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

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

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

$$y_{j}: \begin{cases} 1 & \text{If the stock j is in the Index Fund} \quad j = 1, …, n \\
0 & \text{Other case} \end{cases}$$

Objective function

$$ Z = \quad \text{Max} \quad \sum_{i=1}^n \sum_{j=1}^n \rho_{ij} x_{ij} $$

Subject to

$$\sum_{j=1}^n y_j = q$$

$$\sum_{j=1}^n x_{ij} = 1 \quad _{i=1, …, n}$$

$$x_{ij} \leq y_j \quad _{i,j = 1, …, n}$$

$$x_{ij}, y_j = 0 \quad o \quad 1 \quad _{i,j = 1, …, n}$$

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