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Lecture 4

CIP, UIP, PPP &Empirical testings

2012 International FinanceCYCU

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Fundamentals of Int’l finance

• Three parity theoriesfrom different perspectives

• Capital flow– CIP (covered interest rate parity)– UIP (uncovered interest rate parity)

• Good flow– PPP (purchasing power parity)

• Stemming from LOP (law of one price)

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4.1 International Financial Markets

• Foreign Exchange– General meaning:

A price of foreign currencies: s– No standard way to express– Direct quotations ($domestic/$foreign)

• A price of foreign currencies (in domestic dollars)• e.g., S = 29 (NTD/USD)

– Indirect quotations ($foreign/$domestic)• A price of domestic currency (in foreign dollars)• e.g., e = (1/s =1/29) = 0.0345 (USD/NTD)

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Yahoo finance

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Bank of Taiwan

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Notation: S• Foreign Exchange in this course

– A price of foreign currencies in terms of domestic dollars: (the view of home country)

(s ($domestic/$foreign)

• Terminologies– Under flexible exchange regimes

Appreciation vs Depreciation• S↓ vs S↑

– Under fixed exchange regimesRevaluation vs Devaluations

• S↓ vs S↑

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Foreign Exchange (FX)

• General features– traded over the counter

through a spatially decentralized dealer network– High liquidity: huge transaction volume

• 1998, daily volume of foreign exchange transactions involving the US dollar and executed within in the U.S was 405 billion dollars

• i.e., annual volume of 105.3 trillion dollar …(1998 US GDP was approximately 9 trillion dollars)

• Bilateral-rate vs cross-rate

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Equilibrium condition in cross-rate markets

• given by the absence of unexploited triangular arbitrage profits

• triangular arbitrage– Buy/sell one FX and sell/buy them

• EquilibriumS1 = Sx

3 S2

– S1 be the dollar price of the pound, S2

– be the dollar price of the euro, and – Sx

3 be the euro price of the pound.

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Numerical example• If you get price quotations of

– S1 =1.60 (USD/GBP) (dollars per pound),

– S2 =1.10 (USD/EUR)(dollars per euro, and )

– Sx3 = 1.55 (EUR/GBP)

(euros per pound)• An arbitrage strategy is to

– put up 1.60 dollars to buy one pound, – sell that pound for 1.55 euros and then – sell the euros for 1.1 dollars each. – You begin with 1.6 dollars and end up with 1.705

dollars,

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Three Transaction Types of FX(1)

• 1. spot transactions – for immediate (actually in two working days) d

elivery. – Spot exchange rates are the prices at which fore

ign currencies trade in this spot market.• 2. swap transactions

– agreements in which a currency • sold (bought) today is to be repurchased (sold) at a f

uture date. • The price of both the current and future transaction i

s set today

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Example Swap of FX• Today

– you might agree to buy 1 million euros at 0.98 million dollars

• In six months– sell the 1 million euros back time for 0.95 million dolla

rs.

• The swap rate is the difference between the repurchase (resale) price and the original sale (purchase) price.

• The swap rate and the spot rate together implicitly determine the forward exchange rate.

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Three Transaction Types of FX(2)

• 3. forward transactions– current agreements on the price, quantity, and

maturity or future delivery date for a foreign currency.

• Keys of forward transactions:– Price

• The agreed upon price is the forward exchange rate.

– Quantity– quantity

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Eurocurrency

Important! Not Euro Dollar• Def:

a foreign currency denominated deposit at a bank located outside the country

• offshore bank.– the deposit does not have to be in Europe

• Example:– A US dollar deposit at a London bank is a Eurodollar

deposit – A yen deposit at a San Francisco bank is a Euro-yen

deposit.

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London Interbank Offer Rate (LIBOR)

• LIBOR– The interest rate at which banks are willing to l

end to the most creditworthy banks participating in the London Interbank market.

• premium to LIBOR– the rate for loans to less creditworthy banks and

/or companies outside the London Interbank market

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4.2 Covered Interest Parity• Spot, forward, and Eurocurrency rates are mutually

dependent through the covered interest parity condition.

– Let it: the date t interest ratei∗t:1-period Eurodollar deposit (the interest rate on an Euroeuro deposit rate)St: the spot exchange rate (dollars per euro),Ft: the 1-period forward exchange rate.

– CIP• is the condition that the nominally risk-free dollar re

turn from the Eurodollar and the Euroeuro deposits are equal.

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Interpretation of CIP

home deposit returns = FX returns in future home dollar

s• “Future” FX Rate is fixed by Ft

– No FX riskthat is… “risk” is covered…

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Arbitrages in CIP

• Better deposit returns in home dollars

>

<

• Better deposit returns in FX dollars (after converting them into home dollars)

• In equilibrium:

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Practice Example

• suppose there are– no transactions costs, and you get the above – 12-month eurocurrency forward exchange rate

and spot exchange rate, and interest rate quotations

• Which way you would like to put money?

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Your arbitrage strategy

• (1+it) =1.0678• (1+it)Ft/St = 1.0178• So, your strategy

– borrow 0.9804 euros today– convert them to 1/St =1 dollar, – invest in the eurodollar deposit with future payoff 1.067

8 • But you will need only (1 + i t )Ft/St = 1.0178 dollars to repa∗

y the euro loan. – Note that this arbitrage is a zero-net investment strategy

since it is financed with borrowed funds.

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logarithmic approximation

• After taking log of the above eq. to get an specification for empirical testing

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4.3 Empirical Testing of Theories• Theoretic form

– Sometime no standard math f(.)• Empirical Specifications

– Linear approximation– Log transformation– Taking 1st difference of log variable– Selection of dependant/independent variables

• Stationarity vs Non-stationarity in data– Stationarity => OLS– Non-stationarity => Co-integration

• Hypothesis building• Interpretations

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Theory in math form

• Relationship between variablesY = f(X, W)– Not necessary in linear form– e.g.,

Y = cXaWb

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Theoretic forms of a Theory• In general

– Y = f(X, W)– A theory may only tell that:

X↑ => Y ↑ orW↑ => Y ↑

• e.g., CIPit ↑ => Ft ↑ or

it ↑ => St ↑

• How about an increase in i*t ?

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Empirical Specifications

• Linear approximation– Inference (forecasting) considerations

• Log transformation– Let non-linear form be linear

• Taking 1st difference of log variable– Transform non-stationary variables

• Selection of dependant/independent variables– Which variable causes what?

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Approximations of Theories for empirical testing

• Linear approximation– The linear OLS approach in levels

Y = c + a1 X + a2 W + – c, a1, a2

to be estimated

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About the linear approximation

• Actual f() vs linear approximation

Y

X

Y = c + a1 X + a2 W

Y = f(X, W)

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Forecast in the linear approximation

• Forecasting for actual f() vs linear approximation

Y

X

Y = c + a1 X + a2 W

Y = f(X, W)YOLS

Ytheory