Reading 51: An Introduction to Asset Pricing Models - LOS following, between, stocks, style, black

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1.Given the following data what is the correlation coefficient between the two stocks and the Beta of stock A?

§       standard deviation of returns of Stock A is 10.04 percent

§       standard deviation of returns of Stock B is 2.05 percent

§       standard deviation of the market is 3.01 percent

§       covariance between the two stocks is 0.00109

§       covariance between the market and stock A is 0.002

       Correlation Coefficient    Beta (stock A)

A)                          0.6556        0.06

B)                          0.5296         0.06

C)                          0.6556          2.2

D)                          0.5296        2.2

2.The expected rate of return is twice the 12% expected rate of return from the market. What is the beta if the risk-free rate is 6%.

A)   3.

B)   4.

C)   2.

D)   5.

3.Given a beta of 1.10 and a risk-free rate of 5 percent, what is the expected rate of return assuming a 10 percent market return?

A)   15.5%.

B)   10.5%.

C)   21.5%.

D)   5.5%.

4.Which of the following statements about a stock's beta is TRUE? A beta greater than one is:

A)   risky, while a beta less than one is risk-free.

B)   overvalued, while a beta less than one is undervalued.

C)   is riskier than the market, while a beta less than one is less risky than the market.

D)   undervalued, while a beta less than one is overvalued.

5.If the standard deviation of the market’s returns is 5.8%, the standard deviation of a stock’s returns is 8.2%, and the covariance of the market’s returns with the stock’s returns is 0.003, what is the beta of the stock?

A)   1.07.

B)   0.89.

C)   0.05.

D)   1.12.

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答案和详解如下：

1.Given the following data what is the correlation coefficient between the two stocks and the Beta of stock A?

§       standard deviation of returns of Stock A is 10.04 percent

§       standard deviation of returns of Stock B is 2.05 percent

§       standard deviation of the market is 3.01 percent

§       covariance between the two stocks is 0.00109

§       covariance between the market and stock A is 0.002

       Correlation Coefficient    Beta (stock A)

A)                          0.6556        0.06

B)                          0.5296         0.06

C)                          0.6556          2.2

D)                          0.5296        2.2

The correct answer was D)

correlation coefficient = 0.00109/(0.0205)(0.1004) = 0.5296.

beta of stock A = covariance between stock and the market / variance of the market

Beta = 0.002 / 0.0301² = 2.2

2.The expected rate of return is twice the 12% expected rate of return from the market. What is the beta if the risk-free rate is 6%.

A)   3.

B)   4.

C)   2.

D)   5.

The correct answer was A)

24 = 6 + β (12 - 6)

18 = 6β

β = 3

3.Given a beta of 1.10 and a risk-free rate of 5 percent, what is the expected rate of return assuming a 10 percent market return?

A)   15.5%.

B)   10.5%.

C)   21.5%.

D)   5.5%.

The correct answer was B)

k = 5 + 1.10 (10 - 5)

= 5 + 1.10 (5)

= 5 + 5.5

= 10.5

4.Which of the following statements about a stock's beta is TRUE? A beta greater than one is:

A)   risky, while a beta less than one is risk-free.

B)   overvalued, while a beta less than one is undervalued.

C)   is riskier than the market, while a beta less than one is less risky than the market.

D)   undervalued, while a beta less than one is overvalued.

The correct answer was C)

Beta is a measure of the volatility of a stock.  The overall market's beta is one. A stock with higher systematic risk than the market will have a beta greater than one, while a stock that has a lower systematic risk will have a beta less than one.

5.If the standard deviation of the market’s returns is 5.8%, the standard deviation of a stock’s returns is 8.2%, and the covariance of the market’s returns with the stock’s returns is 0.003, what is the beta of the stock?

A)   1.07.

B)   0.89.

C)   0.05.

D)   1.12.

The correct answer was B)

The formula for beta is: (Cov_stock,market)/(Var_market), or (0.003)/(0.058)² = 0.89.