# Foundations of Financial Management (10248) – Fall I, 2013 – Week 5

Stock A’s beta is 1.5 and Stock B’s beta is 0.5. Which of the following statements must be true about these securities? (Assume market equilibrium.)

a. The expected return on Stock A should be greater than that on B.

b. Stock B must be a more desirable addition to a portfolio than A.

c. The expected return on Stock B should be greater than that on A.

d. Stock A must be a more desirable addition to a portfolio than B.

e. When held in isolation, Stock A has more risk than Stock B.

An individual has $35,000 invested in a stock with a beta of 0.3 and another $75,000 invested in a stock with a beta of 1.7. If these are the only two investments in her portfolio, what is her portfolio’s beta? Round your answer to two decimal places.

Problem 6-6

Required Rate of Return

Suppose rRF = 5%, rM = 11%, and rA = 15%.

a. Calculate Stock A’s beta. Round your answer to two decimal places.

b. If Stock A’s beta were 2.2, then what would be A’s new required rate of return? Round your answer to two decimal places.

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Scheuer Enterprises has a beta of 1.10, the real risk-free rate is 2.00%, investors expect a 3.00% future inflation rate, and the market risk premium is 4.70%. What is Scheuer’s required rate of return?

a. 9.92%

b. 9.43%

c. 10.42%

d. 10.17%

e. 9.67%

Which of the following statements is CORRECT?

a. A large portfolio of randomly selected stocks will always have a standard deviation of returns that is less than the standard deviation of a portfolio with fewer stocks, regardless of how the stocks in the smaller portfolio are selected.

b. If you add enough randomly selected stocks to a portfolio, you can completely eliminate all of the market risk from the portfolio.

c. A large portfolio of randomly selected stocks will have a standard deviation of returns that is greater than the standard deviation of a 1-stock portfolio if that one stock has a beta less than 1.0.

d. A large portfolio of stocks whose betas are greater than 1.0 will have less market risk than a single stock with a beta = 0.8.

e. Diversifiable risk can be reduced by forming a large portfolio, but normally even highly-diversified portfolios are subject to market (or systematic) risk.

Jane has a portfolio of 20 average stocks, and Dick has a portfolio of 2 average stocks. Assuming the market is in equilibrium, which of the following statements is CORRECT?

a. Jane’s portfolio will have less diversifiable risk and also less market risk than Dick’s portfolio.

b. Dick’s portfolio will have more diversifiable risk, the same market risk, and thus more total risk than Jane’s portfolio, but the required (and expected) returns will be the same on both portfolios.

c. The required return on Jane’s portfolio will be lower than that on Dick’s portfolio because Jane’s portfolio will have less total risk.

d. If the two portfolios have the same beta, their required returns will be the same, but Jane’s portfolio will have less market risk than Dick’s.

e. The expected return on Jane’s portfolio must be lower than the expected return on Dick’s portfolio because Jane is more diversified.

Inflation, recession, and high interest rates are economic events that are best characterized as being

a. systematic risk factors that can be diversified away.

b. irrelevant except to governmental authorities like the Federal Reserve.

c. risks that are beyond the control of investors and thus should not be considered by security analysts or portfolio managers.

d. among the factors that are responsible for market risk.

e. company-specific risk factors that can be diversified away.

Assume that investors have recently become more risk averse, so the market risk premium has increased. Also, assume that the risk-free rate and expected inflation have not changed. Which of the following is most likely to occur?

a. The required rate of return for an average stock will increase by an amount equal to the increase in the market risk premium.

b. The required rate of return for each individual stock in the market will increase by an amount equal to the increase in the market risk premium.

c. The required rate of return on the market, rM, will not change as a result of these changes.

d. The required rate of return on a riskless bond will decline.

e. The required rate of return will decline for stocks whose betas are less than 1.0.

Problem 6-13

Historical Returns: Expected and Required Rates of Return

• eBook

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You have observed the following returns over time:

Year Stock X Stock Y Market

2006 13% 13% 10%

2007 21 6 8

2008 -16 -3 -12

2009 5 2 1

2010 19 11 18

Assume that the risk-free rate is 5% and the market risk premium is 16%

a. What is the beta of Stock X? Round your answer to two decimal places.

What is the beta of Stock Y? Round your answer to two decimal places.

b. What is the required rate of return on Stock X? Round your answer to two decimal places.

%

What is the required rate of return on Stock Y? Round your answer to two decimal places.

c. What is the required rate of return on a portfolio consisting of 80% of Stock X and 20% of Stock Y? Round your answer to two decimal places.

%

d. If Stock X’s expected return is 24%, is Stock X under- or overvalued?

I. Stock Y is undervalued, because its expected return is below its required rate of return.

II. Stock X is overvalued, because its expected return exceeds its required rate of return.

III. Stock X is overvalued, because its expected return its is below required rate of return.

IV. Stock Y is undervalued, because its expected return exceeds its required rate of return.

V. Stock X is undervalued, because its expected return is below its required rate of return.

Problem 6-3

Required Rates of Return

10. Assume that the risk-free rate is 3% and that the market risk premium is 6%.

What is the required rate of return on a stock with a beta of 1.1? Round your answer to two decimal places.

%

What is the required rate of return on a stock with a beta of 0.7? Round your answer to two decimal places.

%

11. Stock A has a beta of 0.8 and Stock B has a beta of 1.2. 50% of Portfolio P is invested in Stock A and 50% is invested in Stock B. If the market risk premium (rM ? rRF) were to increase but the risk-free rate (rRF) remained constant, which of the following would occur?

a. The required return would increase for Stock A but decrease for Stock B.

b. The required return on Portfolio P would remain unchanged.

c. The required return would decrease by the same amount for both Stock A and Stock B.

d. The required return would increase for Stock B but decrease for Stock A.

e. The required return would increase for both stocks but the increase would be greater for Stock B than for Stock A.

12. Stock A’s beta is 1.5 and Stock B’s beta is 0.5. Which of the following statements must be true, assuming the CAPM is correct.

a. Stock A would be a more desirable addition to a portfolio then Stock B.

b. When held in isolation, Stock A has more risk than Stock B.

c. In equilibrium, the expected return on Stock B will be greater than that on Stock A.

d. Stock B would be a more desirable addition to a portfolio than A.

e. In equilibrium, the expected return on Stock A will be greater than that on B.

13. Assume that you manage a $10.00 million mutual fund that has a beta of 1.05 and a 9.50% required return. The risk-free rate is 4.20%. You now receive another $5.00 million, which you invest in stocks with an average beta of 0.65. What is the required rate of return on the new portfolio? (Hint: You must first find the market risk premium, then find the new portfolio beta.)

a. 9.74%

b. 9.51%

c. 9.05%

d. 8.83%

e. 9.27%

14. Assume that in recent years both expected inflation and the market risk premium (rM ? rRF) have declined. Assume also that all stocks have positive betas. Which of the following would be most likely to have occurred as a result of these changes?

a. The required returns on all stocks have fallen, but the fall has been greater for stocks with higher betas.

b. The average required return on the market, rM, has remained constant, but the required returns have fallen for stocks that have betas greater than 1.0.

c. The required returns on all stocks have fallen, but the decline has been greater for stocks with lower betas.

d. The required returns on all stocks have fallen by the same amount.

e. Required returns have increased for stocks with betas greater than 1.0 but have declined for stocks with betas less than 1.0.

15. Problem 6-9

Portfolio Required Return

16. Suppose you manage a $4.815 million fund that consists of four stocks with the following investments:

Stock Investment Beta

A $440,000 1.50

B 625,000 -0.50

C 1,100,000 1.25

D 2,650,000 0.75

If the market’s required rate of return is 12% and the risk-free rate is 6%, what is the fund’s required rate of return? Round your answer to two decimal places.

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