Question

You would like to create a $186,000 portfolio that is equally invested in a risk-free asset and two stocks. If one of the stocks has a beta of 2.03 and you want the portfolio to be equally as risky as the market, what must the beta be for the other stock in your portfolio?

Answer 1

The beta of is computed as shown below:

Beta of portfolio = Beta of risk free asset x weight of risk free asset + Beta of 2nd stock x weight of 2nd stock + beta of 3rd stock x weight of 3rd stock

1 = 0 x 1 / 3 + 2.03 x 1 / 3 + Beta of 3rd stock x 1 / 3

1 = 0.676666667 + Beta of 3rd stock x 1 / 3

1 - 0.676666667 = Beta of 3rd stock x 1 / 3

3 x 0.323333333 = Beta of 3rd stock

0.97 = Beta of 3rd stock

Please note beta of market is 1 and beta of risk free asset is zero.

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