Lecture 9: Parity Models and Foreign Exchange Rates

1. Lecture 9: Parity Models and Foreign Exchange Rates Evaluating Current Spot Rates and Forecasting Rates with Parity Models: International Fisher Effect

2. Where is this Financial Center?

3. Dubai, UAE, View From Top of Burj (i.e.,“Tower”) Khalifa (2,717 feet, 162 floors): Opened Jan 4, 2010

4. Recall: Two Major Spot FX Parity Forecasting Models • Purchasing Power Parity (PPP) • Model assumes relative rates of inflation between two countries as the major determinant of the future spot exchange rate. • International Fisher Effect (IFE) • Model assumes relative rates of long term interest between two countries as the major determinant of the future spot exchange rate. • This is the subject of this lecture.

5. International Fisher Effect • The International Fisher Effect (IFE) model uses market interest rates rather than inflation rates to explain why exchange rates change over time. • The model consists of two parts: • (1) Fisher Effect which is an explanation of the market (i.e., nominal) interest rate, and • (2) The International Fisher Effect which is an explanation of the relationship of market interest rates to exchange rates. • The model is attributed to the American economist, Irving Fisher. • Born in upstate New York in 1867. Ph.D. in economics from Yale. - Quantity Theory of Money (MV=PT) - Phillips Curve

6. Explanation of Market Interest Rate • Fisher market interest rate model developed in his book the Theory of Interest (1930) • Fisher’s interest rate model states that the market rate of interest on a default free bond is the sum of: • (1) a real rate requirement. • The real rate requirement reflects the reward that should accrue to a lender for “lending to a productive economy.” • (2) the market’s expected rate of inflation (i.e., an inflation premium which represents the markets’ expectation of future rates of inflation). • This inflation premium protects investors against a loss of purchasing power. • Market (nominal) interest rate on a default free bond = real rate requirement + inflation expectations.

7. Fisher Real Rate Requirement • Defined by Fisher as “The reward for lending into a productive economy.” • Problem: This real rate requirement is much easier to conceptualize than it is to actually measure. • Conceptually, however, it is probably related to economic growth theory, with an economy’s growth dependent upon the productivity of its workforce, capital stock, and population. • While the real rate requirement cannot be observed, different estimation methods relying on theoretical “growth” models have suggested: • A range of 2-3% for both the United States and the euro area. • A rate of 3% for the United Kingdom • Sources: Manrique and Manuel Marques (2004), Laubach and Williams (2003), Giammarioli and Valla (2003), Larsen and McKeown (2004)

8. Estimating the Real Rate Requirement for the United States

9. Relative Stability of Market Interest Rate Components • Given that the market interest rate on a default free bond consists of two components: (1) real rate requirement and (2) inflationary expectations, the question arises as to the relative stability of these two components. • Real rate requirement is assumed to be relatively (more) stable. • Changes in real rate only occur slowly in response to technology changes, population growth, population skills, changes in the capital stock, etc. • Inflationary expectations, however, are subject to potentially wide variations over short periods of time.

10. The Relation of Inflation to Long Term U.S. T-Bond Interest Rates: 1965 – 2011

11. The Relation of Inflation to Short Term U.S. T-Bill Interest Rates: 1965 – 2011

12. International Assumptions of the Fisher Model • On an international level, the Fisher Model assumes that the real rate requirement is similar across major industrial countries. • Thus any observed market interest rate differences between counties according to this model is accounted for on the basis of differences in inflation expectations. • Example: • If the United States 1 year market interest rate is 5% and the United Kingdom 1 year market interest rate is 7%, then: • The expected rate of inflation over the next 12 months must be 2% higher in the U.K. compared to the U.S.

13. The International Fisher Effect • The second part of the Fisher model, the International Fisher (IFE) effect assumes that: • Changes in spot exchange rates are related to differences in market interest rates between countries. • Reason: Because differences in interest rates capture differences in expected inflation, and inflation is assumed to be the major determinant of future exchange rates. • IFE relationship to Exchange Rates • Currencies of high interest rate countries will weaken. • Why: These countries have high inflationary expectations • The annual depreciation of the currency will be equal to the observed interest rate differential. • Currencies of low interest rate countries will strengthen. • Why: These countries have low inflationary expectations. • The annual appreciation of the currency will be equal to the observed interest rate differential.

14. IFE Examples • Assume the following: • I year Government bond rate in U.S. = 5.00% • 1 year Government bond rate Japan = 2.00% • Current spot rate (USD/JPY) = 70.00 • According to the IFE, What should happen to the yen and what should the exchange rate be one year from now? • Now assume the following: • I year Government bond rate in U.S. = 1.00% • 1 year Government bond rate Japan = 3.00% • Current spot rate (USD/JPY) = 70.00 • According to the IFE, What should happen to the yen and what should the exchange rate be one year from now?

15. IFE Examples • Given: • I year Government bond rate in U.S. = 5.00% • 1 year Government bond rate Japan = 2.00% • Spot rate (USD/JPY) = 70.00 • According to the IFE, the yen should appreciate 3.0% per year against the U.S. dollar. • Thus, 1 year from now the spot rate will equal: • 70 - (70 x .03) = 70 – 2.1 = 67.90 • This represents a appreciation of 3% over the current spot rate, and is an amount which is equal to the interest rate differential. • Second example (2% difference in interest rates) • 70 + (70 x .02) = 70 + 1.4 = 71.40 • This represents a depreciation of 2% over the current spot rate, and is an amount which is equal to the interest rate differential.

16. IFE Formula: American Terms • For American Term quoted currency: • IFE Spot RateAT = Current Spot RateAT x (1 + INTUS)n/(1 + INTFC)n • Where: • IFE Spot RateAT forecasted spot rate quoted in American Terms. • Current Spot RateAT is the American Terms spot rate. • INTUS is the current annual market interest rate in the United States. • INTFC is the current annual market interest rate in the foreign country. • N is the number of years in the future (i.e., the forecast horizon).

17. Example: IFE American Terms Forecast • Given data for October 7, 2011: • Current spot rate for British pounds: • GBP/USD 1.5560 • Annual rate of interest on 5 year Government bonds: • United States = 1.07% • United Kingdom = 1.37% • Use the IFE formula below to calculate the spot pound 5 years from now: • IFE Spot RateAT = Current Spot RateAT x (1 + INTUS)n/(1 + INTFC)n • Insert data and solve.

18. IFE American Terms Forecast • Given data for October 7, 2011: • Current spot rate for British pounds: GBP/USD 1.5560 • Annual rate of interest on 5 year Government bonds: • United States = 1.07% • United Kingdom = 1.37% • Use the IFE formula to calculate the spot pound 5 years from now: • IFE Spot RateAT = Current Spot RateAT x (1 + INTUS)n/(1 + INTFC)n • IFE Spot RateAT= 1.5560 x (1 + 0.0107)5/(1 + 0.0137)5 • IFE Spot RateAT = 1.5560 x (1.0107)5/(1.0137)5 • IFE Spot RateAT = 1.5560 x (1.05466/1.0704) • IFE Spot RateAT = 1.5560 x .9853 • IFE Spot RateAT = 1.5331 (This is the forecasted spot rate 5 years from now; is the pound expected to appreciate or depreciate and why?)

19. IFE Formula: European Terms • For European Term quoted currency: • IFE Spot RateET = Current Spot RateET x (1 + INTFC)n/(1 + INTUS)n • Where: • IFE Spot RateET is the forecasted spot rate quoted in European Terms. • Current spot rateET is the European terms spot rate. • INTFC is the current annual market interest rate in the foreign country. • INTUS is the current annual market interest rate in the United States. • N is the number of years in the future (i.e., the forecast horizon).

20. Example: IFE European Terms Forecast • Given data for October 7, 2011: • Current spot rate for Japanese yen: • USD/JPY 76.84 • Annual rate of interest on 2 year Government bonds: • United States = 0.29% • Japan = 0.14% • Use the IFE formula below to calculate the spot yen rate 2 years from now: • IFE Spot RateET = Current Spot RateET x (1 + INTFC)n/(1 + INTUS)n • Insert data and solve.

21. IFE European Terms Forecast • Given data for October 7, 2011: • Current spot rate for Japanese yen: USD/JPY 76.84 • Annual rate of interest on 2 year Government bonds: • United States = 0.29% • Japan = 0.14% • Use the IFE formula to calculate the spot yen rate 2 years from now: • IFE Spot RateET = Current Spot RateET x (1 + INTFC)n/(1 + INTUS)n • IFE Spot RateET = 76.84 x (1 + 0.0014)2/(1 + 0.0029)2 • IFE Spot RateET = 76.84 x (1.0014)2/(1.0029)2 • IFE Spot RateET = 76.84 x (1.0028)/(1.00581) • IFE Spot RateET = 76.84 x .9970 • IFE Spot RateET = 76.61(This is the forecasted spot rate 2 years from now; is the yen expected to appreciate or depreciate and why?)

22. Empirical Tests of IFE • Empirical tests lend some support to the relationship postulated by the international Fisher effect (i.e., currencies with high interest rates tend to depreciate over the long run and currencies with low interest rates tend to appreciate over the long run), although considerable short-run deviations occur. • Emil Sundqvist, 2002 study of the 1993 – 2000 period, correlating quarterly interest rate differentials to quarterly exchange rate changes found the following R-squares: • Swedish krona: 11.5%, Japanese yen: 8.9%, British pound: 3.6%, Canadian dollar: 1.4%, German mark: 1.4%

23. Problematic Issues Regarding the PPP and IFE • PPP model issues: • User needs to “forecast” the future rates of inflation. • How does one do this for very long periods of time? • Perhaps it is easier for shorter time periods (e.g., 1 year). • IFE model issues: • User relies on market interest rate data to “proxy” for future inflation. • However, are real rates similar across countries? • Do real rates change over time? • Inflationary expectations during the forecasted horizon are subject to change.

24. Practical Use of PPP and IFE • Neither model appears appropriate for short term forecasting (less than 1 year). • Both models work better for the long term and in this regard appear to be good indicators of the long term trend in the exchange rate: • Relatively high (low) inflation currencies will exhibit long term depreciation (appreciation). • Relatively high (low) interest rate currencies will exhibit long term depreciation (appreciation).