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THEORIES OF FOREIGN EXCHANGE

THEORIES OF FOREIGN EXCHANGE. International Parity Conditions. Exchange Rate Determination. What determines equilibrium relationships among exchange rates?

sebastian-castillo
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THEORIES OF FOREIGN EXCHANGE

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  1. THEORIES OF FOREIGN EXCHANGE International Parity Conditions

  2. Exchange Rate Determination • What determines equilibrium relationships among exchange rates? • International arbitrageur and the "Law of One-price" insure that risk adjusted expected rates of returns are approximately equal across countries. • There are five key relationships between: • Spot rate • Forward rate • Inflation rate • Interest rate • Exchange rate

  3. Purchasing Power Parity • A unit of domestic currency should purchase the same amount of goods in the home country as it would of identical goods in a foreign country. • Absolute form of PPP: “law of one price”: price of similar products to two countries should be equal when measured in a common currency.

  4. PPP Example • A bottle of wine costs €8 in Paris and $10 in New York. The exchange rate must reflect this price relationship: e0 = Pd/Pf = $10/€8 = $1.25 per € (e0 = $ per FC; direct or American quote) • Equivalent to €0.80 per $ in indirect quote, European terms. • The strictest version of PPP is not supported empirically, but changes in relative inflation rates are related to changes in exchange rates.

  5. Relative form of PPP • Acknowledges market imperfections such as: • transport costs • tariffs and quotas. • Rate of change in the prices of products should be similar when measured in a common currency.

  6. Relative PPP - Example • Example: Suppose the price of wine in Paris increases to € 9 in one year implying an inflation of 12.5%, while in the U.S. the price of wine increases to $10.50 indicating an inflation rate of 5%. The new exchange rate: e1 = Pd,1/Pf,1 = $10.5/€9 = $1.1667 per € or €0.8571 per $ • What is the depreciation in the value of €? 1.1667/1.2500 -1 = -6.67%

  7. PPP Relative PPP: OR OR Approximately: %Δe0 = πd - πf

  8. PPP Implication • According to PPP, the currency of countries with high inflation rates should devalue relative to countries with low inflations rates. • Rationale: if πd > πf, then: • domestic imports increase; domestic exports decrease • foreign imports decrease; foreign exports increase • demand for FC increases; supply decreases • demand for LC decreases; supply increases • FC appreciates; LC depreciates

  9. Relative PPP Example • Suppose the U.S. inflation rate is expected to be 3 percent for the coming year, while the Britain's expected rate of inflation is 5 percent. • The current exchange rate is $1.50 per £. What should be the £ spot rate in one year? 1.50 × 1.03/1.05 = $1.47 per £

  10. II: Fisher Effect • Recall the relationship between nominal and real rates of interest, as expressed in the Fisher theorem: • 1 + i = (1 + r*) (1 + π) • Or • Approximately: i = r* + π and r* = i - π

  11. Generalized Fisher Effect • Real rates of interest are equalized across countries through arbitrage. • Otherwise funds would flows from countries with low expected real rates of interest to countries with high expected real rates of interests (in the absence of segmented markets) • Therefore: r*f = r*d • OR if - πf = id - πd

  12. Generalized Fisher Effect • More precisely: • OR • Approximately:

  13. III. International Fisher Effect Combines the generalized Fisher effect to show the relationship between nominal interest rates and currency exchange rates. From PPP: From GFE: Therefore:

  14. IFE Implications • Currencies with low interest rates would appreciate with respect to currencies with high interest rates. • A long-run tendency for interest rates differentials to offset exchange rate changes has been demonstrated empirically. • Example: Interest rate in U.S. is 4%, while interest rate in Switzerland is 10%. If the current SF spot rate is $0.80, what should be the SF spot rate one year from now? $0.80 × 1.04/1.10 = $0.7564 per SF Or SF depreciates about 5.5%

  15. IV. Forward Rates and Expected Future Spot Rates • Early studies indicated forward exchange rates to be unbiased predictor of future spot exchange rates. f1 = E[e1] • Then the forward rate premium or discount unbiasedly reflects potential gains to be realized from the purchase or sale of forward currencies. • This equality captures the relationship between forward and spot rates. • Recent work has demonstrated the existence of a slight risk premium. The premium, however, changes signs. Therefore, it is fair to assume that the future spot rates would equal forwards rates.

  16. V. Interest Rate Parity • Substituting f1 = E[e1] in the IFE equation:

  17. Covered interest arbitrage • Suppose the interest rates are 4% in the U.S. and 10% in Switzerland. The Swiss Franc spot rate is $0.8000 and 180-day forward rate is $0.7800. Is covered arbitrage possible? • Forward discount on SF = (.78 -.80)/0.80 = -2.5% for 180 days or -5% per year. Id = 4% while If + discount = 10% - 5% = 5% • Therefore, arbitrage is possible.

  18. Covered Arbitrage 1. Borrow $1,000,000 in US @ 4% per year or 2% for half year. Loan plus Interest to be paid in 180 days = $1,020,000 2. Convert $ to SF at the spot rate: $1,000,000/0.80 = SF 1,250,000 3. Invest SF 1,250,000 @ 10% for 180 days: Will receive SF 1,250,000 × (1+10%/2) = SF 1,312,500 in 180 days 4. Sell SF 1,312,500 in forward market @180 forward rate $0.78/SF Will receive 1,312,500 × $0.78/SF = $1,023,750 in 180 days 5. After 180 days receive $1,023,750 from forward contract, and pay-off loan Net profit form arbitrage: $1,023,750 -1,020,000 = $3,750

  19. Forecast change in spot exchange rate + 4 % (yen strengthens) Forward rate as an unbiased predictor ( E ) Purchasing power parity ( A ) Forward premium on foreign currency + 4 % (yen strengthens) International Fisher Effect ( C ) Forecast difference in rates of inflation - 4 % (less in Japan) Difference in nominal interest rates - 4 % (less in Japan) Interest rate parity ( D ) Fisher effect ( B ) Prices, Interest Rates andExchange Rates in Equilibrium

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