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The Value at Risk (VaR) project analyzes portfolio risks using three methods: Parametric (Variance-Covariance), Historical Simulation, and Monte Carlo Simulation. We calculate daily VaR for NIFTY, Infosys, and TCS stocks, applying statistical models to estimate potential losses at 95% and 99% confidence intervals, identifying key risk factors and limitations.
The Value at Risk (VaR) project analyzes portfolio risks using three methods: Parametric (Variance-Covariance), Historical Simulation, and Monte Carlo Simulation. We calculate daily VaR for NIFTY, Infosys, and TCS stocks, applying statistical models to estimate potential losses at 95% and 99% confidence intervals, identifying key risk factors and limitations.
Methodologies Employed for VaR Calculation
Methodologies Employed for VaR Calculation
The report explains three distinct methods used to calculate VaR for a portfolio consisting of NIFTY, Infosys, and TCS stocks:
Parametric (Variance-Covariance) Method: This method assumes that asset returns follow a normal distribution. VaR is calculated using the portfolio’s mean return and standard deviation, with the assumption of linear relationships between the assets. The Z-score is used to determine the loss at different confidence intervals (e.g., 95% and 99%).
Historical Simulation Method: This approach uses historical returns to simulate future losses without making any distributional assumptions. By analyzing actual past data, VaR is calculated based on the worst historical returns, offering an empirical risk measure.
Monte Carlo Simulation: This method involves generating random future scenarios based on the historical distribution of returns using statistical properties such as mean and standard deviation. The Monte Carlo approach allows for more flexibility by simulating a wide range of potential future market conditions and calculating VaR accordingly.
Key Findings
Key Findings
The three methods provided different insights into portfolio risk. The Parametric method is straightforward but assumes normally distributed returns, which may not always be accurate. The Historical Simulation method, by relying on past data, reflects real historical risk but might not account for future market changes. The Monte Carlo method, while computationally intensive, offers a more dynamic view by simulating various potential outcomes.
Limitations of VaR
Limitations of VaR
The report identifies several key limitations of VaR:
Normal Distribution Assumption: Many VaR models assume normality in asset returns, which underestimates risk during extreme market events.
Historical Dependency: Relying on historical data may lead to inaccurate risk assessments when future market conditions differ from past trends.
Neglect of Tail Risks: VaR does not account for the magnitude of losses beyond the specified confidence interval, potentially missing extreme events.
Liquidity Risks: VaR fails to incorporate liquidity risk, meaning it assumes assets can be sold at current market prices, which may not hold during crises.
Recommendations for Improvement
Recommendations for Improvement
To address the limitations, the report recommends supplementing VaR with other risk measures like Conditional Value at Risk (CVaR) and stress testing. Incorporating liquidity-adjusted VaR and dynamic models such as GARCH can further improve the accuracy of risk assessments.
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