MSFT vs AAPL Market Cap Analysis

This project performs Monte Carlo simulations to model the 30-day market cap difference trajectory between Microsoft (MSFT) and Apple (AAPL). It uses both Geometric Brownian Motion (GBM) and GARCH models to estimate probabilities and visualize potential outcomes.

Project Overview

The analysis focuses on predicting the probability that Microsoft's market capitalization will exceed Apple's within a 30-day horizon. It employs:

• Geometric Brownian Motion (GBM): A baseline simulation assuming constant volatility
• GARCH Model: More sophisticated modeling of time-varying volatility and fat-tailed distributions
• Scenario Analysis: Detailed exploration of market cap delta across different return scenarios
• Detailed Visualizations: Confidence intervals, probability projections, and 3D surface plots

Repository Structure

├── advanced_monte_carlo_analysis.py  # Main script for GBM and GARCH comparisons
├── valuation_delta_analysis.py       # Extended valuation gap analysis
├── monte_carlo_simulation.py         # Basic Monte Carlo implementation
├── get_historic_prices.py            # Utility for fetching market data
├── models/                           # Core functionality modules
│   ├── analysis.py                   # Statistical analysis functions
│   ├── data_loader.py                # Data handling and processing
│   ├── simulation.py                 # GBM and GARCH model implementations
│   ├── valuation.py                  # Market cap calculations
│   └── visualization.py              # Chart and plot generation
├── data/                             # Historical price data
│   ├── AAPL.csv
│   ├── MSFT.csv
│   └── SPY.csv
└── analysis_output/                  # generated charts and stats

Features

• Dual Model Approach: Compares GBM with more advanced GARCH modeling
• High-Resolution Scenario Grid: Analyzes market cap delta across 1% return increments
• Interactive Visualizations: 3D surfaces and contour plots for scenario exploration
• Confidence Intervals: Quantified uncertainty in market cap projections
• Decision Boundaries: Identifies critical return combinations for valuation crossover

Key Visualizations

1. GBM vs GARCH Comparison: Visual comparison of both models' projections
2. Probability Trajectory: Time series showing probability of MSFT > AAPL
3. Detailed Scenario Grid: Heatmap showing market cap delta across return scenarios
4. Zoomed Decision Boundary: Close-up of the critical region around current valuation
5. 3D Surface Plots: Interactive visualization of probabilities across scenarios

Dependencies

This project requires Python 3.8 and the following packages:

• numpy
• pandas
• matplotlib
• seaborn
• plotly
• arch
• yfinance

See requirements.txt for specific version requirements.

Results

The analysis produces an assessment of the probability that MSFTs market cap will exceed Apple over the next 30-days. Simulation is visualized in the analysis_output/ folder, including:

• Terminal probability distributions
• Confidence intervals for market cap delta
• Decision boundary visualization
• Scenario grid analysis