Calculating Portfolio Betas: Finding the Beta of the Missing Stock

We can start by using the formula for portfolio beta:

Portfolio Beta = Weight of Stock 1 x Beta of Stock 1 + Weight of Stock 2 x Beta of Stock 2

Since the portfolio is equally invested in the risk-free asset and two stocks, the weights are:

Weight of Stock 1 = 1/3 Weight of Stock 2 = 1/3

We know that the beta of Stock 1 is 1.65, and we want to find the beta of Stock 2, which we can call B2. We also know that the total portfolio is equally as risky as the market, which means its beta is 1. So we can set up the equation:

1 = (1/3) x 1.65 + (1/3) x B2 + (1/3) x 0

Simplifying:

1 = 0.55 + (1/3) x B2

Subtracting 0.55 from both sides:

0.45 = (1/3) x B2

Multiplying both sides by 3:

1.35 = B2

So the beta of the other stock in the portfolio must be 1.35.