Value at Risk (VaR) Calculator

Frequently Asked Questions

What does VaR actually measure?

The maximum expected loss over a given horizon at a given confidence level. A 1-day 95% VaR of $10,000 means there is a 5% chance you lose more than $10,000 tomorrow. It does NOT cap the worst case.

What are common VaR confidence levels?

Banks typically use 99% one-day VaR for market risk capital. Asset managers more often quote 95% one-month VaR. The Basel framework also requires Expected Shortfall (the average loss beyond VaR), which captures tail risk better.

What are the limitations of VaR?

It says nothing about losses beyond the threshold. Historical VaR underestimates risk in calm periods (2007). Parametric VaR assumes normal distributions, which understates fat tails. Use Expected Shortfall (CVaR) as a complement.

How does Expected Shortfall differ?

Expected Shortfall (also called CVaR) is the average of all losses worse than the VaR threshold. It captures tail-risk magnitude. Regulators have shifted toward ES because VaR is "blind" to how bad the tail can be.

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This calculator provides estimates for educational purposes only and is not investment advice. Past performance does not guarantee future results. Consult with a qualified financial advisor before making investment decisions. All investments carry risk, including potential loss of principal.

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How This Calculator Works

You enter a portfolio value, its annualized mean return and standard deviation (volatility), a confidence level, and a horizon in trading days. The tool uses the parametric (variance-covariance) method, which assumes returns are normally distributed. It scales the annual mean and volatility down to your horizon, then uses the one-tailed normal critical value (z) for your confidence level to find the loss threshold. The result, Value at Risk (VaR), is the loss you should not exceed except in the small tail of bad outcomes. It also computes Expected Shortfall (CVaR) - the average loss when that threshold is breached - and the worst-case portfolio value at the chosen confidence.

Formula and Z-Scores

With T = days ÷ 252, the horizon mean μ_T = μ×T and horizon volatility σ_T = σ×√T (the square-root-of-time rule). VaR as a return = z×σ_T − μ_T, and in dollars = VaR×V. Expected Shortfall = σ_T×φ(z) ÷ (1 − α) − μ_T, where φ is the normal density and α the confidence. Critical values: 90% z = 1.282, 95% z = 1.645, 97.5% z = 1.960, 99% z = 2.326, 99.5% z = 2.576.

Worked Example

A $1,000,000 portfolio with 8% mean return, 15% volatility, 95% confidence, 1-day horizon. T = 1 ÷ 252 ≈ 0.004; σ_T = 15% × √0.004 ≈ 0.945%, μ_T ≈ 0.032%. VaR return = 1.645×0.945% − 0.032% ≈ 1.52%, so 1-day 95% VaR ≈ $15,200. In plain terms, there is about a 5% chance of losing more than $15,200 in a single day - and if that tail hits, the average loss (CVaR) is larger, around $19,000.

Common Mistakes

Reading VaR as a maximum possible loss - it is a threshold the loss exceeds with the stated tail probability; CVaR describes how bad it gets beyond it.

Entering daily figures into fields that expect annualized mean and volatility, which corrupts the time-scaling.

Trusting the normal-distribution assumption in a crisis; real returns have fat tails, so VaR understates true risk.

Applying the square-root-of-time rule over long horizons, where it breaks down if returns are serially correlated.

Tips & FAQ

The model assumes independent, normally distributed returns, which held poorly in 2008 and March 2020 when correlations and volatility spiked together. Expected Shortfall is always larger than VaR and is the measure Basel III requires for trading-book capital because it accounts for the severity of tail losses, not just their frequency. For portfolios with options or other non-linear payoffs, parametric VaR is unreliable - Monte Carlo or historical simulation is more appropriate. VaR is also backward-looking, resting on historical volatility. Educational only, not investment advice.

Value at Risk (VaR) Calculator

Frequently Asked Questions

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