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International Parity Conditions

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?. ¥. $.

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International Parity Conditions

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  1. International Parity Conditions (or chapter 4)

  2. 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?

  3. ¥ $ 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.

  4. 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.

  5. 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

  6. Economist, 4/ 2003

  7. 4 P PPP line 3 2 1 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 -1 -2 -3 -4 Relative PPP % change spot rate foreign currency US$/ yen InfJAPAN- InfUS

  8. 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?

  9. 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.

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

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

  12. € €/$ 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 %

  13. 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  • iis nominal rate, r is real rate,  is expected rate of inflation. • FE good for short maturity bonds, NOT long maturity ones. • Why?

  14. FC 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.

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

  16. 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.

  17. Premium or discount? • Forward premium ordiscount : % 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.

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

  19. 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

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

  21. 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.

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

  23. 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.

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

  25. 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 -3 Percent difference between foreign (¥) and domestic ($) interest rates X U -4 Y Z

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

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