Behavior of Nominal Exchange Rates

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Behavior of Nominal Exchange Rates

• International Finance
• Dick Sweeney

2
Beating the Market???

• Not a course in "how to beat the market"
• But talking about whether you can make profits
  introduces you to lots of important topics
• In this introduction, it looks hard to beat the
  market
• But stay tuned for technical analysis

3
The Euro

• Look at graph of Euronumber of USD per Euro
• Looks like a random walk
• Look at graph of percentage rates of change of
  price of Euro (rate of return, R-of-R)
• Looks like they are random
• What does random walk mean in finance terms?
• What does random mean in finance terms?

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U.S. Stock Market Indices
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(No Transcript)
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Euro Easier to See
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Change in Euro
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Change in Euro Easier to See
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The Euro (cont.)

• Points about the Euro apply equally well to
  prices and rates of return of stocks, bonds, etc.
  
• Your understanding about stocks and other assets
  apply to exchange rates
• Later
• What does random walk mean in statistical
  terms? Euro is only approximation
• What does random mean in statistical terms?
• Purpose is to sharpen, clarify understanding

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Random Walks and PredictionDo the Patterns
Allow Profits?

• The Euro is approximately a random walk
• A high value of the Euro today means the value of
  the Euro will be high tomorrow
• But you cant tell whether tomorrows value will
  be higher or lower than todays value
• A low value of the Euro today means the value of
  the Euro will be low tomorrow
• But you cant tell whether tomorrows value will
  be higher or lower than todays value
• Profits come from predicting rates of return

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Regression Log Levels

• Dependent Variable LNEURO (natural logarithm of
  Euro)
• Sample (adjusted) 2 1741
• Variable Coefficient Std. Error t-Statistic Prob. 
   
• C 0.000181 0.000167 1.085198 0.2780
• LNEURO(-1) 0.999666 0.001004 995.4134 0.0000
• R-squared 0.998249     
• Durbin-Watson stat 1.996749     

yt a b xt et yt and xt are observable. a
and b are parameters to estimate. et is an
error. a is the intercept, b is the slope

LNEURO(-1) explains 99.8249 of ups and downs in
LNEURO.
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Random Rates of Return and Prediction

• Each days Euro rate of return fluctuates
  (approximately) unpredictably around mean value
• You may be able to predict (estimate) mean value
• But not whether R-of-R is above or below the
  mean, or how much above (or below)
• Not very favorable for making profitable bets
  about what tomorrows R-of-R will be
• But random walk looked kind of good
• Lots of patterns, reversals etc.

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Detecting a Random Walk

• Random walks have different mean values across
  different time periods
• Rates of return have pretty much the same mean
  across sample
• Random walks show lots of interesting patterns
  across time
• Pretty hard to detect patterns in rates of return
• You make profits by predicting rates of return

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Regression Change in Log Levels(percentage
rates of return)

• Dependent Variable DLNEURO
• Sample (adjusted) 3 1741
• Variable Coefficient Std. Error t-Statistic Pr
  ob.  
• C 0.000148 0.000149 0.991068 0.3218
• DLNEURO(-1) -0.000297 0.023954 -0.012418 0.9901
  
• R-squared 0.000000     
• Durbin-Watson stat 2.000971     

yt a b xt et yt and xt are observable. a
and b are parameters to estimate. et is an
error. a is the intercept, b is the slope

DLNEURO(-1) explains 0.00 of ups and downs in
DLNEURO.
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What exactly is a random series?

• 'Program 1 Random variables.
• 'EViews 5 program for random variables and random
  walks.
• 'Note these programs have to written in Courier.
• SMPL 1 100
• 'This gives a "sample" with 100 observations.
• genr profit_rate nrnd
• 'where "nrnd" means a random variable from a
• 'normal distribution with a mean of zero
• 'and a variance of unity (one).

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Normal Distribution
"Bell-shaped" curve
Standard Normal N(0, 1) Does not have to
be normalconvenient, easy to work with..
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Normal Distributions
Normal, but centered on -2.00.
Small spread
Large spread
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Generated Profit Rates
From Program 1.
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Change in Euro 100 Observations
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Change in Euro Easier to See
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From Random to Random Walk

• Program 2 Random variables AND random walks.
• 'EViews 5 program for random variables and random
  walks.
• SMPL 1 1
• 'This says to look just at the first observation.
  
• genr level profit_rate (could add a
  constant, say 1 or 100)
• SMPL 2 100
• 'Now we look at the next 99 observations
• genr level level(-1) profit_rate
• SMPL 1 100
• 'This puts us back again with 100 observations.

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Generated Random Walk
From Program 2
Random Walk
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Random Walk, Built from Generated Random Rates of
Return
Random Walk
Random
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Generated Random Rates of Return Approximately
Normal
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Generated Level of Random WalkFar from Normal
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Regression Generated Rates of Return
yt a b xt et Yt, xt are observable
variables. a, b are parameters to estimate. et
is a random error term.

• Dependent Variable change
• Method Least Squares
• Sample (adjusted) 3 1741
• Variable Coefficient Std. Error t-Statistic
  Prob.  
• C 0.000148 0.000149 0.991068 0.3218
• change(-1) -0.000297 0.023954 -0.012418 0.9901
• R-squared 0.000297     
• Durbin-Watson stat 2.000971

change(-1) explains 0.0297 of ups and downs in
change.
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Scatter Diagram Generated Rates of Return (from
previous slide)
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Regression Levels (same data)
yt a b xt et Yt, xt are observable
variables. a, b are parameters to estimate. et
is a random error term.

• Dependent Variable LEVEL
• Sample (adjusted) 2 100
• Variable Coefficient Std. Error t-Statistic Prob.
    
• C -0.042629 0.106152 -0.401588 0.6889
• LEVEL(-1) 0.959393 0.029249 32.80094 0.0000
• R-squared 0.917299     
• Durbin-Watson stat 1.583474  

LEVEL(-1) explains 91.37 of ups and Downs in
LEVEL.
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Scatter Diagram Generated Price Levels (same
data as before)
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Example 1 Generated
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Example 2 Generated
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Example 3 Generated
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Example 4 Generated
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Practice 1 Figure
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Practice 1 (same data)

• Dependent Variable PROFIT_RATE
• Sample (adjusted) 2 100
• Variable Coefficient Std.
  Error t-Statistic Prob
• C -0.173938 0.110005 -1.581179
  0.1171
• PROFIT_RATE(-1) -0.011498 0.101046 -0.113792
  0.9096
• R-squared 0.000133     
• Durbin-Watson stat 2.013712

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Practice 1 (cont.same data)

• Dependent Variable LEVEL
• Sample (adjusted) 2 100
• Included observations 99 after adjustments
• Variable Coefficient Std. Error t-Statistic
  Prob.  
• C -0.281801 0.188601 -1.494159 0.1384
• LEVEL(-1) 0.988304 0.016429 60.15428
  0.0000
• R-squared 0.973893     
• Durbin-Watson stat 2.019364     

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Practice 1 (cont.)
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Practice 1 (cont.)
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Practice 2 Figure
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Practice 2 (cont.)

• Dependent Variable PROFIT_RATE
• Sample (adjusted) 2 100
• Variable Coefficient Std. Error t-Statistic
  Prob.  
• C -0.038100 0.104134 -0.365876 0.7153
• PROFIT_RATE(-1) 0.103083 0.100919 1.021445
  0.3096
• R-squared 0.010642     
• Durbin-Watson stat 1.943564     

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Practice 2 (cont.)

• Dependent Variable LEVEL
• Sample (adjusted) 2 100
• Variable Coefficient Std. Error t-Statistic
  Prob.  
• C -0.575786 0.187474 -3.071280 0.0028
• LEVEL(-1) 0.815729 0.054805 14.88426 0.0000
• R-squared 0.695487     
• Durbin-Watson stat 1.667700     

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Practice 2 (cont.)
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Practice 2 (cont.)