Portfolio Optimization & Risk Analysis Using Python

This project demonstrates portfolio optimization and risk analysis using Python.
I've analyzed 5 major US stocks (AAPL, MSFT, TSLA, JNJ, JPM) to build an optimal portfolio using daily returns, risk metrics, and Monte Carlo simulation.

Project Overview

The project workflow includes:

1. Data Collection: Downloading daily stock prices from Yahoo Finance.
2. Exploratory Data Analysis (EDA): Visualizing price movements, computing daily returns, and checking correlations.
3. Portfolio Construction: Building an equal-weighted portfolio and computing performance metrics (returns, volatility, Sharpe ratio, drawdown).
4. Performance Attribution: Determining each stock’s contribution to portfolio returns.
5. Portfolio Optimization: Using Monte Carlo simulation to find the portfolio with maximum Sharpe ratio.
6. Visualization: Plotting cumulative returns, correlation heatmap, and optimal portfolio allocation.

Tools & Libraries:

• Python
• pandas, NumPy
• matplotlib, seaborn
• yfinance

Data

Stocks Analyzed:

• Apple Inc. (AAPL)
• Microsoft Corp. (MSFT)
• Tesla Inc. (TSLA)
• Johnson & Johnson (JNJ)
• JPMorgan Chase & Co. (JPM)

Sample Data (Closing Prices):

Date	AAPL	JNJ	JPM	MSFT	TSLA
2025-01-02	242.53	139.00	233.97	414.57	379.28
2025-01-03	242.04	139.17	237.17	419.29	410.44
2025-01-06	243.67	138.66	236.01	423.75	411.05
2025-01-07	240.89	141.14	238.28	418.32	394.36
2025-01-08	241.38	137.31	238.24	420.49	394.94

Visualization:

• Stock Price Movement Graph

  MSFT is trending highest, followed by TSLA, JPM, AAPL, JNJ.

---

Exploratory Data Analysis (EDA)

Daily Returns (sample):

Date	AAPL	JNJ	JPM	MSFT	TSLA
2025-01-03	-0.00201	0.00118	0.01367	0.01140	0.08216
2025-01-06	0.00674	-0.00368	-0.00488	0.01063	0.00149
2025-01-07	-0.01139	0.01789	0.00963	-0.01281	-0.04060
2025-01-08	0.00202	-0.02708	-0.00016	0.00519	0.00147
2025-01-10	-0.02410	-0.00148	-0.01341	-0.01321	-0.00051

Daily Returns Histogram:

Correlation Heatmap:

---

Portfolio Construction (Equal Weight)

Weights: 20% per stock (equal weight)
Cumulative Return Graph:

• Initial $1 investment grows to ~$1.30 over the year.

Portfolio Metrics:

Metric	Value
Annual Return	0.3055
Volatility	0.2362
Sharpe Ratio	1.2594
Maximum Drawdown	-0.2251

Interpretation:

• Sharpe Ratio 1.26: Portfolio provides good return per unit of risk.
• Max Drawdown -22.5%: Largest peak-to-trough loss.
• Annual Return 30.5%: Total growth over the year.

---

Performance Attribution

Contribution to Portfolio Return (Absolute & %):

Ticker	Absolute	% Contribution
AAPL	0.0329	11.19%
JNJ	0.0824	28.03%
JPM	0.0693	23.57%
MSFT	0.0361	12.28%
TSLA	0.0733	24.92%

Observation: JNJ, TSLA, and JPM contributed the most to portfolio gains.

---

Portfolio Optimization (Monte Carlo Simulation)

Goal: Maximize Sharpe Ratio.

Optimal Portfolio Weights:

Ticker	Weight
MSFT	0.7448
JNJ	0.1151
TSLA	0.0970
JPM	0.0381
AAPL	0.0050

Visualization:

• MSFT dominates the optimal portfolio (>74% allocation).
• Remaining stocks have minor allocations.

---

Visualizations

1. stock_prices.png → Daily stock price movement

2. returns_histogram.png → Daily returns distribution

3. correlation_heatmap.png → Correlation between stocks

4. equal_weight_cum_returns.png → Equal-weight portfolio cumulative returns

5. optimal_portfolio_allocation.png → Optimal weights bar chart

6. Efficient Frontier of Simulated Portfolios Each point represents a portfolio with different weight allocations.

• X-axis: Portfolio risk (volatility)
• Y-axis: Expected return
• Color: Sharpe ratio (risk-adjusted return)
  Bright points represent portfolios with higher Sharpe ratios, indicating optimal trade-offs between risk and return.

7 Efficient Frontier Visualization The scatter plot shows all simulated portfolios with varying weights.

• X-axis: Portfolio Volatility (Risk)
• Y-axis: Portfolio Expected Return
• Color gradient: Sharpe Ratio (reward per unit risk)
• Red Star: Portfolio with highest Sharpe Ratio (Optimal Portfolio)