Asset Diversification & Portfolio Risk Optimization

This repository demonstrates how to analyze diversification in a portfolio through covariance and correlation among assets, and then optimize the portfolio for minimum risk using Python and Object-Oriented Programming (OOP).

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🔹 Motivation

In portfolio theory, risk is not just about individual asset volatility — it depends on how assets move together.
This project implements a Portfolio Optimizer that:

1. Calculates covariance and correlation matrices
2. Builds portfolios (equal-weight & optimized)
3. Shows how diversification reduces risk
4. Finds the optimal risk-minimizing portfolio using numerical optimization

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🔹 Mathematical Background

Portfolio Variance

For n assets with weights ( w ), covariance matrix ( \Sigma ):

$$ \sigma_p^2 = w^T \Sigma w $$

Portfolio Volatility

$$ \sigma_p = \sqrt{w^T \Sigma w} $$

Optimization Problem

We minimize risk subject to full investment:

$$ \min_w , \sigma_p \quad \text{s.t.} \quad \sum_{i=1}^n w_i = 1, , w_i \geq 0 $$

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🔹 Project Structure