Stock J has a beta of 1.17 and an expected return of 14.4 percent, while Stock K has a beta of 0.68 and an expected return of 7.6 percent. You want a portfolio with the same risk as the market. What is the expected return of your portfolio?

Question

BlackTom AI · Accepted Answer

To construct a portfolio with the same risk as the market, we need the portfolio beta to equal 1. Let the weights be wJ for Stock J and wK for Stock K, with wJ + wK = 1. The portfolio beta is: BetaP = wJ*(1.17) + wK*(0.68). Setting BetaP = 1 and using wK = 1 - wJ, we get: 1 = wJ*(1.17) + (1 - wJ)*(0.68).

Expanding: 1 = 1.17 wJ + 0.68 - 0.68 wJ = 0.49 wJ + 0.68. 
Thus 0.49 wJ = 1 - 0.68 = 0.32, so wJ = 0.32 / 0.49 ≈ 0.653 (65.3%). Then wK = 1 - wJ ≈ 0.347 (34.7%).

Now compute the portfolio expected return: E[Rp] = wJ*E[RJ] + wK*E[RK] = 0.653*(14.4%) + 0.347*(7.6%).

First term: 14.4% × 0.653 ≈ 9.4032%. Second term: 7.6% × 0.347 ≈ 2.6372%. Sum ≈ 12.0404%.

Therefore, the portfolio expected return is about 12.04%.

Option analyses:
- 10.67 percent: This value would correspond to a much lower weighted exposure to the high-beta stock or an incorrect beta target; it does not satisfy the required beta of 1 because the weighted average of the given betas cannot produce such a low return when using the calculated weights.
- 11.18 percent: This is closer but still inconsistent with the precise weights needed to achieve BetaP = 1; small miscalculation in weights or arithmetic would be required to land here, but the correct calculation yields a higher value.
- 11.62 percent: This option is a common distractor that might arise if rounding were applied too early or if a student used approximate weights; the exact computation yields 12.04%, not this figure.
- 12.04 percent: This matches the exact weighted return using weights that achieve BetaP = 1, computed from solving 1 = 1.17 wJ + 0.68 (1 - wJ).

Stock J has a beta of 1.17 and an expected return of 14.4 percent, while Stock K has a beta of 0.68 and an expected return of 7.6 percent. You want a portfolio with the same risk as the market. What is the expected return of your portfolio? 单项选择题

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