ch_20_sol - CHAPTER 20 INTERNATIONAL DIVERSIFICATION 1 a...

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CHAPTER 20: INTERNATIONAL DIVERSIFICATION 1. a. 10,000/2 = 5,000 pounds 5,000/40 = 125 shares b. To fill in the table, we use the relation: 1 + r US = ( 1 + r UK ) Price per Share (Pounds) Pound-Denominated Return (%) Dollar-Denominated Return (%) For Year-End Exchange Rate 1.80 2.00 2.20 35 –12.5 –21.25 –12.5 –3.75 40 0 –10.00 0 10.00 45 12.5 1.25 12.5 23.75 c. The dollar-denominated return equals the pound-denominated return in the scenario that the exchange rate remains unchanged over the year. 2. The standard deviation of the pound-denominated return (using 3 degrees of freedom) is 10.21%. The dollar-denominated return has a standard deviation of 13.10% (using 9 degrees of freedom), greater than the pound standard deviation. This is due to the addition of exchange rate risk. 3. First we calculate the dollar value of the 125 shares of stock in each scenario. Then we will add the profits from the forward contract in each scenario. 20-1
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Dollar Value of Stock at given exchange rate Exchange Rate: 1.80 2.00 2.20 Share Price in Pounds 35 7,875 8,750 9,625 40 9,000 10,000 11,000 45 10,125 11,250 12,375 Profits on Forward Exchange: 1,500 500 –500 [= 5000(2.10 – E l )] Total Dollar Proceeds at given exchange rate Exchange Rate: 1.80 2.00 2.20 Share Price in Pounds 35 9,375 9,250 9,125 40 10,500 10,500 10,500 45 11,625 11,750 11,875 Finally, calculate the dollar-denominated rate of return, recalling that the initial investment was $10,000. Rate of return (%) for given exchange rate Exchange Rate: 1.80 2.00 2.20 Share Price in Pounds 35 -6.25 -7.50 –8.75 40 5.00 5.00 5.00 45 16.25 17.50 18.75 b. The standard deviation is now 10.24%. This is lower than the unhedged dollar-denominated standard deviation. 4. Currency Selection EAFE: [.30 × (–10%)] + (.10 × 0) + (.60 × 10%) = 3% Manager: [.35 × (–10%)] + (.15 × 0) + (.50 × 10%) = 1.5% Loss of 1.5% relative to EAFE. Country Selection EAFE: (.30 × 20) + (.10 × 15) + (.60 × 25) = 22.5% Manager: (.35 × 20) + (.15 × 15) + (.50 × 25) = 21.75% Loss of 0.75% relative to EAFE Stock Selection (18 – 20) × .35 + (20 – 15) × .15 + (20 – 25) × .50 = – 2.45% 20-2
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Loss of 2.45% relative to EAFE.
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