Value at Risk (VaR)
Value at Risk (VaR) is a statistical measure that estimates the maximum expected portfolio loss over a specified time horizon at a given confidence level — for example, a one-day 95% VaR of Rs 10 lakh means there is only a 5% probability of losing more than Rs 10 lakh in a single day.
VaR is the most widely adopted quantitative risk measure in financial institutions globally and is deeply embedded in regulatory frameworks. In India, SEBI mandated VaR-based margin systems for the derivatives segment long before global regulators widely adopted similar frameworks. NSE's SPAN margin system for futures and options effectively uses portfolio VaR at a 99% confidence level to determine initial margin requirements.
Three primary VaR methodologies exist. Historical simulation VaR ranks actual historical returns from worst to best and reads off the 5th percentile (for 95% VaR); it is non-parametric and captures fat tails naturally. Parametric (variance-covariance) VaR assumes normality, using mean and standard deviation to compute the tail quantile analytically — computationally fast but underestimates tail risk in non-normal distributions. Monte Carlo VaR simulates thousands of hypothetical portfolio paths using modelled return distributions, offering flexibility to incorporate fat tails but requiring extensive computational resources.
For a portfolio of Indian equities, a one-day 99% VaR is calculated by NSE for margin purposes. If Nifty futures show a daily volatility of 1.5%, the 99th percentile VaR under normality is approximately 3.49% (2.326 standard deviations). Adding a safety factor, NSE's Value at Risk margin typically runs around 3–4% on Nifty contracts. Peak margin rules introduced by SEBI in December 2020 tightened the requirement to use the maximum intraday margin requirement, preventing margin inflation through intraday position building.
Key limitations of VaR include its inability to capture the severity of losses beyond the confidence level (addressed by CVaR), its assumption of stable correlations (violated in crises), and its backward-looking nature when using historical simulation. The 2008 financial crisis globally — and the 2018 credit market freeze in India — demonstrated that historical VaR based on recent benign periods dramatically underestimated actual tail losses.
Regulatory VaR under Basel norms for banks requires a 10-day 99% VaR, often computed using stressed market data from a period of significant financial turbulence. Indian banks following Basel III norms compute trading book VaR using both historical and stressed calibrations, reported periodically to RBI.