1.
An investor is in the 30% tax bracket. If corporate bonds offer 9% yields, what must
municipals offer for the investor to prefer them to corporate bonds?
2.
The Closed Fund is a closed-end
investment company with a portfolio currently worth $200 million. It has liabilities of $3 million and 5
million shares outstanding.
a.
What is the NAV of the fund?
b.
If the fund sells for $36 per
share, what is its premium or discount as a percent of NAV?
3.
Suppose that the rate of
inflation is expected to be 1% over the next five years. What are your best estimates of the expected
rate of return on Treasury bills, Treasury bonds and large capitalization
common stocks?
4.
Assume the expected return on
the S&P 500 portfolio is 14% and the T-bill yield is 5%. The standard deviation of the S&P500
portfolio is 20%. What are the expected
returns and variances of portfolios invested in T-bills and the S&P 500
with S&P weights 0%, 10%, 20%, 30%, 40%, 50%, 60%, 70%, 80%, 90%, and 100%. What is the maximum utility portfolio for an
investor with risk aversion parameter A=3?
What about A=5?
5.
Suppose you manage a risky
portfolio with expected return 18% and standard deviation 28%. The Treasury bill rate is 8%. Suppose your client invests 70% in your
portfolio and 30% in Treasury bills.
a.
What is the expected return and standard
deviation of the client’s portfolio?
b.
What is the Sharpe ratio for
your portfolio? Your client’s portfolio?
c.
Draw the Capital Allocation
Line for your portfolio. What is its’
slope?
d.
Suppose the client’s degree of
risk aversion is 3.5, what should be the proportion of client assets invested
in the risky portfolio?
e.
Suppose there is a passive
portfolio available with expected return 13% and standard deviation 25%. Draw the Capital Market Line and compare it
to your fund’s CAL. What is the
advantage of your fund?
f.
Is there any advantage of your
client moving to the passive fund?
g.
What is the maximum fee you can
charge before it is advantageous for the client to move?
6.
Suppose there are two risky
assets, a stock fund (S) with ER 20% and SD 30% and a bond fund (B) with ER 12%
and SD 15%; the correlation between S and B is 10% and the risk free asset
yields 8%.
a.
What are the investment
proportions in the two funds that create the minimum-variance portfolio?
b.
Draw the investment opportunity
set for the two risky funds.
c.
Draw a tangent line from the
risk-free rate to the opportunity set.
d.
What are the proportions of the
two risky funds in the optimal risky portfolio?
e.
What is the Sharpe Ratio for
the optimal risky portfolio?
7.
Suppose the price per share of
XYZ stock at the beginning of years 2005, 2006, 2007, 2008 is $100, $120, $90
and $100, respectively. The stock pays a
$4 dividend per share each year. Suppose
you buy 3 shares of XYZ at the beginning of 2005, buy another two shares at the
beginning of 2006, sell one share at the beginning of 2007, and sell all four
remaining shares at the beginning of 2008.
What are the arithmetic and geometric average time-weighted rates of
return? What is the dollar weighted rate
of return?
8.
CFA Problem 28.5 – Jarvis
University Endowment fund
9.
Consider Karl, an individual
investor. Karl is 40 years old, earns
after-tax income of $50,000 per year, expects to retire at age 65, and receive
after-tax Social Security payments in retirement of $20,000/year. Karl has a current net worth of $125,000 and
the after-tax return on investment is 1% per year. He believes he will continue to earn $50,000
per year in real terms over the next 25 years.
Assuming Karl believes he may live as long as 100 years, what is the
maximum steady rate of consumption that he can maintain while keeping net worth
positive through age 100? How does your
answer change if the return on investment is 3% per year instead of 1%?
10.
In EXCEL, replicate the five
year financial projections for Bill Ackman’s lemonade business. Extend the projections out to ten years using
the assumption that you invest in as many new lemonade stands you can given the
cash balance at the beginning of the year.
