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# SML, Expected Return, Beta

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5) The rate on Treasury bills is 4 percent, and the equity risk premium is 10 percent. Use the SML to estimate the return on each of the above stocks.
Security Standard deviation Correlation with market

A 0.30 0.70
B 0.75 0.30
C 0.45 0.50
D 0.50 0.16

6) Maria has decided to invest \$5,000 in each of the above stocks. Compute the expected return on the portfolio and the portfolio beta.

Security Standard deviation Correlation with market

A 0.30 0.70
B 0.75 0.30
C 0.45 0.50
D 0.50 0.16

(See attached file for full problem description with data charts)

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#### Solution Summary

Calculates the return on stocks using security market line (SML) and calculates the expected return on the portfolio and the portfolio beta for a portfolio made up of these stocks.

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## Essentials of Investments: SML, CAPM, Beta, expected rate of return

Please see attachment

Textbook: Essentials of Investments

Chapter 7 (1, 2, 3, 6, 16, 18, and 32)

1. Which of the following statements about the security market line (SML) are true?
a. The SML provides a benchmark for evaluating expected investment performance.
b. The SML leads all investors to invest in the same portfolio of risky assets.
c. The SML is a graphic representation of the relationship between expected return
and beta.
d. Properly valued assets plot exactly on the SML.

2. Karen Kay, a portfolio manager at Collins Asset Management, is using the capital asset
pricing model for making recommendations to her clients. Her research department has
developed the information shown in the following exhibit.

Forecasted Returns, Standard Deviations, and Betas
Forecasted Return Standard Deviation Beta
Stock X 14.0% 36% 0.8
Stock Y 17.0 25 1.5
Market index 14.0 15 1.0
Risk-free rate 5.0

3. What must be the beta of a portfolio with E ( r P ) _ 20%, if r f _ 5% and E ( r M ) _ 15%?

6. Are the following statements true or false? Explain.
a. Stocks with a beta of zero offer an expected rate of return of zero.
b. The CAPM implies that investors require a higher return to hold highly volatile
securities.
c. You can construct a portfolio with a beta of 0.75 by investing 0.75 of the budget in
T-bills and the remainder in the market portfolio.

In Problems 16-18 below, assume the risk-free rate is 8% and the expected rate of
return on the market is 18%.
16. A share of stock is now selling for \$100. It will pay a dividend of \$9 per share at the end
of the year. Its beta is 1.0. What do investors expect the stock to sell for at the end of the
year?

18. A stock has an expected return of 6%. What is its beta?

32. The security market line depicts:
a. A security's expected return as a function of its systematic risk.
b. The market portfolio as the optimal portfolio of risky securities.
c. The relationship between a security's return and the return on an index.
d. The complete portfolio as a combination of the market portfolio and the risk-free
asset.

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