Answer:
Beta of stock A (βA) = 1.16
Beta of stock B (βB) = ?
Beta of the portfolio (βP) = 1
Weight of stock A (WA) = 50% = 0.50
Weight of stock B (WB) = 50% = 0.50
β(P) = βA(WA) + βB(WB)
1   =  1.16(0.50) + βB(0.50)
1   = 0.58 + 0.50βB
1 - 0.58 = 0.50βB
0.42 = 0.50βB
0.42  = βB
0.50
βB = 0.84
Explanation:
Beta of a portfolio equals beta of stock A multiplied by weight of stock A plus beta of stock B multiplied by weight of stock B. The beta of the portfolio is 1 because the portfolio is as risky as the market. Beta of stock A has been provided. The weight of stock A and stock B are 50% respectively because equal amount of fund is invested in each security.
