Dynamic Correlation for Risk Assessment in Finance

This repository contains a multivariate econometric study that has been applied to the financial risk management of an equally-weighted (EW) portfolio.

Starting with a set of securities selected through a machine learning (ML) technique and an aggregated macroeconomic-financial index, the study examines the evolution of the pairwise correlations between the purpose-built index and each security over a 5-year horizon (2019-2024), and applies the final results to estimate the Value at Risk (VaR) and the Expected Shortfall (ES) of an EW portfolio.

In addition, the research is carried out on the same dataset, but excluding the most turbulent months of the COVID-19 pandemic (Feb-Apr 2020) in order to analyse differences in both econometric and risk management results.

Repository Structure

The repository is organized into two main directories:

• code/, which contains all the scripts used for data processing,clustering, econometric modelling and portfolio risk estimation;
• docs/, which includes the full thesis and its supporting presentation.

The structure is shown below:

.
├── 01_clustering_and_macro_index/
│ ├── cluster_analysis.py             # Clustering of NASDAQ-100 using KMeans
│ ├── macro_financial_index.m         # Macro-financial index with GARCH(1,1) weights
│ └── macro_index_README.md
│ └── README.md
│
├── 02_dcc_garch_models/
│ ├── dcc_main_driver.m               # Master script for DCC/VAR pipeline
│ ├── dcc_compute_rolling.m           # Rolling correlation benchmark
│ ├── dcc_estimate_all_models.m       # DCC, GJR, TARCH, ADCC variants
│ ├── dcc_model_selection.m           # RMSE-based model selection
│ ├── dcc_compare_with_VAR.m          # VAR-DCC implementation + LRT
│ ├── dcc_generate_plots.m            # Generates all plots
│ └── README.md
│
├── 03_advanced_risk_management/
│ ├── EW_portfolio.m                  # Portfolio P&L based on equal weights
│ ├── VaR_ES.m                        # Dynamic VaR and ES estimation
│ ├── VaR_ES_breaches.m               # VaR and ES exceedance visualization
│ └── README.md
│
├── docs/
├── MSc_Thesis_Giovanni_Pedone.pdf
├── Presentation_Dissertation.pdf
│
├── FUTURE_RESEARCH.md                # Future directions and model improvements
└── README.md                         # This file

Note: each main subdirectory (e.g., 01_clustering_and_macro_index, 02_dcc_garch_models, 03_advanced_risk_management) contains an images/ and images_ex_covid/ folders that store the plots generated within that specific study section.

How to Run

Requirements

• Python 3.11 (or later recommended)
  • Anaconda (recommended for package management)
  • IDE: Spyder (used in development)
• MATLAB R2023a (or later recommended)
  • Econometrics Toolbox
  • Statistics and Machine Learning Toolbox
  • Financial Toolbox
  • MFE Toolbox by Kevin Sheppard (for dcc.m)
    → MFE Toolbox - dcc.m, make sure to add the toolbox to the MATLAB path before running any script

Main Outputs

The repository produces key outputs based on econometric modelling and dynamic risk analysis. Results are presented from two perspectives:

1. Econometric Insights (DCC-GARCH vs. VAR-DCC-GARCH)

The dynamic conditional correlations estimated through the DCC(1,1) and VAR(1)-DCC(1,1) models show substantial convergence over time. Excluding the most volatile months of the Covid-19 pandemic (Feb–Apr 2020) appears to:

• improve the overall stability of correlations, with smoother transitions and fewer spikes;
• reduce frequent regime shifts between positive and negative relationships;
• allow for more accurate modelling of second-order conditional moments.

Even in the absence of exogenous shocks, the trends across models remain largely overlapping, but Ex-COVID data displays less noisy dynamics and more consistent correlation patterns.

2. Risk Measures: VaR and ES (COVID vs. Ex-COVID)

The model provides a set of outputs illustrating the dynamic estimation of daily VaR and ES, derived through a DCC-GARCH framework integrated with Markowitz Portfolio Theory (MPT). The exclusion of the most volatile pandemic months (Feb–Apr 2020) reveals:

• amplified risk exposure when removing COVID months, suggesting that post-pandemic risk dynamics (e.g., supply chain issues, geopolitical tensions, war-related inflation) may have been even more impactful than the initial pandemic shock;
• a more conservative risk profile detected by Expected Shortfall (ES), especially during stress conditions;
• evidence that ES is more precise than VaR in capturing tail risk, particularly post-COVID-peak.

Measure	Covid	Ex-Covid
VaR₉₅%	−271.34	−338.05
VaR₉₉%	−378.82	−466.59
ES₉₅%	−337.24	−416.86
ES₉₉%	−423.27	−530.50

Limits

Despite the robustness of the implemented methodology, several limitations must be acknowledged:

• Variable Scope: the inclusion/exclusion of additional macro-financial variables could significantly alter correlation dynamics and risk estimations.

• Computational Burden: DCC-GARCH models are computationally intensive, especially in high-dimensional settings or during extended sample periods.

• Normality Assumption: the model relies on the assumption of multivariate normality, which may not fully capture the fat tails and asymmetries observed in financial returns.

• Simplified Portfolio Construction: the portfolio assumes equal weights and ignores transaction costs, potentially oversimplifying real-world investment conditions.