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# Finance: CAPM, Portfolio returns and Standard deviation

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1. Abigail Grace has a \$900,000 fully diversified portfolio. She subsequently inherits ABC Company common stock worth \$100,000. Her financial advisor provided her with the following estimates:

Expected Monthly Returns Standard Deviation of Monthly Returns
Original Portfolio 0.67% 2.37%
ABC Company 1.25 2.95

The correlation coefficient of ABC stock returns with the original portfolio returns is 0.40. The inheritance changes Abigail's overall portfolio and she is deciding whether to keep the ABC stock. Assuming Abigail keeps the ABC stock, calculate:
a. the expected return of her new portfolio which includes the ABC stock.
b. covariance of ABC stock returns with the original portfolio returns.
c. the standard deviation of her new portfolio which includes the ABC stock.

2. In previous problems using CAPM Ki=Rf + bi(Km-Rf),we were solving for expected rate of return. How can CAPM be used to calculate expected return, please explain and show calculations.

Karen Kay, a portfolio manager at Collins Asset Management, is using CAPM for making recommendations to her clients. Her research department has developed the following information:

Forecasted Return Standard Deviation Beta

Stock X 14% 36% .8
Stock Y 17 25 1.5
Market Index 14 15 1

Risk-Free rate:5

Calculate expected return for each stock.

#### Solution Summary

The problem deals with different issues in finance.

The problems include portfolio returns, returns under CAPM etc.

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## 4 Problems to do with Finance 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.
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, &#61555;A&#61472;&#61501; 0.1 and &#61555;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?

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?

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?

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(See attached file for full problem description)

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