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[Solution Library] Solve system of linear equations [Portfolio theory] Suppose we need to manage a portfolio of three bonds with weights w_1, w_2, w_3 such

Question: Solve system of linear equations

[Portfolio theory] Suppose we need to manage a portfolio of three bonds with weights \(w_{1}, w_{2}, w_{3}\) such that the following convexity and duration conditions are satisfied

\[\begin{aligned} & \sum\limits_{i=1}^{3}{{{D}_{i}}}{{w}_{i}}=D \\ & \sum\limits_{i=1}^{3}{{{C}_{i}}}{{w}_{i}}=C \\ \end{aligned}\]

and so that

\[\sum_{i=1}^{3} w_{i}=1\]
  1. Assume that \(C_{i}, D_{i}>0\) and \(C, D>0\) are given. Does this imply that there exists \(w_{1}, w_{2}, w_{3}\) with \(w_{i}>0, i=1,2,3 ?\) Is a solution always unique?
  2. Rewrite the above set of equations in matrix form.
  3. Assume that \(C_{1}=1, C_{2}=3, C_{3}=1, D_{1}=2, D_{2}=4, D_{3}=5, C=2\)

\(D=4\). Compute \(w_{1}, w_{2}, w_{3}\)

Price: $2.99
Solution: The downloadable solution consists of 2 pages
Deliverable: Word Document


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