Index Fund to NASDAQ100.

Index Fund

An index fund is a portfolio designed to track the movements of a general market population or a market index.

Variables

$${\rho }_{ij}:\text{Correlation between the stock i and the stock j}$$

$$x_{ij}:\{\begin{array}{ll}1& \text{If j is the stock most correlated stock in the Index Fund}\\ & \text{for the stock i of NASDAQ100}i,j:1,\dots ,n\\ 0& \text{Other case}\end{array}$$

$$y_j:\{\begin{array}{ll}1& \text{If the stock j is in the Index Fund}j=1,\dots ,n\\ 0& \text{Other case}\end{array}$$

Objective function

$$Z=\text{Max}\sum _{i=1}^n\sum _{j=1}^n{\rho }_{ij}{x}_{ij}$$

Subject to

$$\sum _{j=1}^n{y}_j=q$$

$$\sum _{j=1}^n{x}_{ij}=1{}_{i=1,\dots ,n}$$

$$x_{ij}\le y_j{}_{i,j=1,\dots ,n}$$

$$x_{ij},y_j=0o1{}_{i,j=1,\dots ,n}$$

Money management strategies are primarily classified as “active” or “passive.”

• Active portfolio management seeks to achieve superior performance through the use of technical and fundamental analysis, as well as forecasting techniques.

• Passive portfolio management avoids any forecasting technique and relies rather on diversification to achieve the desired performance.

Objective

It is desirable to have an index fund with q stocks, where q is substantially less than the size of the target population (n).

Problem

Create a model that groups assets into similar asset groups and selects a representative asset from each group to be included in the Index Fund’s portfolio.

Approach

• Create an Index Fund with q stocks to track the NASDAQ100 index.

• Each share i has a share j that represents it in the Index Fund

• Each share i can be represented by share j, only if j is in the Index Fund

The objective of the model is to maximize the similarity between the n stocks and their representatives in the Index Fund.

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• 👉 Index Fund - NASDAQ100 App