Chapter 12 Problems - Practice Questions PDF

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Chapter 12 Problems 1. The probability that the economy will experience a recession next year is 0.3, while the probabilities of moderate growth or rapid expansion are 0.5 and 0.2, respectively. The stock of Firm A is expected to return 5%, 15%, or 20% depending on whether the economy experiences a recession, moderate growth or rapid expansion, respectively. The returns for Firm B are expected to be 0%, 16% or 30%, respectively. Calculate the expected returns for each firm’s common stock. (13%, 14%) 2. Based on the following information, calculate the expected return and standard deviation for the two stocks.

State of Economy Recession Normal Boom

Probability of State of Economy 0.15 0.65 0.20

Rate of Return If State Occurs Stock A Stock B 6% -20% 7% 13% 11% 33%

(E(RA ) = 7.65%, σA =1.71%, E(RB ) = 12.05%, σB = 15.57%) 3. Consider the following information:

State of Economy Boom Bust

Probability of State of Economy 0.25 0.75

Rate of Return If State Occurs Stock A Stock B Stock C 14% 12%

15% 3%

33% -6%

What is the expected return and standard deviation of returns on an equally weighted portfolio of these three stocks? (E(Rp) = 7.42%, σp = 7.65%) 4. What are the portfolio weights for a portfolio that includes 80 shares of Stock A that sell for $35 per share and 40 shares of Stock B that sell for $25 per share? (wA = 73.68%, wB = 26.32%)

5. Consider the following information:

State of Economy Boom Growth Normal Recession

Probability of State of Economy 0.10 0.20 0.50 0.20

Rate of Return If State Occurs Stock K Stock M 25% 18% 10% 20% 15% 4% -12% 0%

a. An individual plans to invest $5,000: $3,000 in Stock K and $2,000 in Stock M. What are the stock weights for this portfolio? (wK = 60%, wM = 40%) b. Using the weights computed in Part a, what is the expected return for the portfolio? (E(Rp) = 8.88%) c. Using the weights computed in Part a, calculate the variance and standard deviation of the portfolio. (σ²p = 0.7618% , σp = 8.73%) 6. You own a stock portfolio invested 20% in Stock Q, 20% in Stock R, 10% in Stock S, and 50% in Stock T. The betas for these stocks are 1.4, 0.6, 1.5, and 1.8, respectively. What is the portfolio beta? (βp = 1.45) 7. a. An individual plans to invest in Stock A and/or Stock B. The expected returns are 9% and 10% for Stocks A and B, respectively. The betas are 0.95 and 1.25 for Stocks A and B, respectively. Find the expected return and beta for the portfolio if the individual invests 75% of his funds in Stock A. (E(Rp) = 9.25%, βp = 1.025) b. Suppose the individual described in Part a, forms a portfolio consisting of three assets: 10% invested in Stock A, 30% invested in Stock B, and 60% invested in a risk-free asset with a return of 6%. What is the expected return and beta for this portfolio? (E(Rp) = 7.5%, βp = 0.47) 8. Use the following information to compute the reward-to-risk ratio for Stocks A, B and C:

Stock A Stock B Stock C Risk-free

Expected Return 10.5% 13.0% 14.5% 6.0%

Beta 0.90 1.15 1.20 0.00

(R-to-RA = 5%, R-to-RB = 6.09%, R-to-RC = 7.08%) 9. A stock has a beta of 1.2, the expected return on the market (E(RM)) is 12%, and the riskfree rate is 6%. What is the expected return on this stock? (E(R) = 13.2%) 10. Assume the risk-free return is 6% and the expected return on the market (E(RM)) is 14%. Speiss Corporation has a beta of 2. What are the portfolio weights for a portfolio comprised of Speiss common stock and the risk-free asset if the portfolio beta equals 1.5. What is the expected return for this portfolio? (wSpeiss = 75%, wRF = 25%, E(Rp) = 18%) 11. Assume the risk-free return is 6% and the expected return on the market (E(RM)) is 14%. Dorigan Corporation has a beta of 1.45 and an expected return of 15%. Is Dorigan common stock correctly priced? Explain your answer. (No, because the stock is returning 2.6% less than it should given its systemic risk) 12. A stock has an expected return of 17%, the risk-free rate is 5%, and the market risk premium is 8%. What must the beta of this stock be? (β = 1.5) 13. A stock has an expected return of 10%, its beta is 0.9, and the risk-free rate is 5%. What must the expected return on the market be? (E(RM) = 10.56%) 14. A stock has an expected return of 20%, a beta of 1.5, and the expected return on the market (E(RM)) is 15%. What must the risk-free rate be? (Rf = 5%) 15. A stock has a beta of 1.6 and an expected return of 16%. A risk-free asset currently earns 5%. a. What is the expected return on a portfolio that is equally invested in the two assets? (E(Rp) =10.5%) b. If a portfolio of the two assets has a beta (βp) of 0.6, what are the portfolio weights? (wS = 37.5%, wRF = 62.5%) c. If a portfolio of the two assets has an expected return of 11%, what is its beta? (βp = 0.873)...