Practice
Problems – Chapters 7 and 8
1)
A stock with a beta of .75 has a required return of 8.5%. The risk-free rate is
2.5%.
a) What is the risk premium for the market portfolio?
b) What is the risk premium for the stock?
c) If the risk premium on the market portfolio
increases by 3 percentage points (e.g., from x% to x+3%), what is the new
required return for the stock?
2) Andy’s Candies has a beta of 0.86 and an expected return of 9.266% per year. The risk-free rate is 2.3% per year.
a) What is the expected return on the market portfolio?
b) At the end of the year you find that the actual return on the market portfolio is 6%. What return do you now expect from the stock for this year?
3) The expected return on a stock is 13.55%.
The expected return on the market portfolio is 11.5%. The risk-free rate
is 3.3%.
a) What is the beta of the stock?
b) If the actual return on the market portfolio for
the year turns out to be 15%, what return would you now expect from the stock
for the year?
4) XYZ's stock has an expected
return of 10.48. The riskfree rate
is 2.20%, while the risk premium on the market portfolio is 9%.
a) What
is the beta of XYZ's stock?
b) What
is the risk premium for the stock?
c) What
is the expected return for the market portfolio?
d) The actual return for the
market portfolio at the end of the year turns out to be 8%. What performance would you now expect from XYZ's stock?
5) BBC Corp.'s stock has a
beta of 0.86 and an expected return of 10.525%.
The market portfolio has an expected return of 11.75%
a) What
is the riskfree return?
b) What
is the risk premium for the market portfolio?
c) What
is the risk premium for BBC's stock?
d) If the actual
return on the market portfolio at the end of the year turns out to be -5%, what
return would you now expect from the stock?
6)
Peculiar Pumpkins Inc.
has a beta of 1.15, and a required return of 11.19% per year.
A stock portfolio with beta of 0.3 has a required return of 4.73% per
year.
a)
What is the risk free rate?
b)
What is the expected return on the market portfolio?
c)
At the end of
the year, the return on the market portfolio turns out to be 16%, and the return
on PPI’s stock turns out to be 15%. What
is PPI’s abnormal return for the year?
7) Last year the market went up 10%. A stock with a beta of 1.2 went up by 11%. If the riskless rate was 3%, what was the stock's abnormal return?
8) Last year the market went down 16%. A stock with a beta of 0.8 went down 10%. If the riskless rate was 2%, what was the stock's abnormal return?
9)
Mark the following statements with a T or a F to indicate whether
they are true or false (no explanations required):
a)
A risk averse investor is one who will invest in riskfree assets rather
than hold risky assets and bear risk.
b) A higher beta necessarily means a higher required return.
c) If the beta of a stock doubles, the required return on the stock will
double.
d) Firm-specific news constitutes diversifiable risk only because the
firm-specific news of different firms is uncorrelated.
e) On a given day, you cannot predict whether economy-wide
news will be randomly positive or negative.
If it is randomly positive or negative, it should cancel out in a large
portfolio and constitute diversifiable risk.
f) Beta is used to measure
the systematic risk of a stock because the numerator of beta measures the
marginal risk the stock contributes to the market portfolio.
g) Risk averse investors
will not be willing to hold a risky stock if the expected return is less than
the riskless rate.
h) If two stocks have the same standard deviation of returns, the one which
has a lower correlation with the market portfolio always has the smaller beta.
i) If the beta of the market portfolio increases, E(Rm) will increase.