For the maximum risk portfolio, the weight vector isw = \How can I modify the equation, so that I have additional constraints, such as setting a particular weight to 0.3?

Lagrange multipliers

Your equation arises because you have the constraint {1 1 1 1 1 ... 1} w = 1. You want another contraint like {0 0 0 0 1 0 0 ..... 0} w = 0.3 to achieve what you ask. Then use the Lagrange Multiplier method as before (assuming you know how you arrived at the equation in the first place).

Hello,I have tried using Lagrange Multipliers, but without luck. I have LaTeXed up how far I have got below: Working from http://www.maths.sussex.ac.uk/Staff/QT/FO/Chapter4.doc, 4.4 The Maximum Return Risk Ratio Portfolio:. I want to add another constraint on the first weight:such that For example, C would be 0.3 if I wanted to constrain the first weight to be 30% of the portfolio. Equation 1 Becomes: Where are the Lagrange Multipliers Differentiating we get Multiply by w, to get In the unconstrained example, we get only have one Lagrange multiplier,, so we can conclude that . However, in this constrained example, things aren't so convenient and we cannot do that. In the worked example, is used in (2). However, I cannot do that in the constrained case.

Must be insomnia or something. Anyway, if anyone is interested and wants to know the answer, it'sWhere u and C are respectively the expected returns and covariance matrix. The constraints are given by Aw=bI can't simplify it really any further but would be interested if some knows if a simplification exists.