Finance Work out problems
1. You have the following data on
(1) the average annual returns of the market for the past 5 years
(2) similar information on Stocks A and B. Which of the possible answers best describes the historical betas for A and B?
Years Market Stock A Stock B
1 0.03 0.16 0.05
2 -0.05 0.20 0.05
3 0.01 0.18 0.05
4 -0.10 0.25 0.05
5 0.06 0.14 0.05
a. bA > 0; bB = 1.
b. bA > +1; bB = 0.
c. bA = 0; bB = -1.
d. bA < 0; bB = 0.
e. bA < -1; bB = 1.
2. Which of the following statements is CORRECT?
a. “Characteristic line” is another name for the Security Market Line.
b. The characteristic line is the regression line that results from plotting the returns on a
c. particular stock versus the returns on a stock from a different industry.
d. The slope of the characteristic line is the stock’s standard deviation.
e. The distance of the plot points from the characteristic line is a measure of the stock’s
3. Assume an economy in which there are three securities: Stock A with rA = 10% and A = 10%; Stock B with rB = 15% and B = 20%; and a riskless asset with rRF = 7%. Stocks A and B are uncorrelated (rAB = 0). Which of the following statements is most CORRECT?
a. The expected return on the investor’s portfolio will probably have an expected return that is somewhat above 15% and a standard deviation (SD) of approximately 20%.
b. The expected return on the investor’s portfolio will probably have an expected return that is somewhat below 10% and a standard deviation (SD) of approximately 10%.
c. The expected return on the investor’s portfolio will probably have an expected return that is somewhat below 15% and a standard deviation (SD) that is between 10% and 20%.
d. The investor’s risk/return indifference curve will be tangent to the CML at a point where the expected return is in the range of 7% to 10%.
e. Since the two stocks have a zero correlation coefficient, the investor can form a riskless portfolio whose expected return is in the range of 10% to 15%.
4. Consider the following information and then calculate the required rate of return for the Scientific Investment Fund, which holds 4 stocks. The market’s required rate of return is 15.0%, the risk-free rate is 7.0%, and the Fund’s assets are as follows:
Stock Investment Beta
A $ 200,000 1.50
B 300,000 -0.50
C 500,000 1.25
D 1,000,000 0.75
5. You plan to invest in Stock X, Stock Y, or some combination of the two. The expected return for X is 10% and X = 5%. The expected return for Y is 12% and Y = 6%. The correlation coefficient, rXY, is 0.75.
a. Calculate rp and p for 100%, 75%, 50%, 25%, and 0% in Stock X.
b. Use the values you calculated for rp and p to graph the attainable set of portfolios. Which part of the attainable set is efficient? Also, draw in a set of hypothetical indifference curves to show how an investor might select a portfolio comprised of Stocks X and Y. Let an indifference curve be tangent to the efficient set at the point where rp = 11%.
c. Now suppose we add a riskless asset to the investment possibilities. What effects will this have on the construction of portfolios?
d. Suppose rM = 12%, M = 4%, and rRF = 6%. What would be the required and expected return on a portfolio with P = 10%?
e. Suppose the correlation of Stock X with the market, rXM, is 0.8, while rYM = 0.9. Use this information, along with data given previously, to determine Stock X’s and Stock Y’s beta coefficients.
f. What is the required rate of return on Stocks X and Y? Do these stocks appear to be in equilibrium? If not, what would happen to bring about an equilibrium?