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.webp "Value at Risk")
Value at Risk (VaR) estimates the possible loss in a portfolio's value under normal market conditions over a given timeframe and confidence level. It serves as a standard tool across financial institutions for quantifying equity market and portfolio risk. This article explains what VaR is, why it matters, the primary methods used, and how to calculate and interpret it effectively.
To begin, let’s clarify the purpose and role of VaR in risk metrics:
VaR represents the maximum expected loss over a specified period (e.g., one day or ten days) at a certain confidence interval (such as 95% or 99%). For instance, a one-day 95% VaR of ₹1 Lakh indicates there is only a 5% chance of losing more than ₹1 Lakh in a day under normal market conditions.
VaR informs financial firms, regulators, and investors about capital reserves required to cover potential losses. Market regulators also use VaR to ensure institutions maintain adequate margins and avoid systemic risks.
Different calculation methods exist, each with unique assumptions and strengths:
This analytical method assumes normally distributed returns. It uses mean, standard deviation, and confidence level (Z-score) to compute risk. For diversified portfolios, the covariance matrix between assets is employed to improve accuracy.
This model uses actual historical return data—reordering past losses to determine the loss at a given percentile. It avoids assumptions about return distributions and offers an empirical approach to estimating VaR.
This method simulates thousands of possible future paths by generating random returns based on statistical models. The VaR is taken as the percentile outcome of simulated losses, making it flexible but computationally intensive.
Here is the standard parametric VaR formula:
VaR = Z × σ × √t
Where:
Z = confidence-level Z-score (e.g., 1.65 for 95%)
σ = standard deviation of portfolio returns
t = time horizon (in days)
This provides the portfolio’s potential loss, scaled for the target timeframe. For longer horizons such as monthly, scale using √T (e.g., √20 for 20 trading days).
Let’s consider a practical example using the parametric method:
Portfolio value: ₹10 Lakh
Daily standard deviation: 2%
Time horizon: 1 day
Confidence level: 95% (Z = 1.65)
VaR = 1.65 × 0.02 × √1 = 3.3%
Estimated loss = ₹10 Lakh × 3.3% = ₹33,000
This implies a 95% confidence that the portfolio will not lose more than ₹33,000 in a single day.
Understanding its use and its boundaries is essential:
VaR aids firms, banks, and brokers in risk oversight, margin setting, financial controls, and capital allocation. It plays a central role in regulatory frameworks and internal risk policies.
VaR assumes normal distribution of returns, which may underestimate extreme events. It does not capture losses beyond the VaR threshold and is sensitive to model choice and historical data quality.
Since VaR has gaps, complementary metrics help provide a fuller risk profile:
CVaR, or Conditional Value at Risk, evaluates the average losses incurred when the actual loss exceeds the VaR threshold. It offers deeper insight into potential extreme losses and provides a more comprehensive picture of tail-end risk.
These methods model extreme market conditions—such as crashes—providing insight into vulnerabilities beyond normal assumptions. They are especially useful for robust financial planning.
Value at Risk is a widely used, standardised measure that offers a probabilistic estimate of loss potential under normal market conditions. While it helps institutions measure and manage everyday risk, VaR should be used alongside other methods like CVaR and stress testing to address extreme scenarios.
This content is for informational purposes only and the same should not be construed as investment advice. Bajaj Finserv Direct Limited shall not be liable or responsible for any investment decision that you may take based on this content.
It indicates the maximum expected loss over a set time period at a given confidence level under normal conditions.
CVaR—or Expected Shortfall—averages losses that exceed the VaR threshold and captures tail risk better.
The main methods are Parametric (variance-covariance), Historical Simulation, and Monte Carlo Simulation.
The parametric formula: VaR = Z × σ × √t, where Z is the Z-score, σ standard deviation, and t time horizon.
Yes. SEBI requires brokers to collect upfront VaR margins based on this calculation method.
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