Question:

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(R_m)            = Standard deviation of the market portfolio = 0.10

SD(R_b)            = Standard deviation of stock B's return = 0.12

R_b                    = Expected return on stock B = 0.10

Corr(R_a,R_m)     = The correlation of stock A and the market = 0.7

Corr(R_b,R_m)     = The correlation of stock B and the market = 0.34

Corr(R_a,R_b)      = 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?