There are two stocks in the market, Stock A and Stock B . The price of Stock A today is $79. The price of Stock A next year will be $68 if the economy is in a recession, $91 if the economy is normal, and $101 if the economy is expanding. The probabilities of recession, normal times, and expansion are .24, .56, and .20, respectively. Stock A pays no dividends and has a correlation of .74 with the market portfolio. Stock B has an expected return of 14.4 percent, a standard deviation of 34.4 percent, a correlation with the market portfolio of .28, and a correlation with Stock A of .40. The market portfolio has a standard deviation of 18.4 percent. Assume the CAPM holds. The expected return of Stock A is 10.74%. The recession return of stock A is -13.92%. The normal return is 15.19%. The expansion return is 27.85%. The standard deviation of stock A is 14.68%. The beta of stock A is .590.
How do you solve for and what is the variance Stock A? (Do not round intermediate calculations and round your answer to 4 decimal places, e.g., 32.1616.)