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# CAPM and Beta of Stocks

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You have been asked to use a CAPM analysis to choose between Stocks R and S, with your choice being the one whose expected rate of return exceeds its required return by the widest margin. The risk-free rate is 6%, and the required return on an average stock (or "the market") is 10%. Your security analyst tells you that Stock S's expected rate of return, , is equal to 11%, while Stock R's expected rate of return, , is equal to 12%. The CAPM is assumed to be a valid method for selecting stocks, but the expected return for any given investor (such as you) can differ from the required rate of return for a given stock. The following past rates of return are to be used to calculate the two stocks' beta coefficients, which are then to be used to determine the stocks' required rates of return:

Year Stock R Stock S Market
1 -15% 0% -5%
2 5 5 5
3 25 10 15

Note: The averages of the historical returns are not needed, and they are generally not equal to the expected future returns.

Required: Set up the SML equation and use it to calculate both stocks' required rates of return, and compare those required returns with the expected returns given above. You should invest in the stock whose expected return exceeds its required return by the widest margin. What is the widest margin, or greatest excess return ( - r)?

#### Solution Preview

You have been asked to use a CAPM analysis to choose between Stocks R and S, with your choice being the one whose expected rate of return exceeds its required return by the widest margin. The risk-free rate is 6%, and the required return on an average stock (or "the market") is 10%. Your security analyst tells you that Stock S's expected rate of return, , is equal to 11%, while Stock R's expected rate of return, , is equal to 12%. The CAPM is assumed to be a valid method for selecting stocks, but the expected return for any given investor (such as you) can differ from the required rate of return for a given stock. The following past rates of return are to be used to calculate the two stocks' beta coefficients, which are then to be used to determine the stocks' required rates of return:

Year Stock R Stock S Market
1 -15% 0% -5%
2 5 5 5
3 25 10 15

Note: The averages of the historical returns are not needed, and they are generally not equal to the expected future returns.

Required: Set up the SML equation and use it to calculate both stocks' required rates of return, and compare those required returns with the expected returns ...

#### Solution Summary

The solution uses CAPM analysis to choose between two Stocks the criterion being that the expected rate of return of the stock exceeds its required return by the widest margin. The beta for the two stocks is calculated first using the data given and then the beta valueas are input in the CAPM (Capital Asset Pricing Model) equation to calculate the required returns. These then are compared with the expected rate of return.

\$2.19

## 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?