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Exchange Rates and Interest Rates Interest Parity

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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.

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

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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 $/€

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

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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.

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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.

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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.

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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.

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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 $/€ )

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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.

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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 $/€

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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.

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

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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.

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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.

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

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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

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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.

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Exchange rates, interest rates and inflation Fisher equations for two countries: i $ = r $ + US e i ¥ = r ¥ + J e If the real rate is the same between two countries, that is, r $ = r ¥, then i $ - i ¥ = US e - J e = (F $/¥ -E $/¥ ) /E $/¥

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CIP, PPP, and FE Covered Interest Parity: i $ - i ¥ = (F $/¥ -E $/¥ ) /E $/¥ Relative PPP: US e - J e = % E $/¥ = (F $/¥ -E $/¥ ) /E $/¥ Fisher equations for two countries: i $ = r $ + US e i ¥ = r ¥ + J e “CIP + Relative PPP + FE” implies r $ = r ¥

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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, US e . (Why?) This implies i $ by Fisher equation (Why?)

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Three possible cases 1. Possibly, E e . Then F . (Why?) 2. More likely, E e does not change. Then E . (Why?) 3. 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?)

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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.

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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.

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Chapter 2 Foreign Exchange Parity Relations. Problem 1: Because the interest rate in A is greater than the interest rate in B, is expected to depreciate.

Chapter 2 Foreign Exchange Parity Relations. Problem 1: Because the interest rate in A is greater than the interest rate in B, is expected to depreciate.

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