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360-15 - Chapter 15 Exchange Rates Interest Rates and...

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Chapter 15 – Exchange Rates, Interest Rates, and Interest Parity (IP) International Trade: Goods/services AND financial assets (stocks, bonds, CDs, FDI), and ex- rates change in response to both types of trade. PPP and LOP apply to goods, and we learned in CH 14 that deviations from PPP are typical, partly because of the differential speeds of adjustment between financial asset prices (ex-rates) and individual goods prices (and price indexes). We now consider the relationship between interest rates (or bond prices) and ex- rates , which are both part of the financial markets, and should respond quickly to new information (economic news). As we might expect, the Interest Parity (IP) condition holds much more closely than PPP. INTEREST PARITY (IP) IP condition results from the possibility of covered interest arbitrage, or covered interest parity. Full IP formula is: 1 + i $ = (1 + i £ ) (F/E), which can be approximated as: (15.1) i $ i £ + F E or (15.4) E ( i $ - i £ ) F – E , where (15.3) E i $ = interest rate in the U.S. on bond or bank CD i £ = interest rate in the U.K. on an equivalent bond or CD (T-bill, bank CD) F = Forward Ex-rate ($/£) for the same maturity as the interest rate (3-month, 1-year) E = Spot Ex-rate ($/£) Equation (15.1) and IP says that if financial markets for bonds and ex-rates are efficient, an investor should receive the same payoff investing in either the U.S. or U.K. bond market. Since a U.S. investor would face currency risk investing in the U.K., he/she could cover the ex-rate risk with a forward contract, selling the BPs forward. For example, IP says that $100 invested for one year in either the U.S. or U.K. should have the same payoff at the end of the year, measured in a common currency. Example: i $ = 5% for one year CD in U.S. i £ = 4% for one year CD in U.K. F = $1.61538/£ for one-year forward contract E = $1.60/£ Payoff in U.S. = $100 x (1.05) = $105 in one year January 23, 2012 1
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Investing $100 in U.K. involves: a. Sell $100 for BP = $100 / $1.60 = £62.50 b. Invest £62.50 @ 4% in U.K. for payoff = £62.50 (1.04) = £65 in one year c. Sell BP for $ at the forward rate = £65 x $1.61538 = $105 in one year The currency risk (of BP _____ ) has been covered with a one-year forward contract. Payoff = $105 in either country when IP holds, and is like LOP for financial securities. Also using 15.1, we can show that 1.05 = 1.04 (1.61538 / 1.60) We can also calculate the forward discount or premium for the BP from E and F, which is the formula (F – E ) / E: ($1.61538 - $1.60) / $1.60 = +.0096 or +.96% ≈ +1% (BP premium) or (F / E) – 1 = $1.61538 / 1.60 = 1.00961 – 1 = .00961 x 100 = +.961% Using (15.3) we would have the following relationships: 5% = 4% + 1% or (5% - 4%) = +1% IP says that an investor earns 5% in either country, measured in a common currency. A U.S. investor earns 5% in the U.S. in dollars, and can also earn 5% in the U.K. in dollars: 4% return on the British bond PLUS +1% return on the appreciation of the BP. A U.K. investor earns 4% in the U.K. in BPs and also earns 4% in the U.S. in BPs: 5% on the U.S. bond MINUS -1% depreciation of the USD.
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