Lecture 4 CIP UIP PPP Empirical testings 2012

Lecture 4 CIP, UIP, PPP & Empirical testings 2012 International Finance CYCU 1

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) 2

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) 3

Yahoo finance 4

Bank of Taiwan 5

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↑ 6

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 7

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 S 1 = Sx 3 S 2 – S 1 be the dollar price of the pound, S 2 – be the dollar price of the euro, and – Sx 3 be the euro price of the pound. 8

Numerical example • If you get price quotations of – S 1 =1. 60 (USD/GBP) (dollars per pound), – S 2 =1. 10 (USD/EUR) (dollars per euro, and ) – Sx 3 = 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, 9

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 10

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. 11

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 12

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. 13

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 14

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. 15

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… 16

Arbitrages in CIP > • Better deposit returns in home dollars < • Better deposit returns in FX dollars (after converting them into home dollars) • In equilibrium: 17

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? 18

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. 19

logarithmic approximation • After taking log of the above eq. to get an specification for empirical testing 20

4. 3 Empirical Testing of Theories • Theoretic form – Sometime no standard math f(. ) • Empirical Specifications – – Linear approximation Log transformation Taking 1 st difference of log variable Selection of dependant/independent variables • Stationarity vs Non-stationarity in data – Stationarity => OLS – Non-stationarity => Co-integration • Hypothesis building • Interpretations 21

Theory in math form • Relationship between variables Y = f(X, W) – Not necessary in linear form – e. g. , Y = c. Xa. Wb 22

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 ? 23

Empirical Specifications • Linear approximation – Inference (forecasting) considerations • Log transformation – Let non-linear form be linear • Taking 1 st difference of log variable – Transform non-stationary variables • Selection of dependant/independent variables – Which variable causes what? 24

Approximations of Theories for empirical testing • Linear approximation – The linear OLS approach in levels Y = c + a 1 X + a 2 W + e – c, a 1, a 2 to be estimated 25

About the linear approximation • Actual f() vs linear approximation Y Y = f(X, W) Y = c + a 1 X + a 2 W X 26

Forecast in the linear approximation • Forecasting for actual f() vs linear approximation Y Ytheory YOLS Y = f(X, W) Y = c + a 1 X + a 2 W X 27