A one-day 95% VaR of $20,000 means that on 19 days out of 20 losses should be smaller than $20,000. VaR says nothing about how bad the worst days can be – real returns have fatter tails than the normal distribution assumes.
How to use the Value at Risk Calculator
- Portfolio value
- Annual standard deviation (volatility)
- Expected annual return
- Time horizon
- Confidence level
Results update as you type, and every field accepts the units shown in its menu.
How it works
Enter the portfolio value, annual volatility, expected annual return, the time horizon in trading days and the confidence level.
Tips
- Use the nominal annual rate and pick the compounding frequency your bank or broker states.
- Small differences in return or fees compound into large differences over decades.
- Run the calculation with a cautious, a central and an optimistic return to see the range of outcomes.
- Past returns do not guarantee future returns – nothing here is investment advice.
Common mistakes to avoid
- Comparing an APR with an APY or effective rate.
- Ignoring inflation, taxes and fees when judging a real return.
- Entering a percentage as a decimal (5 instead of 0.05 is correct here).
Inputs explained
| Field | What to enter |
|---|---|
| Portfolio value | Amount in your currency |
| Annual standard deviation (volatility) | In % |
| Expected annual return | In % |
| Time horizon | In trading days |
| Confidence level | Choose one: 90%, 95%, 97.5%, 99% … |
What each result means
- Value at risk = max([Portfolio value]×([Confidence level]×[Annual standard deviation (volatility)]÷100×sqrt([Time horizon]÷252) – [Expected annual return]÷100×[Time horizon]÷252), 0)
- VaR as a share of the portfolio = [Value at risk]÷[Portfolio value]×100
- 10-day VaR at the same confidence = max([Portfolio value]×([Confidence level]×[Annual standard deviation (volatility)]÷100×sqrt(10÷252) – [Expected annual return]÷100×10÷252), 0)
Example values
How the main result changes when Portfolio value changes and everything else stays at the example values above:
| Portfolio value | Value at risk |
|---|---|
| 500,000 | 10,203.8 |
| 750,000 | 15,305.69 |
| 1,000,000 | 20,407.59 |
| 1,250,000 | 25,509.49 |
| 1,500,000 | 30,611.39 |
| 2,000,000 | 40,815.18 |
Formula
VaR = portfolio value × (Z × σ × √(days ÷ 252) − μ × days ÷ 252)Z = 1.645 (95%), 2.326 (99%)Worked example
Inputs — Portfolio value: $1,000,000; Annual standard deviation (volatility): 20 %; Expected annual return: 8 %; Time horizon: 1 trading days; Confidence level: 95%.
Results — Value at risk = $20,407.59; VaR as a share of the portfolio = 2.04 %; 10-day VaR at the same confidence = $62,363.77.
Frequently asked questions
What does VaR mean?
The loss level that should not be exceeded with a given confidence over a period.
How do I scale one-day VaR?
Multiply by the square root of the number of days (ignoring drift).
What are VaR's limitations?
It assumes normal returns and says nothing about losses beyond the threshold.
What formula does the Value at Risk Calculator use?
VaR = portfolio value × (Z × σ × √(days ÷ 252) − μ × days ÷ 252).