# 12 Multiple choice questions on portfolio of stocks, beta of stocks, beta of portfolio, CAPM, market rate, market risk premium , diversified portfolio , market risk , Security Market Line, unsystematic risk, default-free rate, expected inflation rate, etc.

1 In a portfolio of three different stocks, which of the following could not be true?

a. The riskiness of the portfolio is less than the riskiness of each of the stocks if they were held in isola-tion.

b. The riskiness of the portfolio is greater than the riskiness of one or two of the stocks.

c. The beta of the portfolio is less than the beta of each of the individual stocks.

d. The beta of the portfolio is greater than the beta of one or two of the individual stocks' betas.

e. None of the above (that is, they all could be true, but not necessarily at the same time).

2.. Stock A has a beta = 0.8, while Stock B has a beta = 1.6. Which of the following statements is most correct?

a. Stock B's required return is double that of Stock A's.

b. An equally weighted portfolio of Stock A and Stock B will have a beta less than 1.2.

c. If market participants become more risk averse, the required return on Stock B will increase more than the required return for Stock A.

d. All of the statements above are correct.

e. Statements a and c are correct.

3.. Which of the following statements is most correct?

a. The beta coefficient of a stock is normally found by running a regression of past returns on the stock against past returns on a stock market index. One could also construct a scatter diagram of returns on the stock versus those on the market, estimate the slope of the line of best fit, and use it as beta.

b. It is theoretically possible for a stock to have a beta of 1.0. If a stock did have a beta of 1.0, then, at least in theory, its required rate of return would be equal to the riskless (default-free) rate of return, kRF.

c. If you found a stock with a zero beta and held it as the only stock in your portfolio, you would by definition have a riskless portfolio. Your 1-stock portfolio would be even less risky if the stock had a negative beta.

d. The beta of a portfolio of stocks is always larger than the betas of any of the individual stocks.

e. All of the statements above are correct.

4. Other things held constant, (1) if the expected inflation rate decreases, and (2) investors become more risk averse, the Security Market Line would shift

a. Down and have steeper slope.

b. Up and have less steep slope.

c. Up and keep same slope.

d. Down and keep same slope.

e. Down and have less steep slope.

5. Which of the following statements is most correct?

a. If the returns from two stocks are perfectly positively correlated (that is, the correlation coefficient is +1) and the two stocks have equal variance, an equally weighted portfolio of the two stocks will have a variance which is less than that of the individual stocks.

b. If a stock has a negative beta, its expected return must be negative.

c. According to the CAPM, stocks with higher standard deviations of returns will have higher expected returns.

d. A portfolio with a large number of randomly selected stocks will have less market risk than a single stock which has a beta equal to 0.5.

e. None of the statements above is correct.

6. Which of the following statements is most correct?

a. It is possible to have a situation where the market risk of a single stock is less than the market risk of a portfolio of stocks.

b. The market risk premium will increase if, on average, market participants become more risk averse.

c. If you selected a group of stocks whose returns are perfectly positively correlated, then you could end up with a portfolio for which none of the unsystematic risk is diversified away.

d. Statements a and b are correct.

e. All of the statements above are correct.

7. Given the following information, determine which beta coefficient for Stock A is consistent with equilibrium:

kA = 11.3%; kRF = 5%; kM = 10%

a. 0.86

b. 1.26

c. 1.10

d. 0.80

e. 1.35

8. You are an investor in common stock, and you currently hold a well-diversified portfolio that has an expected return of 12 percent, a beta of 1.2, and a total value of $9,000. You plan to increase your portfolio by buying 100 shares of AT&E at $10 a share. AT&E has an expected return of 20 percent with a beta of 2.0. What will be the expected return and the beta of your portfolio after you purchase the new stock?

a. = 20.0%; bp = 2.00

b. = 12.8%; bp = 1.28

c. = 12.8%; bp = 1.20

d. = 13.2%; bp = 1.28

e. = 14.0%; bp = 1.32

9. Given the following probability distribution, what is the expected return and the standard deviation of returns for Security J?

State Pi kJ

_____ ____ ____

1 0.2 10%

2 0.6 15

3 0.2 20

a. 15%; 6.50%

b. 12%; 5.18%

c. 15%; 3.16%

d. 15%; 10.00%

e. 20%; 5.00%

10. Currently, the risk-free rate is 5 percent and the market risk premium is 6 percent.

You have your money invested in three assets: an index fund that has a beta of

1.0, a risk-free security that has a beta of 0, and an international fund that has a

beta of 1.5. You want to have 20 percent of your portfolio invested in the risk-

free asset, and you want your overall portfolio to have an expected return of 11

percent. What portion of your overall portfolio should you invest in the inter-

national fund?

a. 0%

b. 40%

c. 50%

d. 60%

e. 80%

11. Walter Jasper currently manages a $500,000 portfolio. He is expecting to receive an additional $250,000 from a new client. The existing portfolio has a required return of 10.75 percent. The risk-free rate is 4 percent and the return on the market is 9 percent. If Walter wants the required return on the new portfolio to be 11.5 percent, what should be the average beta for the new stocks added to the portfolio?

a. 1.50

b. 2.00

c. 1.67

d. 1.35

e. 1.80

12. You have been scouring The Wall Street Journal looking for stocks that are "good values" and have calculated expected returns for five stocks. Assume the risk-free rate (kRF) is 7 percent and the market risk premium ( - ) is 2 percent. Which security would be the best investment? (Assume you must choose just one.)

Expected Return Beta

a. 9.01% 1.70

b. 7.06% 0.00

c. 5.04% -0.67

d. 8.74% 0.87

e. 11.50% 2.50

#### Solution Preview

...ta.

d. The beta of a portfolio of stocks is always larger than the betas of any of the individual stocks.

e. All of the statements above are correct.

A is correct.

B is wrong. For beta=1 the required rate of return is market rate.

Second part of C is incorrect. Any beta (either positive or negative) means risk.

D is wrong. Beta of the portfolio is the average beta. It cannot be larger than the betas of any of the individual stocks.

(Answer A)

4. Other things held constant, (1) if the expected inflation rate decreases, and (2) investors become more risk averse, the Security Market Line would shift

a. Down and have steeper slope.

b. Up and have less steep slope.

c. Up and keep same slope.

d. Down and keep same slope.

e. Down and have less steep slope.

Answer a is correct.

Risk free rate will come down and market rate will go up (investors would demand higher return for the same risk). both come down but not by the same amount. Hence SML will shift down and have steeper slope.

5. Which of the following statements is most correct?

a. If the returns from two stocks are perfectly positively correlated (that is, the correlation coefficient is +1) and the two stocks have equal variance, an equally weighted portfolio of the two stocks will have a variance which is less than that of the individual stocks.

b. If a stock has a negative beta, its expected return must be negative.

c. According to the CAPM, stocks with higher standard deviations of returns will have higher expected returns.

d. A portfolio with a large number of randomly selected stocks will have less market risk than a single stock which has a beta equal to 0.5.

e. None of the statements above is correct.

A is wrong because the portfolio will have exactly the same variance as the stocks.

B is wrong as expected return may be negative but not in all the cases.

C is wrong as according to CAPM Stocks with higher betas will have higher expected returns.

D is wrong as a portfolio with a large number of randomly selected stocks will have a beta close to 1. It cannot have less risk than a stock with beta equal to 0.5.

Hence answer e is correct.

6. Which of the following statements is most correct?

a. It is possible to have a situation where the market risk of a single stock is less than the market risk of a portfolio of stocks.

b. The market risk premium will ...