a. What is the expected return on the market portfolio?
b. What would be the expected return on a zero-beta stock?
c. Suppose you consider buying a share of stock at a price of $41. The stock is expected to pay a dividend of $2 next year and to sell then for $43. The stock risk has been evaluated at beta = -.5. Is the stock overpriced or underpriced?
|Portfolio||Beta on M1||Beta on M2||Expected Return (%)|
What is the expected return-beta relationship in this economy?
a. Find the bond’s price today and six months from now after the next coupon is paid.
b. What is the total rate of return on the bond?
Suppose the risk-free rate is 4%. Suppose that the expected market risk premium is 5%, the excess return of a stock for a small firm over that of a stock for a large firm is 3%, the excess return of a stock for a firm with a high book-market value over that of a stock for a firm with a high book-market value is 4%. Suppose that company XYZ has the following exposures:
Market factor: 1.2
Size factor: .7
Book-market factor: .9
Find the expected return for Stock XYZ.
Suppose that today’s interest rate on a 10-year security is 8%. Suppose that today’s interest rate on a 7-year security is 9%? Find the 3-year interest rate expected in 7 years if the interest rate on the 10-year security carries no liquidity premium. What if the interest rate on the 10-year security carries a .7% liquidity premium?
Suppose that today’s date is December 13, 2016. A Treasury bond with a 4¼ % coupon paid semiannually every January 15 and July 15 is listed in The Wall Street Journal as selling at an ask price of 102-4+. If you buy the bond from a dealer today,
a. What is clean (list or quoted) price?
b. What is the accrued interest?
c. What is dirty (full or invoice) price?
d. What is the ask yield?
e. What is your expected overall return on this investment?
a. What is the yield to call?
b. What is the yield to call if the call price is only $1,050?
c. What is the yield to call if the call price is $1,100 but the bond can be called in five years instead of ten years?
a. At what price and P/E ratio would you expect the firm to sell?
b. What is the present value of growth opportunities?
c. What would be the P/E ratio and the present value of growth opportunities if the firm planned to reinvest only 20% of its earnings?
a. Calculate the yield to maturity of the bond.
b. Calculate the realized compound yield of the bond.
c. Explain why the realized compound yield is different form the yield to maturity computed in part (a).
a. Find its Macaulay duration.
b. Find its modified duration.
c. If the yield increases by 25 basis points, find:
i. The exact percentage change in the price of the bond.
ii. The approximate percentage change in the price of the bond.
a. What is the present value and duration of your obligation?
b. What maturity zero-coupon bond would immunize your obligation?
c. Suppose you buy a zero-coupon bond with value and duration equal to your obligation. Now suppose that rates immediately increase to 11%. What happens to your net position, that is, to the difference between the value of the bond and that of your tuition obligation? What if rates fall to 9%?
You are managing a portfolio of $2 million. Your target duration is 15 years, and you can choose from two bonds: a zero-coupon bond with maturity 10 years, and a perpetuity, each currently yielding 10%.
a. How much of each bond will you hold in your portfolio?
b. How will these fractions change next year if target duration is now 14 years.
a. Find the price of the bond if its yield to maturity falls to 7.5% or rises to 8.5%.
b. What prices for the bond at these new yields would be predicted by the duration rule?
c. What prices for the bond at these new yields would be predicted by the duration-with-convexity rule?
d. What is the percent error for each rule?
e. What do you conclude about the accuracy of the two rules?
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|
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 6% or 22%?
c. If the T-bill rate is 5%, and the market return is equally likely to be 6% or 22%, 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?