Here is the problem:
I have 40 shares in an index and I want to weight them based on their market value, define the known value as $x_i$
In the traditional way, the weight of each share is calculated as:
$w_i = x_i / \sum^M_{j=1} x_j $ for $M = 40$
However, now I want to apply the following restrictions:
- $w^{k}_s <= 0.05$
- $\sum^{N_k}_{s=1} w^{k}_s <= 0.10$ for all $k = 1...K$
- $\sum^{K}_{k=1} \sum^{N_k}_{s=1} w^{k}_s = 1$
Moreover, each share belongs to one sector $k$, the sum of the weights of the shares within each of these sectors should be less or equal to 0.10. In addition, the weight of each individual share $i$ should be less or equal than 0.05. Summing up all the weight $w^{k}_s$ should add up to 1.
My questions are:
- How to solve this?
- What is the solution?
- Is there an objective function and what is it?
Many many thanks!