Dr. P.V. Viswanath
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Risk and Return: Diversification, Portfolio Selection and the Capital Asset Pricing Model
Problem 1. (solution) A. Assume that investors' horizons are exactly 1 year. Hence assume that the CAPM describes asset returns over 1 year holding periods. Suppose a 10 year zero-coupon sells for $295 and is known to have a beta of 0.15. Suppose further that the expected rate of return on the market is 25% per annum. What do you expect a 9 year bond to cost next year if the current yield on a 1 year bond is 5%?
The following data apply to questions B through D:
Hennessey & Associates manages a $30 million equity portfolio for the multimanager Wilstead Pension Fund. Jason Jones, financial vice president of Wilstead, noted that Hennessy had rather consistently achieved the best record among the Wilstead's six equity managers. Performance of the Hennessy portfolio had been clearly superior to that of the S&P 500 in 4 of the past 5 years. In the one less favorable year, the shortfall was trivial.
Hennessy is a "bottom-up" manager. The firm largely avoids any attempt to "time the market." It also focuses on selection of individual stocks, rather than the weighting of favored industries.
There is no apparent conformity of style among the six equity managers. The five managers, other than Hennessy, manage portfolios aggregating $250 million made of more than 150 individual issues.
Jones is convinced that Hennessy is able to apply superior skill to stock selection, but the favorable results are limited by the high degree of diversification in the portfolio. Over the years, the portfolio generally held 40 to 50 stocks, with about 2% to 3% of total funds committed to each issue. The reason Hennessy seemed to do well most years was because the firm was able to identify each year 10 or 12 issues which registered particularly large gains.
Based on this overview, Jones outlined the following plan to the Wilstead pension committee:
"Let's tell Hennessy to limit the portfolio to no more than 20 stocks. Hennessy will double the commitments to the stocks that it really favors, and eliminate the remainder. Except for this one new restriction, Hennessy should be free to manage the portfolio exactly as before."
All the members of the pension committee generally supported Jones' proposal, because all agreed that Hennessy had seemed to demonstrate superior skill in selecting stocks. Yet, the proposal was a considerable departure from previous practice, and several committee members raise questions.
Respond to each of these questions, using no more than 5 lines each:
B. Answer the following:
a. Will the limitation of 20 stocks likely increase or decrease the risk of the portfolio? Explain.
b. Is there any way Hennessy could reduce the number of issues from 40 to 20 without significantly affecting risk? Explain.
C. One committee member was particularly enthusiastic concerning Jones' proposal. He suggested that Hennessy's performance might benefit further from reduction in the number of issues to 10. If the reduction to 20 could be expected to be advantageous, explain why reduction to 10 might be less likely to be advantageous. (Assume that Wilstead will evaluate the Hennessy portfolio independently of the other portfolios in the fund.)
D. Another committee member suggested that, rather than evaluate each managed portfolio independently of other portfolios, it might be better to consider the effects of a change in the Hennessy portfolio on the total fund. Explain how this broader point of view could affect the committee decision to limit the holdings in the Hennessy portfolio to either 10 or 20 issues.
E. Consider the following table, which gives a security analyst's expected return on two stocks for two particular market returns:
Note: SML stands for Security Market Line. This line is typically drawn with the expected return on assets on the y-axis, and the asset beta on the x-axis.
The expected return should be equal to the required rate of return, but this equality will hold only if the market is in equilibrium.
Problem 2. (Fall
the following article and answer the following questions:
Warner-Lambert Discuss Merger --- Transaction for $65 Billion Could Spur
Consolidation Among Drug Companies
Home Products Corp. and Warner-Lambert Co. are in talks to merge in a
$65 billion deal that would unite two of the largest pharmaceutical companies
in the world, according to people familiar with the situation.
a deal -- which would be the largest drug merger in history and one of
the largest transactions ever -- could trigger a new wave of consolidation
in what remains a relatively fragmented industry, despite some major deals
in recent years.
combining Warner-Lambert, of Morris Plains, N.J., with American Home,
located just down the road in Madison, would bring together the companies
behind such household names as Advil, Anacin and Chap Stick (American
Home) and Dentyne gum and Certs breath mints (Warner-Lambert). American
Home also makes Premarin, a fast-selling drug for menopause and osteoporosis,
and Warner-Lambert manufactures blockbuster cholesterol drug Lipitor.
announcement could come as soon as tomorrow, though, as is often the case
with delicate merger talks, the discussions could fall through at the
for American Home and Warner-Lambert declined to comment.
talks come at a time when American Home's stock has been hit by a series
of product and legal-related setbacks. American Home recently took a $4.75
billion charge to settle thousands of lawsuits related to the diet drugs
Redux and Pondimin. American Home also is restructuring its struggling
Cyanamid agricultural unit.
its share price has perked up a bit in recent weeks, American Home has
been concerned about the possibility of a hostile overture by a rival
drug company, according to people close to the company. It recently adopted
a "poison pill" shareholder-rights plan.
New York Stock Exchange trading at 4 p.m., American Home shares fell 43.75
cents to $50.375. Warner-Lambert shares fell $1.5625 to $78.4375, also
on the Big Board.
Home is poised to launch some promising new drugs, including a vaccine
for pneumonia in children, but some of its strongest existing sellers,
like Premarin, are aging and a deal with Warner-Lambert would greatly
expand its portfolio of medicines.
As for Warner-Lambert, Wall Street analysts have expressed concerns
about whether it has enough potentially profitable new drugs in its pipeline,
though profit growth has been robust because of Lipitor's success.
Home has looked for a merger partner in the recent past. Just last year,
it announced a deal to merge with Monsanto Co. and held merger talks with
SmithKline Beecham PLC. Both sets of talks fell through, partly because
of issues about who would run the combined firm.
Home's chairman, John Stafford, 62 years old, is expected to be chairman
of the combined firm, and WarnerLambert's chairman, Lodewijk J.R. de Vink,
who is nearly a decade younger, is likely to be chief executive, these
people said. Under a scenario being discussed, the board of the combined
company would be split evenly between the two sides.
Home and Warner Lambert shareholders each are expected to end up with
about 50% of the stock of the combined company. Under the structure being
considered, AHP shares would be used to acquire the shares of Warner-Lambert.
headquarters is expected to be at American Home's base in Madison.
(20 points) What are
the unlevered betas of American Home Products (AHP)and Warner-Lambert
(5 points; bonus) The actual average returns on AHP (using data for the
last five years from http://chart.yahoo.com)
is 30.25% p.a. and that on WLA is 42.61%.
Compare these numbers to your answers from d) above.
How would you explain the discrepancy, if any?
f) (10 points) What do you think the correlation coefficient between the stock returns of the two companies would be? Provide a numerical estimate and justify your answer.
(20 points) Use your estimate in f) above to compute the variance
of returns on a portfolio consisting of $10,000 invested in American Health
Products and $20,000 in Warner-Lambert (assuming that the merger does
not go through). The following
additional information is available:
The standard deviation of returns on WLA stock is 93.32% per year,
computed using stock-split and dividend adjusted return data from Yahoo
(http://chart.yahoo.com) for the
last five years. The same
number for AHP is 93.76%. (If
you have not been able to answer part e), you can use any arbitrary figure
for the correlation, other than zero.)
(10 points) Compute the expected return on the portfolio in g)
above, using your computations from d) above.
Problem 3. (Spring 1999): Read the following WSJ article from March 15, 1999 and answer this question, using no more than two sides of a page. Rambling answers will be penalized.
Problem 4: (Spring
1999) Here are the prices and betas, as of March 17, 1999 for three
stocks that I own:
If I have 100 shares of each company in my portfolio, compute the
portfolio proportions for each stock.
You have the following additional information on these stocks standard deviations (in percentages, on diagonal) and correlation coefficients (off-diagonal numbers):
b. Compute the standard deviation of returns on your portfolio.
c. If the expected return on the market portfolio is 15%, and the yield on the one-year T-bill is 5%, what is the required rate of return on your portfolio?