Quantitative Risk Modeling: Portfolio VaR Estimation

This project calculates the 1-day 95% Value-at-Risk (VaR) of a mixed asset portfolio containing a SOFR swap and equity positions (AAPL, MSFT, F, BAC), using three major VaR methodologies:

Methods Implemented

• Parametric VaR (Variance-Covariance)
• Monte Carlo VaR
  • Full Revaluation
  • Sensitivity-Based
• Historical VaR
  • Full Revaluation
  • Sensitivity-Based

Portfolio Overview

• 10Y Payer SOFR Swap ($100M notional, 4.2% strike)
• Equity: $1M each in AAPL, MSFT, Ford, and Bank of America

Project Workflow

1. Preprocess the Market Data

   • Compute daily returns for equities and daily changes for SOFR zero rates.
   • Merge into a unified dataset of 34 risk factors.
   • Interpolate missing data points linearly.

2. Swap Pricing & Sensitivity

   • Calculate present value of the 10Y payer SOFR swap.
   • Estimate the PV01 vector (rate sensitivities) using bump-and-reprice.

3. Value-at-Risk Modeling

   • Compute Parametric VaR based on portfolio variance and expected return.
   • Run Monte Carlo simulations:
     • Full revaluation: simulate future returns using a multivariate normal distribution; reprice the swap under each simulated scenario.
     • Sensitivity-based: estimate swap PnL using the dot product of PV01 and rate shocks.
   • Apply Historical VaR using actual past risk factor changes:
     • Full revaluation: shift the SOFR curve by historical deltas and reprice the swap.
     • Sensitivity-based: approximate PnL using PV01 × historical changes in zero rates.

4. Compare Results

   • Print all 1-day 95% VaR results across all models.
   • Evaluate consistency, model assumptions, and sensitivity of outcomes.

Data Used

• 1 year of historical SOFR curve data
• Stock price data (31/10/2022 - 30/10/2023)
• Provided Excel-based swap pricer for full revaluation

How to Run

Follow these steps to set up and run the project locally:

1. Clone the Repository

git clone https://github.com/PPH-Myat/multi-asset-var-analysis.git
cd multi-asset-var-analysis

2. Set Up Python Environment

Make sure you have Python 3.10+ installed. Then install all required dependencies:

pip install -r requirements.txt

3. Prepare the Excel File

Place the Excel file in the following path:

data/hist_data.xlsm

The file must include the following sheets:

• SofrCurve — daily SOFR curve (with tenor columns and date rows)
• AAPL, MSFT, F, and BAC — each with:
  • Date column
  • Adj Close column (for adjusted closing prices)

4. Run the Main Script

From the root directory, execute:

python main.py

5. Output

You will see results printed in the terminal like this:

----- 1-Day 95% Value at Risk (VaR) Summary -----
Parametric VaR: $X,XXX,XXX.XX
Monte Carlo VaR (Full Revaluation): $X,XXX,XXX.XX
Monte Carlo VaR (Sensitivity-Based): $X,XXX,XXX.XX
Historical VaR (Full Revaluation): $X,XXX,XXX.XX
Historical VaR (Sensitivity-Based): $X,XXX,XXX.XX

Academic Context

This project was submitted as part of the QF609 (AY2024-2025) group assignment at Singapore Management University.

Acknowledgements

Baseline modeling references and data templates provided by the professor and senior cohorts. Modified and extended by our team for educational use.