Question

You own a portfolio equally invested in a risk-free asset and two stocks. One of the stocks has a beta of 1.25 and the total portfolio is equally as risky as the market. What must the beta be for the other stock in your portfolio?

Answer 1

The answer is "1.75"

Step-by-step explanation:

The portfolio is equally weighted with three parts, which each weighs 33,33%. The risk-free asset (Rf) is available worldwide and beta 0 is given for the market portfolio.

`Return \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ Beta \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ Probability (Pi)\\\\\text{Risk free Return (Rf)} \ \ \ \ \ \ \ \ \ \ \ 0 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 33.33\%\\\\Stock 1\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 1.25 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 33.33\%\\\\Stock 2\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ? \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 33.33\%\\\\`

`\text{Portfolio Beta = (Pi Rf * Beta Rf) + (Pi Stock1 * Beta Stock1) + (Pi Stock2 * Beta Stock2)}\\\\1 = (33.33\% * 0) + (33.33\% * 1.25) + (33.33\% * x)\\\\1 = 0 + 0.416625 + 0.3333x\\\\1 - 0.416625 = 0.3333x\\\\0.583375 = 0.3333x\\\\x =(0.583375)/(0.3333)\\\\x = 1.75`