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# Expected return, standard deviation of stocks/portfolio

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Week 6 - Problem 1

10.6 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 percent A and 65 percent B when the correlation between the returns on A and B is 0.6.

b. Calculate the standard deviation of a portfolio that is composed of 35 percent A and 65 percent 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 of the portfolio?

Week 6 - 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?

Week 6 - 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?

#### Solution Preview

Week 6 - Problem 1

10.6 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 percent A and 65 percent B when the correlation between the returns on A and B is 0.6.

b. Calculate the standard deviation of a portfolio that is composed of 35 percent A and
65 percent 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
of the portfolio?
SHOW ALL CALCULATIONS

a. Calculate the expected return and standard deviation of a portfolio that is composed of 35 percent A and 65 percent B when the correlation between the returns on A and B is 0.6.

Stock Weights (x) Expected return ( r ) Standard deviation (&#963;) Correlation (&#961;)
A 0.35 0.17 0.12 0.6
B 0.65 0.27 0.21

Expected return = xA rA + xB rB= 0.235 =0.35*0.17+0.65*0.27
Standard deviation =&#8730; (xA^2&#963;A^2 + xB^2&#963;B^2+ 2 xAxB&#961;&#963;A&#963;B)= 0.1652
=&#8730;(0.35^2*0.12^2+0.65^2*0.21^2+2*0.35*0.65*0.6*0.12*0.21)

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

Stock Weights (x) Expected return ( r ) Standard ...

#### Solution Summary

The solution calculate the expected return and standard deviation of a portfolio and expected return of a stock using capital-asset-pricing model (CAPM).

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