Fin 6310-Investment Theory and Practice Homework 6: Chapter - 9
Fin 6310-Investment Theory and Practice Homework 6: Chapter - 9
Fin 6310-Investment Theory and Practice Homework 6: Chapter - 9
Homework 6
Chapter -9
Q4. Here are data on two companies. The T-bill rate is 4% and the market risk premium is 6%.
What would be the fair return for each company according to the capital asset pricing model (CAPM)?
Answer-
Company 1
E(company1) = 0.04 + 1.5 * (0.10-0.04)
= 0.13 or 13%
Company 2
E(company2) = 0.04 + 1 * (0.10- 0.04)
= 0.10 or 10%
Q9. Consider the following table, which gives a security analyst’s expected return on two stocks in two
particular scenarios for the rate of return on the market:
5% −2% 6%
25 38 12
b. What is the expected rate of return on each stock if the two scenarios for the market return are
equally likely?
c. If the T-bill rate is 6% and the market return is equally likely to be 5% or 25%, draw the SML for this
economy.
d. Plot the two securities on the SML graph. What are the alphas of each?
e. What hurdle rate should be used by the management of the aggressive firm for a project with the risk
characteristics of the defensive firm’s stock?
Answer-
Q20. Two investment advisers are comparing performance. One averaged a 19% rate of return and the
other a 16% rate of return. However, the beta of the first investor was 1.5, whereas that of the second
investor was 1.
a. Can you tell which investor was a better selector of individual stocks (aside from the issue of general
movements in the market)?
b. If the T-bill rate was 6% and the market return during the period was 14%, which investor would be
considered the superior stock selector?
c. What if the T-bill rate was 3% and the market return was 15%?
Answer-
a. To determine which one is the best, we need to calculate each investor’s abnormal return, i.e.
the returns above what was expected for the same level of risk. Without knowing the risk free
rate and the market premium, we cannot determine which investor is better at picking stocks.
b. If rf = 6% and rM = 14%, then (using the notation alpha for the abnormal return):
Here, not only does the second investor appear to be the superior stock selector, but the first
investor's predictions appear valueless (or worse).
Q21. Suppose the rate of return on short-term government securities (perceived to be risk-free) is about
5%. Suppose also that the expected rate of return required by the market for a portfolio with a beta of 1
is 12%. According to the capital asset pricing model:
c. Suppose you consider buying a share of stock at $40. The stock is expected to pay $3 dividends next
year and you expect it to sell then for $41. The stock risk has been evaluated at β = −0.5. Is the stock
overpriced or underpriced?
Answer-
a. Since the market portfolio, by definition, has a beta of 1, its expected rate of return is 12%.
b. beta = 0 means no systematic risk. Hence, the stock's expected rate of return in market
equilibrium is the risk-free rate, 5%.
c. Using the SML, the fair expected rate of return for a stock with beta = -0.5 is:
E(r)= 0.05 + [(-0.5) * (0.12 - 0.05)]
= 1.5%
The actually expected rate of return, using the expected price and dividend for next year is:
E(r) = (41 + 3) / 40 - 1
= 0.10 or 10%
Because the actually expected return exceeds the fair return, the stock is underpriced.
Chapter-10
Q1. Suppose that two factors have been identified for the U.S. economy: the growth rate of industrial
production, IP, and the inflation rate, IR. IP is expected to be 3%, and IR 5%. A stock with a beta of 1 on
IP and 0.5 on IR currently is expected to provide a rate of return of 12%. If industrial production actually
grows by 5%, while the inflation rate turns out to be 8%, what is your revised estimate of the expected
rate of return on the stock?
Answer-
Q4. Suppose that there are two independent economic factors, F1 and F2. The risk-free rate is 6%, and
all stocks have independent firm-specific components with a standard deviation of 45%. Portfolios A and
B are both well-diversified with the following properties:
Answer-
We need to find the risk premium [rp] for each of the two factors-
To do so, the following system of two equations with to unknowns must be solved-
rp1 = 10%
rp2 = 5%
Q8. Assume that security returns are generated by the single-index model,
Ri = αi + βiRM + ei
where Ri is the excess return for security i and RM is the market’s excess return. The risk-free rate is 2%.
Suppose also that there are three securities, A, B, and C, characterized by the following data:
B 1.0 12 10
C 1.2 14 20
c. Is there an arbitrage opportunity in this market? What is it? Analyze the opportunity graphically.
Answer-
b. If there are infinite number of assets with return characteristics identical to those of A,B AND C,
Mean = 10
= 256
Mean = 12
= 400
Mean = 14
= 576