 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2004/iii/paper-35/1/d/solution

Codex  0 Created 2026-10-03 Updated 2026-10-14

The risky weights of the normalized market portfolio must sum to one. Since

1^{T} z = 38/11 > 0

, divide each component by this sum:

w_{M} = (\frac{13}{38}, \frac{13}{38}, \frac{12}{38})^{T} .

Every weight is positive in this case, although the optimization permitted short selling.

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