Ch 7 - F

Dothan Inc.'s stock has a 25% chance of producing a 30% return, a 50% chance of producing a 12% return, and a 25% chance of producing a −18% return. What is the firm's expected rate of return?

• 8.12%

• 9.00%

• 8.55%

• 7.72%

Answer explanation

In a portfolio of three different stocks, which of the following could NOT be true?

• The riskiness of the portfolio is greater than the riskiness of one or two of the stocks.

• The beta of the portfolio is greater than the beta of one or two of the individual stocks.

• The beta of the portfolio is less than the beta of each of the individual stocks.

• The riskiness of the portfolio is less than the riskiness of each stock held in isolation.

Answer explanation

The beta of the portfolio is a weighted average of the individual securities' betas, so it could not be less than the betas of all of the stocks.

If r_RF = 5%, r_M = 11%, and b = 1.3 for Stock X, what is r_X, the required rate of return for Stock X?

• 14.8%

• 18.7%

• 16.7%

• 12.8%

Answer explanation

r_X = r_RF + (r_M – r_RF)b_X = 5% + (11% – 5%)1.3 = 12.8%

Which of the following statements is CORRECT?

• The slope of the SML is determined by the value of beta.

• Both the SML and a company's position on it change over time due to changes in interest rates, investors' aversion to risk, and individual companies' betas.

• If you plotted the returns of a given stock against those of the market, and if you found that the slope of the regression line was negative, then the CAPM would indicate that the risk-free rate of return on the stock should be less than the required rate of return for a well-diversified investor, assuming that the observed relationship is expected to continue into the future.

• The SML relates required returns to firms' market risk. The slope and intercept of this line can be controlled by the financial manager.

Answer explanation

The slope (r_M – r_RF) and intercept (r_RF) of the SML cannot be controlled by the financial manager. The slope of the SML is r_M - r_RF, not beta. A negative beta in the CAPM would indicate that the stock's required rate of return is less than the risk-free rate. Finally, if investors become less risk averse, the slope of the SML will decline, not increase.

Consider the following information for the Alachua Retirement Fund, with a total investment of $4 million. The market required rate of return is 12%, and the risk-free rate is 6%. What is its required rate of return?

• 10.45%

• 11.50%

• 11.01%

• 9.98%

Answer explanation

Determine the weight each stock represents in the portfolio and multiply that by each beta, then add them together to get the portfolio beta, which is bp = 0.8350 = portfolio beta. Then, write out the SML equation and substitute the known values, including the portfolio beta. Solve for the required portfolio return: r_p = r_RF + (r_M – r_RF)bp = 6% + (12% – 6%)0.8350 = 6% + 5.01% = 11.01%.

A stock has a required return of 12%. The risk-free rate is 6% and the market risk premium is 5%. What is the stock's beta coefficient?

• 0.95

• 1.50

• 1.20

• 0.80

Answer explanation

Last year you bought 100 Nova Telcom stocks at $34. One year later you sold these stocks at $36.50. What is your return on investment? Assume that the stock did not pay any dividends.

• 6.60%

• 7.35%

• 6.85%

• 3.68%

Answer explanation

R = (36.5 – 34)/34 = 7.35%

If a stock has a beta of zero, it will be riskless when held in isolation.

• True

• False

Answer explanation

A zero beta stock could be made riskless if it were combined with enough other zero beta stocks, but it would still have diversifiable risk and be risky when held in isolation.

You are managing a portfolio of 10 stocks that are held in equal dollar amounts. The current beta of the portfolio is 1.8, and the beta of Stock A is 2.0. If Stock A is sold and the proceeds are used to purchase a replacement stock, what does the beta of the replacement stock have to be to lower the portfolio beta to 1.7?

• 1.2

• 1.4

• 1.3

• 1.0

Answer explanation

If r_RF = 5%, r_M = 11%, and b = 1.3 for Stock X, what would r_X be if investors expected the inflation rate to increase by 2 percentage points? Assume that investors' risk aversion has not changed.

• 14.8%

• 18.7%

• 16.7%

• 12.8%

Answer explanation

r_X = r_RF + (r_M – r_RF)b_X = 7% + (13% – 7%)1.3 = 14.8%. A change in the inflation premium does not change the market risk premium (r_M - r_RF) as both r_M and r_RF are affected. Changes in the market risk premium reflect changes in investors' risk aversion.