International Finance
FIN456 ♦ Fall 2012Michael Dimond
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International Parity Conditions
•The economic theories which link exchange rates, pricelevels, and interest rates together are called internationalparity conditions
•These theories may not always work out to be “true” whencompared to what students and practitioners observe in thereal world, but they are central to any understanding of howmultinational business is conducted
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P$ S = P¥
Where the price of the product in US dollars (P$), multipliedby the spot exchange rate (S, yen per dollar), equals theprice of the product in Japanese yen (P¥)
Prices and Exchange Rates
•The Law of one price states that all else being equal (notransaction costs) a product’s price should be the same in allmarkets
•Even if prices for a particular product are in differentcurrencies, the law of one price states that
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¥
$
Prices and Exchange Rates
•Conversely, if the prices were stated in local currencies,and markets were efficient, the exchange rate could bededuced from the relative local product prices
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Purchasing Power Parity & The Law of One Price
•If the Law of One Price were true for all goods, thepurchasing power parity (PPP) exchange rate could befound from any set of prices
•Through price comparison, prices of individual products canbe determined through the PPP exchange rate
•This is the absolute theory of purchasing power parity
•Absolute PPP states that the spot exchange rate isdetermined by the relative prices of similar basket of goods
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The Hamburger Standard
•The “Big Mac Index,” as it has been christened by TheEconomist is a prime example of this law of one price:
–Assuming that the Big Mac is identical in all countries, it serves as acomparison point as to whether or not currencies are trading at marketprices
–Big Mac in China costs Yuan 13.2 (local currency), while the same BigMac in the US costs $3.73
–The actual exchange rate was Yuan 6.78/$ at the time. Therefore, theprice of a Big Mac in Chinese Yuan in U.S. dollar-terms was
–The Economist then calculates the implied purchasing power parityrate of exchange using the actual price of the Big Mac in China overthe price of the Big Mac in U.S. dollars
Yuan 13.2
Yuan 6.78/$
=
$1.95
Yuan 13.2
$3.73
=
Yuan3.54/$
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The Hamburger Standard
•Now comparing the implied PPP rate of exchange, Yuan 3.54/$, with theactual market rate of exchange at that time, Yuan 6.78/$, the degree towhich the Chinese yuan is either undervalued or overvalued versus theU.S. dollar is calculated:
Yuan 3.54/$ - Yuan 6.78/$ = -48%
Yuan 6.78/$
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Selected Rates from the Big Mac Index
•Does the Big Mac Index view of PPP really hold true?
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Relative Purchasing Power Parity
•If the assumptions of absolute PPP theory are relaxed, weobserve relative purchasing power parity
–This idea is that PPP is not particularly helpful in determining what thespot rate is today, but that the relative change in prices betweencountries over a period of time determines the change in exchangerates
–Moreover, if the spot rate rate between 2 countries starts inequilibrium, any change in the differential rate of inflation betweenthem tends to be offset over the long run by an equal but oppositechange in the spot rate
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Relative Purchasing Power Parity (PPP)
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Relative Purchasing Power Parity
•Empirical tests of both relative and absolute purchasingpower parity show that for the most part, PPP tends to notbe accurate in predicting future exchange rates
•Two general conclusions can be drawn from the tests:
–PPP holds up well over the very long term but is poor for short termestimates
–The theory holds better for countries with relatively high rates ofinflation and underdeveloped capital markets
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Exchange Rate Indices: Real and Nominal
•In order to evaluate a single currency’s value against all othercurrencies in terms of whether or not the currency is “over” or“undervalued,” exchange rate indices were created
–These indices are formed by trade-weighting the bilateral exchangerates between the home country and its trading partners
•The nominal exchange rate index uses actual exchangerates to create an index on a weighted average basis of thevalue of the subject currency over a period of time
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Exchange Rate Indices: Real and Nominal
•The real effective exchange rate index indicates how theweighted average purchasing power of the currency haschanged relative to some arbitrarily selected base period
–Example: The real effective rate for the US dollar (E$ ) is found bymultiplying the nominal rate index (E$ ) by the ratio of US dollar costs(C$) over foreign currency costs (CFC)
R
N
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Exchange Rate Indices: Real and Nominal
–If changes in exchange rates just offset differential inflation rates – ifpurchasing power parity holds – all the real effective exchange rateindices would stay at 100
–If a rate strengthened (overvalued) or weakened (undervalue) then theindex value would be ± 100
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€
€/$
Exchange Rate Pass-Through
•Incomplete exchange rate pass-through is one reasonthat country’s real effective exchange rate index candeviate from it’s PPP equilibrium point
–The degree to which the prices of imported & exported goodschange as a result of exchange rate changes is termed pass-through
–Example: assume BMW produces a car in Germany and all costsare incurred in euros. When the car is exported to the US, theprice of the BMW should be the euro value converted to dollarsat the spot rate
–Where P$ is the BMW price in dollars, P€ is the BMW price ineuros and S is the spot rate
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The degree of pass-through in this case is partial, 14.29% ÷ 20.00% orapproximately 0.71. Only 71.0% of the change has been passed through tothe US dollar price
Exchange Rate Pass-Through
–Incomplete exchange rate pass-through is one reason that a country’s realeffective exchange rate index can deviate for lengthy periods from its PPP-equilibrium level
–If the euro appreciated 20% against the dollar, but the price of the BMW in the USmarket rose to only $40,000, and not $42,000 as is the case under complete pass-through, the pass-through is partial
–The degree of pass-through is measured by the proportion of the exchange ratechange reflected in dollar prices
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Exchange Rate Pass-Through
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i = r + + r
Where i is the nominal rate, r is the real rate of interest, and is the expected rate of inflation over the period of time
The cross-product term, r , is usually dropped due to itsrelatively minor value
Interest Rates and Exchange Rates
•Prices between countries are related by exchange rates and now wediscuss how exchange rates are linked to interest rates
•The Fisher Effect states that nominal interest rates in each country areequal to the required real rate of return plus compensation for expectedinflation. As a formula, The Fisher Effect is
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i = r + ; i = r +
$
$
$
¥
¥
¥
It should be noted that this requires a forecast of the future rate ofinflation, not what inflation has been, and predicting the future canbe difficult!
Interest Rates and Exchange Rates
•Applied to two different countries, like theUS and Japan, the Fisher Effect would be stated as
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¥
Interest Rates and Exchange Rates
•The international Fisher effect, or Fisher-open, statesthat the spot exchange rate should change in an amountequal to but in the opposite direction of the difference ininterest rates between countries
–if we were to use the US dollar and the Japanese yen, theexpected change in the spot exchange rate between the dollarand yen should be (in approximate form)
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Interest Rates and Exchange Rates
•Justification for the international Fisher effect is that investorsmust be rewarded or penalized to offset the expected changein exchange rates
•The international Fisher effect predicts that with unrestrictedcapital flows, an investor should be indifferent betweeninvesting in dollar or yen bonds, since investors worldwidewould see the same opportunity and compete it away
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Interest Rates and Exchange Rates
•The Forward Rate
–A forward rate is an exchange rate quoted today for settlement atsome future date
–The forward exchange agreement between currencies states the rateof exchange at which a foreign currency will be bought or soldforward at a specific date in the future (typically 30, 60, 90, 180, 270or 360 days)
–The forward rate is calculated by adjusting the current spot rate by theratio of euro currency interest rates of the same maturity for the twosubject currencies
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Interest Rates and Exchange Rates
•The Forward Rate
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Interest Rates and Exchange Rates
•The Forward Rate example with spot rate of Sfr1.4800/$, a90-day euro Swiss franc deposit rate of 4.00% p.a. and a 90-day euro-dollar deposit rate of 8.00% p.a.
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For direct quotes ($/FC), then (F-S)/S should be applied
Interest Rates and Exchange Rates
•The forward premium or discount is the percentagedifference between the spot and forward rates stated inannual percentage terms
–When stated in indirect terms (foreign currency per home currencyunits, FC/$) then formula is
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Currency Yield Curves and the Forward Premium
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The positive sign indicates that the Swiss franc is sellingforward at a premium of 3.96% per annum (it takes 3.96%more dollars to get a franc at the 90-day forward rate)
Interest Rates and Exchange Rates
–Using the previous Sfr example, the forward discount or premiumwould be as follows:
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Interest Rate Parity (IRP)
•Interest rate parity theory provides the linkage betweenforeign exchange markets and international money markets
•The theory states that the difference in the national interestrates for securities of similar risk and maturity should beequal to, but opposite sign to, the forward rate discount orpremium for the foreign currency, except for transaction costs
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Interest Rate Parity (IRP)
–In this diagram, a US dollar-based investor with $1 million to invest, isshown indifferent between dollar-denominated securities for 90 daysearning 8.00% per annum, or Swiss franc-denominated securities ofsimilar risk and maturity earning 4.00% per annum, when “cover”against currency risk is obtained with a forward contract
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Covered Interest Arbitrage (CIA)
•Because the spot and forward markets are not always in astate of equilibrium as described by IRP, the opportunity forarbitrage exists
•The arbitrageur who recognizes this imbalance can invest inthe currency that offers the higher return on a covered basis
•This is known as covered interest arbitrage (CIA)
•The following slide describes a CIA transaction in much thesame way as IRP was transacted
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Covered Interest Arbitrage (CIA)
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Covered Interest Arbitrage (CIA)
•A deviation from CIA is uncovered interest arbitrage, UIA,wherein investors borrow in currencies exhibiting relativelylow interest rates and convert the proceeds into currencieswhich offer higher interest rates
•The transaction is “uncovered” because the investor does notsell the currency forward, thus remaining uncovered to anyrisk of the currency deviating
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Covered Interest Arbitrage (CIA)
•Rule of Thumb:
–If the difference in interest rates is greater than the forwardpremium (or expected change in the spot rate), invest in thehigher yielding currency.
–If the difference in interest rates is less than the forward premium(or expected change in the spot rate), invest in the lower yieldingcurrency.
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UIA: The Yen Carry Trade
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Interest Rate Parity (IRP) and Equilibrium
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Forward Rates as an Unbiased Predictor
•If the foreign exchange markets are thought to be “efficient”then the forward rate should be an unbiased predictor of thefuture spot rate
•This is roughly equivalent to saying that the forward rate canact as a prediction of the future spot exchange rate, and it willoften “miss” the actual future spot rate, but it will miss withequal probabilities (directions) and magnitudes (distances)
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Forward Rate as an Unbiased Predictor
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Prices, Interest and Exchange Rates in Equilibrium
•(A) Purchasing power parity
–forecasts the change in the spot rate on the basis of differences in expected rates ofinflation
•(B) Fisher effect
–nominal interest rates in each country are equal to the required real rate of return (r)plus compensation for expected inflation ()
•(C) International Fisher effect
–the spot exchange rate should change in an amount equal to but in the oppositedirection of the difference in interest rates between countries
•(D) Interest rate parity
–the difference in the national interest rates should be equal to, but opposite in sign to,the forward rate discount or premium for the foreign currency, except for transactioncosts
•(E) Forward rate as an unbiased predictor
–the forward rate is an efficient predictor of the future spot rate, assuming that the foreignexchange market is reasonably efficient
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International Parity Conditions in Equilibrium
