I Am Buying A Firm With An Expected Perpetual Cash Flow Of 1 000 But Am Unsure Of Its Risk. If I Think The Beta Of The Firm Is Zero When The Beta Is Really 1.0 How Much More Will I Offer For The Firm Than It Is Truly Worth
In problems 15-17 below, assume the risk-free rate is 8% and the expected rate of return on the market is 18%.
15. A share of stock is now selling for $100. It will pay a dividend of $9 per share at the end of the year. Its beta is 1.0. What do investors expect the stock to sell for at the end of the year?
I am buying a firm with an expected perpetual cash flow of $1,000 but am unsure of its risk. If I think the beta of the firm is zero, when the beta is really 1.0, how much more will I offer for the firm than it is truly worth? A stock has an expected return of 6%. What is its beta?
Two investment advisers are comparing performance. One averaged a 19% return and the other a 16% return. However, the beta of the first adviser was 1.5, while that of the second was 1.0.
a. Can you tell which adviser was a better selector of individual stocks (aside from the issue of general movements in the market)?
b. If the T-bill rate were 6%, and the market return during the period were 14%, which adviser would be the superior stock selector?
c. What if the T-bill rate were 3% and the market return 15%? In 2002, the yield on short-term government securities (perceived to be risk-free) was about 4%. Suppose the expected return required by the market for a portfolio with a beta of 1.0 is 12%. According to the capital asset pricing model:
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 $40. The stock is expected to pay a dividend of $3 next year and to sell then for $41. The stock risk has been evaluated at (3 = -0.5. Is the stock overpriced or underpriced?
20. Based on current dividend yields and expected capital gains, the expected rates of return on portfolio A and B are 11% and 14%, respectively. The beta of A is 0.8 while that of B is 1.5. The T-bill rate is currently 6%, while the expected rate of return of the S&P 500 Index is 12%. The standard deviation of portfolio A is 10% annually, while that of B is 31%, and that of the index is 20%.
a. If you currently hold a market index portfolio, would you choose to add either of these portfolios to your holdings? Explain.
b. If instead you could invest only in bills and one of these portfolios, which would you choose?
21. Consider the following data for a one-factor economy. All portfolios are well diversified.
Portfolio E(r) Beta
Suppose another portfolio E is well diversified with a beta of 2/3 and expected return of 9%. Would an arbitrage opportunity exist? If so, what would the arbitrage strategy be? 22. Following is a scenario for three stocks constructed by the security analysts of PF Inc.
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Stock |
Price ($) |
Recession |
Average |
Boom |
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