# Problems in CAPM / Beta / Return and standard deviations

(See attached file for full problem description)

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1.1 Solve Problems 10.3 on page 289, RWJ Chapter 10

Mr Henry can invest in Highbull stock and Slowbear stock.

His projection of the returns on these two stocks is as follows:

State of Probability of Return on Return on

Economy State Occurring Highbull Stock (%) Slowbear Stock (%)

Recession 0.25 - 2.00 5.00

Normal 0.60 9.20 6.20

Boom 0.15 15.40 7.40

a. Calculate the expected return on each stock.

b. Calculate the standard deviation returns on each stock.

c. Calculate the covariance and correlation between the returns on the

two stocks.

Answers

a.

b.

c.

1.2 Solve Problems 10.6 on page 289, RWJ Chapter 10

Suppose the expected returns and standard deviations of stocks A and B are E(RA) = 0.15, E(RB) = 0.25, A 0.1 and B = 0.2 respectively.

a. Calculate the expected returns and standard deviations of a portfolio that is composed of 40 percent A and 60 percent B when the correlation between the returns on A and B is 0.5.

b. Calculate the standard deviation of portfolio that is comprised of 40 percent A and 60 percent B when the correlation coefficient between the returns on A and B is -0.5.

c. How does the correlation between the returns on A and B affect the standard deviation of the portfolio?

Answers:

a.

b.

c.

1.3 Solve Problems 10.28 on page 292, RWJ Chapter 10

Suppose you observe the following situation:

Return if State Occurs

State of Economy Probability of State Stock A Stock B

Bust 0.25 -0.1 -0.3

Normal 0.5 0.1 0.05

Boom 0.25 0.2 0.4

a. Calculate the expected return on each stock

b. Assuming the capital asset pricing model holds and stock A's beta is greater than stock B's beta by 0.25, what is the expected market risk premium?

Answers:

a.

b.

1.4 Solve Problems 10.38 on page 293, RWJ Chapter 10

Suppose you have invested $30,000 in the following Stocks:

Security Amount Invested Beta

Stock A $ 5,000 0.75

Stock B 10,000 1.1

Stock C 8,000 1.36

Stock D 7,000 1.88

Question:

The risk-free rate is 4 percent and the expected return on the market portfolio is 15 percent. Based on the capital asset pricing model, what is the expected return on the above portfolio?

Answer:

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(See attached file for full problem description)

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#### Solution Summary

The solution has 4 problems dealing with Finance CAPM / Beta / Return and standard deviations from the book by Ross, Westerfield and Jaffe Chapter 10

Expected return and Standard Deviation of a portfolio, CAPM

The following four questions need to be addressed with regards to each problem.

1. What financial concept or principle is the problem asking you to solve?

2. In the context of the problem, what are some business decisions that a manager would be able to make after solving the problem?

3. Is there any additional information missing from the problem that would enhance the decision making process?

4. Without showing mathematical equations, explain in writing how you would solve the problem.

PROBLEM 1

Suppose the expected returns and standard deviations of stocks A and B are E(RA)= 0.17, E(RB) = 0.27, StdDevA = 0.12, and StdDevB = 0.21, respectively.

a. Calculate the expected return and standard deviation of a portfolio that is composed of 35% A and 65% B when the correlation between the returns on A and B is 0.06.

b. Calculate the standard deviation of a portfolio that is composed of 35% A and 65% B when the correlation coefficient between the returns on A and B is -0.6.

c. How does the correlation between the returns on A and B affect the standard deviation?

PROBLEM 2

Suppose the expected return on the market portfolio is 14.7 percent and the risk-free rate is 4.9 percent. Morrow Inc. stock has a beta of 1.3. Assume the capital-asset-pricing model holds.

a. What is the expected return on Morrow's stock?

b. If the risk-free rate decreases to 4 percent, what is the expected return on Morrow's stock?

PROBLEM 3

A portfolio that combines the risk-free asset and the market portfolio has an expected return of 22 percent and a standard deviation of 5 percent. The risk-free rate is 4.9 percent, and the expected return on the market portfolio is 19 percent. Assume the capital-asset-pricing model holds.

What expected rate of return would a security earn if it had a 0.6 correlation with the market portfolio and a standard deviation of 3 percent?

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