Question

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. A random sample of 15 high-technology stocks was selected at the end of 2009, and the sample mean and sample standard deviation of the beta coefficients were computed to be 1.23 and s=.37, respectively. (Assume that beta coefficient follows a normal distribution.)

a. (4 points) State the null and alternative hypothesis to test
whether the average high-technology stock is riskier than the
market as a whole.

b. (2 points) Establish the appropriate test statistics for this
problem.

c. (4 points) Determine an appropriate decision rule for testing
the hypothesis in part a at the level of significance α =
.01.

d. (6 points) Make an appropriate conclusion based on the summary
statistics provided in the problem and the decision rule you
specified in part c.

e. (3 points) What is the p-value of the test.

f. (2 points) Based on the p-value calculated in part (e), do you
reject the null hypothesis at the level of significance α=.01? Say
how you made your decision.

g. (3 points) How does your conclusion change if instead of α=.01
we chose a smaller level of significance? Explain.

Answer #1

a)

Below are the null and alternative Hypothesis,

Null Hypothesis, H0: μ = 1

Alternative Hypothesis, Ha: μ > 1

b)

Test statistic,

t = (xbar - mu)/(s/sqrt(n))

t = (1.23 - 1)/(0.37/sqrt(15))

t = 2.408

c)

Rejection Region

This is right tailed test, for α = 0.01 and df = 14

Critical value of t is 2.624.

Hence reject H0 if t > 2.624

d)

Failed to reject null hypothesis

e)

P-value = 0.0152

f)

Failed to reject the null hypothesis as p-value is greater than
0.01

g)

There is no change in the conclusion on decreasing the alpha
because p-value will be greater than alpha and we will conclude to
reject the null hypothesis.

Which of the following statements about the beta coefficient is
false?
A
A stock’s beta coefficient measures its volatility relative to
the market portfolio.
B
A stock’s beta coefficient can be estimated by plotting the
stock’s returns versus the market portfolio’s returns.
C
A stock’s reported beta coefficient is based on forecasted
future volatility.
D
A stock with a beta coefficient greater than 1.0 is said to be
riskier than the market portfolio.
E
Using the capital asset pricing model,...

You are a risk averse investor. You are willing to add an
investment with high volatility provided the correlation
coefficient of this investment with other stocks in the portfolio
is not less than +1.
True
False
10 points
The stock A has 25% standard deviation on its expected return
and the stock B has 25% standard deviation on its expected return.
The expected return for the portfolio of these two stocks will have
a standard deviation of 25%.
True...

Stock X has a 10.0% expected return, a beta coefficient of 0.9,
and a 40% standard deviation of expected returns. Stock Y has a
13.0% expected return, a beta coefficient of 1.3, and a 20%
standard deviation. The risk-free rate is 6%, and the market risk
premium is 5%.
Calculate each stock's coefficient of variation. Do not round
intermediate calculations. Round your answers to two decimal
places.
CVx =
CVy =
Which stock is riskier for a diversified investor?
For...

Stock X has a 9.0% expected return, a beta coefficient of 0.7,
and a 35% standard deviation of expected returns. Stock Y has a
13.0% expected return, a beta coefficient of 1.3, and a 25%
standard deviation. The risk-free rate is 6%, and the market risk
premium is 5%.
Calculate each stock's coefficient of variation. Do not round
intermediate calculations. Round your answers to two decimal
places.
CVx =
CVy =
Which stock is riskier for a diversified investor?
For...

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and a 30% standard deviation of expected returns. Stock Y has a
12.0% expected return, a beta coefficient of 1.1, and a 25.0%
standard deviation. The risk-free rate is 6%, and the market risk
premium is 5%.
Calculate each stock's coefficient of variation. Round your
answers to two decimal places. Do not round intermediate
calculations.
CVx =
CVy =
Which stock is riskier for a diversified investor?
For...

Stock X has a 10.5% expected return, a beta coefficient of 1.0,
and a 35% standard deviation of expected returns. Stock Y has a
12.0% expected return, a beta coefficient of 1.1, and a 30.0%
standard deviation. The risk-free rate is 6%, and the market risk
premium is 5%.
Calculate each stock's coefficient of variation. Round your
answers to two decimal places. Do not round intermediate
calculations.
CVx =
CVy =
Which stock is riskier for a diversified investor?
For...

Stock X has a 10.5% expected return, a beta coefficient of 1.0,
and a 35% standard deviation of expected returns. Stock Y has a
12.5% expected return, a beta coefficient of 1.2, and a 20.0%
standard deviation. The risk-free rate is 6%, and the market risk
premium is 5%. Calculate each stock's coefficient of variation.
Round your answers to two decimal places. Do not round intermediate
calculations. CVx = CVy = Which stock is riskier for a diversified
investor? For...

Stock X has a 10.0% expected return, a beta coefficient of 0.9,
and a 35% standard deviation of expected returns. Stock Y has a
12.0% expected return, a beta coefficient of 1.1, and a 25.0%
standard deviation. The risk-free rate is 6%, and the market risk
premium is 5%.
Calculate each stock's coefficient of variation. Round your
answers to two decimal places. Do not round intermediate
calculations.
CVx =
CVy =
Which stock is riskier for a diversified investor?
For...

Stock X has a 9.5% expected return, a beta coefficient of 0.8,
and a 35% standard deviation of expected returns. Stock Y has a
12.5% expected return, a beta coefficient of 1.2, and a 30.0%
standard deviation. The risk-free rate is 6%, and the market risk
premium is 5%.
Calculate each stock's coefficient of variation. Round your
answers to two decimal places. Do not round intermediate
calculations.
CVx = _____
CVy = _____
Which stock is riskier for a diversified...

Stock X has a 10.5% expected return, a beta coefficient of 1.0,
and a 30% standard deviation of expected returns. Stock Y has a
12.0% expected return, a beta coefficient of 1.1, and a 30.0%
standard deviation. The risk-free rate is 6%, and the market risk
premium is 5%.
Calculate each stock's coefficient of variation. Round your
answers to two decimal places. Do not round intermediate
calculations.
CVx =
CVy =
Which stock is riskier for a diversified investor?
For...

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