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

To tackle this problem, I’ll start by noting the given weights and betas: wR = 0.20 with betaR = 0.75, wS = 0.38 with betaS = 1.30, and the remaining weight wT = 1 - (0.20 + 0.38) = 0.42. The portfolio beta is the weighted sum of the constituent betas, so we have: betaP = wR*betaR + wS*betaS + wT*betaT.

Compute the known part: 0.20 * 0.75 = 0.15, and 0.38 * 1.30 = 0.494. Their sum is 0.644.

Set up the equation with betaP = 1.18 to solve for betaT: 0.644 + 0.42*betaT = 1.18. Subtract 0.644 from both sides to get 0.42*betaT = 0.536.

Divide both sides by 0.42 to isolate betaT: betaT = 0.536 / 0.42 ≈ 1.27619, which rounds to about 1.28.

Now evaluate the provided options one by one:

Option A: 1.03. If betaT were 1.03, then 0.42*betaT would be 0.4326. Adding to the known 0.644 would yield 1.0766, far below the required 1.18. This makes Option A inconsistent with the given portfolio beta.

Option B: 1.45. If betaT were 1.45, then 0.42*betaT would be 0.609. Adding to 0.644 gives 1.253, which is higher than 1.18. So this would overshoot the target betaP.

Option C: 1.09. If betaT were 1.09, then 0.42*betaT would be 0.4578. Adding to 0.644 yields 1.1018, again short of 1.18. This does not match the given portfolio beta.

Option D: 1.18. If betaT were 1.18, then 0.42*betaT would be 0.4956. Adding to 0.644 gives 1.1396, not equal to 1.18. This fails to reproduce the target portfolio beta.

Option E: 1.28. If betaT were 1.28, then 0.42*betaT would be 0.5376. Adding to 0.644 yields 1.1816, which is essentially the specified portfolio beta of 1.18 when rounded. This aligns with the given information.

Putting it together, the value that brings the portfolio beta to the stated 1.18 is approximately 1.28, while the other options produce results noticeably off from 1.18.

BUSFIN 3220 AU2025 (2910) 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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