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?

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. ¥ $

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.

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

Economist, 4/ 2003

Relative PPP P PPP line % change spot rate foreign currency US$/ yen 2 4 -5 -4 -1 -3 -2 1 3 5 -6 6 % change spot rate foreign currency US$/ yen P InfJAPAN- InfUS

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…

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.

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

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

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 $40,000. Pass-through: Degree of pass-through: 14.29 % / 20 % = 0.71 or 71 % € €/$

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?

International Fisher effect International Fisher effect (Fisher-open): spot exchange rate change equals opposite of interest rate differential. 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. FC

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

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.

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.

Currency Yield Curve & Forwards Months Interest yield 2 4 1 3 5 6 1.0 % 3.0 % 4.0 % 5.0 % 6.0 % 2.0 % Euro yield curve Forward premium on low interest rate currrency Eurodollar yield curve

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 for foreign currency. or

Interest Rate Parity (IRP) Dollar money market $1,000,000 $1,020,000  1.02 Start End i $ = 8 % per annum (2 % 90 days) S = SF 1.4800/$ SF 1,480,000 F90 = SF 1.4655/$ $1,019,993 90 days Swiss franc money market SF 1,494,800  1.01 i SF = 4 % per annum (1 % 90 days)

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.

Covered Interest Arbitrage (CIA) Eurodollar rate = 8.00 % per annum Dollar money market $1,000,000 $1,040,000  1.04 Start End F180 = ¥ 103.50/$ Arbitrage Potential $1,044,638 S =¥ 106.00/$ ¥ 106,000,000 180 days Yen money market ¥ 108,120,000  1.02 Euroyen rate = 4.00 % per annum

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.

Uncovered Interest Arbitrage (UIA): The Yen Carry Trade Investors borrow yen at 0.40% per annum Japanese yen money market ¥ 10,000,000 ¥ 10,040,000 Repay  1.004 Start End S360 = ¥ 120.00/$ ¥ 10,500,000 Earn ¥ 460,000 Profit Then exchanges the yen proceeds for US dollars, investing in US dollar money markets for one year S =¥ 120.00/$ $ 83,333,333 360 days US dollar money market $ 87,500,000  1.05 Invest dollars at 5.00% per annum

Interest Rate Parity (IRP) & Equilibrium 4 3 2 Percentage premium on foreign currency (¥) 1 4.83 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 -1 -2 -3 Percent difference between foreign (¥) and domestic ($) interest rates X U -4 Y Z

Forward Rate - Unbiased Predictor? Exchange rate Time S2 Error F2 S3 S4 F1 Error S1 F3 Error t 2 t 3 t 4 t 1