Portfolio Management and Performance Analysis

This project was created as part of the Mathematics of Finance class to construct, manage, and evaluate the performance of a financial portfolio. The project aims to provide hands-on experience with portfolio management concepts and financial metrics, leveraging tools like Python and Jupyter Notebooks.

Project Overview

• Initial Budget: $1,000,000
• Portfolio Composition: 5 stocks
• Duration: Weekly tracking and analysis over the semester
• Stocks Selected:
  • Broadcom Inc. (AVGO)
  • Fidelity Blue Chip Growth Fund (FBGRX)
  • Alphabet Inc. (GOOGL)
  • Intuitive Surgical Inc. (ISRG)
  • Nvidia Corporation (NVDA)

Key Features

1. Portfolio Construction:

   • Application of the Markowitz Model to determine optimal portfolio weights.
   • Focus on minimizing variance and achieving a target return.

2. Performance Metrics:

   • Rate of Return: Weekly and overall returns.
   • Standard Deviation: Volatility assessment.
   • Beta: Sensitivity to market movements.
   • Jensen Index: Excess return evaluation.
   • Sharpe Ratio: Risk-adjusted returns.
   • Value at Risk (VaR): Downside risk quantification.

3. Visualization:

   • Weekly performance trends for the portfolio and individual stocks.
   • Comparisons against the S&P 500 as a benchmark.

4. Reporting:

   • Comprehensive analysis of portfolio performance.
   • Insights into risk-return trade-offs and investment strategies.

Tools and Technologies

• Python:
  • Libraries: pandas, numpy, matplotlib, scipy, yfinance
  • Historical stock data is fetched using the Yahoo Finance API (yfinance).
• Jupyter Notebook: For interactive analysis and visualization.

How to Run the Project

• Open the Jupyter Notebook portfolio_mgmt_and_analysis.ipynb and run the cells sequentially to replicate the analysis.

Insights and Learnings

• Practical application of theoretical finance concepts.
• Analysis of risk and return metrics to guide portfolio management decisions.
• Hands-on experience with data-driven financial modeling.

Results

A detailed performance report is included, showcasing:

• Portfolio returns relative to market benchmarks.
• Risk assessment and optimization strategies.
• Key takeaways for improving investment strategies.

Stock Overview

Stock	Return	Standard Deviation	Beta	Jensen Index	Sharpe Ratio	VaR (h=0.05)
S&P 500	-0.0025	0.0075	N/A	N/A	N/A	N/A
AVGO	-0.0526	0.0314	2.7075	0.0166	-0.5154	8.3612
FBGRX	-0.0462	0.0129	1.5851	0.0067	-0.4524	4.6489
GOOGL	-0.0832	0.0174	1.6225	0.0076	-0.3069	5.1598
ISRG	-0.0800	0.0227	0.3694	-0.0083	0.0451	6.3156
NVDA	-0.0848	0.2925	3.0843	0.0079	-0.0760	6.9969

Summary

• Negative Returns: All stocks experienced negative returns, with NVDA and GOOGL showing the largest losses.
• Volatility: NVDA and AVGO exhibit the highest volatility
• Risk Indicators: Positive Jensen Index values indicate some excess return relative to the risk-free rate, but Sharpe Ratios are mostly negative, except for ISRG.
• Investor Considerations: Diversification, rebalancing, and focusing on lower-risk assets may help optimize returns and reduce risk.