# 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.

**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

market risk.

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

a. 10.67%

b. 11.23%

c. 11.82%

d. 12.45%

e. 13.10%

**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?