You would like to create a portfolio that is equally invested in a risk-free asset and two stocks. One stock has a beta of 1.14. What does the beta of the second stock have to be if you want the portfolio to be equally as risky as the overall market?

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BlackTom AI · Accepted Answer

We’re told the portfolio should be equally invested in a risk-free asset and two stocks. Since the risk-free asset has beta 0, the portfolio beta is the average of the betas of the two stocks:

Portfolio beta = (1/3)*0 + (1/3)*beta_A + (1/3)*beta_B = (1/3)*(beta_A + beta_B).
Here, beta_A = 1.14, and we want the portfolio beta to equal the market beta of 1, so (1/3)*(1.14 + beta_B) = 1.

Multiply both sides by 3: 1.14 + beta_B = 3.

Solve for beta_B: beta_B = 3 - 1.14 = 1.86.

Now, evaluate the given options to see which one satisfies the equation for the portfolio to mirror market risk:

- 0.62: (1/3)*(1.14 + 0.62) = (1/3)*1.76 ≈ 0.587, which is much less than 1, so this stock would not make the portfolio as risky as the market.
- 0.97: (1/3)*(1.14 + 0.97) = (1/3)*2.11 ≈ 0.703, still below 1, not meeting the requirement.
- 1.23: (1/3)*(1.14 + 1.23) = (1/3)*2.37 ≈ 0.790, which remains short of market risk.
- 1.55: (1/3)*(1.14 + 1.55) = (1/3)*2.69 ≈ 0.896, closer but not equal to 1.
- 1.86: (1/3)*(1.14 + 1.86) = (1/3)*3.00 = 1.00, exactly the market beta, meaning this stock provides the needed level of systematic risk.

Thus, among the options, 1.86 is the value that makes the portfolio’s risk equal to the market risk, while the other choices yield portfolio betas below 1.0 and fail to match the market.

FNBSLW 344-23 Chapter 11 Practice Quiz (not graded)

You would like to create a portfolio that is equally invested in a risk-free asset and two stocks. One stock has a beta of 1.14. What does the beta of the second stock have to be if you want the portfolio to be equally as risky as the overall market?

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