There are two stocks in the market, Stock A and Stock B . The price of Stock A today is $83. The price of Stock A next year will be $72 if the economy is in a recession, $95 if the economy is normal, and $105 if the economy is expanding. The probabilities of recession, normal times, and expansion are .28, .52, and .20, respectively. Stock A pays no dividends and has a correlation of .78 with the market portfolio. Stock B has an expected return of 14.8 percent, a standard deviation of 34.8 percent, a correlation with the market portfolio of .32, and a correlation with Stock A of .44. The market portfolio has a standard deviation of 18.8 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.)
Return Recession % Normal % Expansion %
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.)
Expected return %
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.)
Variance
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.)
Standard deviation %
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.)
Beta of Stock A 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.) Beta of Stock B
If you are a typical, risk-averse investor with a well-diversified portfolio, which stock would you prefer?
Stock A Stock B
b-1. What is the expected return of a portfolio consisting of 65 percent of Stock A and 35 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.)
Expected return %
b-2. What is standard deviation of a portfolio consisting of 65 percent of Stock A and 35 percent of Stock B? (Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.)
Standard deviation %
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.)
Beta of the portfolio