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R$ = RLC + S + (RLC)(S)
R$ = return on the foreign asset in U.S. dollar terms
RLC = return on the foreign asset in local currency terms
S = percentage change in the foreign currency
Return = 0.14 + (-0.05) + (0.14) (-0.05) = 8.30%
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σ2$ = σ2LC + σ2S + 2σLCσSρLC,S
where:
σ2$ = variance of the returns on the foreign asset in U.S. dollar terms
σ2LC, σLC = variance and standard deviation of the foreign asset in local currency terms
σ2S, σS = variance and standard deviation of foreign currency
ρLC,S = correlation between returns for the foreign asset in local currency terms and movements in the foreign currency.
Variance = (0.30)2 + (0.10)2 + 2(0.3)(0.1)(0.3) = 0.118
Standard deviation = √(0.118) = 34.35%
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Contribution of currency risk = σ$ - σLC
Contribution of currency risk = 34.35% - 30.00% = 4.35%
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Exhibit 1 – Emerging Markets Investing
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U.S.
portfolioKorean
portfolioExpected Return 8.00% 12.00% Standard Deviation 22.00% 32.00% Correlation 0.60
Return on Japanese stock in yen 16% Beginning spot rate (yen/$) 100 Ending spot rate (yen/$) 125
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Developed | Emerging |
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R$ = RLC + S + RLCSwhere:
R$ = Return on foreign asset in U.S. dollar terms RLC = Return on foreign asset in local currency terms S = Percentage change in foreign currency
Return on King’s bond = (8.0 + 98.0 – 95.0) / 95.0 = 0.115789
Solving for S we get:
R$ King = 0.115789 + S + 0.115789S -0.1074 = 0.115789 + 1.115789S -0.22319 = 1.115789S
S = -0.20 or 20.0% depreciation of the foreign currency.
Return on Waite’s bond in the local currency = (8.5 + 98.0 - 96.5) / 96.5 = 0.103627
R$ Waite = 0.103627 – 0.20 + (.1036)(-0.20)
= 0.103627 - 0.20 - 0.02072 = -0.117 or -11.7%
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Standard Deviation | Expected Return |
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