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# The Efficiency of the Market Portfolio

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Question 1
The Debt Cost of Capital
14. In mid-2012, Ralston Purina had AA-rated, 10-year bonds outstanding with a yield to maturity
of 2.05%.
a. What is the highest expected return these bonds could have?
b. At the time, similar maturity Treasuries have a yield of 1.5%. Could these bonds actually
c. If you believe Ralston Purina's bonds have 0.5% chance of default per year, and that expected
loss rate in the event of default is 60%, what is your estimate of the expected return for these
bonds?

Question 2
The Behavior of Individual Investors
9. Your brother Joe is a surgeon who suffers badly from the overconfidence bias. He loves to trade
stocks and believes his predictions with 100% confidence. In fact, he is uninformed like most investors.
Rumors are that Vital Signs (a startup that makes warning labels in the medical industry) will
receive a takeover offer at \$20 per share. Absent the takeover offer, the stock will trade at \$15 per
share. The uncertainty will be resolved in the next few hours. Your brother believes that the takeover
will occur with certainty and has instructed his broker to buy the stock at any price less than \$20. In
fact, the true probability of a takeover is 50%, but a few people are informed and know whether the
takeover will actually occur. They also have submitted orders. Nobody else is trading in the stock.

a. Describe what will happen to the market price once these orders are submitted if in fact the takeover
will occur in a few hours. What will your brother's profits be: positive, negative, or zero?
b. What range of possible prices could result once these orders are submitted if the takeover
does not occur? What will your brother's profits be: positive, negative, or zero?
c. What are your brother's expected profits?

Question 3
The Efficiency of the Market Portfolio
14. Davita Spencer is a manager at Half Dome Asset Management. She can generate an alpha of
2% a year up to \$100 million. After that her skills are spread too thin, so cannot add value and
her alpha is zero. Half Dome charges a fee of 1% per year on the total amount of money under
management (at the beginning of each year). Assume that there are always investors looking for
positive alpha and no investor would invest in a fund with a negative alpha. In equilibrium, that
is, when no investor either takes out money or wishes to invest new money,
a. What alpha do investors in Davita's fund expect to receive?
b. How much money will Davita have under management?
c. How much money will Half Dome generate in fee income?

#### Solution Preview

See the attached file. Thanks

Question 1
The Debt Cost of Capital
14. In mid-2012, Ralston Purina had AA-rated, 10-year bonds outstanding with a yield to maturity
of 2.05%.
a. What is the highest expected return these bonds could have?
The highest expected return we can get on these bonds is equal to the yield to maturity. Hence. highest return y=2.05%

b. At the time, similar maturity Treasuries have a yield of 1.5%. Could these bonds actually
No. Since, treasuries are risk free and have a yield of 1.5%, the expected return on AA rated bonds cannot not be 2.05%

c. If you believe Ralston Purina's bonds have 0.5% chance of default per year, and that expected
loss rate in the event of default is 60%, what is your estimate of the expected return for these
bonds?
y 2.05%
d 0.50%
l 60%
Expected return = y - d*l 1.7500%

Question 2
The Behavior of ...

#### Solution Summary

This solution contains step-by-step calculations to solve three questions from Corporate finance concerning the concepts of debt cost of capital, behavior of individual investors, and the efficient of the market portfolio. All steps are shown in an Excel file.

\$2.19