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Quantitative Problem Set

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solution


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Question;Question #1: Capital Allocation;Consider the following capital market: a risk-free asset yielding;1.75% per year and a mutual fund consisting of 65% stocks and 35% bonds. The;expected return on stocks is 12.50% per year and the expected return on bonds is;3.25% per year. The standard deviation of stock returns is 29.00% and the;standard deviation of bond returns 8.75%. The stock, bond and risk-free returns;are all uncorrelated.;1. What is the expected return on the mutual fund?;2. What is the standard deviation of returns for the mutual fund?;Now, assume the correlation between stock and bond returns is 0.40;and the correlations between stock and risk-free returns and between the bond;and risk-free returns are 0 (by construction, correlations with the risk-free;asset are always zero).;3. What is the standard deviation of returns for the mutual fund?;Is it higher or lower than the standard deviation found in part 2? Why?;Now, assume that the standard deviation of the mutual fund;portfolio is exactly 18.00% per year and a potential customer has a;risk-aversion coefficient of 2.75.;4. What correlation between the stock and bond returns is;consistent with this portfolio standard deviation?;5. What is the optimal allocation to the risky mutual fund (the;fund with exactly 18.00% standard deviation) for this investor?;6. What is the expected return on the complete portfolio?;7. What is the standard deviation of the complete portfolio?;8. What is the Sharpe ratio of the complete portfolio?;Question #2: Markowitz Optimization;Open the associated Excel file named QPS2-2 input.xlsx in My;Course Content::Problem Set Spreadsheets. Version A: Use;Excel column K observation numbers 64 through 123 (2002m01 ? 2006m12) to answer;the following questions;1. What is the average;return for each of the nine indexes?;2. Show the covariance matrix of returns.;Briefly describe how you constructed the covariance matrix.;Consider the simple case where short sales are allowed. Use Excel;Solver to find the Minimum Variance Portfolio (MVP).;3. What is the expected;portfolio return for the MVP portfolio?;4. What is the portfolio;standard deviation for the MVP portfolio?;5. What is the portfolio;composition (i.e., what are the weights for the nine assets)?;Consider the simple case where short sales are allowed. Use Excel;Solver to find the Maximum return portfolio with a standard deviation of;exactly 10.25%.;6. What is the expected;portfolio return for this portfolio?;7. What is the portfolio;composition (i.e., what are the weights for the nine assets)?;Consider the more realistic case where short sales are NOT allowed;and no more than 30% of the portfolio and no less than 5% is invested in any;country index. Use Excel Solver to find the Minimum Variance Portfolio (MVP).;8. What is the expected;portfolio return for the MVP portfolio?;9. What is the portfolio;standard deviation for the MVP portfolio?;10. What is the portfolio;composition (i.e., what are the weights for the nine assets)?;Consider the simple case where short sales are NOT allowed and no;more than 35% and no less than 2% of the portfolio is invested in any country;index. Use Excel Solver to find the Market Portfolio if the risk-free rate is;0.20%/month (2.4%/year).;11. What is the;expected portfolio return for this portfolio?;12. What is the;portfolio standard deviation for this portfolio?;13. What is the;portfolio composition (i.e., what are the weights for the nine assets)?;14. What is the maximum;Sharpe ratio?

 

Paper#49893 | Written in 18-Jul-2015

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