Lecture 4
CIP, UIP, PPP &
Empirical testings
2012 International Finance
CYCU
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Fundamentals of Int’l finance
• Three parity theories
from 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 regimes
Revaluation 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
• Equilibrium
S1 = Sx3 S2
– S1 be the dollar price of the pound, S2
– be the dollar price of the euro, and
– Sx3 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)
delivery.
– Spot exchange rates are the prices at which
foreign currencies trade in this spot market.
• 2. swap transactions
– agreements in which a currency
• sold (bought) today is to be repurchased (sold) at a
future date.
• The price of both the current and future transaction
is 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
dollars.
• 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
lend 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 rate
i∗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
return from the Eurodollar and the Euroeuro
deposits are equal.
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Interpretation of CIP
home deposit returns
= FX returns in future home dollars
• “Future” FX Rate is fixed by Ft
– No FX risk
that 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
1.0678
• But you will need only (1 + i∗t )Ft/St = 1.0178 dollars to repay
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 variables
Y = 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 ↑ or
W↑ => Y ↑
• e.g., CIP
it ↑ => 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 + e
– c, a1, a2
to be estimated
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About the linear approximation
• Actual f() vs linear approximation
Y
Y = f(X, W)
Y = c + a1 X + a2 W
X
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Forecast in the linear approximation
• Forecasting for actual f() vs linear approximation
Y
Ytheory
YOLS
Y = f(X, W)
Y = c + a1 X + a2 W
X
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