Lecture 9: Parity Models and Foreign Exchange Rates

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Lecture 9 Parity Models and Foreign Exchange
Rates

• Evaluating Current Spot Rates and Forecasting
  Rates with Parity Models
• International Fisher Effect

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Where is this?
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What Else is Egypt Noted For? 4,000 year old
Pyramids of Giza
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Also Noted for Strange Behavior At the Top --
455 Ft
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View From the Top
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Islamic Law (Sharia)

• Sharia, or Islamic law, influences the legal code
  in most Muslim countries.
• Sharia (an Arabic word meaning "the right path)
  originated as an important part of the Islamic
  religion.
• It is estimated that 1.3 billion people in the
  world practice the Islamic religion, second only
  to Christianity (with 2.5 billion people).
• Saudi Arabia and Iran apply Islamic law most
  extensively, and other countries uses it to
  varying degrees (including Egypt).

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Islamic Capital Markets

• Islamic financial markets and institutions are
  based on Sharia Law. As such, Islamic financial
  institutions and financial instruments (banking,
  bonds and equities) must comply (i.e., be sharia
  compliant) with the following
• Prohibition of Riba (Interest).
• Avoidance of Gharar (Ambiguity) in agreements.
• Prohibition of Maisir (Gambling/Speculation).
• No involvement in production and/or distribution
  of prohibited commodities (e.g., alcoholic
  beverages).
• The total Islamic capital market has been
  estimated a 1.2 trillion USD and includes banking
  (31 of the market), and the bond and equity
  markets (69).

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Islamic Financial Institutions/Markets

• These include
• Islamic Banking Institutions Estimated at 15 of
  the worlds banking sector.
• Islamic Bonds Called a sukuk (sue-coat). Sukuk
  bonds are based on a pool of reference assets
  (land, fixed assets). Holders receive rental
  returns based on the future profits generated by
  these assets (asset-backed certificates).
• Malaysia accounts for about 2/3rd of the
  outstanding sukuk market. There are currently
  USD226b worth of sukuk outstanding with 64
  denominated in Malaysian ringgits and 15 in USD.
  
• Secondary market Sukuk bonds trade on the Paris
  platform of NYSE-Euronext.
• Islamic Equities.
• Major market is Malaysia. Almost 90 of the
  stocks trading on the Malaysian stock (Bursa
  Malaysia) exchange are sharia compliant. Market
  also reports an Islamic Equity Index (Kuala
  Lumpur Sharia Index). Dow Jones also publishes
  Islamic Equity Indexes http//www.djindexes.com/i
  slamicmarket/

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Islamic Bonds (Sukuk)

• Issued by sovereigns (e.g., Malaysia, Saudi
  Arabia, Kuwait) and corporates (e.g., Dana Gas
  based in the UAE).
• Like conventional bonds subject to
• Interest rate risk
• Need to adjust to changes in the opportunity
  cost of investing (thus inverse relationship).
• Default risk
• Investors need to assess the value of the
  reference assets.
• Exchange rate risk Results from a mismatch of
  the currency of the reference assets and the
  currency of denomination of the Sukuk.
• And can be insured through the CDS market.

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Recall Two Major Spot FX Parity Forecasting
Models

• Purchasing Power Parity (PPP)
• Model assumes relative rates of inflation between
  two countries as the major determinant of the
  future spot exchange rate.
• International Fisher Effect (IFE)
• Model assumes relative rates of long term
  interest between two countries as the major
  determinant of the future spot exchange rate.
• This is the subject of this lecture.

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International Fisher Effect

• The International Fisher Effect (IFE) model uses
  market interest rates rather than inflation rates
  to explain why exchange rates change over time.
• The model consists of two parts
• (1) Fisher Effect which is an explanation of the
  market (i.e., nominal) interest rate, and
• (2) The International Fisher Effect which is an
  explanation of the relationship of market
  interest rates to exchange rates.
• The model is attributed to the
• American economist, Irving Fisher.
• Born in upstate New York in 1867.
• Ph.D. in economics from Yale.
• - Quantity Theory of Money (MVPT)
• - Phillips Curve

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Explanation of Market Interest Rate

• Fisher market interest rate model developed in
  his book the Theory of Interest (1930)
• Fishers interest rate model states that the
  market rate of interest on a default free bond is
  the sum of
• (1) a real rate requirement.
• The real rate requirement reflects the reward
  that should accrue to a lender for lending to a
  productive economy.
• (2) the markets expected rate of inflation
  (i.e., an inflation premium which represents the
  markets expectation of future rates of
  inflation).
• This inflation premium protects investors against
  a loss of purchasing power.
• Market (nominal) interest rate on a default free
  bond real rate requirement inflation
  expectations.

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Fisher Real Rate Requirement

• Defined by Fisher as The reward for lending into
  a productive economy.
• Problem This real rate requirement is much
  easier to conceptualize than it is to actually
  measure.
• Conceptually, however, it is probably related to
  economic growth theory, with an economys growth
  dependent upon the productivity of its workforce,
  capital stock, and population.
• While the real rate requirement cannot be
  observed, different estimation methods relying on
  theoretical growth models have suggested
• A range of 2-3 for both the United States and
  the euro area.
• A rate of 3 for the United Kingdom
• Sources Manrique and Manuel Marques (2004),
  Laubach and Williams (2003), Giammarioli and
  Valla (2003), Larsen and McKeown (2004)

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Estimating the Real Rate Requirement for the
United States
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Relative Stability of Market Interest Rate
Components

• Given that the market interest rate on a default
  free bond consists of two components (1) real
  rate requirement and (2) inflationary
  expectations, the question arises as to the
  relative stability of these two components.
• Real rate requirement is assumed to be relatively
  (more) stable.
• Changes in real rate only occur slowly in
  response to technology changes, population
  growth, population skills, changes in the capital
  stock, etc.
• Inflationary expectations, however, are subject
  to potentially wide variations over short periods
  of time.

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The Relation of Inflation to Long Term U.S.
T-Bond Interest Rates 1965 2011
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The Relation of Inflation to Short Term U.S.
T-Bill Interest Rates 1965 2011
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The Relation of Inflation to Interest Rates in
the U.K. 1989 2011
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The Relation of Inflation to Interest Rates in
Canada 1961 2005
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International Assumptions of the Fisher Model

• On an international level, the Fisher Model
  assumes that the real rate requirement is similar
  across major industrial countries.
• Thus any observed market interest rate
  differences between counties according to this
  model is accounted for on the basis of
  differences in inflation expectations.
• Example
• If the United States 1 year market interest rate
  is 5 and the United Kingdom 1 year market
  interest rate is 7, then
• The expected rate of inflation over the next 12
  months must be 2 higher in the U.K. compared to
  the U.S.

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The International Fisher Effect

• The second part of the Fisher model, the
  International Fisher (IFE) effect assumes that
• Changes in spot exchange rates are related to
  differences in market interest rates between
  countries.
• Reason Because differences in interest rates
  capture differences in expected inflation, and
  inflation is assumed to be the major determinant
  of future exchange rates.
• IFE relationship to Exchange Rates
• Currencies of high interest rate countries will
  weaken.
• Why These countries have high inflationary
  expectations
• The annual depreciation of the currency will be
  equal to the observed interest rate differential.
• Currencies of low interest rate countries will
  strengthen.
• Why These countries have low inflationary
  expectations.
• The annual appreciation of the currency will be
  equal to the observed interest rate differential.

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IFE Examples

• Assume the following
• I year Government bond rate in U.S. 5.00
• 1 year Government bond rate Japan 2.00
• Current spot rate (USD/JPY) 70.00
• According to the IFE, What should happen to the
  yen and why. And by how much (percent) should the
  yen exchange rate change per year?
• Now assume the following
• I year Government bond rate in U.S. 1.00
• 1 year Government bond rate Japan 3.00
• Current spot rate (USD/JPY) 70.00
• According to the IFE, What should happen to the
  yen and why? And by how much (percent) should the
  yen exchange rate change per year?

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Answers

• Given
• 1 year Government bond rate in U.S. 5.00
• 1 year Government bond rate Japan 2.00
• Spot rate (USD/JPY) 70.00
• According to the IFE, the yen should appreciate
  3.0 per year against the U.S. dollar.
• Why Lower rate of inflation in Japan.
• 1 year from now the spot rate will equal
• 70 - (70 x .03) 70 2.1 67.90
• This represents a appreciation of 3 over the
  current spot rate, and is an amount which is
  equal to the interest rate differential.
• Second example (2 higher interest rate in Japan)
• According to the IFR, the yen should depreciate
  2 per year against the U.S. dollar.
• Why Higher rate of inflation in Japan.
• 70 (70 x .02) 70 1.4 71.40
• This represents a depreciation of 2 over the
  current spot rate, and is an amount which is
  equal to the interest rate differential.

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IFE Formula American Terms

• For American Term quoted currency
• IFE Spot RateAT Current Spot RateAT x (1
  INTUS)n/(1 INTFC)n
• Where
• IFE Spot RateAT forecasted spot rate quoted in
  American Terms.
• Current Spot RateAT is the American Terms spot
  rate.
• INTUS is the current annual market interest rate
  in the United States (in decimal form).
• INTFC is the current annual market interest rate
  in the foreign country (in decimal form).
• N is the number of years in the future (i.e., the
  forecast horizon).

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Example IFE American Terms Forecast

• Assume
• Current spot rate for British pounds
• GBP/USD 1.5560
• Annual rate of interest on 5 year Government
  bonds
• United States 1.07
• United Kingdom 1.37
• Use the IFE formula below to calculate the spot
  pound 5 years from now
• IFE Spot RateAT Current Spot RateAT x (1
  INTUS)n/(1 INTFC)n
• Insert data and solve.

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Answer

• Given
• Current spot rate for British pounds GBP/USD
  1.5560
• Annual rate of interest on 5 year Government
  bonds
• United States 1.07
• United Kingdom 1.37
• Use the IFE formula to calculate the spot pound
  5 years from now
• IFE Spot RateAT Current Spot RateAT x (1
  INTUS)n/(1 INTFC)n
• IFE Spot RateAT 1.5560 x (1 0.0107)5/(1
  0.0137)5
• IFE Spot RateAT 1.5560 x (1.0107)5/(1.0137)5
• IFE Spot RateAT 1.5560 x (1.05466/1.0704)
• IFE Spot RateAT 1.5560 x .9853
• IFE Spot RateAT 1.5331 (This is the forecasted
  spot rate 5 years from now is the pound expected
  to appreciate or depreciate and why?)

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IFE Formula European Terms

• For European Term quoted currency
• IFE Spot RateET Current Spot RateET x (1
  INTFC)n/(1 INTUS)n
• Where
• IFE Spot RateET is the forecasted spot rate
  quoted in European Terms.
• Current spot rateET is the European terms spot
  rate.
• INTFC is the current annual market interest rate
  in the foreign country (in decimal form).
• INTUS is the current annual market interest rate
  in the United State (in decimal form).
• N is the number of years in the future (i.e., the
  forecast horizon).

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Example IFE European Terms Forecast

• Assume
• Current spot rate for Japanese yen
• USD/JPY 76.84
• Annual rate of interest on 2 year Government
  bonds
• United States 0.29
• Japan 0.14
• Use the IFE formula below to calculate the spot
  yen rate 2 years from now
• IFE Spot RateET Current Spot RateET x (1
  INTFC)n/(1 INTUS)n
• Insert data and solve.

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Answer

• Given
• Current spot rate for Japanese yen USD/JPY
  76.84
• Annual rate of interest on 2 year Government
  bonds
• United States 0.29
• Japan 0.14
• Use the IFE formula to calculate the spot yen
  rate 2 years from now
• IFE Spot RateET Current Spot RateET x (1
  INTFC)n/(1 INTUS)n
• IFE Spot RateET 76.84 x (1 0.0014)2/(1
  0.0029)2
• IFE Spot RateET 76.84 x (1.0014)2/(1.0029)2
• IFE Spot RateET 76.84 x (1.0028)/(1.00581)
• IFE Spot RateET 76.84 x .9970
• IFE Spot RateET 76.61(This is the forecasted
  spot rate 2 years from now is the yen expected
  to appreciate or depreciate and why?)

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Empirical Tests of IFE

• Empirical tests of the long term relationship
  lend some support to the relationship postulated
  by the international Fisher effect.
• See slides which follow
• Over the short term substantial deviations can
  occur
• Emil Sundqvist, 2002 study of 1993 2000 data,
  correlating quarterly interest rate differentials
  to quarterly exchange rate changes found the
  following R-squares
• Swedish krona 11.5, Japanese yen 8.9,
  British pound 3.6, Canadian dollar 1.4,
  German mark 1.4

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Evidence in Support of the IFE Japan
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Evidence in Support of the IFE The Euro-Zone
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Evidence in Support of the IFE New Zealand
(NZD-USD)
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Evidence in Support of the IFE New Zealand
(NZD-AUD)
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Evidence in Support of the IFE Norway (Exchange
Rate Index)
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Problematic Issues Regarding the PPP and IFE

• PPP model issues
• User needs to forecast the future rates of
  inflation.
• How does one do this for very long periods of
  time?
• Perhaps it is easier for shorter time periods
  (e.g., 1 year).
• IFE model issues
• User relies on market interest rate data to
  proxy for future inflation.
• However, are real rates similar across countries?
• See slide next page.
• Do real rates change over time?
• Inflationary expectations during the forecasted
  horizon are subject to change.

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Are Real Rates Similar?
Country Average Annual Growth Rate in Real GDP 1990 2006
United States 3.3 (3.25 1947 2012)
Australia 3.6 (3.51 1960 2012)
New Zealand 3.3 (2.24 1988 2012)
Canada 3.2 (3.34 1962 2012)
United Kingdom 2.7 (2.57 1956 2012)
Total OECD 2.7
Euro Area 1.9 (1.77 1995 2012)
Japan 1.3 (2.12 1981 2012)
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Practical Use of PPP and IFE

• Neither model appears appropriate for short term
  forecasting (less than 1 year).
• Both models work better for the long term and in
  this regard appear to be good indicators of the
  long term trend in the exchange rate
• Relatively high (low) inflation currencies will
  exhibit long term depreciation (appreciation).
• Relatively high (low) interest rate currencies
  will exhibit long term depreciation
  (appreciation).