You own a portfolio equally invested in a risk-free asset and two stocks. If one of the stocks has a beta of 1.16 and the total portfolio is exactly as risky as the market, what must the beta be for the other stock in your portfolio

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.