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Selena invests the following sum of money in common stock having expected returns as follows:

Common Stock Amount Invested in $ Expected Return Beta of Stock
β
WOOPS 5,000 0.14 0.6
KBOOM 10,000 0.16 0.8
JUDY 6,000 0.17 0.85
UPDWN 8,000 0.13 0.5
SPROUT 4,500 0.20 1.1
RINGG 7,500 0.15 0.65
EIEIO 9,000 0.18 0.9


a) What is the expected return on her portfolio based on the amount invested above?


b) Calculate the systematic risk, β of the portfolio.


c) Does the portfolio have more or less systematic risk compared to the average market portfolio?


d) If return on the market (Rm) is 14% and the risk free rate (Rf) is 4%, what would be the return of the portfolio according to Capital Asset Pricing Model (CAPM)?


e) If Selena wants to get 12% return from this portfolio, is this the appropriate portfolio for her? Explain your reason using your answer in (A) and (D).


f) If she still wants to invest in this portfolio, what should she do in terms of adjusting the weight of the stock? Give your answer based on the amount invested in UPDWN and SPROUT stocks.

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Sixta Kovacek
Sixta KovacekLv2
28 Sep 2019

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Related questions

A portfolio manager is managing a portfolio which is invested in the following manner:

Investment Dollar Amount Invested Beta

Stock 1 $1 million 0.4

Stock 2 2 million 0.8

Stock 3 3 million 1.4

Stock 4 4 million 1.7

Currently, the market risk premium is 5 percent and the portfolio has an expected return of 13 percent. Assume that the market is in equilibrium so that expected returns equal required returns. The manager wants to reduce the risk of the portfolio and wants to earn an expected return of 10.5 percent on the portfolio. Her plan is to sell Stock 3 and use the proceeds to buy another stock. In order to reach her goal, what should be the beta of the stock that the manager selects to replace Stock 3?

1 . a. Lawrence used $20,000 to purchase $5000 each of four stocks: Stock A has βΑ = 1.2; stock B has βΒ = 1.4; stock C has βc = 1.6; and stock D has βD = 1.8. What is Lawrence's portfolio beta? If the risk-free rate is 2%, and the market risk premium (Rmbar – Rf) is 8%, what is Lawrence's expected rate of return on this portfolio?

b. Claire has $10,000. She is very competitive with her brother Lawrence, and wants a portfolio that has the same expected rate of return as his. However, she plans to invest in a stock mutual fund (like an S&P 500 index fund, for instance), while possibly borrowing at the risk-free rate from her broker, to achieve her goal. What are her portfolio weights, and what is the standard deviation of her portfolio's return? Assume the market standard deviation is σm = 9%.

c. Can we assume that Lawrence's portfolio has the same standard deviation of return as Claire's? Why or why not? Which strategy is generally considered more prudent, Lawrence's or Claire's, and why?

1. If we are able to eliminate all of the unsystematic or diversifiable risk in a portfolio then, what is the result?

a.

a risk-free portfolio
b.
a portfolio that has an expected return of zero
c.

a portfolio that contains only systematic risk

2. A portfolio consists 20% of a risk-free asset and 80% of a stock. The risk-free return is 4%. The stock has an expected return of 15% and a standard deviation of 30%. What’s the expected return of the portfolio?

a.
9.5%
b.
15.0%
c.
12.8%

d.
2%


3. The risk-free rate is 5% and the expected return on the market portfolio is 13%. A stock has a beta of 1.5, what is its expected return?


a.
12%
b.
19.5%
c.

17%

4. For what value of the correlation coefficient for the returns of a pair of stocks will the benefits of diversification the largest?


a.

1.0
b.

-1.0
c.

0.0
d.

0.5


5. Which of the following is an example of systematic risk?
a.
IBM posts lower than expected earnings.
b.
The overall stock market becomes more risky due to super fasting trading algorithms.
c.

Intel announces record earnings.

6. According to the CAPM (capital asset pricing model), the security market line is a straight line. The intercept of this line should be equal to

a.
zero
b.
the expected risk premium on the market portfolio
c.
the expected return on the market portfolio
d.
the risk-free rate


7. A portfolio has 40% invested in Asset 1, 50% invested in Asset 2 and 10% invested in Asset 3. Asset 1 has a beta of 1.2, Asset 2 has a beta of 0.8 and Asset 3 has a beta of 1.8, what’s the beta of the portfolio?

a.
0.80
b.
1.06
c.
1.27


8. Suppose you can borrow and lend at the risk free-rate of 3%. Which of the following four risky portfolios has the best return relative to risk. (Hint: Calculate Sharpe Ratios the ratio of risk premium to standard deviation for each portfolio)

a.
portfolio with a standard deviation of 15% and an expected return of 12%
b.
portfolio with a standard deviation of 12% and an expected return of 9%
c.
portfolio with a standard deviation of 25% and an expected return of 18%
d.
portfolio with a standard deviation of 19% and an expected return of 15%


9. Which statements are TRUE regarding risk and return?

Statement I:
Diversification is the process of removing systematic risk from a portfolio.
Statement II:
In general, the greater the risk, the greater the return required by an investor.
Statement III:
Investors should focus on real returns if they are concerned about the purchasing power of their wealth.


a.
Statements II and III only
b.
Statement I only
c.
Statements I and III only
d.
Statements I and II only

10. The beta of the risk-free asset is:
a.

1.0
b.

0.5
c.

0.0
d.

-1.0

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