# Required rate of return on an individual stock equation

The equation for the required rate of return on an individual stock given by the Capital Asset Pricing Model is

kj = Rf + á(Rf - km)

kj = Rf - á(km - Rf)

kj = Rf + á(km - Rf)

kj = km + á(km - kf)

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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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