2. A pension fund manager is considering three mutual funds. The first is a stock fund, the second is a long-term government and corporate bond fund, and the third is a T-bill money market fund that yields a sure rate of 4%. The risk-return characteristics of the risky funds are:

Expected Return Stock fund 18%(stock fund) 9%(bond fund)

Standard Deviation 35%(stock fund) 20%(bond fund)

The correlation between the fund returns is .15.

a. Using Excel, tabulate and plot the investment opportunity set of the two risky funds.

Use investment proportions for the stock fund of -20% to 120% in increments of 10%.

Attach your spreadsheet and plot to your writeup.

b. Using the Solver tool, find the minimum variance portfolio. What are the corresponding

weights to the stock and bond fund? What is the level of expected return and standard deviation for the minimum variance portfolio? (If you dont see Solver under the Datatab, search enable add-in in Excel on Google. Microsoft Office Support websites would be useful.)

c. Using Solver, find the optimal risky portfolio. What is the expected return and standard deviation? What is the Sharpe ratio?

d. Suppose now that your portfolio must yield an expected return of 15% and be efficient, that is, on the best feasible CAL. What is the standard deviation of your portfolio?

e. If you were to use only the two risky funds and still require an expected return of 15%, what would be the standard deviation in that case? How does it compare to your answer in part (d)? What do you conclude?

2. Suppose it is possible to lend and borrow at the risk-free rate, , and that there are no

restrictions on short selling. You spotted two stocks with the following characteristics:

Stock Expected Return Standard Deviation

A 8% 40%

B 13% 60%

Correlation = -1

Could the equilibrium be greater than 10%? (Hint: Think in terms of an arbitrage argument.)

3. Pick the stock that has given you the best returns so far in the stock trading game. (You can also choose the stock that destroyed you.) Go to finance.yahoo.com and download five years of monthly closing prices for your stock and the S&P 500 Index (GSPC). Download the data into an Excel file and use the Adjusted-Close prices, which adjust for dividend payments, to calculate the monthly rate of return for each price series. Use the data on T-bills that I provided (T-bill rates.xlsx) to calculate excess returns. Draw the scatter plot representing excess returns on your company and on S&P 500, and also draw the security characteristic line (SCL). Use the regression tool in Excel for estimation (Data -> Data Analysis -> Regression). What is the beta of the security? How can you interpret it? What is the alpha? Looking at the t-statistic, evaluate if it is significantly different from zero. How do you interpret the alpha? What is the ^2 and how do you interpret it? Attach your scatter plot and SCL to your writeup. Label your axes properly.