You have a portfolio that is invested 20 percent in Stock R, 38 percent in Stock S, and the remainder in Stock T. The beta of Stock R is .75, and the beta of Stock S is 1.30. The beta of your portfolio is 1.18. What is the beta of the Stock T?

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BlackTom AI · Accepted Answer

We are given a portfolio with weights: R = 20% (0.20), S = 38% (0.38), and T = remainder (1 - 0.20 - 0.38 = 0.42).

The betas are: beta_R = 0.75, beta_S = 1.30, and beta_T is unknown. The portfolio beta is a weighted average: beta_P = w_R*beta_R + w_S*beta_S + w_T*beta_T.

First, compute the contributions from the known stocks:
- w_R*beta_R = 0.20 * 0.75 = 0.15
- w_S*beta_S = 0.38 * 1.30 = 0.494
These sum to 0.15 + 0.494 = 0.644.

The target portfolio beta is 1.18, so:
1.18 = 0.644 + 0.42*beta_T
Subtract 0.644 from both sides: 1.18 - 0.644 = 0.536
Solve for beta_T: beta_T = 0.536 / 0.42 ≈ 1.27619, which rounds to about 1.28.

Now evaluate each option by checking whether it reproduces the given portfolio beta when combined with R and S.

Option A: 1.09
Compute portfolio beta with beta_T = 1.09:
0.644 + 0.42*1.09 = 0.644 + 0.4578 = 1.1018, which is far from 1.18. This option is incorrect.

Option B: 1.45
0.644 + 0.42*1.45 = 0.644 + 0.609 = 1.253, also not equal to 1.18. Incorrect.

Option C: 1.18
0.644 + 0.42*1.18 = 0.644 + 0.4956 = 1.1396, not 1.18. Incorrect.

Option D: 1.03
0.644 + 0.42*1.03 = 0.644 + 0.4326 = 1.0766, not 1.18. Incorrect.

Option E: 1.28
0.644 + 0.42*1.28 = 0.644 + 0.5376 = 1.1816, which matches the target 1.18 when rounded. This option is consistent with the given portfolio beta.

In summary, each option was tested by replacing beta_T and checking if the resulting portfolio beta equals 1.18. Only the last option yields a result close to the required portfolio beta after accounting for rounding, while the others produce noticeably different totals.

BUSFIN 3220 AU2025 (2110) Exam 3 - Requires Respondus LockDown Browser

You have a portfolio that is invested 20 percent in Stock R, 38 percent in Stock S, and the remainder in Stock T. The beta of Stock R is .75, and the beta of Stock S is 1.30. The beta of your portfolio is 1.18. What is the beta of the Stock T?

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