International Finance

1
International Finance

• Chapter 5
• Part 1 International Parity Relationships

2
FORWARD RATES

• Involves contracting today for the future
  purchase or sale of foreign exchange.
• Forward rate is set today!
• Forward rate can be
• Equal to spot (flat)
• Worth more than spot (premium)
• Worth less than spot (discount)

3
EXAMPLES OF FORWARD RATES

• Wednesday, June 4, 2004
• American Terms
• U.K. (Pound) 1.8343
• 1 month forward 1.8289
• European Terms
• Japan (yen) 110.07
• 1 month forward 109.95

4
FORWARD DISCOUNTS AND PREMIUMS

• Is the pound selling at a forward discount or
  forward premium?
• U.K. (Pound) 1.8343
• 1 month forward 1.8289
• Answer
• Discount 1 month forward is less than the spot
  by .0054

5
FORWARD PREMIUMS AND DISCOUNTS

• Is the Japanese yen selling at a forward premium
  or forward discount?
• Japan (yen) 110.07
• 1 month forward 109.95
• Answer
• Premium Dollar is selling at a discount with
  the 1 month forward less than the spot by .12
  yen.
• Convert to American terms (110.07 .009085
  109.95 .009095). Yen 1 month forward is worth
  .000010 more than the spot.

6
WHAT DETERMINES THE FORWARD RATE?

• What does NOT determine forward rate
• Markets expectation about where spot rate will
  be in the future.
• What does determine forward rate
• Assuming no capital controls, in equilibrium the
  rate represents the difference in interest rates
  between the two currencies in question.

7
INTEREST RATE PARITY

• Interest rate parity theory provides a linkage
  (and explanation) between international money
  markets and (forward) foreign exchange markets.
• The theory states that the difference in the
  national interest rates for securities of similar
  risk and maturity should be equal to, but
  opposite in sign to, the forward rate discount or
  premium for the foreign currency (except for
  transaction costs)

8
EXAMPLE

• Assume a US dollar-based investor has 1 million
  to invest for 90 days and can select from two
  investments
• Invest in the U.S. and earn 4.0 p.a.
• Invest in Switzerland and earn 8.0 p.a.
• Problem with Swiss franc investment
• Uncertainty about the future spot rate, or what
  if the franc depreciates against the dollar!
• Solution for investor
• Cover the Swiss franc investment by selling the
  Swiss francs anticipated from the investment
  forward 90 days.
• But what will the forward rate be?

9
FORWARD RATE UNDER INTEREST RATE PARITY

• In equilibrium, the forward rate must settle at a
  rate to offset the interest rate differential
  between the two currencies in question.
• This is to insure that the two investments will
  yield similar returns.
• To prevent covered interest arbitrage
  opportunities!!!

10
COVERED INTEREST ARBITRIGE

• Assume
• 90 day Interest rate in U.S. is 4
• 90 day Interest rate in Switzerland is 8
• Assume the spot rate and the 90 day forward rate
  are the same
• A U.S. investor could invest in Switzerland, and
  cover (sell francs forward) and obtain a (foreign
  exchange) riskless return of 8 which is 400
  basis points greater than investing in the U.S.
• This is covered interest arbitrage!

11
EQUILIBRIUM

• In equilibrium the forward rate will price the
  currency to offset the interest rate
  differential.
• In the previous example, the correct 90 day
  forward Swiss franc rate will be at a discount of
  4 of its spot.
• When the U.S. investor covers, the 8 Swiss
  return is reduced by the 4 discount, resulting
  in a covered return of 4.

12
VIEWING IRP
90 days
13
EQUILIBRIUM
90 days
14
HOW IS THE FORWARD RATE CALCULATED?

• The forward rate is calculated from three
  observable elements
• The (current) spot rate
• The foreign currency deposit rate
• The home (U.S.) currency deposit rate

15
FORWARD RATE FORMULA

• Where
• Fn forward rate (FC/), n business days in the
  future.
• S spot rate (FC/)
• N number of days in forward contract
• iFC interest rate on foreign currency deposit
• i interest rate on U.S. dollar deposit

16
EXAMPLE

• Assume
• Current Yen Spot rate 120.0000
• 90 day dollar rate 2.0
• 90 day yen rate .5
• Calculate the 90-day yen forward rate

17
SOLUTION
18
SOLUTION TO SWISS FRANC EXAMPLE

• Recall, the following information about the Swiss
  franc example
• Swiss franc spot rate of Sfr1.4800/,
• a 90-day Swiss franc deposit rate of 8.00
• a 90-day dollar deposit rate of 4.00.

19
COVERED INTEREST ARBITRAGE

• If the forward rate is not correct, the chance of
  covered interest arbitrage exists.
• Generally, these situations will not last long
• As the market takes advantage of them,
  equilibrium will be restored.

20
EXAMPLE
90 days

• Assume the forward rate is 1.48. Then, the
  covered Swiss investment yields 1,020,000,
• 10,000 more than the U.S. investment.

21
USING IRP TO FORECAST

• While the forward rate under the assumption of
  the Interest Rate Parity model assumes
• The forward rate simply represents interest rate
  differentials
• And NOT the markets view of the future spot
  rate.
• Some forecasters do use this model to forecast
  future spot rates.

22
Forward Rates as anUnbiased Predictor

• Some forecasters believe that the forward rate is
  an unbiased predictor of the future spot rate.
• This is roughly equivalent to saying that the
  forward rate can act as a prediction of the
  future spot exchange rate, but
• it will generally miss the actual future spot
  rate
• and it will miss with equal probabilities
  (directions) and magnitudes (distances) which
  offset the errors of the individual forecasts!

23
Forward Rates Unbiased Predictor
S1
The forward rate available today (Ft,t1), time
t, for delivery at future time t1, is used as a
predictor of the spot rate that will exist at
that day in the future. Therefore, the forecast
spot rate for time St2 is F1 the actual spot
rate turns out to be S2. The vertical distance
between the prediction and the actual spot rate
is the forecast error. When the forward rate is
termed an unbiased predictor, it means that the
forward rate over or underestimates the future
spot rate with relatively equal frequency and
amount, therefore it misses the mark in a regular
and orderly manner. Over time, the sum of the
errors equals zero.
24
Other Parity Models

• Two other important parity models are
• Purchasing Power Parity
• Exchange rate between two countries should be
  equal to the ratio of the two countries price
  level.
• The change in the exchange rate will be equal to
  the difference in inflation.
• International Fisher Effect
• The change in the exchange rate will be equal to
  the difference in the nominal interest rate
  between two countries.

25
LAW OF ONE PRICE

• The Purchasing Power Parity model is based on the
  Law of One Price
• The Law of one price states that all else being
  equal (i.e., no transaction costs or other
  frictions) a products price should be the same
  in all markets (countries).
• Why? The principle of competitive markets assumes
  that prices will equalize if costs of moving such
  goods does not exist.

26
LAW OF ONE PRICE

• When prices for a particular product are
  expressed in different currencies, the law of one
  price states that after adjusting for exchange
  rates, prices will be the same.
• Example (U.S. and Japan)
• The price of a product in US dollars (P),
  multiplied by the spot exchange rate (S yen per
  dollar), equals the price of the product in
  Japanese yen (P), or
• P ? S P

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EXAMPLE

• If a Big Mac costs 2.00 in the United States and
  if the current spot rate is 110, then the Law of
  One Price would suggest a price in Japan of
• 2.00 x 111 222.00

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PPP EXCHANGE RATE

• Conversely, if the prices for similar goods were
  known in local currencies, the appropriate (PPP)
  spot exchange rate (S) could be calculated from
  relative product prices, or
• Spot PPP rate Foreign Price/Home Price

29
PPP Example Sept 11, 2003

• Big Mac Boulder, Colorado 2.29
• Big Mac Osaka, Japan 250
• PPP Exchange Rate Yen Price/Dollar Price
• PPP Exchange Rate 250/2.29 109.17
• The PPP rate can be compared to the actual rate,
  and if
• Actual gt PPP currency may be undervalued!
• Actual lt PPP currency may be overvalued!
• Rate on September 11, 2003 117.1240
• Thus, this model suggested the yen was
  undervalued at that time (or dollar was
  overvalued).

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ABSOLUTE PPP

• The absolute PPP measures the correctness of
  the current spot rate on the bases of similar
  goods in different countries.
• A popular version of the absolute PPP technique
  is found in the Economist Big Mac index.

31
Big Mac Index Explanation From the Economist
Magazine

• Burgernomics is based on the theory of
  purchasing-power parity, the notion that a dollar
  should buy the same amount in all countries.
• Thus in the long run, the exchange rate between
  two countries should move towards the rate that
  equalizes the prices of an identical basket of
  goods and services in each country.
• The Economist "basket" is a McDonald's Big Mac,
  which is produced in about 120 countries.
• The Big Mac PPP is the exchange rate that would
  mean hamburgers cost the same in America as
  abroad.
• Comparing actual exchange rates with PPPs
  indicates whether a currency is under- or
  overvalued.

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Big Mac Index Web Site

• The Economist Magazine publishes their Big Mac
  Index twice a year.
• http//www.economist.com/markets/Bigmac/Index.cfm
• Currently the index (May 27, 2004) suggests
• Swiss franc PPP 2.19 actual 1.25
• Worlds most overvalued currency!
• Philippine peso PPP 23.8 actual 55.8
• Worlds most undervalued currency!

33
OECD PPP MEASURES

• A more comprehensive measure of a countrys PPP
  is provided by the OECD for 30 member countries.
  It can be found on the following web-site
• http//www.oecd.org/home/
• Or
• http//www.oecd.org/department/0,2688,en_2649_3435
  7_1_1_1_1_1,00.html

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RELATIVE PPP

• The relative Purchasing Power Parity model is
  concerned with the rate of change in the
  exchange rate.
• Model suggests that the percent change in the
  exchange rate should be equal to the difference
  in the rates of inflation between countries, or
• change in FX rate Home inflation rate
  Foreign inflation rate.

35
RELATIVE PPP EXAMPLE

• Assume the following
• Annual rate of inflation in U.S. 2.0
• Annual rate of inflation in U.K. 3.0
• The British pound should depreciate 1 per year
  against the U.S. dollar.
• If the current rate is 1.80, then
• 1 year from now the rate should be 1.7820
• 2 years from now the rate should be 1.7642
• Etc.

36
TESTS OF THE PPP

• The existing empirical tests of the PPP have
  proved disappointing.
• Generally the results do not support the PPP.
• However, PPP can still provide us with a
  benchmark test of whether a currency is
  overvalued or undervalued against other
  currencies.

37
INTERNATIONAL FISHER EFFECT

• The last major parity model is the International
  Fisher Effect.
• Begins with the Fisher Effect
• A change in the expected rate of inflation will
  result in a direct and proportionate change in
  the market rate of interest.

38
FISHER EFFECT

• Market rate of interest is comprised of two
  components
• Real rate requirement
• Relates to the real growth rate in the economy
• Expected rate of inflation
• Real rate requirement is assumed to be relatively
  stable
• Thus, changes in market interest rates occur
  because of changes in expected inflation!

39
FISHER EFFECT EXAMPLE

• Assume the following
• real rate requirement is 3.0
• Expected rate of inflation is 1.0
• Under these conditions, the market interest rate
  would be 4
• If the expected rate of inflation increases to
  2.0, the market interest rate would rise to 5.

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FISHER EFFECT DATA

• CPI Forecast 2 Year Govt
• Country 2004 2005 Bond Rate
• Australia 2.2 2.5 5.27
• U.S. 1.9 1.8 2.45
• Switzerland 0.7 0.4 1.13
• Japan -0.1 nil 0.14
• Forecast The Economist Poll,
• Date May 29, 2004

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FISHER EFFECT ASSUMPTIONS

• Model assumes that the real rate requirement is
  the same across countries.
• Thus market interest rate differences between
  counties is accounted for on the basis of
  differences in inflation expectations.
• If the interest rate is 5 in the U.S. and 7 in
  the U.K. then
• The expected rate of inflation is 2 higher in
  the U.K.

42
INTERNATIONAL FISHER EFFECT

• Changes in exchange rates will be driven by
  differences in market interest rates between
  countries.
• Because differences in interest rates capture
  differences in expected inflation.
• High interest rate countries (due to high
  expected rates of inflation) will experience
  currency depreciation.
• Low interest rate countries (due to low expected
  rates of inflation) will experience currency
  appreciation.

43
INTERNATIONAL FISHER EFFECT EXAMPLE

• Using interest rate data from Bloombergs web
  site (rates and bonds)
• http//www.bloomberg.com/markets/index.html
• 2 year U.S. Government rate 2.65
• 2 year Japanese Government rate 0.14
• Higher U.S. rate is accounted for on the basis of
  higher expected U.S. inflation
• 2.65 0.14 2.51

44
EXCHANGE RATE CHANGE

• Given the expected inflation differences, the yen
  will appreciate 2.51 per year.
• Current spot rate 110.
• Spot rate 1 year from now 107.239
• Spot rate 2 years from now 104.547
• Etc