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What to do with this practice set?

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FIN-469 Investments Analysis Professor Michel A. Robe
Practice Set #4 and Solutions.
What to do with this practice set?
To help students prepare for the assignment and the exams, practice sets with solutions will be
handed out. These sets contain worked-out end-of-chapter problems from BKM3 and BKM4.
These sets will not be graded, but students are strongly encouraged to try hard to solve them and
to use office hours to discuss any problems they may have doing so. One of the best self-tests
for a student of his or her command of the material before a case or the exam is whether he or
she can handle the questions of the relevant practice sets. The questions on the exam will cover
the reading material, and will be very similar to those in the practice sets.
Consider the following statement to answer Questions 1 to 5:
You manage a risky portfolio with an expected rate of return of 17% and a standard deviation of
27%. The Treasury-bill rate is 7%.
Question 1:
One of your clients chooses to invest 70% of a portfolio in your fund and 30% in a T-bill money
market fund. What is the expected value and standard deviation of the rate of return on your
client’s portfolio?
Question 2:
Suppose that your client decides to invest in your portfolio a proportion y of the total investment
budget so that the overall portfolio will have an expected rate of return of 15%.
(a) What is the proportion y?
(b) Further suppose that your risky portfolio includes the following investments in the given
proportions: Stock A (27%), Stock B (33%), and Stock C (40%). What are your client’s
investment proportions in your three stocks and the T-bill fund.
Question 3:
Now suppose that your client prefers to invest in your fund a proportion y that maximizes the
expected return on the overall portfolio subject to the constraint that the overall portfolio’s
standard deviation will not exceed 20%.

(a) What is the investment proportion, y?
(b) What is the expected rate of return on the overall portfolio?
Question 4:
Suppose that your client’s degree of risk aversion is A = 3.5. What proportion, y, of the total
investment should you suggest that he invest in your fund?
Question 5:
You estimate that a passive portfolio (that is, one entirely invested in a risky portfolio that
mimics the S&P 500 stock index) yields an expected rate of return of 13% with a standard
deviation of 25%.
(a) What is the slope of the CML?
(b) Characterize in one short paragraph the advantage of your fund over the passive fund.
(c) Your client is considering whether to switch to the passive portfolio the 70% of his wealth
currently invested in your fund. Show your client that he is better off staying with you.
(Hint 1: show your client the maximum fee you could charge — as a percentage of the
investment in your fund deducted at the end of the year — that would still leave him
at least as well off investing in your fund as in the passive one)
(Hint 2: the fee will lower the slope of your client’s CAL by reducing the expected return net
of the fee)
Question 6:
Suppose that there are many stocks in the market and that the characteristics of Stocks A and B
are given as follows:
Stock Expected Return Standard Deviation
——————————————————————————————-
A 10% 5%
B 15% 10%
——————————————————————————————-
Correlation = -1
——————————————————————————————-
Suppose that it is possible to borrow at the risk-free rate, Rf. What must be the value of the riskfree
rate?
(Hint: think about constructing a risk-free portfolio from Stocks A and B).

Question 7:
The market price of a security is $40. Its expected rate of return is 13%. The risk-free rate is 7%
and the market risk premium is 8%. What will be the market price of the security if its
covariance with the market portfolio doubles (and all other variables remain unchanged)?
Assume that the stock is expected to pay a constant dividend in perpetuity.
Question 8:
Consider the following table, which gives a security analyst’s expected return on two stocks for
two particular market returns:
Market Return Aggressive Stock Defensive Stock
——————————————————————————————-
5% 2% 3.5%
20% 32% 14%
——————————————————————————————-
(a) What are the betas of the two stocks?
(b) What is the expected rate of return on each stock if the market return is equally likely to be
5% or 20%?
(c) If the T-bill rate is 8% and the market return is equally likely to be 5% or 20%, 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?
Question 9:
Two investment advisors 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 was 1.
(a) Can you tell which investor was a better predictor of individual stocks (aside from the issue
of general movements in the market)?
(b) If the T-bill rate were 6% and the market return during the period were 14%, which investor
would be the superior stock selector?
(c) What if the T-bill rate were 3% and the market return were 15%?



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