There are two stocks in the market: Stock A and Stock B. The price of Stock A today is $74. The price of Stock A next year will be $63 if the economy is in a recession, $86 if the economy is normal, and $96 if the economy is expanding. The probabilities of recession, normal times, and expansion are .19, .61, and .20, respectively. Stock A pays no dividends and has a correlation of .69 with the market portfolio. Stock B has an expected return of 13.9 percent, a standard deviation of 33.9 percent, a correlation with the market portfolio of .23, and a correlation with Stock A of .35. The market portfolio has a standard deviation of 17.9 percent. Assume the CAPM holds.
Please show all work/formulas step by step!
a1. 
What is the return for each state of the economy for Stock A? (Negative amount should be indicated by a minus sign. Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places (e.g., 32.16).)

a2. 
What is the expected return of Stock A? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places (e.g., 32.16).)

a3. 
What is the variance of Stock A? (Do not round intermediate calculations and round your final answer to 4 decimal places (e.g., 32.1616).)

a4. 
What is the standard deviation of Stock A?(Do not round intermediate calculations.Enter your answer as a percent rounded to 2 decimal places (e.g., 32.16).)

a5. 
What is the beta of Stock A? (Do not round intermediate calculations and round your final answer to 3 decimal places (e.g., 32.161).)

a6. 
What is the beta of Stock B? (Do not round intermediate calculations and round your final answer to 3 decimal places (e.g., 32.161).)

If you are a typical, riskaverse investor with a welldiversified portfolio, which stock would you prefer? 

b1. 
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.Enter your answer as a percent rounded to 2 decimal places (e.g., 32.16).)

b2. 
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.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 final answer to 3 decimal places (e.g., 32.161).)
