Value at Risk (VaR) Calculator

Value at Risk (VaR)

Value at Risk is the loss a portfolio will not exceed over a given period, at a specified confidence level, under normal market conditions.

It is not the maximum loss, and the difference matters

VaR is very widely described as a maximum, including by people who should know better, and that description is wrong in a way that has cost real money. A 95% one-day VaR of $24,675 does not say you cannot lose more than $24,675. It says you will lose more than that on roughly one day in twenty. It is a threshold, not a ceiling.

VaR is completely silent about what happens on those days. Two portfolios can report the same VaR to the dollar while one loses a little beyond it and the other loses everything. That blind spot is the reason Expected Shortfall exists: it answers “when the bad day does arrive, how bad is it on average?” This calculator reports both, because the second number is the one that tells you whether you survive.

Basel III moved bank capital requirements from VaR to Expected Shortfall in 2016, for exactly this reason.

Parametric VaR Formula:

VaR = Portfolio Value × z × σ_daily × √t

Z-scores by confidence level:

That last column is the part worth staring at. Raising confidence from 95% to 99% makes the VaR number bigger, which feels more conservative, but it also makes the gap between VaR and the average breach smaller. A high-confidence VaR is a rarer event, not a safer one, and it still says nothing about the day it happens.

Example:

• Portfolio: $1,000,000
• Daily volatility: 1.5%
• Confidence: 95%, Holding period: 1 day
• VaR = $1,000,000 × 1.6449 × 0.015 × √1 = $24,674
• Expected Shortfall = $30,938
• Interpretation: on about 13 trading days a year the loss is worse than $24,674, and on those days it averages $30,938

Scaling VaR across time:

VaR scales with the square root of time (for normally distributed returns).

10-day VaR = 1-day VaR × √10

Getting the volatility input right

This field wants a daily standard deviation, and it is where most wrong answers on this page come from. Volatility is usually quoted annualized: an option chain showing 30% means 30% a year, not a day. Feed 30 into a daily field and the answer comes back larger than the portfolio itself.

To convert, divide by the square root of the number of trading days in a year:

Daily volatility = Annual volatility ÷ √252

So 30% annual is 30 ÷ 15.87 = 1.89% daily. For reference, a broad equity index typically runs 0.8% to 1.2% daily in calm conditions and 3% or more in a crisis. A single stock is usually 1.5% to 3%. If your number is above 5%, check it before trusting the result.

Limitations of parametric VaR:

• Assumes normally distributed returns, and real markets have fat tails, so large losses happen more often than the model predicts
• Underestimates risk during stress events (2008, the COVID crash)
• The square-root-of-time scaling assumes each day is independent of the last, which breaks down precisely when markets trend hard
• Historical and Monte Carlo VaR handle fat tails better

That first limitation is worth a number. Under a normal distribution a 5-standard-deviation daily move should turn up about once every 7,000 years. Equity markets deliver them every few decades, and October 1987 was north of 20 standard deviations, which the normal model puts at odds no human vocabulary covers. The model is a useful summary of ordinary weather. It is not a description of storms.

Regulatory use: Banks used 99% confidence, 10-day VaR under Basel II. The 2016 revision (FRTB) replaced it with 97.5% Expected Shortfall, a deliberate move away from a measure that ignores the tail. This calculator uses the parametric (variance-covariance) method.