MAN 441: International Finance

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MAN 441 International Finance

• Parity Conditions and Currency Forecasting

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Chapter Objective

• Understand
• Parity conditions, and
• 1. Purchasing Power Parity (PPP)
• 2. The Fisher Effect (FE)
• 3. The International Fisher Effect
• (IFE)
• 4. Interest Rate Parity (IRP)
• 5. Unbiased Forward Rate (UFR)
• Alternative methods of currency forecasting

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Arbitrage

• So many relationships in international finance,
  including the parity conditions, depends on
  arbitrage activities.
• Arbitrage is defined as simultaneous purchase and
  sale of the same assets or commodities on
  different markets to profit from price
  discrepancies.

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Parity Conditions
UFRForward rates as unbiased predictors of
future spot rates PPPPurchasing power
parity IFEInternational Fisher effect FEFisher
effect IRPInterest rate parity
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Arbitrage and Law of One Price

• So many relationships in international finance,
  including the parity conditions, depends on
  arbitrage activities.
• Arbitrage is defined as simultaneous purchase and
  sale of the same assets or commodities on
  different markets to profit from price
  discrepancies.
• Law of one price (LOP) stems from arbitrage and
  states that
• In competitive markets free of transportation
  costs and official barriers to trade, identical
  goods sold in different countries must sell for
  the same price when their prices are expressed in
  terms of the same currency.
• Mathematically, for good i

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Arbitrage and Law of One Price

• Example
• If a DVD sells for 30 in New York, and if the
  /BP1.50 (BPBritish Pound), based on the law of
  one price, same DVD must sell for 20 BP in
  London.
• Suppose the price in US is 28 for the same DVD.
  In that case, US exporters and British importers
  will have an incentive to buy the DVD in New York
  and ship it to London for a profit (of course, in
  the absence of any transportation costs and
  barriers to trade). This will
• ? push the prices up in New York, and
• ? push the prices down in London
• until the price of same DVD equalized in both
  locations.
• Hence, international arbitrage enforces the law
  of one price.

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Purchasing Power Parity

• In its absolute version, PPP states that price
  levels should be equal worldwide when expressed
  in a common currency a unit of home currency
  should have the same purchasing power around the
  world. In other words, exchange rate between two
  currencies should be equal to the ratio of the
  countries price levels.

where PUS and PGBR are the prices of the
reference currency baskets. Hence, PPP theory
predicts that a fall in a currency's domestic
purchasing power (increase in the domestic price
level) will be associated with a proportional
currency depreciation in the foreign exchange
market. If, for example, the reference basket
costs 200 in US and 120 British pounds in UK,
PPP predicts price of BP as 1.67 (200/120).
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Purchasing Power Parity

• If law of one price holds (for all commodities),
  then absolute PPP must hold. Could we say that
  law of one price must hold if absolute PPP holds?
  
• Note that absolute PPP ignores
• Transportation costs
• Tariffs, quotas and other restrictions
• Product differentiation
• Law of one price and absolute PPP (to a degree)
  are best illustrated by the Big Mac index
  (initially put together by The Economist).

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Purchasing Power Parity
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Purchasing Power Parity

• For example, a Big Mac cost 1.99 BP in London,
  while its price is 2.71 in US.
• Implied PPP exchange rate for /BP can be
  calculated by (2.71/1.99)1.36
• Implied PPP exchange rate for BP/ can be
  calculated by (1.99/2.71)0.73
• Actual price of dollar was 0.63 BP on that date,
  implying US dollar was undervalued and BP was
  overvalued.
• 0.73 - 0.63 16 (note we used Price of
  dollar)
• 0.63
• What are the problems with the Big Mac approach?

Ignores what is included in the price of a Big
Mac - cost of real estate local taxes local
services In other words, it includes both traded
and non-traded goods and services. So, absolute
PPP doesnt make sense if the baskets are
different.
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Purchasing Power Parity

• Relative PPP, which is mostly used, states that
  the percentage change in the exchange rate over
  any period equals the difference between the
  percentage changes in national price levels. In
  other words, exchange rates should change to
  offset differences in inflation rates.
• For example, if inflation is 5 in US and 1 in
  Japan, then the dollar value of Japanese Yen must
  rise by about 4 to equalize the dollar price of
  goods in the two countries (dollar depreciates).
• In mathematical terms,

where e1 future spot rate e0 spot rate
ih home inflation if foreign inflation
t time period and e is the price of foreign
currency (/BP)
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Purchasing Power Parity

• If purchasing power parity is expected to hold,
  then the best prediction for the one-period spot
  rate should be

A more simplified but less precise relationship
is
PPP says the currency with the higher inflation
rate is expected to depreciate relative to the
currency with the lower rate of inflation.
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Purchasing Power Parity

• Example Projected inflation rates for the U.S.
  and Germany for the next twelve months are 10
  and 4, respectively. If the current exchange
  rate is .50/dm, what should the future spot rate
  be at the end of next twelve months?

0.529 is the best prediction for the future /DM
exchange rate.
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Purchasing Power Parity

• As it is clear now, exchange rate changes may
  indicate nothing more than the reality that
  countries have different inflation rates (outcome
  of PPP). Hence, changes in nominal exchange rates
  may not be significant to evaluate the true
  effects of currency changes on a firm.
• Real exchange rate is the nominal exchange rate
  adjusted for changes in relative purchasing power
  of each currency since some base period (so home
  price of the foreign basket relative to home
  basket).

Where Pf is the foreign price level and Ph is the
home price level at time 1, both indexed to 100
at time 0. Note that increases in the foreign
price level and foreign currency depreciation
have offsetting effects on real exchange
rates. An alternative way is using the inflation
rates. Note if PPP holds than ere0.
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Purchasing Power Parity

• Example1 Assume Canadian reference commodity
  basket costs Can100, and US basket costs 50 and
  the nominal exchange rate is E/Can0.5 per
  Canadian dollar.
• Er/Can 0.5(100/50)(50 per Canadian
  basket)/(50 per US basket)
• 1 US basket per Canadian basket
• Assume the Canadian baskets cost increases to
  Can110. Real exchange rate becomes 1.1 so we need
  to give 1.1 US basket for one Canadian basket
  real depreciation of dollar against Canadian
  dollar (Fall in the purchasing power of a US
  dollar within Canadian borders relative to its
  purchasing power within US).

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Purchasing Power Parity

• Example2 Assume Yen/ exchange rate moved from
  Yen226.63/ to Yen93.96/ between 1980 and 1995.
  CPI in Japan rose from 91.0 to 119.2, and US CPI
  rose from 82.4 to 152.4.
• (a) If PPP hold, what would be the exchange rate
  in 1995 (according to PPP real rates do not
  change)?
• Inflation in Japan was 31, and in US was 85
  over that time period
• Yen/ PPP rate226.63(1.31/1.85)Yen160.51/ gt
  Yen93.96/ , so Yen appreciated more than PPP
  would suggest.
• (b) What happened to real value of Yen?
• Real rate93.96(1.85/1.31)Yen132.69/ in 1995
• Real rate in 1980 is just equal to nominal rate,
  Yen226.63/. Yen appreciated in real terms by
  71.

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Purchasing Power Parity

• The distinction between nominal and real exchange
  rate has important implications for foreign
  exchange risk management. If real exchange rate
  remains constant, changes in nominal exchange
  rate will be less important.
• Empirical Evidence
• Law of one price doesnt hold (no surprise here)
• There is a clear relationship between relative
  inflation rates and changes in exchange rates. In
  general, it appears that PPP holds well in the
  long-run, but doesnt perform well in the
  short-run
• we observe substantial deviations from PPP
  predicted rates in the short-run, but there is a
  tendency to move back to PPP predicted rates in
  the long-run. This is called mean reversion and
  it is important for currency risk management.

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Purchasing Power Parity

• Why do we see deviations in the short-run?
• sticky prices in the short-run
• transportation costs and restrictions
• departures from free competition
• differently constructed price indices
• relative price changes
• Non-traded goods and services

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Fisher Effect

• Investors care about real interest rates and not
  about the nominal interest rates. However, almost
  all financial contracts are stated in nominal
  terms.
• The Fisher effect states that nominal interest
  rate, r, is a function of
• Real required rate of return, a, and
• An inflation premium equal to the expected amount
  of inflation, i
• Formally,
• 1Nominal rate(1Real rate)(1Expected
  inflation rate)
• ?1r(1a)(1i)
• ? raiai
• This equation can be approximated by
• ? rai (under what conditions?)

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Fisher Effect

• Example if a3 and i10, Fisher equation tells
  us that nominal interest rate, r, should be 13.
  
• Generalized version of Fisher effect
• Real returns tend towards equality across
  countries (ahaf)
• If ahgtaf then capital will flow from foreign to
  home currency.
• In the absence of government intervention,
  nominal interest rate differential should be
  equal to expected inflation differential between
  two currencies.
• rh-rf ih-if How did we obtain this
  condition (remember ahaf)?
• Currencies with high rates of inflation should
  bear higher nominal interest rates than
  currencies with lower inflation rates.

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Fisher Effect

• Example if inflation rates are 4 and 7 in US
  and UK, respectively, nominal interest rates
  should be higher by about 3 in UK.

Is D an equilibrium point? Do we expect capital
to flow from home country to foreign country to
take advantage of the real difference?
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Fisher Effect

• Empirical Evidence
• - Evidence is consistent with the hypothesis that
  most of the variation in nominal interest rates
  across countries can be attributed to differences
  in inflationary expectations.
• It is much harder to test the hypothesis that
  real returns are equal between countries.
  However, arbitrage will force pre-tax real
  interest rates to converge across all the major
  nations, if arbitrage is permitted to operate
  unhindered and capital markets are integrated
  worldwide.
• Capital market integration means that real
  interest rates are determined by the global
  supply and demand for funds.
• Capital market segmentation means that real
  interest rates are determined by local credit
  conditions.

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Fisher Effect

• Empirical evidence shows that capital markets are
  becoming increasingly integrated worldwide.
• However, we still observe real interest rate
  differential across countries (not arbitraged
  away).
• - Political risk and currency risk (higher
  inflation risk Canada example)
• - Different tax policies
• - Regulatory barriers to free flow of capital
• Hence, real interest rates tend to be higher in
  developing countries.
• Furthermore, integration of capital markets (and
  resulting flow of funds) impose some discipline
  on mismanagement of economies in developing
  nations.

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International Fisher Effect

• Combine PPP and FE to find IFE.
• Remember PPP is denoted as

And FE as rh-rf ih-if.
Is this familiar? Currencies with low interest
rates are expected to appreciate relative to
currencies with high interest rates. Is this
consistent with our earlier discussions?
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International Fisher Effect

• Fisher postulated
• 1. The nominal interest rate differential should
  reflect the inflation rate differential.
• 2. Expected rates of return are equal in the
  absence of government intervention.
• Remember, changes in the nominal interest
  differential can have two sources
• 1. Changes in real interest differential
• 2. Changes in inflationary expectations
• These two have opposite effects on currency
  values.
• If the change is due to a higher real interest
  rate in the home country, value of home countrys
  currency will rise.
• If the change is because of an increase in
  inflationary expectations in home country, value
  of home countrys currency will fall.

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International Fisher Effect

• If the / spot rate is 108/ and the interest
  rates in Tokyo and New York are 6 and 12,
  respectively, what is the future spot rate two
  years from now?

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Interest Rate Parity Theory
The Theory states The forward rate (F) differs
from the spot rate (S) at equilibrium by an
amount equal to the interest differential (rh -
rf) between two countries. The forward premium
or discount equals the interest rate
differential. F - S/S (rh - rf) where rh
the home rate rf the foreign
rate THE UNBIASED FORWARD RATE States that if
the forward rate is unbiased, then it should
reflect the expected future spot rate. ft
et
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Currency Forecasting

• Important for financial executives of
  multinational corporations
• Currency forecasting can lead to consistent
  profits only if the forecaster
• Has superior forecasting model
• Has access to private information consistently,
  or has access to public information with a time
  lead
• Can exploit small, temporary deviations from
  equilibrium
• Can predict the nature of government intervention
  in the foreign exchange market (more applicable
  for countries who manage their currencies to some
  extent)

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Currency Forecasting

• Market-Based Forecasts
• Extract the predictions already included in
  interest and forward rates
• Forward rate is an unbiased estimate of the
  future spot rate limited to forecast horizon of
  one year
• Interest rate differential can be used to predict
  future interest rates exist for longer time
  periods
• Model-Based Forecasts
• Fundamental analysis involves the examination of
  macroeconomic variables and policies. Simplest is
  to use PPP.
• Technical analysis focuses on the past price and
  volume movements try to discover price
  patterns.

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Currency Forecasting

• The possibility of consistent profit-making
  through currency forecasting is inconsistent with
  the efficient market hypothesis. According to
  efficient market hypothesis current exchange
  rates reflect all publicly available information.
  
• Note the forecast doesnt have to be accurate. It
  needs to be profitable.
• Example Yen/ spot rate is Yen110 per . A
  90-day forward rate is Yen109/. If our forecast
  for 90-day is Yen102/, we should buy the Yen
  forward.
• Buy 1million worth of Yen forward 109,000,000
  Yen. If the spot exchange rate 90-day from now
  turns out to be Yen108/, sell Yen spot for a
  profit of 9259. Our forecast was off by 6, but
  we made a profit.
• Assume our forecast was Yen111/. We would sell
  Yen forward and we would lose 9259. Our forecast
  was more accurate, it was off by 3 only.