Question

You own a portfolio equally invested in a risk-free asset and two stocks. If one of the stocks has a beta of 1.50 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

1. Risk of the portfolio is measured by beta
2. Beta for the portfolio can be calculated as a weighed average of betas for individual assets included in it:

$\beta_{port}=1/3*0+1/3*1.5+1/3*\beta=0.5+\frac{\beta}{3}=1=\beta_{market}$

All weights are 1/3 as we equally invested in a risk-free asset and two stocks. Beta of risk-free asset is 0 by definition, beta of one stock is given and equials 1.5. Beta of the market portfolio is 1 by definition.

Thus, beta for the other stock is 1.50