Problem 11-37 Standard Deviation and Beta There are two stocks in the market, Stock A and Stock B. The price of Stock A today is $85. The price of Stock A next year will be $74 if the economy is in a recession, $97 if the economy is normal, and $107 if the economy is expanding. The probabilities of recession, normal times, and expansion are .30, .50, and .20, respectively. Stock A pays no dividends and has a correlation of .80 with the market portfolio. Stock B has an expected return of 15.0 percent, a standard deviation of 35.0 percent, a correlation with the market portfolio of .34, and a correlation with Stock A of .46. The market portfolio has a standard deviation of 19.0 percent. Assume the CAPM holds. a-1.What is the return for each state of the economy for Stock A? (A negative answer should be indicated by a minus sign. Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.) a- What is the expected return of Stock A? (Do not round intermediate calculations 2. and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) a- What is the variance of Stock A? (Do not round intermediate calculations and round 3. your answer to 4 decimal places, e.g., .1616.) a- What is the standard deviation of Stock A? (Do not round intermediate calculations 4. and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) a- What is the beta of Stock A? (Do not round intermediate calculations and round 5. your answer to 3 decimal places, e.g., 32.161.) a- What is the beta of Stock B? (Do not round intermediate calculations and round 6. your answer to 3 decimal places, e.g., 32.161.) a-1. Recession -12.94 % a-1. Normal 14.12 % a-1. Expansion 25.88 % a-2. Expected return 8.35% a-3. Variance a-4. Standard deviation % a-5. Beta of Stock A a-6. Beta of Stock B
Problem 11-37 Standard Deviation and Beta There are two stocks in the market, Stock A and Stock B. The price of Stock A today is $85. The price of Stock A next year will be $74 if the economy is in a recession, $97 if the economy is normal, and $107 if the economy is expanding. The probabilities of recession, normal times, and expansion are .30, .50, and .20, respectively. Stock A pays no dividends and has a correlation of .80 with the market portfolio. Stock B has an expected return of 15.0 percent, a standard deviation of 35.0 percent, a correlation with the market portfolio of .34, and a correlation with Stock A of .46. The market portfolio has a standard deviation of 19.0 percent. Assume the CAPM holds. a-1.What is the return for each state of the economy for Stock A? (A negative answer should be indicated by a minus sign. Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.) a- What is the expected return of Stock A? (Do not round intermediate calculations 2. and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) a- What is the variance of Stock A? (Do not round intermediate calculations and round 3. your answer to 4 decimal places, e.g., .1616.) a- What is the standard deviation of Stock A? (Do not round intermediate calculations 4. and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) a- What is the beta of Stock A? (Do not round intermediate calculations and round 5. your answer to 3 decimal places, e.g., 32.161.) a- What is the beta of Stock B? (Do not round intermediate calculations and round 6. your answer to 3 decimal places, e.g., 32.161.) a-1. Recession -12.94 % a-1. Normal 14.12 % a-1. Expansion 25.88 % a-2. Expected return 8.35% a-3. Variance a-4. Standard deviation % a-5. Beta of Stock A a-6. Beta of Stock B
Essentials Of Investments
11th Edition
ISBN:9781260013924
Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Chapter1: Investments: Background And Issues
Section: Chapter Questions
Problem 1PS
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Transcribed Image Text:Problem 11-37 Standard Deviation and Beta
There are two stocks in the market, Stock A and Stock B. The price of Stock A today is
$85. The price of Stock A next year will be $74 if the economy is in a recession, $97 if
the economy is normal, and $107 if the economy is expanding. The probabilities of
recession, normal times, and expansion are .30, .50, and .20, respectively. Stock A pays
no dividends and has a correlation of .80 with the market portfolio. Stock B has an
expected return of 15.0 percent, a standard deviation of 35.0 percent, a correlation with
the market portfolio of .34, and a correlation with Stock A of .46. The market portfolio
has a standard deviation of 19.0 percent. Assume the CAPM holds.
a-1.What is the return for each state of the economy for Stock A? (A negative answer
should be indicated by a minus sign. Do not round intermediate calculations and
enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.)
a- What is the expected return of Stock A? (Do not round intermediate calculations
2. and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)
a- What is the variance of Stock A? (Do not round intermediate calculations and round
3. your answer to 4 decimal places, e.g., .1616.)
a- What is the standard deviation of Stock A? (Do not round intermediate calculations
4. and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)
a- What is the beta of Stock A? (Do not round intermediate calculations and round
5. your answer to 3 decimal places, e.g., 32.161.)
a- What is the beta of Stock B? (Do not round intermediate calculations and round
6. your answer to 3 decimal places, e.g., 32.161.)
a-1. Recession
-12.94 %
a-1. Normal
14.12 %
a-1. Expansion
25.88 %
a-2. Expected return
8.35%
a-3. Variance
a-4. Standard deviation
%
a-5. Beta of Stock A
a-6. Beta of Stock B
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