# Portfolio Theory: Standard Deviation of Stock Returns, Required Return, Risk Premium

1. The standards deviation of stock returns for stock A is 40%. The standard deviation of the market return is 20%. If the correlation between stocks A and the market is 0.70, what is Stock A's Beta

2. An analyst has molded the stock of Crisp Trucking using a two- factor APT model. The risk- free rate is 6%, the expected return on the first factor (r1) is 12%, and the expected return on the second factor (r2) is 8%. If (bi1) = 0.7 and bi2 = 0.9, what is Crisp's required return?

3. An analyst has molded the stock of a company using Fame-French three factor model. The risk- free rate is 5%, the required market return is 10%, the risk premium for small stocks (rsmb) is 3.2%, and the risk premium for value stocks (rhml) is 4.8%. if ai= 0, bi= 1.2, ci= -0.4 and di= 1.3, what is the stock's required return?

Must be done using Excel worksheet.

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#### Solution Summary

The solution is attached as an Excel files and calculates the beta of certain stocks when given their standard deviation and the required turn of two types of stock.

Portfolio Theory, Stock Valuation, & Market Equilibrium

Portfolio Theory, Stock Valuation, & Market Equilibrium

1. Consider the following information and then calculate the required rate of return for the Scientific Investment Fund, which holds 4 stocks. The market's required rate of return is 15.0%, the risk-free rate is 7.0%, and the Fund's assets are as follows: 30

Stock Investment Beta

A $ 200,000 1.50

B 300,000 -0.50

C 500,000 1.25

D 1,000,000 0.75

a. 10.67%

b. 11.23%

c. 11.82%

d. 13.10%

Question 2.2. Calculate the required rate of return for Mercury, Inc., assuming that (1) investors expect a 4.0% rate of inflation in the future, (2) the real risk-free rate is 3.0%, (3) the market risk premium is 5.0%, (4) Mercury has a beta of 1.00, and (5) its realized rate of return has averaged 15.0% over the last 5 years.

a. 10.29%

b. 10.83%

c. 11.40%

d. 12.00%

Question 3.3. The SML relates required returns to firms' systematic (or market) risk. The slope and intercept of this line can be influenced by managerial actions.

a. True

b. False

Question 4.4. We will almost always find that the beta of a diversified portfolio is less stable over time than the beta of a single security.

a. True

b. False

Question 5.5. If the returns of two firms are negatively correlated, then one of them must have a negative beta.

a. True

b. False

Question 6.6. Stock A's beta is 1.5 and Stock B's beta is 0.5. Which of the following statements must be true about these securities? (Assume market equilibrium.)

a. When held in isolation, Stock A has greater risk than Stock B.

b. Stock B must be a more desirable addition to a portfolio than Stock A.

c. Stock A must be a more desirable addition to a portfolio than Stock B.

d. The expected return on Stock A should be greater than that on Stock B.

Question 7.7. It is possible for a firm to have a positive beta, even if the correlation between its returns and those of another firm are negative.

a. True

b. False

Question 8.8. Which of the following is NOT a potential problem with beta and its estimation?

a. Sometimes a security or project does not have a past history which can be used as a basis for calculating beta.

b. Sometimes, during a period when the company is undergoing a change such as toward more leverage, or riskier assets, the calculated beta will be drastically different than the "true" or "expected future" beta.

c. The beta of "the market," can change over time, sometimes drastically.

d. Sometimes the past data used to calculate beta do not reflect the likely risk of the firm for the future because conditions have changed.

Question 9.9. The CAPM is a multi-period model which takes account of differences in securities' maturities, and it can be used to determine the required rate of return for any given level of systematic risk.

a. True

b. False

Question 10.10. Which is the best measure of risk for an asset held in isolation, and which is the best measure for an asset held in a diversified portfolio?

a. Variance; correlation coefficient.

b. Standard deviation; correlation coefficient.

c. Beta; variance.

d. Coefficient of variation; beta.