BUS593 homework 1

BUS593 homework 1

Question

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.