6. (20 points) You are a US-based investor and you have all your wealth of $1m...

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6. (20 points) You are a US-based investor and you have all your wealth of $1m in- vested in fund A. Fund A is tracking a broad US equity index. You are being offered an investment in a US dollar denominated internationally diversified fund B. Fund B invests 60% in the same broad US equity index and 40% in a broad international equities index that does not contain US stocks (that is ex-US). You have the following information on the US equities index and the international equities index. Note, these are the two separate components of fund B. Expected Return Standard Deviation US Equities Index (and fund A) International Equities Index (ex-US) 10% 22% 12% 28% The correlation between returns on the US and international equity indices is 0.5. The US riskfree rate is 4% per year and all returns are in US dollars. (a) (8 points) What are the expected return and standard deviation of the interna- tionally diversified fund B? (b) (10 points) Show how you can invest your $1m in a portfolio of fund B and the riskfree asset (only) that has the same expected return but a lower volatility than your current investment in fund A. Clearly identify the dollar investments in fund B and the riskfree asset as well as the volatility of the position. (c) (2 points) Would it make sense to invest in both fund A and B at the same time? If so, explain under what conditions. If not, please explain why not. Qualitative answer only. 6. (20 points) You are a US-based investor and you have all your wealth of $1m in- vested in fund A. Fund A is tracking a broad US equity index. You are being offered an investment in a US dollar denominated internationally diversified fund B. Fund B invests 60% in the same broad US equity index and 40% in a broad international equities index that does not contain US stocks (that is ex-US). You have the following information on the US equities index and the international equities index. Note, these are the two separate components of fund B. Expected Return Standard Deviation US Equities Index (and fund A) International Equities Index (ex-US) 10% 22% 12% 28% The correlation between returns on the US and international equity indices is 0.5. The US riskfree rate is 4% per year and all returns are in US dollars. (a) (8 points) What are the expected return and standard deviation of the interna- tionally diversified fund B? (b) (10 points) Show how you can invest your $1m in a portfolio of fund B and the riskfree asset (only) that has the same expected return but a lower volatility than your current investment in fund A. Clearly identify the dollar investments in fund B and the riskfree asset as well as the volatility of the position. (c) (2 points) Would it make sense to invest in both fund A and B at the same time? If so, explain under what conditions. If not, please explain why not. Qualitative answer only.