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Beta value of a stock. The “beta coefficient” of a stock
Chapter 7, Problem 121SE(choose chapter or problem)
Problem 121SE
Beta value of a stock. The “beta coefficient” of a stock is a measure of the stock’s volatility (or risk) relative to the market as a whole. Stocks with beta coefficients greater than 1 generally bear greater risk (more volatility) than the market, whereas stocks with beta coefficients less than 1 are less risky (less volatile) than the overall market (Alexander, Sharpe, and Bailey, Fundamentals of Investments, 2000). A random sample of 15 high-technology stocks was selected at the end of 2009, and the mean and standard deviation of the beta coefficients were calculated: = 1.23, s = .37.
a. Set up the appropriate null and alternative hypotheses to test whether the average high-technology stock is riskier than the market as a whole.
b. Establish the appropriate test statistic and rejection region for the test. Use = .10.
c. What assumptions are necessary to ensure the validity of the test?
d. Calculate the test statistic and state your conclusion.
e. What is the approximate p-value associated with this test? Interpret it.
f. Conduct a test to determine if the variance of the stock beta values differs from .15. Use = .05.
Questions & Answers
QUESTION:
Problem 121SE
Beta value of a stock. The “beta coefficient” of a stock is a measure of the stock’s volatility (or risk) relative to the market as a whole. Stocks with beta coefficients greater than 1 generally bear greater risk (more volatility) than the market, whereas stocks with beta coefficients less than 1 are less risky (less volatile) than the overall market (Alexander, Sharpe, and Bailey, Fundamentals of Investments, 2000). A random sample of 15 high-technology stocks was selected at the end of 2009, and the mean and standard deviation of the beta coefficients were calculated: = 1.23, s = .37.
a. Set up the appropriate null and alternative hypotheses to test whether the average high-technology stock is riskier than the market as a whole.
b. Establish the appropriate test statistic and rejection region for the test. Use = .10.
c. What assumptions are necessary to ensure the validity of the test?
d. Calculate the test statistic and state your conclusion.
e. What is the approximate p-value associated with this test? Interpret it.
f. Conduct a test to determine if the variance of the stock beta values differs from .15. Use = .05.
ANSWER:
Solution:
Step 1 of 7:
It is given that beta coefficient denotes the measure of stock’s risk relative to the market as a whole.
The beta coefficient greater than 1 indicates the greater risk and beta coefficient less than 1 indicates less risk
The beta coefficients of the randomly selected 15 high technology stocks have the mean
=1.23 and the standard deviation s=0.37.
Using this data we need to find the required values.