topic 15.1
INTEREST PARITY
Countries trade goods and services at a point in time. They also trade over time through buying and selling financial assets.
Under free trade with costless arbitrage the price of 'bonds' is constrained in a manner similar to that of goods. Just as traded goods should (in theory) conform to the 'law of one price', so too assets should exhibit parity conditions. Assets are actually a much better candidate for parity conditions than goods because they are homogeneous and easily traded, unlike goods which are neither.
The best known parity condition applies to international trade in bonds: 'interest rate parity'.
Assume there are two bonds, a US bond denominated in dollars and a UK bond denominated in pounds. Assume both are risk free.
Then
(1 + i)$ = (1 + i) pounds * (F/E)
where:
i$ and ipounds are the returns on the US and UK bonds
F and E are future and spot exchange rates ($/pounds)
To explain this - consider a US person with $1 to spend on a US one-year bond or a UK one-year bond. Absent any risk differences or transaction costs the investor should be indifferent between:
- investing in a US bond today or
- investing in a UK bond today with the necessary use of the exchange rate to convert dollars to pounds today (E), and then back the other way one year from now (F)
Another way to express the equation is:
i$ - ipound = (F-E)/E
In this example (F-E)/E is the 'forward premium'
The intuition here is that if US bonds paid a higher nominal interest rate than UK bonds then the higher expected US return must be offset by an expectation that the dollar will depreciate against the pound (F is higher than E).
If the forward premium is insufficient to cover exchange rate risk the traders will move into US bonds, driving the US bond price up and theUS bond expected return down (and the opposite for the UK bond) - this will drive the system toward parity.
There are reasons why interest rate parity may not hold: different risks between the bonds or the forward rate is not certain - it is an expected rate.
We can extend a similar analysis to equities.
The advantage of parity conditions is that they allow us to cut through the complexity of international finace to establish core fundamental relationships.
