1. Exchange Rate Determination
Lecture 2
Exchange Rate Determination

2. Some basic questions Why aren’t FX rates all equal to one?
Why do FX rates change over time?
Why don’t all FX rates change in the same direction?
What drives forward rates – the rates at which you can trade currencies at some future date?
FIN 509 Spring 2004

3. Definitions f€/$ : forward rate of exchange
r$ : dollar rate of interest (r¥, rHK$,…)
i$ : expected dollar inflation rate
f€/$ : forward rate of exchange
s€/$ : spot rate of exchange
“Indirect quote”:
s€/$ =  1 $ buys €
“Direct quote”:
s$/€ =  1 € buys $1.2017
FIN 509 Spring 2004

4. 3. Four theories . Difference in Exp. difference in interest rates
Fisher
Theory
Difference in
interest rates
1 + r€
1 + r$
Exp. difference in
inflation rates
1 + iSFr
1 + i$
Interest
Rate
parity
Relative PPP
Difference between
forward & spot rates
F€/$
s€/$
Expected change
in spot rate
E(s€/$)
S€/$
Exp. Theory
of forward
rates
FIN 509 Spring 2004

5. Theory #1: Purchasing power parity
Law of One Price
Versions of
PURCHASING
POWER
PARITY
Absolute PPP
Relative PPP
FIN 509 Spring 2004

6. The Law of One Price
A commodity will have the same price in terms of common currency in every country
In the absence of frictions (e.g. shipping costs, tariffs,..)
Example
Price of wheat in France (per bushel): P€
Price of wheat in U.S. (per bushel): P$
S€/$ = spot exchange rate
P€ = s€/$  P$
FIN 509 Spring 2004

7. The Law of One Price, continued
Example:
Price of wheat in France per bushel (p€) = 3.45 €
Price of wheat in U.S. per bushel (p$) = $4.15
S€/$ = (s$/€ = )
Dollar equivalent price
of wheat in France = s$/€ x p€
= $/€ x 3.45 € = $4.15
 When law of one price does not hold, supply and demand forces help restore the equality
FIN 509 Spring 2004

8. Absolute PPP Extension of law of one price to a basket of goods
Absolute PPP examines price levels
Apply the law of one price to a basket of goods with price P€ and PUS (use upper-case P for the price of the basket):
where P€ = i (wFR,i  p€,i )
PUS = i (wUS,i  pUS,i )
S€/$ = P€ / PUS
FIN 509 Spring 2004

9. Absolute PPP
If the price of the basket in the U.S. rises relative to the price in Euros, the U.S. dollar depreciates:
May 21 : s€/$ = P€ / PUS
= € / $ = €/$
May 24: s€/$ = € / $ = €/$
FIN 509 Spring 2004

10. Relative PPP Absolute PPP: Relative PPP: P€ = s€/$  P$
For PPP to hold in one year:
P€ (1 + i€) = E(s€/$)  P$ (1 + i$),
or: P€ (1 + i€) = s€/$ [E(s€/$)/s€/$ )]  P$ (1 + i$)
Using absolute PPP to cancel terms and rearranging:
Relative PPP:
P€ = s€/$  P$
1 + i€ = E(s€/$)
1 + i$ s€/$
FIN 509 Spring 2004

11. Relative PPP
Main idea – The difference between (expected) inflation rates equals the (expected) rate of change in exchange rates:
1 + i€ = E(s€/$)
1 + i$ s€/$
FIN 509 Spring 2004

12. The Purchasing Power Parity Theory (PPP)
The PPP theory was developed by Swedish economists Gustav Cassel in 1920 to determine the exchange rate between countries on inconvertible paper currencies.
This theory states that, the rate of exchange between two countries is determined by purchasing power in two different countries
PPP have two versions:
The absolute purchasing power parity theory
The relative purchasing power parity theory 12

13. 1) Absolute Purchasing power parity
The absolute version states that the exchange rates between two countries is equal to the ratio of the price level in the two countries. The formula is, R AB = PA /PB where RAB is the exchange rate between two countries A and B and PA and PB refers to general price level in two countries 13

14. Absolute Purchasing power parity (cont..)
For example if price of one bushel of wheat is $1 in U.S and £1 in U.K then exchange rate between $ and £ is equal to 1
According to the law of one price, a given commodity should have same price
So purchasing power of two currencies is at parity in both countries
If the price of one bushel of wheat in term of $ were $0.50 in U.S and £1.50 in U.K …firm would purchase wheat in U.S and resell it in U.K at profit

15. Absolute Purchasing power parity (cont..)
This commodity arbitrage would cause the price of wheat to fall in U.K and rise in U.S until the prices were equal to $1per bushel in both economies
Criticisms
This version is not used because it ignore the transportation cost and other factors.

16. 2) The Second Version ( Relative purchasing parity)
According to this version the change in the exchange rate over a specific period of time should be proportional to the relative change in price level in the two nations over the same period of time The formula used for determination of exchange rate is R1 =P1a/P0 . R0 where R1 shows exchange rate in period 1, and R0 shows exchange rate in base period for example if general price level does not change in foreign nation from the base period to period 1 Where as general price level in the home nation increase by 50%
P1b/P0 16

17. The Second Version ( Relative purchasing parity)
So according to PPP theory the exchange rate (price of a unit of foreign currency in term of domestic currency) should be 50% higher in period 1 as compared to the base period (home currency depreciated by 50%)
This theory can be explain with the help of other example.
Suppose India and England are on inconvertible paper standard and by spending Rs.60, the bundle of goods can be purchased in India as can be bought by spending £ 1 in England. Thus, according to PPP, the rate of exchange will be Rs. 60= £ 1
Suppose domestic price index increase by 300 and foreign price index rises to 200 the new exchange rate will be Rs 60 =£1.5

18. Explanation (PPP)
The exchange rate would be a proper reflection of the purchasing power in each country if the relative values bought the same amount of goods in each country. 18

19. BOP theory for Determination of exchange rate
According to this theory ,exchange rate of a currency depends on its BOP position
A favorable BOP raise the exchange rate
And unfavorable BOP reduces the exchange rate
Thus according to this theory exchange rate is determined by the demand and supply of foreign exchange
Demand for foreign exchange arises from the debit side of the balance sheet
Supply of foreign exchange arises from credit side of balance sheet

20. BOP theory for Determination of exchange rate (Cont…)
When BOP is unfavorable it means that demand for foreign currency is more than its supply
It means that external value of domestic currency in relation to foreign currency fall
Consequently exchange rate to fall…..how ?
Suppose RS 60=$1 , external value of domestic currency is .017
Due to unfavorable BOP Rs90=$1 so external value of domestic currency is ……… .011
On other hand if BOP is favorable it means that supply of foreign is greater than demand
It means that external value of domestic currency in relation to foreign currency rise

21. BOP theory for Determination of exchange rate (Cont…)
Consequently exchange rate to rise
Suppose RS 60=$1 , so external value of domestic currency is .017
Due to favorable BOP Rs 40=$1 so external value of domestic currency is ……… .025
In conclusion, in foreign exchange determination BOP is important

22. BOP theory for Determination of exchange rate (Cont…)
price of $ in Rupee S R2 R
Exchange rate R1 S D Q
Dollars

23. What is the evidence? The Law of One Price frequently does not hold.
Absolute PPP does not hold, at least in the short run.
See The Economist’s Big McCurrencies
Homework: Use The Economist Big Mac Index: July 2013
Identify whether Euro, Japanese Yen, Great British Pound, Chinese Yuan, Swiss Frank and your own countries currency s are overvalued or undervalued against USA$.
Compare today's exchanage rates with July rates and discuss whether the big mac index gives right directions or not.
The data largely are consistent with Relative PPP, at least over longer periods.
FIN 509 Spring 2004

24. Statistical difficulties
Deviations from PPP
Simplistic model
Why does
PPP
not
hold?
Imperfect Markets
Statistical difficulties
FIN 509 Spring 2004

25. Statistical difficulties
Deviations from PPP
Transportation costs
Tariffs and taxes
Consumption patterns differ
Non-traded goods & services
Sticky prices
Markets don’t work well
Construction of price indexes
- Different goods
- Goods of different qualities
Simplistic model
Imperfect Markets
Statistical difficulties
FIN 509 Spring 2004

26. Summary of theory #1: . Exp. difference in inflation rates 1 + i€
Relative PPP
Expected change
in spot rate
E(s€/$)
S€/$
FIN 509 Spring 2004

27. Theory #2: Interest rate parity
Main idea: There is no fundamental advantage to borrowing or lending in one currency over another
This establishes a relation between interest rates, spot exchange rates, and forward exchange rates
Forward market: Transaction occurs at some point in future
BUY: Agree to purchase the underlying currency at a predetermined exchange rate at a specific time in the future
SELL: Agree to deliver the underlying currency at a predetermined exchange rate at a specific time in the future
FIN 509 Spring 2004

28. PART IV. INTEREST RATE PARITY THEORY
I. INTRODUCTION
A. The Theory states:
the forward rate (F) differs from the spot rate (S) at equilibrium by an amount equal to the interest differential (rh - rf) between two countries.

29. INTEREST RATE PARITY THEORY
2. The forward premium or
discount equals the interest
rate differential.
(F - S)/S = (rh - rf)
where rh = the home rate
rf = the foreign rate

30. INTEREST RATE PARITY THEORY
3. In equilibrium, returns on
currencies will be the same
i. e. No profit will be realized
and interest parity exists
which can be written
(1 + rh) = F
(1 + rf) S

31. INTEREST RATE PARITY THEORY
B. Covered Interest Arbitrage
1. Conditions required:
interest rate differential does
not equal the forward premium or discount.
2. Funds will move to a country
with a more attractive rate.

32. INTEREST RATE PARITY THEORY
3. Market pressures develop:
a. As one currency is more
demanded spot and sold
forward.
b. Inflow of fund depresses
interest rates.
c. Parity eventually reached.

33. INTEREST RATE PARITY THEORY
C. Summary:
Interest Rate Parity states:
1. Higher interest rates on a
currency offset by forward discounts.
2. Lower interest rates are offset by forward premiums.

34. Example of a forward market transaction
Suppose you will need 100,000€ in one year
Through a forward contract, you can commit to lock in the exchange rate
f$/€ : forward rate of exchange
Currently, f$/€ =  1 € buys $
 1 $ buys €
At this forward rate, you need to provide $119,854 in 12 months.
FIN 509 Spring 2004

35. Interest Rate Parity START (today) END (in one year) r$=2.24% $117,228
$117,228  = $119,854
(Invest in $)
One year
s€/$=
f€/$=
(Invest in €)
$117,228  = 97,551€
97,551€  = 100,000€
r€=2.51%
FIN 509 Spring 2004

36. Interest rate parity
Main idea: Either strategy gets you the 100,000€ when you need it.
This implies that the difference in interest rates must reflect the difference between forward and spot exchange rates
Interest
Rate Parity:
1 + r€ = f€/$
1 + r$ s€/$
FIN 509 Spring 2004

37. Interest rate parity example
Suppose the following were true:
Does interest rate parity hold?
Which way will funds flow?
How will this affect exchange rates?
U.S Dollar
Euro
12 month interest rate
2.24%
2.70%
Spot rate
€ / $
Forward rate
€ / $
FIN 509 Spring 2004

38. Evidence on interest rate parity
Generally, it holds
Why would interest rate parity hold better than PPP?
Lower transactions costs in moving currencies than real goods
Financial markets are more efficient that real goods markets
FIN 509 Spring 2004

39. Summary of theories #1 and #2:.
Difference in
interest rates
1 + r€
1 + r$
Exp. difference in
inflation rates
1 + i€
1 + i$
Interest
Rate
parity
Relative PPP
Difference between
forward & spot rates
f€r/$
s€/$
Expected change
in spot rate
E(s€/$)
s€/$
FIN 509 Spring 2004

40. Theory #3: The Fisher condition
Main idea: Market forces tend to allocate resources to their most productive uses
So all countries should have equal real rates of interest
Relation between real and nominal interest rates:
(1 + rNominal) = (1 + rReal)(1 + i )
(1 + rReal) = (1 + rNominal) / (1 + i )
FIN 509 Spring 2004

41. Example of capital market equilibrium
Fisher condition in U.S. and France:
(1 + r$(Real)) = (1 + r$) / (1 + i$)
(1 + r€(Real)) = (1 + r€) / (1 + i€)
If real rates are equal, then the Fisher condition implies:
The difference in interest rates is equal to the expected difference in inflation rates
1 + r€ = i€
1 + r$ i$
FIN 509 Spring 2004

42. Summary of theories 1-3: . Difference in Exp. difference in
Fisher
Theory
Difference in
interest rates
1 + r€
1 + r$
Exp. difference in
inflation rates
1 + i€
1 + i$
Interest
Rate
parity
Relative PPP
Difference between
forward & spot rates
f€/$
s€/$
Expected change
in spot rate
E(s€/$)
s€/$
FIN 509 Spring 2004

43. Theory #4: Expectations theory of forward rates
Main idea:
The forward rate equals expected spot exchange rate
Expectations theory
of forward rates:
f€/$ = E(s€/$)
f€/$ = E(s€/$ )
s€/$ s€/$
FIN 509 Spring 2004

44. Expectations theory of forward rates
With risk, the forward rate may not equal the spot rate
If Group 1 predominates, then E(s€/$) < f€/$
If Group 2 predominates, then E(s€/$) > f€/$
Group 1: Receive €
in six months, want $
Wait six months and
convert € to $ or
Sell € forward
Group 2: Contracted to
pay out € in six months
Wait six months and
convert $ to € or
Buy € forward
FIN 509 Spring 2004

45. Takeaway: Summary of all four theories.
Fisher
Theory
Difference in
interest rates
1 + r€
1 + r$
Exp. difference in
inflation rates
1 + i€
1 + i$
Interest
Rate
parity
Relative PPP
Difference between
forward & spot rates
f€/$
s€/$
Expected change
in spot rate
E(s€/$)
s€/$
Exp. Theory
of forward
rates
FIN 509 Spring 2004