There are two stocks, stock A and stock B. The price of stock A today is $70. The price of stock A next year will be $50 if the economy is in recession, $80 if the economy is normal and $95 if the economy is expanding. The attendant probabilities of recession, normal times, and expansion are 0.2, 0.6, 0.2, respectively. Stock A pays no dividend. Assume the CAPM is true. Other information about the market includes:
SD(Rm)= Standard deviation of the market portfolio = 0.10
SD(Rb)= Standard deviation of stock B's return = 0.12
Rb= Expected return on stock B = 0.10
Corr(Ra,Rm)= The correlation of stock A and the market = 0.7
Corr(Rb,Rm)= The correlation of stock B and the market = 0.34
Corr(Ra,Rb)= The correlation of stock A and stock B = 0.6
What is the beta of the portfolio consisting of 30% of stock A and 70% of stock B?
Please refer attached file for better clarity of tables and formulas.
State of economy Probability Price Return*
P R P*R P*(R-Mean)^2
Recession 0.2 50 -0.28571 -0.05714285 0.029755102
Normal 0.6 80 0.14286 ...
Solution describes the steps to calculate beta of stock A and B with the help of statistics given. It also calculates beta of portfolio consisting of stock A and stock B.