IBUS 302:
International Finance
Topic 9–Fisher Effects
Lawrence Schrenk, Instructor
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Learning Objectives
1.
2.
3.
4.
Distinguish real versus nominal values. ▪
Calculate the real exchange rate and
discuss its implications for international
competition.
Describe the evidence for PPP and the
reasons there may be deviations from it.
Explain the international Fischer effect and
the forward expectations parity.▪
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Real versus Nominal Values

Nominal Values




Values before an adjustment for inflation
The price stated in a contract
The actual price you will pay either now or later
Real Values



Values after an adjustment for inflation
‘Constant’ dollars
Incorporates only productivity changes
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The Fisher Effect (FE)

Variables




Nominal return (i)
Real Return (r)
Inflation (p)
Relationship
1 + i 

1
+ r  1 + E p  
NOTE: Do not use the approximation: i ≈ r + p
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If PPP Holds
If PPP holds



There is inflation (i.e., price levels change)
FX rates change cancelling the effects of inflation

So the changes have been only nominal
Real exchange rate (q) = 1.
International competitiveness does not
change



The amount you can buy in dollar terms has not
changed.
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If PPP Does Not Hold
If PPP does not hold



There is inflation (i.e., price levels change)
FX rates may change, but do not completely
cancel the effects of inflation

So some part of the changes are real
Real exchange rate (q) ≠ 1.
International competitiveness does change



The amount you can buy in dollar terms has
changed.
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Real Exchange Rate


q is the deviation from PPP
q is the real exchange rate
1+ p $
q
1+ e 1+ p x 

e is the (empirical) percentage change in F based on
current data. (Do not confuse it with ePPP which is the
(theoretical) percentage change in F consistent with
relative PPP.)
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ePPP versus e
F S
e
S

Formula:

Notation (not in the textbook)

ePPP is the percentage change in F predicted by PPP.
e is the (empirical) percentage change in F based on
current data.
If e = ePPP, then

PPP holds, i.e., no deviation and q = 1

International competitiveness does not change.
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Real Exchange Rate and
Competitiveness
q and competitiveness




< 1 domestic more competitive
= 1 no change
> 1 domestic less competitive
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Real Exchange Rate Example





p$ = 5%
p€ = 4%
S($/€) = 1.4300
F($/€) = 1.4500
What is q?
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Solution

Actual Change in Forward Rate
F  S 1.4500  1.4300
e

S
1.4300
 0.0140 1.40%

Real Exchange Rate
1+ p $
1.05
q

 1.0212
1+ e 1+ p x  1.01401.014 
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Analysis

If PPP held, then the forward rate should be:
ePPP
FPPP

 p $  p x   0.05  0.04 

 0.0096


1.04

 1+ p x  
 1.4300  1.0096  1.4438
The actual forward rate, F, is 1.4500, so


PPP does not hold, and
q > 1, so domestic trade is less competitive
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Practice: Absolute PPP

Data




US Big Mac $3.54
UK Big Mac £2.29
S($/£) = 1.4689
Questions


What is SPPP($/£)?
Does absolute PPP hold?
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Practice: Relative PPP

S($/£) = 1.4689, F12($/£) = 1.4722, p$ = 7.4%, p£ = 6.1%

Question: Does relative PPP hold?

What is ePPP?
ePPP

p $  p x 


 1+ p x 
What is FPPP?
FPPP ($/x)  S($/x)  1 + e
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Practice: Relative PPP

S($/£) = 1.4689, F12($/£) = 1.4722, p$ = 7.4%, p£ = 6.1%

Question: If not what is the real exchange rate?

What is e ? (Remember this is different from ePPP)
F S
e
S

What is q?
1+ p $
q
1+ e 1+ p x 
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Practice: Relative PPP


S($/£) = 1.4689, F12($/£) = 1.4722, p$ = 7.4%, p£ = 6.1%
Question: What are the implications for
international competition?
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Evidence: Absolute PPP
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Evidence: Relative PPP
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PPP Deviations

Transportation Costs


Trade Restrictions




Shipping costs can remove arbitrage
opportunity; imports become relatively more
expensive.
Example: Pharmaceutical Industry
Cost of Non-Tradable Inputs
Taxes
Productivity
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‘Big Mac’ Index



Index
Analysis
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International Fischer
Effect and the Forward
Expectations Parity
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Overview

Interest Rate Parity
interest rates (i) →

Purchasing Power Parity
inflation (p)

forward rate
→
forward rate
↔
inflation (p)
Fisher Effect
interest rates (i)
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Implications



IRP connects FX and interest rates
PPP connects FX and inflation
Fisher Effect connects interest rates and
inflation
FX
Inflation
Interest Rates
Fisher Effect
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Fisher Effect (FE)


Inflation increases causes interest rate increase.
Recall time value of money (TVM) motivations




Opportunity Costs
Inflation
Risk
Interest rates must compensate the investor for
expected inflation:
i  1 + r  1 + E p    1
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Fisher Effect

Fisher Effect applies to all currencies
individually:


i $  1 + r$  1 + E p $   1
i £  1 + r £  1 + E p £    1
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International Fisher Effect
(IFE)

Combine PPP and FE to get IFE




The real rate should be equal r$ = r£
i x  rx
Rewrite FE as: E p x  
1+ rx 
p $  p x 
Recall PPP: E  ePPP   

1
+
p

x 
 i$  i x 

IFE   
1
+
i

x 
Substitute FE into PPP: E  e
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Forward Expectations Parity
(FEP)

Combine IFE and IRP to get FEP

 i$  i x 
Recall IFE: E  eIFE   

 1+ i x 

FIRP  S i$  i x
Recall IRP (in a different form):

S
1+ ix

Combine IFE and IRP for FEP:
i$  i x
FIRP  S
 E  eIFE  
S
1+ i x
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Forward Expectations Parity
(FEP): Implications I

Percentage Change Analysis
i$  i x
FFEP  S
 E  eIFE  
S
1+ i x

The percentage change in the exchange rate, i.e.,
the forward premium or discount, is equal to the
expected change in the exchange rate.
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Forward Expectations Parity
(FEP): Implications II

Forward Rate Analysis
E  FFEP   S 1 + E  eIFE  
i$  i x
where E  eIFE  
1+ ix

The expected forward rate is equal to the spot
rate increased by the expected change in the
exchange rate.
29 (of 18)
FEP Example

S($/A$) = 0.6495, i$ = 4.2%, iA$ = 3.3%
 i $  i A$ 
E  FFEP   S 1 +

 1 + i A$ 
 0.042  0.033 
 0.6495 1 +
 0.6552

1.033


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Implications



IRP connects FX and interest rates
PPP connects FX and inflation
Fisher Effect connects interest rates and
inflation ▪
FX
FEP ▪
Inflation
Interest Rates
Fisher Effect
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Fisher Required Formulae

Fisher Effect (FE)
i  1 + r  1 + E p    1

International Fisher Effect (IFE)
 i$  i x 
E  eIFE   

1
+
i

x 

Forward Expectations Parity (FEP)
i$  i x
FFEP  S
 E  eIFE  
S
1+ i x
32 (of 18)