# FINCapital Allocation pROBLEMS

Capital AllocationConsider the following capital market: a risk-free asset yielding 2.00% per year and a mutual fund consisting of 75% stocks and 25% bonds. The expected return on stocks is 7.00% per year and the expected return on bonds is 4.50% per year. The standard deviation of stock returns is 17.00% and the standard deviation of bond returns 10.00%. 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 0.70 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 14.00% per year and a potential customer has a risk-aversion coefficient of 2.5.4. 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 14.00% 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 2Markowitz OptimizationOpen the associated Excel file named QPS2-2 input.xlsx in My Course Content::Problem Set Spreadsheets. Use observation numbers 52 through 111 (2001m01 â 2005m12) 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 7%.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. 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. Use Excel Solver to find the Market Portfolio if the risk-free rate is 0.25%/month (3%/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?