1. Foreign Exchange Markets,
Purchasing Power Parity, and Real Interest Parity
ECO Money & Banking - Dr. D. Foster

2. Perspective! The U.S. E $ depreciates; the price rises; we buy less
$ appreciates; the price falls; we buy more
D £
S £
$ (per £) Q£ E
Equilibrium in the market for pounds (£)
Exchange rate changes as S & D change . . .

3. Exchange rate changes as S & D change . . .
Perspective! Britain
£ depreciates; the price rises; we buy less
D $
S $
£ (per $) Q$
1 𝐸
$ appreciates
£ appreciates; the price falls; we buy more
$ depreciates
Exchange rate changes as S & D change . . .

4. Purchasing Power Parity
Where . . .
transportation costs are zero.
tax differentials do not exist.
there are no trade restrictions.
goods are homogeneous.
Law of One Price: A unit of goods in one country trades for the same price in another country.

5. Example - Apples in U.S. & Britain
Purchasing Power Parity
Example - Apples in U.S. & Britain
U.S. price = $.50; British = £.75
If exchange rate is .667 ($/£) then the apple sells for the same price in both.
What if the exchange rate is .75?
Sell apple in Britain for .75 (£) and convert to $: (£.75)*(.75) = $.562 for a 6.2 cent profit!

6. On your own - show this from the British perspective.
Purchasing Power Parity
Arbitrage results
U.S. -  demand for apples -  apple prices
Britain -  supply of apples -  apple prices
or …
.75 S£ D£
$/£ Q£
.667
S£1
In U.S. foreign exchange market,  S£ as arbitrageurs convert back to $.
On your own - show this from the British perspective.

7. Purchasing Power Parity
Different PPP models
Absolute PPP: CPIUS = E(CPIBrit)
if this can be applied to all goods,
assumes goods mix the same in both.
Solve for rate: E = (CPIUS)/(CPIBrit)
Relative PPP: %ΔE = %Δ(CPIUS) - %Δ(CPIBrit)
differences in inflation rates explain . . .
appreciating/depreciating exchange rates.
Long-run data tends to confirm this.

8. Hedging your bets - Futures Market
Buying Future Dollars
Hedging your bets - Futures Market
You want to buy British bonds . . .
earning iBrit
but you face the risk of changing E . . .
So, you buy $ futures contract.
Locks in your financial outcome . . .

9. What if the risk premiums differed? Wait …
Buying Future Dollars
Let iUS=6% and iBrit=8% with E=1.2
E aka “spot rate.”
Let the forward rate be Ef=1.18
With $1200, should you invest in US bonds or British bonds?
US bonds earn $1200*1.06 = $1272.
For British bonds: $1200/1.2 = £1000;
in one year, bond earns £1080;
converts back at (1.18)*(1080) = $ 
What if the risk premiums differed? Wait …

10. Buying Future Dollars iBrit + [(Ef - E)/E]
In US terms, the British bond earns:
iBrit + iBrit*[(Ef - E)/E] + [(Ef - E)/E]
iBrit + [(Ef - E)/E]
(.08)*[( )/1.2] + (-.02/1.2) = 6.2%
With well functioning markets in equilibrium, this equals ius
Noting relative PPP: %Ee = eUS - eBrit
where e=expected and =inflation.
Using “r” to represent real interest, rewrite as:
(Ee - E)/E = (ius-reUS) - (iBrit-reBrit)

11. Real Interest Rate Parity
Substituting for iUS
(Ee - E)/E = (iBrit + [(Ef - E)/E] -reUS) - (iBrit-reBrit)
We can cancel out both iBrit
If Ee=Ef, we can cancel them out
reUS = reBrit

12. Revisit Bond Problem
What if the UK bond had a risk premium of +0.3% over the US bond?
U.K. return = $74.4/1200 = 6.2% … but adjusted for risk = 5.9%
U.S. return = 6%; take the U.S. bond!!!

13. Foreign Exchange & Monetary Policy
Gold Standard
Fixed X∆ rates, K flows, $ policy
Bretton Woods System
Fixed X∆ rates, K flows, $ policy
Unmanaged free floating rates
Volatile X∆ rates, K flows, $ policy
Managed rates
Semi-fixed X∆ rates, K flows, ???$ policy

14. Foreign Exchange Markets,
Purchasing Power Parity, and Real Interest Parity
ECO Money & Banking - Dr. D. Foster