LongerTerm Exchange Rate and Price Movements

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Longer-Term Exchange Rate and Price Movements

• International Finance
• Dick Sweeney

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Take Aways

• Using PPP to help value projects, firms
• Reduces uncertainty
• PPP helps to estimate your uncertainty
• PPP more useful at longer time horizons
• But much uncertainty even at longer horizons
• Technical analysis better for shorter horizons
• PPPs usefulness, limitations in predicting
  longer-term exchange rates and prices
• PPP helps but is no guarantee
• Very useful for 100 projects with modest
  correlation

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I. PPP and Trends

• PPP relevant for high-inflation countries trends
• Look at Brazil or Argentina in old days
• But did exchange rate depreciate as much as
  inflation? More? Less?
• Floating (Zambia) crawling peg (Brazil)
  adjustable peg (Indonesia)
• What about low-inflation, low-depreciation
  countries Dont have dominant long-run trends
• Conclusion Not exchange rate, but exchange rate
  versus prices, that mattersreal exchange rate

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II. Real Rate and Competitiveness

• A competitiveness approach to PPP
• S is spot rate in European terms for DEM relative
  to USD (DEM for one USD)
• Hey! What about the Euro? Come back in 3-4 years
• PUS, price of basket of goods in U.S. in USD
• PGer, price of same basket in Germany in DEM
• Which basket? bit arbitrary
• Look at CPIs common choice

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II. Real Rate (cont.)

• Compare US prices and German prices
• Convert German price index to USD divide by S,
  so PGer,USD PGer /S
• Or multiply by S' ( 1/S S' is rate in American
  terms)
• Define real exchange rate R as the ratio
  PUS / PGer,USD R
• Arbitrary Could look at R' 1/R
• Often look at lnR, log of R
• Often compare lnSt versus lnRt

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III. Behavior of Real Rate

• Two possible ways to think about the real
  exchange rate (see following graph)
• The real exchange rate is a non-stationary,
  "random walk" variable
• Changes are mostly not forecastable
• Alternative PPP holds in long runmean-reverting
  real rate
• May take a very long time
• Actual path to long run fairly uncertain new
  shocks
• Forecastable, but still substantial uncertainty

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Mean Reversion? or Not?
Et lnRth lnRt, h gt 0
? ?
?
lnRt
a / (1 - b)
lnR
Talk about in few minutes
?
time
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IV. ExampleWhy you care

• DEM FCFs of German operation directly
  proportionate to German price level
• Hold constant US price level in example
• Keep it simple!
• Receiving DEM 2m now S DEM 2/USD, RR 10
• PV ECF/RR (2m/2)/.1 1m/.1
  USD 10m
• DEM now depreciates to DEM 3/USD--what is new PV?
  With random-walk real rate, PV (2m/3)/.1
  USD 6.67m

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IV. Example (cont.)

• What if mean-reverting real exchange rate?
• Suppose S doesnt adjust but PGer does
• Pass through of depreciation to prices,
  familiar in countries with inflation
• Might have both S and Pger adjust
• Keep it simple!
• In long run, S up by 50 means PGer up by 50,
  DEM FCFs up by 50 to DEM 3m
• In long run, PV (3m/3)/.1 USD 10m, as before

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IV. Example (cont.)

• Short run effects suppose gap between initial
  and long-run real rate made up at 20 per year of
  initial gap
• Future FCFs are then DEM 2.2m, 2.4m, 2.6m, 2.8m,
  3m, 3m
• PV (2.2m/3)/(1.1) (2.4m/3)/(1.1)2
  (2.6m/3)/(1.1)3 (2.8m/3)/(1.1)4
  (3m/3)/(1.1)5 (3m/3)/.1/(1.1)5 9.447m
  versus 6.67m versus 10.0m

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V. Basic Forecasting Model

• Need to know Mean reversion? Random-walk real
  rate?
• Basic forecasting model (in logs)
  lnRt a b lnRt-1
  ut, ut ? N(0, ?2u)
• Long-Run Mean lnR
• lnR a b lnR ? lnR a / (1-b)
• Makes sense only if b lt 1
• Imagine b ? 1 from below (1 - b) ? 0, a / (1 -
  b) ? ? ? as a gt,lt 0
• Graphical interpretation of model (previous
  graph) lnR is (log of) long run real exchange
  rate
• Disturbances move lnRt away from long run level

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V. Forecasting Model (cont.)

• How to use estimates to forecast real exchange
  rate
• Need a, b for long-run equilibrium real rate
  a / (1 - b) lnR
• Need (1 - b) for speed of adjustment (see below)
• Need estimate of error variance, ?2u, to
  estimate the uncertainty of real-rate forecast
• ?2u ? ?u, standard deviation of disturbance ut
  

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VI. Testing for mean reversion

• For single currencies by themselves, cannot
  reject null of b 1
• Random walk, no mean reversion
• But tests on a system of currencies,for G-10
  countries relative to US
• Usually some econometric gain to pooling like
  this--Like adding more observations for any one
  country
• Jorion and Sweeney (1996) Often reject null
  hypothesis of b 1 in favor of alternative that
  b lt 1 ? mean reversion!

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VI. Testing Notes

• For your information, in dealing with
  econometrics geeks
• b lt 1? or b 1?
• b 1 ? real rate non-stationary, mean reversion
  doesnt work
• Econometric problems Mainstream statistics are
  for stationary, mean-reverting variables
• But if b ? 1, lnRt is non-stationary cannot use
  standard t-statistic critical values (2.0, etc.)
  
• Can still calculate t-statistics, of course, but
  have to find new critical values
• Use simulation based on your data set to find
  critical values Jorion and Sweeney (1996) use
  simulation

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VII. Forecasting Results

• Acid test How do different approaches do out
  of sample?
• This is what you need in decisions
• On average, mean reversion models work better
  than random walk models
• For any one MA deal like German firm, may lose
  if bet on mean reversion
• For 100 MA deals like German firm,
• very high probability that bets on mean
  reversion pay off if modest correlation

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VII. Forecasting Results (cont.)

• Using PPP model, benefits increase as the
  forecast horizon lengthens
• Benefits increase with longer estimating period
  (Siddique and Sweeney 1998)
• Even at one-year horizons, PPP calculations
  reduce uncertainty by only about 10 percent
  relative to random-walk forecasts