interest rate parity condition (also known as the International Fisher Equation):
E(e1- e0)/e0 = r$ - r£
P.V. Viswanath

11. Deviations from Covered Interest Parity
Although covered interest parity generally holds, there could be deviations because of:
Transactions costs
Political Risks
Potential tax advantages to foreign exchange gains versus interest earnings
Liquidity differences between foreign and domestic securities.
P.V. Viswanath

12. Fisher Open condition
Take the uncovered interest rate parity condition, E(e1- e0)/e0 = r$ - r£ together with
the expectations form of the PPP: E(e1- e0)/e0 = E($- £). This gives us:
r$ - r£ = E($- £)
This is known as the Fisher Open Condition
P.V. Viswanath

13. The Fisher Effect
Irving Fisher decomposed the nominal interest rate into the real interest and the expected inflation rate.
If capital is mobile across countries, then real interest rates should equalize.
This implies that differences in nominal interest rates across countries should reflect differences in expected inflation.
Combining this with the expectations form of the PPP, we have the International Fisher Effect
the interest rate differential between two countries is an unbiased predictor of the future change in the spot rate of exchange.
P.V. Viswanath