Value at Risk Calculator
Reviewed by Hamza Gujjar, Algorithm Architect & Software Developer
Last updated: August 19, 2026Putting a Dollar Figure on "How Bad Could It Get?"
Value at Risk answers a specific question: over a given time horizon, how much could this portfolio plausibly lose, with a stated level of confidence? It doesn't predict the worst possible outcome — it estimates a loss threshold that shouldn't be exceeded except in the tail of outcomes beyond the chosen confidence level.
The Formula
This is the parametric (variance-covariance) method. Z is the z-score for the chosen confidence level, σ is the portfolio's standard deviation per period (as a decimal), and T is the time horizon in periods. The square root of time scales single-period volatility up to the chosen horizon, assuming returns are independent day to day.
Z-Scores Used
| Confidence Level | Z-Score |
|---|---|
| 90% | 1.2816 |
| 95% | 1.6450 |
| 99% | 2.3263 |
$100,000 Portfolio, 2% Daily Volatility
| Confidence | VaR (1 day) |
|---|---|
| 90% | $2,563.20 |
| 95% | $3,290.00 |
| 99% | $4,652.60 |
Extending the same portfolio to a 10-day horizon at 95% confidence raises VaR to $10,403.89 — risk scales with the square root of time, not linearly.
Where This Is Used
- Risk limits — trading desks and funds often cap positions based on a maximum acceptable VaR.
- Regulatory capital — banks use VaR-based models as part of regulatory capital requirement calculations.
- Portfolio monitoring — tracking VaR over time flags when a portfolio's risk profile is drifting higher.
How to Use This Calculator
- Enter the Portfolio Value.
- Enter the Portfolio Standard Deviation per period, as a percentage.
- Enter the Time Horizon in days.
- Select the Confidence Level — 90%, 95%, or 99%.
- Select Calculate to see the estimated Value at Risk.
Related Calculations
Need the standard deviation input first? Calculate it with the Risk Calculator, or check a multi-asset portfolio's combined volatility with the Portfolio Standard Deviation Calculator.
Statistical Principles of Value at Risk (VaR)
Value at Risk (VaR) is the industry-standard statistical risk management metric used by commercial investment banks, hedge funds, sovereign wealth funds, and institutional regulatory bodies (such as the Basel Committee on Banking Supervision) to quantify the maximum expected potential financial loss of an asset portfolio over a specified holding horizon at a predetermined statistical confidence level under normal market conditions.
For instance, stating that a $100 million investment portfolio has a 1-Day 95% VaR of $2.5 million means there is a 95% statistical probability that the portfolio will not lose more than $2.5 million during any single trading day (or conversely, there is a 5% chance that the daily loss will equal or exceed $2.5 million).
The Three Methodologies for Calculating VaR
- 1. Parametric (Variance-Covariance / Delta-Normal) Method: Assumes portfolio returns follow a normal distribution. For a portfolio with mean return μ, standard deviation σ, and standard normal critical value Z (Z = 1.645 for 95% confidence; Z = 2.326 for 99% confidence):
VaR = Portfolio Value × (Z × σ - μ) × √t
- 2. Historical Simulation Method: Applies actual historical percentage price returns from the past 500 to 1,000 trading days directly to the current portfolio, ranking simulated daily P&L outcomes from worst to best and reading the corresponding percentile loss value directly. Captures fat tails and empirical skewness without parametric distribution assumptions.
- 3. Monte Carlo Simulation Method: Generates tens of thousands of pseudo-random market scenarios using geometric Brownian motion stochastic paths and copula dependency structures, ideal for non-linear derivative option portfolios.
Expected Shortfall (Conditional VaR / CVaR)
A critical limitation of traditional VaR is that it reports only the threshold cutoff loss without describing the severity of losses that occur in the extreme tail beyond the cutoff point. Modern banking regulations (Basel III / Basel IV) mandate Expected Shortfall (ES or CVaR), which computes the expected average loss conditional upon the loss exceeding the VaR threshold:
Step-by-Step Worked Calculation Example
Example: Calculating 10-Day 99% Basel Regulatory VaR for a Trading Desk
Problem: A commercial bank proprietary trading desk holds an equity portfolio with a current market valuation of $50,000,000. The daily return standard deviation (σdaily) is 1.50% (0.0150), and expected daily drift μ is assumed to be 0. Calculate: (1) The 1-day 99% Parametric VaR (Z = 2.326); and (2) The 10-day 99% Regulatory Capital VaR using the square-root-of-time scaling rule.
Step 1: Calculate 1-Day 99% Value at Risk:
VaR1-day, 99% = Portfolio Value × Z × σdaily
VaR1-day, 99% = $50,000,000 × 2.3263 × 0.0150 = $1,744,725.00
Step 2: Scale to 10-day holding horizon using square-root-of-time:
VaR10-day, 99% = VaR1-day × √10 = $1,744,725.00 × 3.162277 = $5,517,304.50
Conclusion: The bank faces a 99% 10-day Value at Risk of $5.52 million (11.03% of portfolio value), requiring minimum regulatory capital reserves to absorb potential market declines.
Common Pitfalls in VaR Risk Analysis
- Assuming Stationarity During Market Crises: Historical asset correlations often surge toward 1.0 during liquidity panics, causing portfolio diversification benefits to evaporate precisely when VaR models predict low risk.
- Square-Root-of-Time Scaling Errors: Multiplying 1-day VaR by √t assumes independent identically distributed (i.i.d.) returns; if returns exhibit positive autocorrelation or volatility clustering, √t scaling severely underestimates multi-week risk.
Basel III Regulatory Capital Requirements and the FRTB
Under international bank solvency regulations established by the Basel Committee on Banking Supervision — specifically the Fundamental Review of the Trading Book (FRTB) — commercial banking institutions must maintain Tier 1 regulatory capital reserves determined by standardized and internal risk model metrics. FRTB transitions regulatory market risk standards from 99% 10-day Value at Risk to 97.5% Expected Shortfall (ES) across multiple liquidity horizons (10, 20, 40, 60, and 120 days) to better protect banking solvency during systemic liquidity shocks.
Backtesting VaR Models: Kupiec's Proportion of Failures Test
Risk management divisions validate internal VaR models using empirical backtesting. Under Kupiec's POF likelihood-ratio test, if a 95% 1-day VaR model records significantly more than 5 exceptions (days where actual loss exceeded predicted VaR) across 100 trading days, the model is statistically rejected for underestimating market volatility, triggering regulatory supervisory capital surcharges.
Stress Testing and Historical Crisis Scenario Analysis
Because statistical VaR models rely on stationary historical market windows, bank risk committees augment VaR with deterministic crisis stress testing. Risk engines revalue trading books against historical systemic shocks: the 1987 Black Monday crash (-22.6% in 1 day), the 2008 Lehman Brothers liquidity freeze, and the March 2020 COVID-19 pandemic market volatility spike, ensuring capital adequacy under extreme market dislocations.
Marginal VaR and Component Risk Allocation
Institutional portfolio managers calculate Component Value at Risk (CVaR) to decompose total portfolio risk across individual asset positions, identifying specific trades that contribute disproportionate volatility to total firm capital exposure.
Incremental VaR in Portfolio Optimization
Incremental VaR (IVaR) quantifies the exact change in total portfolio risk resulting from adding or removing a specific prospective trade position from the existing portfolio.