1. International Parity Conditions
(or chapter 4)

2. Agenda What is PPP & law of one price?
What is exchange rate pass-through?
How do interest rates & exchange rates link?
Interest rate parity?
What is covered interest arbitrage?
What is uncovered interest arbitrage?

3. Prices and Exchange Rates
Law of one price:
product’s price same in all markets
P$  S = P¥
where spot exchange rate is S, yen per dollar. $

4. Purchasing Power Parity & Law of One Price
Absolute purchasing power parity:
spot exchange rate is determined by relative prices of similar basket of goods.
Relative purchasing power parity:
Relative change in prices b/n countries determines change in forex rate.

5. Absolute PPP: Big Mac Index
Economist’s Big Mac PPP:
Big Mac in China costs Yuan 9.90.
Big Mac in US costs $2.71.
Implied PPP exchange rate

6. Economist,
4/ 2003

7. Relative PPP P PPP line % change spot rate foreign currency US$/ yen2 4 -5 -4 -1 -3 -2 1 3 5 -6 6
% change spot rate foreign currency
US$/ yen P
InfJAPAN- InfUS

8. But: PPP is not very accurate predictor…
Why?
PPP holds well over very long term…
PPP holds better for countries w/ high inflation & underdeveloped capital markets…

9. Is forex under-/over- valued?
Use forex indices: trade-weighted bilateral exchange rates b/n the home country & trading partners
Nominal exchange rate index : use actual exchange rates.
Real effective exchange rate index indicates how the weighted average purchasing power of the currency has changed relative to some arbitrarily selected base period.

10. Q: Can you tell when a currency is overvalued?
Why the real exchange rate deviates from 100?

11. Real Effective Exchange Rate Indices
United States & Japan (1995 = 100)

12. Exchange Rate Pass-Through
Pass-through: change in prices of imported/exported goods when exchange rate changes
BMW made in Germany spot rate US$ 35,000.
where P$ is the price in US$, P€ is price in euros, S is spot rate
Euro appreciates by 20%. But BMW is now only $40,000.
Pass-through:
Degree of pass-through: % / 20 % = 0.71 or 71 % €
€/$

13. Interest Rates & Exchange Rates?
What is a fair nominal interest rate?
Well, can ask a banker … or read Irvin Fisher…
Fisher Effect: nominal interest rates in each country are equal to the required real rate of return plus compensation for expected inflation.
i = r +  + r 
i is nominal rate, r is real rate,  is expected rate of inflation.
FE good for short maturity bonds, NOT long maturity ones.
Why?

14. International Fisher effect
International Fisher effect (Fisher-open):
spot exchange rate change equals opposite of interest rate differential.
where S is indirect quote.
Direct Quotes: US$/ Foreign Currency.
Indirect Quotes: Foreign Currency / US$.
Fisher-open not precise in short-term.
Why?
Should include forex risk premium. FC

15. Forward Rate Forward Rate
A forward rate: exchange rate quoted today for future date

16. Forward Rate Spot rate SF 1.48/$
90-day euro Swiss franc deposit rate 4% p.a.
90-day euro-dollar deposit rate 8% p.a.

17. Premium or discount?
Forward premium or discount : % difference b/n spot & forward rates in annual percentage terms.
For indirect quotes (FC per home currency, FC/$) then
Swiss franc sells premium 3.96% p. a.
(takes 3.96% more US$ to get franc at 90-day forward rate)
For direct quotes ($/FC), use (F-S)/S.

18. Currency Yield Curve & Forwards
Months
Interest
yield 2 4 1 3 5 6
1.0 %
3.0 %
4.0 %
5.0 %
6.0 %
2.0 %
Euro yield curve
Forward premium on
low interest rate currrency
Eurodollar
yield curve

19. Interest Rate Parity (IRP)
Interest rate parity:difference in national interest rates for securities of similar risk & maturity should be equal to opposite of forward rate discount/ premium for foreign currency. or

20. Interest Rate Parity (IRP)
Dollar money market
$1,000,000
$1,020,000
 1.02
Start
End
i $ = 8 % per annum
(2 % 90 days)
S = SF /$
SF 1,480,000
F90 = SF /$
$1,019,993
90 days
Swiss franc money market
SF 1,494,800
 1.01
i SF = 4 % per annum
(1 % 90 days)

21. Covered Interest Arbitrage (CIA)
Because spot & forward markets are not in equilibrium, arbitrage exists.
Covered interest arbitrage (CIA): invests in currency that offers higher return on covered basis.

22. Covered Interest Arbitrage (CIA)
Eurodollar rate = 8.00 % per annum
Dollar money market
$1,000,000
$1,040,000
 1.04
Start
End
F180 = ¥ /$
Arbitrage
Potential
$1,044,638
S =¥ /$
¥ 106,000,000
180 days
Yen money market
¥ 108,120,000
 1.02
Euroyen rate = 4.00 % per annum

23. Uncovered Interest Arbitrage (UIA)
Uncovered interest arbitrage (UIA): investors borrow in currencies w/ low interest rates & convert proceeds into currencies w/ high interest rates.
“Uncovered” because investor does not sell the currency forward.

24. Uncovered Interest Arbitrage (UIA): The Yen Carry Trade
Investors borrow yen at 0.40% per annum
Japanese yen money market
¥ 10,000,000
¥ 10,040,000 Repay
 1.004
Start
End
S360 = ¥ /$
¥ 10,500,000 Earn
¥ ,000 Profit
Then exchanges
the yen proceeds
for US dollars,
investing in US
dollar money
markets for
one year
S =¥ /$
$ 83,333,333
360 days
US dollar money market
$ 87,500,000
 1.05
Invest dollars at 5.00% per annum

25. Interest Rate Parity (IRP) & Equilibrium4 3 2
Percentage premium on
foreign currency (¥) 1
4.83 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 -1 -2 -3
Percent difference between
foreign (¥) and domestic ($)
interest rates X U -4 Y Z

26. Forward Rate - Unbiased Predictor?
Exchange rate
Time S2
Error F2 S3 S4 F1
Error S1 F3
Error
t 2
t 3
t 4
t 1