International Parity Conditions

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International Parity Conditions

• Reading Chapter 4

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Class Outline

• Introduction to Parity Conditions
• Absolute Relative Purchasing Power Parity
• Real Exchange Rate
• Fisher Effect (FE)
• International Fisher Effect (IFE)
• Unbiased Forward Rate (UFR)
• Interest Rate Parity (IRP)
• Covered Interest Arbitrage
• Currency Forecasting gt PROJECT

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Introduction

• Managers of multinational firms, international
  investors, importers and exporters, and
  government officials must deal with these
  fundamental issues
• Are changes in exchange rates predictable?
• How are exchange rates related to interest rates?
• What, at least theoretically, is the proper
  exchange rate?
• To answer these questions we need to first
  understand the economic fundamentals of
  international finance, known as parity conditions.

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Parity Conditions

• Parity Conditions provide an intuitive
  explanation of the movement of prices and
  interest rates in different markets in relation
  to exchange rates.
• The derivation of these conditions requires the
  assumption of Perfect Capital Markets (PCM).
• no transaction costs
• no taxes
• complete certainty
• NOTE Parity Conditions are expected to hold in
  the long-run, but not always in the short term.

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Purchasing Power Parity (PPP)

• PPP is based on the notion of arbitrage across
  goods markets and the basic building block of PPP
  is the Law of One Price (LOP).
• LOP states that the price of an identical good
  should be the same in all markets (assuming no
  transactions costs).
• Otherwise, one could make profits by buying the
  good in the cheap market and reselling it in the
  expensive market.

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The Law of One Price

• LOP states that a products price may be stated
  in different currency terms, but the price of the
  product should remain the same.
• Comparison of prices would only require
  conversion from one currency to the other
• Conversely, the exchange rate could be deduced
  from the relative local product prices

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LOP Example

• Pwheat, Aust 4/bushel and Pwheat, UK
  2.5/bushel
• Spot rate (A/) 1.70
• A equivalent price of wheat in UK is A1.70/
  2.5
• 4.25/bushel
• Implication The demand for Australian wheat
  will increase forcing up its price. The price of
  UK wheat will drop.

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The Big Mac Index

• The most famous test is The Economist magazines
  Big Mac Hamburger standard.
• First launched in 1986, updated ever since.
• For example, see
• http//www.oanda.com/products/bigmac/bigmac.shtml

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Research on the Big Mac Index

• Pakko and Pollard (1996) conclude that Big Mac
  PPP holds in the long-run, but currencies can
  deviate from it for lengthy periods. They note
  several reasons why the Big Mac index may be
  flawed
• It assumes that there are NO barriers to trade.
• Prices are distorted by taxes.
• Profit margins may vary according to competition.
• Prices of non-traded goods (real estate,
  utilities, labor) are also inputs that affect
  production costs.

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Working for a Big Mac
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A New Index Starbucks Index
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Absolute PPP

• A less extreme form of the Law of One Price is
  ABSOLUTE PPP which says that the price of a
  basket of goods should be the same in each
  market.
• The PPP exchange rate between the two countries
  should then be

Absolute PPP
PID,t (PIF,t) is the domestic (foreign) price
index (e.g., consumer price index) at time t.
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Relative Purchasing Power Parity

• Relative PPP claims that exchange rate movements
  should exactly offset any inflation differential
  between two countries

Percentage change in domestic prices
Relative PPP

• We can also write

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Relative PPP

• Relative PPP implies that the change in the
  exchange rate will offset the difference between
  the relative inflation of two countries.
• The previous formula can be approximated as
• where, pD and pF refers to the percentage change
  in domestic and foreign price levels respectively
  and ?s to the percentage change in the exchange
  rate.
• If domestic inflation gt (lt) foreign inflation,
  PPP predicts the domestic currency should
  depreciate (appreciate).

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Relative PPP Example

• Given inflation rates of 5 and 10 in Australia
  and the UK respectively, what is the prediction
  of PPP with regards to A/GBP exchange rate?
• (0.05 0.10)/(1 0.10) - 0.045 - 4.5
• The general implication of relative PPP is that
  countries with high rates of inflation will see
  their currencies depreciate against those with
  low rates of inflation.

Relative PPP
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How well does PPP work?

• We have seen that the strictest version of PPP
  that all goods and financial assets obey the law
  of one price is demonstrably false.
• However, there is clearly a relationship between
  relative inflation rates and changes in exchange
  rates.
• Currencies that have had the largest relative
  decline (gain) in purchasing power see the
  sharpest erosion (appreciation) in their foreign
  exchange values.

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Relative Purchasing Power Parity

• Applications of Relative PPP
• Forecasting future spot exchange rates.
• Calculating appreciation in real exchange
  rates. This will provide a measure of how
  expensive a countrys goods have become (relative
  to another countrys).

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Forecasting Future Spot Rates

• Suppose the spot exchange rate and expected
  inflation rates are
• What is the expected / exchange rate if
  relative PPP holds?

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Real Exchange Rate

• By definition, the real exchange rate measures
  deviations from PPP.
• That is, changes in the spot exchange rate that
  do not reflect differences in inflation rates
  between the two currencies in question.

Real Exchange Rate
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Real Exchange Rate

• Appreciation/depreciation in the real exchange
  rate measures deviations from PPP.
• When E 1, the denominator currency is valued
  correctly. The competitiveness of this country
  is unaltered.
• When E lt 1, the denominator currency is
  undervalued. Products from the other country seem
  expensive relative to the base year. That is,
  the competitiveness of the denominator country
  improves.
• When E gt 1, the denominator currency is
  overvalued. Products from the other country seem
  cheap relative to the base year. That is, the
  competitiveness of the denominator country
  deteriorates.

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The Fisher Effect

• The international Fisher relation is inspired by
  the domestic relation postulated by Irving Fisher
  (1930).
• The Fisher effect (also called Fisher-closed)
  states

• This relation is often presented as a linear
  approximation stating that the nominal interest
  rate is equal to a real interest rate plus
  expected inflation

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The Fisher Effect

• Applied to two different countries, like
  Australia and Japan, The Fisher Effect would be
  stated as
• It should be noted that this requires a forecast
  of the future rate of inflation, not what
  inflation has been in the past.

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The International Fisher Effect

• The International Fisher Effect (also called
  Fisher-open) states that the spot exchange rate
  should change to adjust for differences in
  interest rates between two countries

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The International Fisher Effect

• The Fisher effect applied to two different
  countries like Australia and Japan would be
• (1i) (1r)(1?)
• (1i) (1r)(1?)
• Dividing (1) by (2), we get
• (3)

1
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The International Fisher Effect

• If real interest rates are equalized across
  countries, then for equation (3) we get r r

(4)
(5)
E(St1)
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Tests of the International Fisher Effect

• Empirical tests lend some support to the
  relationship postulated by the international
  Fisher effect (currencies with high interest
  rates tend to depreciate and currencies with low
  interest rates tend to appreciate), although
  considerable short-run deviations occur.

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Unbiased Forward Rate (UFR)

• Some forecasters believe that for the major
  floating currencies, foreign exchange markets are
  efficient and forward exchange rates are
  unbiased predictors of future exchange rates.
• The unbiased forward rate (UFR) concept states
  that the forward exchange rate, quoted at time t
  for delivery at time t1, is equal to the
  expected value of the spot exchange rate at time
  t1.

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Unbiased Forward Rate (UFR)

• UFR can be written as

• An unbiased predictor, however, does not mean the
  future spot rate will actually be equal to what
  the forward rate predicts.
• Unbiased prediction means that the forward rate
  will, on average, overestimate and underestimate
  the actual future spot rate in equal frequency
  and degree.

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Empirical Tests of UFR

• A consensus is developing that rejects the
  efficient market hypothesis.
• It appears that the forward rate is not an
  unbiased predictor of the future spot rate and
  that it does pay to use resources in an attempt
  to forecast exchange rates.
• The existence and success of foreign exchange
  forecasting services suggest that managers are
  willing to pay a price for forecast information
  even though they can use the forward rate to
  forecast at no cost.

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Interest Rate Parity

• Interest rate parity (IRP) is an arbitrage
  condition that provides the linkage between the
  foreign exchange markets and the international
  money markets.

Interest Rate Parity (IRP)
where, Ft and St are the forward and spot rates
and id and if are domestic and foreign interest
rates respectively.
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Interest Rate Parity

• The approximate form of IRP says that the
  forward premium equals the difference in interest
  rates.

Approximation of IRP

• In general, the currency trading at a forward
  premium (discount) is the one from the country
  with the lower (higher) interest rate.

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Interest Rate Parity An Example

• Basic idea Two alternative ways to invest funds
  over same time period should earn the same
  return.
• Suppose the 3-month money market rate is 8 p.a.
  (2 for 3-months) in the U.S. and 4 p.a. (1 for
  3-months) in Switzerland, and the spot exchange
  rate is SFr1.48/.
• The 3-month forward rate must be SFr1.4655/ to
  prevent arbitrage opportunities (i.e., interest
  rate parity must hold).

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The Example Continued
90 days
Rounding error.
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Interest Rate Parity Why It Holds

• This must hold by arbitrage. Otherwise riskless
  profits could be made. This is known as covered
  interest arbitrage (CIA) and occurs whenever IRP
  does not hold. CIA can involve the following
  steps
• Borrow the domestic currency
• Exchange the domestic currency for the foreign
  currency in the spot market
• Invest the foreign currency in an
  interest-bearing instrument and then
• Sign a forward contract to lock in a future
  exchange rate at which to convert the foreign
  currency proceeds back to the domestic currency.

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Covered Interest Arbitrage Example

• The annual interest rate in the AUS and UK are 5
  and 8 respectively. The current spot rate is
  1.50/ and the 1 year forward rate is 1.48/.
  Can arbitrage profits be made?
• Borrow 1m (at 5)
• Purchase 666,667 using 1m
• Invest at 8 (will receive 720,000 in one
  years time)
• Simultaneously sell 720,000 forward (1,065,600)
• Repay loan interest of 1,050,000
• ARBITRAGE PROFIT 15,600

1.05 ? 1.0656
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The Example Continued
lt1,050,000gt
1,065,600
Profit 15,600
720,000
666,667
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Covered Interest Arbitrage

• Covered interest arbitrage should continue until
  interest rate parity is re-established, because
  the arbitrageurs are able to earn risk-free
  profits by repeating the cycle.
• But their actions nudge the foreign exchange and
  money markets back toward equilibrium
• Purchase of Pounds in the spot market and sale of
  in the forward market narrow the premium on
  forward pounds.
• The demand for pound-denominated securities
  causes pound interest rates to fall, while the
  higher level of borrowing in Australia causes
  dollar interest rates to rise.

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Uncovered Interest Arbitrage
0

• A deviation from covered interest arbitrage is
  uncovered interest arbitrage (UIA).
• In this case, investors borrow in countries and
  currencies exhibiting relatively low interest
  rates and convert the proceed into currencies
  that offer much higher interest rates.
• The transaction is uncovered because the
  investor does no sell the higher yielding
  currency proceeds forward, choosing to remain
  uncovered and accept the currency risk of
  exchanging the higher yield currency into the
  lower yielding currency at the end of the period.

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Currency Forecasting

• What have we learnt about currency forecasting
  this week?
• Unbiased forward rate
• Long-term equilibrium relationships (RPPP and
  IFE)
• More methodologies next week.