FIN 500: Case Study 1 Assignment

Notes

Your first case assignment deals with the concepts of risk and return. Please read the

case questions through and give some thought to your answers before you commence.

Answer all parts of the ten (10) questions presented below. Your report should be wellorganized, type-written/word processed, and independently prepared. Each student's

report must be his/her own original work and the write-up must also be individually

prepared.

1. Buxton Corporation is planning to invest in a security that has several potential rates of

return. Using the following probability distribution of returns during different states of

the economy, what is the expected rate of return on this investment? In addition,

compute the standard deviation of the returns (σ). Finally, briefly explain what these

numbers represent.

Probability

0.10

0.20

0.30

0.40 2. Expected Return

-10%

5%

10%

25% Using the capital asset pricing model (CAPM), estimate the appropriate required rate of

return for the following three stocks, assuming that the risk-free rate (r RF) is 5 percent

and the expected return for the market (rM) is 17 percent.

Stock

A

B

C 3. Based on the following table of actual (or ex post) returns for both Inquiry Corporation

and the market from 2007 through 2010, calculate the average return and the standard

deviation for both Inquiry and the market (keep in mind that this data is historical and

not based on a probability distribution, so be sure to use the correct formulas).

Year

2007

2008

2009

2010 4. Beta (β)

0.75

0.90

1.40 Inquiry Corporation

4%

6%

0%

2% Market

2%

3%

1%

-1% (a) Derive the expected return (rP) and beta (βP) for a portfolio based on the

following information:

Stock Percentage of

Portfolio

40%

25%

35% 1

2

3

(b) 5. Beta (β)

1.00

0.75

1.30 Expected

Return

12%

11%

15% Given the information in the table above, present the equation for the security

market line and explain where the return for this specific portfolio would lie (plot)

relative to the SML (i.e., below or above the line). Assume that the risk-free rate

(rRF) is 8 percent and that the expected return on the market portfolio (r M) is 12

percent. Reliable Printing is evaluating a security. One-year Treasury bills (r RF) are currently

paying 3.1 percent. Calculate the following investment’s expected return and its

standard deviation (σ). Should Reliable Printing invest in this security? Briefly explain.

Probability

0.15

0.30

0.40

0.15 Expected Return

-1%

2%

3%

8% 6. You have researched the common stock of two companies (A and B) and have

compiled the following information:

COMPANY A

Probability

0.20

0.50

0.30 COMPANY B

Return

Probability

-2%

0.10

18%

0.30

27%

0.40

0.20 Return

4%

6%

10%

15% Calculate the expected return, standard deviation (σ), and the coefficient of variation

(CV) for each stock and, based on the CV, which stock should you invest in? Briefly

explain.

7. Assume you own a portfolio consisting of the following stocks:

Stock

1

2

3 Percentage of

Portfolio

20%

30%

15% Beta (β)

1.00

0.85

1.20 Expected

Return

16%

14%

20% 4

5 25%

10% 0.60

1.60 12%

24% (a) Determine the expected return on your portfolio.

(b) Determine the portfolio beta (βP).

(c) Given the portfolio beta and the assumptions that the risk-free rate (r RF) is 7 percent

and the expected return on the market portfolio (rMKT) is 15.5 percent, present the

equation for the security market line (SML).

(d) Based on your equation for the SML and the expected returns from the data in the

table, which stocks appear to be winners (i.e., underpriced) and which stocks

appear to be losers (i.e., overpriced)?

8. The common stock for a particular company is known to have a beta (β) of 1.20. The

expected return on the market (rM) is 9 percent and the risk-free rate (rRF) is 5 percent.

(a) Compute a fair rate of return based on this information.

(b) What would be a fair rate of return if the beta were 0.85?

(c) What would be a fair rate of return if the expected return on the market increased to

12 percent and the beta remained at 0.85? 9.

The expected return for the general market (rMKT) is 12.8 percent, and the market risk

premium (i.e., RPM) is 4.3 percent. Moe, Larry, and Curley have betas of 0.82, 0.57,

and 0.68, respectively. What are the required rates of return for the three securities? 10. Hickory Stick’s common stock has a beta (β) of 0.95. The expected return for the

market (rM) is 7 percent and the risk-free rate (rRF) is 4 percent.

(a) What is the required rate of return based on this information?

(b) What would be the required rate of return if the beta were 1.25? 11. An exhaustive financial analysis has produced the following returns on two investments

under three different scenarios:

Scenario

S1

S2

S3 Expected Returns

Probability

0.3

0.4

0.3 Stock X

10%

16%

12% Stock Y

8%

15%

20% (a) Calculate the expected return on each investment.

(b) Calculate the standard deviations (σ) for both X and Y.

(c) Calculate the coefficient of variation (CV) for both X and Y.

(d) If you were to create a portfolio consisting of 67% of Stock X and 33% of Stock Y,

what will be the expected return (rP) and the standard deviation (σP) for your

portfolio?