Busn Week 5 Homework

Chapter 11: 4, 7, 17, and 29

Problem 4

Portfolio Expected Return. You have $10,000 to invest in a stock portfolio. Your choices are Stock X with an expected return of 14 percent and Stock Y with an expected return of 11 percent. If your goal is to create a portfolio with an expected return of 12.4 percent, how much money will you invest in Stock X? In Stock Y?

Solution

ER = W1 ER1 +W2 ER2

12.4% = w1 *14% + (1-w1)*11%

12.4% = W1*3% +11%

W1 = (12.4%-11%)/ 3%

=0.4667

W2 = 1-0.4667 = 0.5333

Amount invested in X = 10000*0.4667 = $4667

Amount invested in Y= 10000*0.5333 = $5333

Problem 7

7. Calculating Returns and Standard Deviations. Based on the following information, calculate the expected return and standard deviation for the two stocks.

Solution

As given in the solution expected return for stock A = 10.3%

Stock B = 14.7%

Problem 17

Using CAPM. A stock has a beta of 1.15 and an expected return of 10.4 percent. A risk-free asset currently earns 3.8 percent.

a. What is the expected return on a portfolio that is equally invested in the two assets?

b. If a portfolio of the two assets has a beta of .7, what are the portfolio weights?

c. If a portfolio of the two assets has an expected return of 9 percent, what is its beta?

d. If a portfolio of the two assets has a beta of 2.3, what are the portfolio weights? How do you interpret the weights for the two assets in this case? Explain.

Solution

R= 3.8+1.15 (10.4-3.8) = 11.39%

a) Return on portfolio = 0.5*3.8% +0.5*11.39 =7.6%

b) As the beta of risk free asset is zero and other assets is 1.15 the weight of other assets =0.7/1.15 = 61%

Risk free assets = 39%

c)

stock A as stock percent of portfolio = 3.8% *pa + (1-Pa)*11.39% = 9%

= 31.5

stock B as stock percent of portfolio = 1-0.315 =0.685

Portfolio Beta = 0.315* 0 +0.685...