Exchange Rates and Interest Rates

1. Exchange Rates and Interest Rates Interest Parity

2. PPP and IP • Relationship between exchange rates and prices ------ Purchasing Power Parity • PPP is expected to hold when there is no arbitrage opportunity in goods markets. • Relationship between exchange rates and interest rates ------ Interest Parity • IP is expected to hold when there is no arbitrage opportunity in financial markets.

3. PPP and IP • Financial- asset prices adjust to new information more quickly than goods prices  PPP does not hold in the short run

4. Interest Parity • 1/30/02 FT • US$ Libor (3 months): 1.870 = i$ • Euro Libor (3 months): 3.351 = i€ • Euro spot: 0.8617 = E$/€ • Euro 3 months forward: 0.8585 = F$/€

5. Euro currency • Offshore Banking • Euro dollar, Euro yen • Euro banks • Libor = London Interbank Offer Rate

6. Interest Parity • By investing $1,000 for 3 months, an investor in the US can earn 1,000 x (1+i$) = 1,000 x [1+(0.018704)] = 1,004.67 dollars at home. • Alternatively, she can invest in the EU by converting dollars to euros and then investing the euros.

7. Interest Parity • $1,000 equal to 1,000 E$/€ = 1,000  0.8617 = 1,160.50 euros, which is the quantity of euros resulting from the 1,000 dollars invested. • After three months, she will receive 1,160.50 x (1+i€) = 1,160.50 x [1+(0.03351 4)] = 1,170.22 euros.

8. Interest Parity • She will have to convert this investment return to dollars at the exchange rate that will prevail 3 months later, which is unknown today. • To avoid this uncertainty, she can cover the investment in euro with a forward contract.

9. Interest Parity • She sells €1,170.22 to be received in 3 months in the forward market today. • The covered return is (1,000  E$/€) x (1+i€) x F$/€ = 1,170.22 x F$/€= 1,170.22 x 0.8585 = 1,004.64 dollars, which is pretty close to $1,004.67.

10. Interest Parity • Arbitrage makes the difference between the returns on two investment opportunities equal to zero. • In other words, 1+i$= (1+i€)(F$/€ /E$/€) or (1+i$)/ (1+i€) = (F$/€ /E$/€)

11. Interest Parity • Interest rate parity condition is given by (i$-i€)/ (1+i€) = (F$/€-E$/€) /E$/€ which is approximated by i$-i€ = (F$/€-E$/€) /E$/€ (Covered Interest Parity) • In other words, the interest differential between the US and the EU is equal to the forward premium of the euro.

12. Interest Parity • To check CIP: • (i$-i€) = (1.870 – 3.351)400 = -0.0037 • (F$/€-E$/€) /E$/€ = (0.8585 – 0.8617)0.8617 = -0.0037 • CIP can be rewritten as i$ =i€ + (forward premium) where (forward premium) = (F$/€-E$/€) /E$/€

13. Uncovered Interest Parity • Suppose that a US investor is buying a UK bond without using the forward market. • The 6 months £ Libor is 4.17250 %, but this is not the rate of return relevant for the US investor.

14. UIP • The effective rate is given by i£ + (Ee$/€-E$/€) /E$/€ = (UK interest rate) + (Expected rate of depreciation) where Ee$/€ stands for the expected exchange rate 3 month ahead.

15. UIP • In other words, the expected return on a pound investment is the UK interest rate plus the expected rate of depreciation of the dollar against the pound.

16. UIP: an example • Suppose an investor expects the dollar to appreciate by 1.15% over six months. • Then, the expected return on a UK bond is (4.172502) – 1.15 = 0.936 %. • This is almost same as the return on a US bond: 1.8702 = 0.935 %. • In such a case, we say that Uncovered Interest Parity holds.

17. Inflation and Interest Rates • Nominal interest rate = i : the observed rate • Real interest rate = r : the rate adjusted for inflation

18. Fisher Effect • Nobody lends someone money at 5% interest rate when the inflation rate is expected to be 6% for the next year. (Why?) • The nominal interest rate incorporates inflation expectations to provide lenders enough level of real return. Fisher Effect

19. Fisher Equation • i = r + e where e = expected rate of inflation • Higher the inflation expectations, higher will be the nominal interest rates. • The interest rates were high in 1970s and 80s.

20. Exchange rates, interest rates and inflation • Fisher equations for two countries: i$ = r$ + USe i¥ = r¥ + Je • If the real rate is the same between two countries, that is, r$ = r¥ , then i$ - i¥ = USe - Je = (F$/¥-E$/¥) /E$/¥

21. CIP, PPP, and FE • Covered Interest Parity: i$ - i¥ = (F$/¥-E$/¥) /E$/¥ • Relative PPP: USe - Je = % E$/¥ = (F$/¥-E$/¥) /E$/¥ • Fisher equations for two countries: i$ = r$ + USe i¥ = r¥ + Je • “CIP + Relative PPP + FE” implies r$ = r¥

22. Implications • Suppose initially CIP holds: i$ - i¥ = (F$/¥-E$/¥) /E$/¥ • Suppose further that the Democrats take over the senate and congress and start massive spending. • Then, USe. (Why?) • This implies i$ by Fisher equation (Why?)

23. Three possible cases • Possibly, Ee . Then F . (Why?) • More likely, Ee does not change. Then E . (Why?) • Suppose that the US or Japan or both intervene the FX markets, trying to keep the exchange rate constant. Then, there will be no change in i$ - i¥ (Why?) But i$ (Why?) So, i¥ has to go up. Then, J will also go up. (Why?)

24. Expected exchange rate and the Term Structure of Interest Rates • How different are the interest rates for different maturities? Term Structure of Interest Rates • In bonds market, there are 3-month, 6-month, 1-year, 3-year, 10-year, and 30-year bonds. • Short-term, medium-term, long-term interest rates.

25. Term Structure of Interest Rates • Expectations Hypothesis: The expected return from the long-term bond tends to be equal to the return generated from holding the series of short-term bonds. • Liquidity Premium Risk-averse investors more prefer lending short-term than long-term. (Why?) Long-term bonds incorporate a risk-premium.