Question

You own a portfolio equally invested in a risk-free asset and two stocks. If one of the stocks has a beta of 1.35 and the total portfolio is equally as risky as the market, what must the beta be for the other stock in your portfolio? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Answer 1

The beta for the other stock is 1.68

Step-by-step explanation:

`\beta_(2)`: The beta of the second stock

The weighted beta of the portfolio is given by ∑
`x_(i) \beta _(i)` where x is the weight of the individual stock/asset,
`\beta_(i)` is the beta of the individual stock/asset

As your portfolio is as equally risky as the market it's beta should be 1

Risk-free asset has beta 0

=> ∑
`x_(i) \beta _(i)` = 1

=> (0.33 * 0) + (0.33 * 1.35) + 0.33 *
`beta _(2)` = 1

=>
`\beta_(2)` = 1.68