International Parity Conditions or chapter 4 Agenda

International Parity Conditions (or chapter 4)

Agenda • • • What is PPP & law of one price? What is exchange rate pass-through? How do interest rates & exchange rates link? Interest rate parity? What is covered interest arbitrage? What is uncovered interest arbitrage? 2

Prices and Exchange Rates § Law of one price: § product’s price same in all markets P$ S = P ¥ § where spot exchange rate is S, yen per dollar. ¥ $ 3

Purchasing Power Parity & Law of One Price Absolute purchasing power parity: § spot exchange rate is determined by relative prices of similar basket of goods. Relative purchasing power parity: § Relative change in prices b/n countries determines change in forex rate. 4

Absolute PPP: Big Mac Index § Economist’s Big Mac PPP: • Big Mac in China costs Yuan 9. 90. • Big Mac in US costs $2. 71. • Implied PPP exchange rate 5

Economist, 4/ 2003 6

Relative PPP 4 PP P % change spot rate foreign currency US$/ yen P lin 3 e 2 1 -6 -5 -4 -3 -2 -1 1 -1 2 3 4 5 6 Inf. JAPAN- Inf. US -2 -3 -4 7

But: § PPP is not very accurate predictor… • Why? § PPP holds well over very long term… § PPP holds better for countries w/ high inflation & underdeveloped capital markets… • Why? 8

Is forex under-/over- valued? § Use forex indices: trade-weighted bilateral exchange rates b/n the home country & trading partners § Nominal exchange rate index : use actual exchange § rates. Real effective exchange rate index indicates how the weighted average purchasing power of the currency has changed relative to some arbitrarily selected base period. 9

Q: • Can you tell when a currency is overvalued? • Why the real exchange rate deviates from 100? 10

Real Effective Exchange Rate Indices United States & Japan (1995 = 100) 11

Exchange Rate Pass-Through § Pass-through: change in prices of imported/exported goods when exchange rate changes • BMW made in Germany cost @ spot rate US$ 35, 000. € €/$ • where P$ is the price in US$, P€ is price in euros, S is spot • • rate Euro appreciates by 20%. But BMW is now only $40, 000. Pass-through: • Degree of pass-through: 14. 29 % / 20 % = 0. 71 or 71 % 12

Interest Rates & Exchange Rates? § What is a fair nominal interest rate? – Well, can ask a banker … or read Irvin Fisher… • Fisher Effect: nominal interest rates in each country are equal to the required real rate of return plus compensation for expected inflation. i = r + + r • i is nominal rate, r is real rate, is expected rate of inflation. • FE good for short maturity bonds, NOT long maturity ones. – Why? 13

International Fisher effect § International Fisher effect (Fisher-open): spot exchange rate change equals opposite of interest rate differential. FC where S is indirect quote. § Direct Quotes: US$/ Foreign Currency. § Indirect Quotes: Foreign Currency / US$. § Fisher-open not precise in short-term. § • Why? Should include forex risk premium. 14

Forward Rate § Forward Rate • A forward rate: exchange rate quoted today for settlement @ future date 15

Forward Rate § Spot rate SF 1. 48/$ § 90 -day euro Swiss franc deposit rate 4% p. a. § 90 -day euro-dollar deposit rate 8% p. a. 16

Premium or discount? § Forward premium or discount : % difference b/n spot & forward rates in annual percentage terms. • For indirect quotes (FC per home currency, FC/$) then • Swiss franc sells forward @ premium 3. 96% p. a. (takes 3. 96% more US$ to get franc at 90 -day forward rate) • For direct quotes ($/FC), use (F-S)/S. 17

Currency Yield Curve & Forwards Interest yield 6. 0 % Euro yield curve 5. 0 % 4. 0 % Forward premium on low interest rate currrency 3. 0 % 2. 0 % Eurodollar yield curve 1. 0 % 1 2 3 4 Months 5 6 18

Interest Rate Parity (IRP) § Interest rate parity: difference in national interest rates for securities of similar risk & maturity should be equal to opposite of forward rate discount/ premium foreign currency. or 19

Interest Rate Parity (IRP) i $ = 8 % per annum (2 % 90 days) Start End S = SF 1. 4800/$ 1. 02 $1, 020, 000 Dollar money market $1, 000 $1, 019, 993 90 days F 90 = SF 1. 4655/$ Swiss franc money market SF 1, 480, 000 1. 01 SF 1, 494, 800 i SF = 4 % per annum (1 % 90 days) 20

Covered Interest Arbitrage (CIA) § Because spot & forward markets are not in § equilibrium, arbitrage exists. Covered interest arbitrage (CIA): invests in currency that offers higher return on covered basis. 21

Covered Interest Arbitrage (CIA) Eurodollar rate = 8. 00 % per annum Start $1, 000 End 1. 04 Dollar money market S =¥ 106. 00/$ 180 days $1, 040, 000 $1, 044, 638 Arbitrage Potential F 180 = ¥ 103. 50/$ Yen money market ¥ 106, 000 1. 02 ¥ 108, 120, 000 Euroyen rate = 4. 00 % per annum 22

Uncovered Interest Arbitrage (UIA) § Uncovered interest arbitrage (UIA): investors § borrow in currencies w/ low interest rates & convert proceeds into currencies w/ high interest rates. “Uncovered” because investor does not sell the currency forward. 23

Uncovered Interest Arbitrage (UIA): The Yen Carry Trade Investors borrow yen at 0. 40% per annum Start ¥ 10, 000 Then exchanges the yen proceeds for US dollars, S =¥ 120. 00/$ investing in US dollar money markets for one year End 1. 004 Japanese yen money market 360 days ¥ 10, 040, 000 Repay ¥ 10, 500, 000 Earn ¥ 460, 000 Profit S 360 = ¥ 120. 00/$ US dollar money market $ 83, 333 1. 05 $ 87, 500, 000 Invest dollars at 5. 00% per annum 24

Interest Rate Parity (IRP) & Equilibrium 4 3 Percentage premium on foreign currency (¥) 2 1 4. 83 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 -1 -2 Percent difference between foreign (¥) and domestic ($) interest rates -3 -4 X U Y Z 25

Forward Rate - Unbiased Predictor? Exchange rate F 2 S 2 Error S 1 F 3 Error S 3 S 4 Time t 1 t 2 t 3 t 4 26