There are two stocks in the market: Stock A and Stock B . The price of Stock A t

Question

There are two stocks in the market: Stock A and Stock B. The price of Stock A today is $72. The price of Stock A next year will be $61 if the economy is in a recession, $84 if the economy is normal, and $94 if the economy is expanding. The probabilities of recession, normal times, and expansion are .17, .63, and .20, respectively. Stock A pays no dividends and has a correlation of .67 with the market portfolio. Stock B has an expected return of 16.1 percent, a standard deviation of 33.7 percent, a correlation with the market portfolio of .21, and a correlation with Stock A of .33. The market portfolio has a standard deviation of 17.7 percent. Assume the CAPM holds.

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).)

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).)

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).)

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).)

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).)

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).)

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

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

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).)

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).)

Explanation / Answer

Calculate the return on the stock A:

Recession = ($61-$72)/$72 = - 0.15278

Normal =($84-$72)/72=0.1667

Expanding =($94-72)/72=0.3056

Expected return = 0.17(.15278)+0.63(.1667)+0.20(.3056)=0.1921 or 19.21%

Calculate the variance of stock is ;

.17(-0. 153-0.1921)^2+.63(0.1667-0.1921)^2+.20(.30560.-.

1921)^2 =0.02025

Standard deviation = square root of 0.02025=0.14229 or 14.23%

Calculate the stock beta for A:

Beta =( correlation A)(Standard deviation A)/standard deviation of the portfolio

(.67)(.1423)/.177=0.5387

Calculate stock beta for stock B

(.21)(33.7)/17.7=0.3998

Beta of the stock A is greater than that of the stock B , hence stock b has to be opted.

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