Value at Risk Calculator

Parametric and historical loss estimates

Value at Risk Calculator

Estimate portfolio Value at Risk (VaR) and Expected Shortfall (ES/CVaR) from normal-distribution assumptions or an empirical return series. Results are loss thresholds, not guarantees.

Use returns and volatility measured over compatible periods.
Formatting only; no exchange-rate conversion.
A 95% level leaves a 5% modeled loss tail.

Parametric assumptions
Enter 0 to ignore expected return.
Mean scales by h; volatility scales by √h.

Risk estimate

Value at Risk—
Expected Shortfall—
VaR as portfolio %—
Tail probability—

Risk detail

Value at Risk and Expected Shortfall formulas

Value at Risk estimates a loss threshold over a defined horizon and confidence level. Expected Shortfall, also called Conditional VaR, estimates the average loss inside the modeled tail beyond that threshold.

Parametric horizon mean: μh = h × μ
Parametric horizon volatility: σh = √h × σ
Normal VaR rate: max(0, zc × σh − μh)
Normal Expected Shortfall rate: max(0, σh × φ(zc) ÷ (1 − c) − μh)

Here c is the confidence level, zc is its standard-normal quantile and φ is the standard-normal density. Monetary VaR or ES equals the rate multiplied by portfolio value. The historical method sorts observed returns, selects the worst ceiling of (1 − c) × N observations, uses the least-bad return in that tail as the VaR boundary and averages the tail for Expected Shortfall.

Verified parametric example

For a US$100,000 portfolio, 0.05% mean return per period, 1.5% volatility, 95% confidence and a 10-period horizon, the calculator uses a 0.50% horizon mean and 4.7434% horizon volatility. The independently verified VaR is US$7,302.23 and Expected Shortfall is US$9,284.31.

How to use the calculator

  1. Choose parametric normal or historical return-series mode.
  2. Enter a portfolio value and confidence level.
  3. For parametric VaR, use mean and volatility from the same return interval and enter the holding periods.
  4. For historical VaR, paste returns whose interval already matches the risk horizon.
  5. Compare VaR with Expected Shortfall and review the assumptions before using the estimate.

What the result means

A 95% VaR is not the maximum possible loss. It states that the modeled threshold is exceeded in roughly 5% of periods under the selected assumptions or empirical sample. Expected Shortfall describes the average modeled loss in that tail and is therefore normally at least as large as VaR.

Limits and assumptions

  • Parametric mode assumes normally distributed, independent and identically distributed returns with constant mean and volatility. Real returns can have skewness, fat tails, volatility clustering and changing correlations.
  • Square-root-of-time scaling can be misleading across long horizons or stressed markets. Historical mode assumes the selected sample represents future risk and uses a discrete order-statistic convention without interpolation.
  • VaR and Expected Shortfall do not predict the worst possible loss, timing, liquidity costs, gaps, leverage calls, taxes or model error. Losses can exceed both measures.
  • Portfolio value must be greater than zero and no more than 1,000,000,000,000,000. Numeric inputs accept up to six decimals; holding periods are whole numbers from 1 through 10,000.
  • Historical mode accepts 20–10,000 returns from −100% through 1,000%. Returns must use a period as the decimal separator.

Risk warning: VaR is a model-dependent summary, not a capital guarantee or investment recommendation. Stress testing and scenario analysis are still necessary.

Related calculators

Use the Portfolio Variance Calculator to estimate covariance-based volatility, the Maximum Drawdown Calculator for observed peak-to-trough loss, the Risk Parity Calculator for equal risk contributions, and the Sharpe Ratio Calculator for risk-adjusted return.