Estimate the maximum expected loss of a portfolio at a chosen confidence level over a specified time horizon using parametric VaR.
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Risk Management
Value at Risk (VaR) estimates the maximum expected loss of a portfolio over a specified time horizon at a chosen confidence level. This parametric VaR calculator uses the variance-covariance method with daily return statistics.
A 95% 10-day VaR of 50,000 means there is a 5% chance the portfolio will lose more than 50,000 over the next 10 trading days. VaR does not tell you how bad the loss could be in that 5% tail — for that, you need Expected Shortfall (CVaR).
VaR is widely used by banks, asset managers, and regulators (Basel framework) to quantify market risk exposure and set capital reserves.
The variance-covariance method assumes normally distributed returns.
VaR = Portfolio × (z × σ × √t − μ × t)
μ = daily mean return, σ = daily standard deviation, z = z-score for confidence level (1.65 for 95%, 2.33 for 99%), t = holding period in days.
Parametric VaR assumes returns are normally distributed. In reality, financial returns exhibit fat tails (kurtosis) and skewness, meaning extreme losses occur more often than the normal distribution predicts. Historical simulation and Monte Carlo methods address this but are more complex.
Frequently asked questions
95% is standard for internal risk reporting. 99% is used by Basel regulatory frameworks for bank capital requirements. Higher confidence means higher VaR (wider tail).
The parametric method uses the normal distribution for computational simplicity. It works reasonably well for diversified portfolios over short horizons but understates tail risk for concentrated or leveraged positions.
VaR tells you the threshold: “95% of the time, losses won’t exceed X.” Expected Shortfall (CVaR) tells you the average loss in the worst 5% of cases — it captures tail severity, not just frequency.
Calculate from historical daily returns over a representative period (typically 1–3 years). Use log returns for accuracy. Many financial data providers (Bloomberg, Yahoo Finance) provide these statistics.
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