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The expected return of the stock is:

14. XYZ stock price and dividend history are as follows:

Year Beginning-of-Year Price Dividend Paid at Year-End

An investor buys three shares of XYZ at the beginning of 1999 buys another two shares at the beginning of 2000, sells one share at the beginning of 2001, and sells all four remaining shares at the beginning of 2002.

a. What are the arithmetic and geometric average time-weighted rates of return for the investor?

b. What is the dollar-weighted rate of return. Hint: Carefully prepare a chart of cash flows for the four dates corresponding to the turns of the year for January 1, 1999, to January 1, 2002. If your calculator cannot calculate internal rate of return, you will have to use trial and error.

15. a. Suppose you forecast that the standard deviation of the market return will be 20% in the coming year. If the measure of risk aversion in equation 5.6 is A = 4, what would be a reasonable guess for the expected market risk premium?

b. What value of A is consistent with a risk premium of 9%?

c. What will happen to the risk premium if investors become more risk tolerant?

16. Using the historical risk premiums as your guide, what is your estimate of the expected annual HPR on the S&P 500 stock portfolio if the current risk-free interest rate is 5%?

17. What has been the historical average real rate of return on stocks, Treasury bonds, and Treasury notes?

18. Consider a risky portfolio. The end-of-year cash flow derived from the portfolio will be either $50,000 or $150,000, with equal probabilities of 0.5. The alternative riskless investment in T-bills pays 5%.

a. If you require a risk premium of 10%, how much will you be willing to pay for the portfolio?

b. Suppose the portfolio can be purchased for the amount you found in (a). What will the expected rate of return on the portfolio be?

c. Now suppose you require a risk premium of 15%. What is the price you will be willing to pay now?

d. Comparing your answers to (a) and (c), what do you conclude about the relationship between the required risk premium on a portfolio and the price at which the portfolio will sell?

For problems 19-23, assume that you manage a risky portfolio with an expected rate of return of 17% and a standard deviation of 27%. The T-bill rate is 7%. 19. a. Your client chooses to invest 70% of a portfolio in your fund and 30% in a T-bill money market fund. What is the expected return and standard deviation of your client's portfolio?

b. Suppose your risky portfolio includes the following investments in the given proportions:

Stock A 27%

Stock B 33%

Stock C 40%

What are the investment proportions of your client's overall portfolio, including the position in T-bills?

c. What is the reward-to-variability ratio (S) of your risky portfolio and your client's overall portfolio?

d. Draw the CAL of your portfolio on an expected return/standard deviation diagram. What is the slope of the CAL? Show the position of your client on your fund's CAL.

20. Suppose the same client in problem 19 decides to invest in your risky portfolio a proportion (y) of his total investment budget so that his overall portfolio will have an expected rate of return of 15%.

a. What is the proportion y?

b. What are your client's investment proportions in your three stocks and the T-bill fund?

c. What is the standard deviation of the rate of return on your client's portfolio?

21. Suppose the same client in problem 19 prefers to invest in your portfolio a proportion (y) that maximizes the expected return on the overall portfolio subject to the constraint that the overall portfolio's standard deviation will not exceed 20%.

a. What is the investment proportion, y?

b. What is the expected rate of return on the overall portfolio?

22. You estimate that a passive portfolio invested to mimic the S&P 500 stock index yields an expected rate of return of 13% with a standard deviation of 25%. Draw the CML and your fund's CAL on an expected return/standard deviation diagram.

a. What is the slope of the CML?

b. Characterize in one short paragraph the advantage of your fund over the passive fund.

23. Your client (see problem 19) wonders whether to switch the 70% that is invested in your fund to the passive portfolio.

a. Explain to your client the disadvantage of the switch.

Bodie-Kane-Marcus: Essentials of Investments, Fifth Edition

II. Portfolio Theory

5. Risk and Return: Past and Prologue

© The McGraw-H Companies, 2003

Part TWO Portfolio Theory

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