Exchange Rates and Interest Rates Interest Parity PPP

Exchange Rates and Interest Rates Interest Parity

PPP and IP n n 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.

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

Interest Parity n n n 1/30/02 FT US$ Libor (3 months): 1. 870 = i$ Euro Libor (3 months): 3. 351 = i€ Euro spot: 0. 8617 = E$/€ Euro 3 months forward: 0. 8585 = F$/€

Euro currency n n Offshore Banking Euro dollar, Euro yen Euro banks Libor = London Interbank Offer Rate

Interest Parity n n 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.

Interest Parity n n $1, 000 equal to 1, 000 E$/€ = 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.

Interest Parity n n 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.

Interest Parity n n 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 0. 8585 = 1, 004. 64 dollars, which is pretty close to $1, 004. 67.

Interest Parity n n 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$/€)

Interest Parity n 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) n In other words, the interest differential between the US and the EU is equal to the forward premium of the euro.

Interest Parity n n 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$/€

Uncovered Interest Parity n n 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.

UIP n 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.

UIP n 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.

UIP: an example n n 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.

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

Fisher Effect n n 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

Fisher Equation n 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 1970 s and 80 s.

Exchange rates, interest rates and inflation n n 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$/¥

CIP, PPP, and FE n n 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¥

Implications n n 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? )

Three possible cases 1. 2. 3. 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? )

Expected exchange rate and the Term Structure of Interest Rates n n n 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.

Term Structure of Interest Rates n n 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.