# Index Fund to NASDAQ100.

In this post, I present a dashboard that optimizes through an Index Fund the NASDAQðŸ’¯.

## 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 FundEach 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.