Value at Risk (VaR) Calculator (Parametric, With Expected Shortfall)
The loss a portfolio is not expected to exceed over a few trading days at a chosen confidence level, and the average loss in the cases beyond it, assuming normal returns.
Results
The dashed line marks the value you entered.
What this tool does
Parametric VaR scales the annual volatility to the horizon with the square-root-of-time rule (using 252 trading days a year) and multiplies by the normal quantile: 1.645 standard deviations for 95 %, 2.326 for 99 %. It answers "how much could I lose on a bad day that happens 1 time in 20 or 100", not "what is the worst that can happen". Real returns have fatter tails than the normal curve, so actual extreme losses are usually larger; expected shortfall, the average loss once VaR is breached, is the more cautious measure. This is a risk illustration, not a forecast or a recommendation.
Formula
VaR = V × (z × σ√(t ÷ 252) − μ t ÷ 252) · ES = V × (σ√(t ÷ 252) × φ(z) ÷ (1 − c) − μ t ÷ 252)
Variables
| Symbol | Meaning | Unit |
|---|---|---|
v | Value of the portfolio or position | — |
mu | Expected return per year | % |
sg | Volatility per year (standard deviation of returns) | % |
dd | Horizon in trading days | d |
cl | Confidence level | — |
VR | Value at Risk (loss not expected to be exceeded) | — |
ES | Expected shortfall (average loss in the worst cases) | — |
VP | VaR as a share of the value | % |
SH | Volatility over the horizon | % |
Worked example
- Value of the portfolio or position100,000
- Expected return per year0 %
- Volatility per year (standard deviation of returns)20 %
- Horizon in trading days10 d
- Confidence level99
- Value at Risk (loss not expected to be exceeded)9268
- Expected shortfall (average loss in the worst cases)10,618
- VaR as a share of the value9.27 %
- Volatility over the horizon3.98 %
Limitations
- This is an informational calculator, not personalised financial advice. Rates, fees, taxes and contract conditions vary between institutions and countries.
- The result is an estimate based only on the values you type. Real situations often include factors this calculator does not know about.