# 566-6 - CHAPTER 6 INTERNATIONAL PARITY RELATIONSHIPS We now...

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CHAPTER 6 - INTERNATIONAL PARITY RELATIONSHIPS We now look at Int'l. Parity Relationships, starting with the Law of One Price (LOP), extended to: Purchasing Power Parity (PPP) and Interest Rate Parity (IRP). These parity relationships help us to understand: 1) how ex-rates are determined, and 2) how to forecast ex-rates. Int'l. Parity is based on EMH (Efficient Market Hypothesis). FX/securities markets are efficient when: 1) securities/FX are priced efficiently reflecting all currently available information, and 2) no arbitrage opportunities exist. Arbitrage : Riskless, certain profit opportunities by exploiting price discrepancies. Simultaneously buying and selling mispriced securities/FX to make a guaranteed, riskless profit without any investment. "Picking up dimes with a bulldozer." Example: triangular arbitrage. Int'l. parity conditions exist when there are no arbitrage opportunities and markets are in equilibrium. "No \$100 bills lying on the sidewalk." Law of One Price (LOP) : P D = S (\$/£) P F , where P D = Domestic Price (\$) P F = Foreign Price (£) S (\$/£) = spot ex-rate. Example: Gold in U.S. is \$1,200/oz., gold in U.K. = £750 and S= \$1.600/£ In USD: £750 x \$1.6000/£ = \$1,200, Gold is selling in both countries for the same price in USD In BP: \$1,200/oz. ÷ \$1.6000/£ = £750/oz, Gold is selling in both countries for the same price in BP If Law of One Price (Price Equalization Principle) did not hold, arbitrage would be possible, and would quickly restore parity. For example, what if gold in U.K. was \$1,250? What if gold in U.S. was £775? INTEREST RATE PARITY (IRP) IRP: “No Arbitrage condition” when int'l. financial markets (FX and money markets) are in equilibrium. Assuming free movement of capital, int'l. financial markets should be efficient. "Smell of profits" eliminates any discrepancies. Covered Interest Rate Parity = Parity conditions in fin. mkts., when forward markets are used to eliminate or "cover" any FX risk. Example: U.S. investor has \$1 to invest for one year. You consider two strategies: 1) Invest in U.S. treasury securities at i \$ , the domestic interest rate, for one year; or 2) Invest in foreign U.K. treasury securities at i £ , and hedge FX risk by selling maturity value of £s forward one year. In U.S., your payoff (maturity value) in one year will be: \$1(1 + i \$ ) In equilibrium this should be the same as your payoff in U.K. MGT 566: International Finance – CH 6 Professor Mark J. Perry 1

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In U.K., your investment strategy involves: 1. Sell \$1 for £s to get \$1 ÷ S(\$/£) pounds. (We assume that S = S(\$/£)). 2. Invest £s at U.K. int. rate ( i £ ) with payoff = \$1/S x (1 + i £ ) 3. Sell £s forward at F 360 (\$/£) for the maturity value of the UK investment, to get a guaranteed amount of \$s. For either investment, you start and end with U.S. dollars. For Strategy #2, you have completely
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566-6 - CHAPTER 6 INTERNATIONAL PARITY RELATIONSHIPS We now...

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