Question

There are two stocks in the market, Stock A and Stock B. The price of Stock A today is $85. The price of Stock A next year will be $74 if the economy is in a recession, $97 if the economy is normal, and $107 if the economy is expanding. The probabilities of recession, normal times, and expansion are .30, .50, and .20, respectively. Stock A pays no dividends and has a correlation of .80 with the market portfolio. Stock B has an expected return of 15.0 percent, a standard deviation of 35.0 percent, a correlation with the market portfolio of .34, and a correlation with Stock A of .46. The market portfolio has a standard deviation of 19.0 percent. Assume the CAPM holds a-1. What is the return for each state of the economy for Stock A? (A negative answer should be indicated by a minus sign. Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.) a-2. What is the expected return of Stock A? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) a-3. What is the variance of Stock A? (Do not round intermediate calculations and round your answer to 4 decimal places, e.g., 32.1616.) a-4. What is the standard deviation of Stock A? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) a-5. What is the beta of Stock A? (Do not round intermediate calculations and round your answer to 3 decimal places, e.g., 32.161.) a-6. What is the beta of Stock B? (Do not round intermediate calculations and round your answer to 3 decimal places, e.g., 32.161.)

If you are a typical, risk-averse investor with a well-diversified portfolio, which stock would you prefer?

b-1.	What is the expected return of a portfolio consisting of 75 percent of Stock A and 25 percent of Stock B? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

b-2.	What is the standard deviation of a portfolio consisting of 75 percent of Stock A and 25 percent of Stock B? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

c.	What is the beta of the portfolio in part (b)? (Do not round intermediate calculations and round your answer to 3 decimal places, e.g., 32.161.)

Answer 1

A1) return of recession= -12.94%

Return of normal economy= 14.12%

Return of expanding economy=25.88%

A2) Expected return of A = 8.35%

A3) variance of stock A =2.1386%

A4) Standard deviation of A= 14.62%

A5) Beta of A = 0.6155

A6) Beta of B = 0.6263

B1) Expected return of portfolio= 10.0125%

B2) Standard deviation of portfolio= 19.715%

C) Beta of C = 0.6182