Consider the following capital market: a risk-free asset yielding 1.50% per year and a mutual fund consisting of 55% stocks and 45% bonds. The expected return

on stocks is 9.00% per year and the expected return on bonds is 2.50% per year. The standard deviation of stock returns is 23.00% and the standard deviation of

bond returns 8.00%. 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 11.00% per year and a potential customer has a risk-aversion coefficient of

2.0.

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 11.00% 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?

2. Markowitz Optimization

Open the associated Excel file named QPS2-2 input.xlsx in My Course Content::Problem Set Spreadsheets. Use observation numbers 40 through 99 (2000m01 %u2013

2004m12) 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 6.5%.

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 0.30%/month (3.6%/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?