Dynamic Interactions in Financial Markets

Overview

This projects conducts a detailed financial analysis of three major Indian cement companies—Shree Cement Ltd (SHREECEM.NS), UltraTech Cement Ltd (ULTRACEMCO.NS), and Ambuja Cements Ltd (AMBUJACEM.NS)—from January 1, 2020, to December 30, 2024. It uses advanced econometric techniques, including GARCH models, Vector Autoregression (VAR), Johansen cointegration tests, and risk metrics, with data from Yahoo Finance. The analysis examines price trends, volatility, inter-stock relationships, and risk profiles.

Objectives

• Price Trends: Analyze stock price movements.
• Volatility: Model risk using GARCH.
• Inter-Stock Relationships: Investigate dependencies via VAR and cointegration.
• Risk Metrics: Calculate annualized returns, volatility, and Sharpe ratios.

Project Structure

The notebook is divided into sections with code and markdown cells. Below is a detailed breakdown of key sections, actions, outputs, and interpretations.

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Section 1: Data Collection and Preparation

Code Cell 1: Import Libraries

Purpose: Sets up the Python environment.

Libraries:

• yfinance: Fetches stock data.
• pandas: Manages DataFrames.
• numpy: Numerical computations.
• matplotlib.pyplot: Visualizations.
• statsmodels.tsa.api.VAR: VAR models.
• arch.arch_model: GARCH models.
• statsmodels.tsa.vector_ar.vecm.coint_johansen: Cointegration tests.
• seaborn: Enhances plots.
• warnings: Suppresses warnings.

Output: None (sets seaborn-v0_8 style with husl palette).

Explanation: Libraries enable data fetching, modeling, and visualization. Styling ensures professional plots.

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Code Cell 2: Download Stock Data

Purpose: Retrieves daily closing prices for the three stocks.

Actions:

1. Defines tickers: ['SHREECEM.NS', 'ULTRACEMCO.NS', 'AMBUJACEM.NS'] and names: ['Shree Cement', 'UltraTech Cement', 'Ambuja Cement'].
2. Uses yf.download for closing prices, drops missing values.
3. Prints trading days, date range, and descriptive statistics.

Output:

 Downloading stock data...
YF.download() has changed argument auto_adjust default to True
 Successfully downloaded data for 1237 trading days
 Date range: 2020-01-01 to 2024-12-30

 Stock Price Summary:
Ticker  AMBUJACEM.NS  SHREECEM.NS  ULTRACEMCO.NS
count        1237.00      1237.00        1237.00
mean          393.02     24407.68        7179.11
std           145.05      2810.42        2282.04
min           125.00     15537.85        2945.90
25%           283.07     22671.52        5852.44
50%           381.42     24624.12        7041.03
75%           513.20     26415.12        8276.17
max           695.00     31254.03       12083.90

Interpretation:

• Data: 1237 trading days (~5 years).
• Prices:
  • Ambuja: Mean ₹393, std ₹145, range ₹125–₹695.
  • Shree: Mean ₹24,408, std ₹2,810, range ₹15,538–₹31,254.
  • UltraTech: Mean ₹7,179, std ₹2,282, range ₹2,946–₹12,084.
• Insights: Shree has the highest price/volatility, Ambuja the lowest.
• Error Handling: try-except ensures robust data retrieval.

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Section 2: Returns Calculation and Basic Analysis

Code Cell 3: Calculate Returns

Purpose: Computes simple and log returns.

Actions:

1. Simple returns: (P_t - P_{t-1}) / P_{t-1} using data.pct_change().dropna().
2. Log returns: ln(P_t / P_{t-1}) using np.log(data / data.shift(1)).dropna().
3. Prints simple returns statistics.

Output:

 Calculating returns...
 Returns Summary:
Ticker  AMBUJACEM.NS  SHREECEM.NS  ULTRACEMCO.NS
count      1236.0000    1236.0000      1236.0000
mean          0.0012       0.0004         0.0010
std           0.0225       0.0184         0.0174
min          -0.1733      -0.1029        -0.1452
25%          -0.0094      -0.0096        -0.0083
50%           0.0017       0.0007         0.0008
75%           0.0121       0.0101         0.0099
max           0.0933       0.0777         0.1288

Interpretation:

• Simple Returns:
  • Ambuja: 0.12% mean, 2.25% std (highest).
  • Shree: 0.04% mean, 1.84% std (lowest return).
  • UltraTech: 0.10% mean, 1.74% std (lowest volatility).
• Range: Largest loss (Ambuja: -17.33%), gain (UltraTech: 12.88%).
• Log Returns: Used for GARCH (not printed).
• Insights: Ambuja is high-return/high-risk, Shree underperforms.

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Section 3: Comprehensive Visualization Dashboard

Code Cell 4: Multi-Panel Dashboard

Purpose: Visualizes price trends, returns, volatility, and correlations.

Actions:

1. Creates subplots for:
   • Normalized price trends.
   • Daily returns.
   • Rolling volatility (e.g., 21-day).
   • Correlation heatmap.
2. Uses matplotlib and seaborn.

Output:

 Creating price trend visualization...

Interpretation:

• Price Trends: Normalized plots show relative changes.
• Returns: Highlights volatility spikes.
• Volatility: Shows risk evolution.
• Correlation: Visualizes co-movement (values near 1 indicate strong correlation).
• Insights: Comprehensive view of stock behavior.

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Section 4: Bollinger Bands

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Section 5: GARCH (1,1) Modeling

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Section 6: VAR Analysis

Code Cell 9: Build VAR Model

Purpose: Models interdependencies between stock returns.

Actions:

1. Uses returns.dropna().
2. Selects lag length with model.select_order(maxlags=10).
3. Fits VAR model using AIC-selected lag.
4. Prints model summary and plots IRFs.

Output:

 Building VAR model...
 VAR Lag Selection Results:
   • AIC: 2 lags
   • BIC: 1 lags
   • FPE: 2 lags
   • HQIC: 1 lags

 VAR(2) model fitted successfully
 Model Summary:
   • Number of equations: 3
   • Number of observations: 1234
   • Log-Likelihood: 11328.67
   • AIC: -18.34

 Computing Impulse Response Functions...

Interpretation:

• VAR: Models returns based on past returns (3 equations).
• Lags: AIC/FPE select 2 lags.
• Fit: 1234 observations, log-likelihood 11328.67, AIC -18.34.
• IRFs: Show shock propagation over 10 days.
• Insights: Captures short-term interdependencies.

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Section 7: Cointegration Analysis

Code Cell 10: Johansen Cointegration Test

Purpose: Tests for long-run equilibrium relationships.

Actions:

1. Runs coint_johansen on prices (det_order=0, k_ar_diff=2).
2. Compares trace statistics to 5% critical values.
3. Prints results and interpretation.

Output:

 Performing Johansen Cointegration Test...

 Johansen Cointegration Test Results:
Null Hypothesis      Trace Stat   5% Critical  Reject? 
-------------------------------------------------------
r <= 0                 18.36        29.80        No      
r <= 1                 4.66         15.49        No      
r <= 2                 0.09         3.84         No      

 Interpretation:
   • Number of cointegrating relationships: 0
   • No cointegration found - stocks move independently in long run

Interpretation:

• Cointegration: Tests for long-term price relationships.
• Results: No cointegration (trace < critical values).
• Insights: Stocks move independently, no mean-reverting opportunities.

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Section 8: Summary and Risk Metrics

Code Cell 11: Final Summary

Purpose: Summarizes risk metrics and correlations.

Actions:

1. Recalculates returns.
2. Computes annualized metrics:
   • Return: Mean × 252.
   • Volatility: Std × √252.
   • Sharpe: Return ÷ Volatility.
3. Prints metrics and correlation summary.

Output:

 FINAL SUMMARY
==================================================

 Risk Metrics (Annualized):
               Annual Return  Annual Volatility  Sharpe Ratio
AMBUJACEM.NS          0.2947             0.3575        0.8244
SHREECEM.NS           0.0949             0.2918        0.3254
ULTRACEMCO.NS         0.2516             0.2767        0.9093

 Correlation Summary:
   • Highest correlation: 0.6629
   • Lowest correlation: 0.5095
   • Average correlation: 0.5699

 Analysis completed successfully!
 All visualizations have been generated and displayed.

Interpretation:

• Metrics:
  • Ambuja: 29.47% return, 35.75% volatility, Sharpe 0.8244.
  • Shree: 9.49% return, 29.18% volatility, Sharpe 0.3254.
  • UltraTech: 25.16% return, 27.67% volatility, Sharpe 0.9093.
• Correlations: Moderate (0.5095–0.6629, avg 0.5699).
• Insights: UltraTech is best risk-adjusted, Ambuja high-risk/high-return, Shree underperforms.

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Further Extensions

• Risk Management: Value at Risk, Expected Shortfall.
• Advanced Models: Multivariate GARCH, regime-switching.
• Trading Strategies: Explore if cointegration exists.
• Economic Indicators: Add macroeconomic factors.

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Overall Insights

• Performance: UltraTech excels, Ambuja high-risk/high-return, Shree underperforms.
• Volatility: GARCH (implied) would show clustering.
• Interdependencies: VAR shows short-term effects, no long-run cointegration.
• Sector Dynamics: Moderate correlations suggest diversification.

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