Value at Risk (VaR)

Risk & Portfolio
Updated Apr 2026 • Has calculator

The maximum dollar loss not expected to be exceeded over a given period at a specified confidence level.

What is Value at Risk?

Value at Risk (VaR) is a statistical measure of the potential loss in value of a portfolio over a defined period, given a specified confidence level. A 1-day 95% VaR of $16,449 means: under normal market conditions, there is a 95% chance that the portfolio will not lose more than $16,449 in a single day (or, equivalently, a 5% chance it will lose that amount or more). This calculator uses the parametric (variance-covariance) method, which assumes returns are normally distributed. It requires only the portfolio value, mean daily return, daily standard deviation, and confidence level. VaR is widely used by banks, hedge funds, and regulators (Basel III) as a risk limit metric, though it has limitations: it underestimates tail risk and does not measure the size of losses beyond the threshold.

Formula

VaR = Portfolio Value × (z_α × σ − μ)

Worked Example

Worked example — Hypothetical $1M Equity Portfolio

1-Day Parametric VaR at 95% Confidence

Step 1  Portfolio value: $1,000,000
Step 2  Daily mean return: 0.0003 (≈ 0.03%/day)
Step 3  Daily standard deviation: 0.0100 (1.00%/day)
Step 4  Confidence: 95% → z₀.₉₅ ≈ 1.6449
Step 5  VaR = $1,000,000 × (1.6449 × 0.0100 − 0.0003)
Step 6  VaR = $1,000,000 × 0.016149 = $16,149
Step 7  → 95% confident the portfolio won't lose more than ~$16,149 in a day

Source: CFA Institute — Risk Management, 2nd ed., Ch. 3 (2023-01-01)

Calculate Value at Risk

Current market value of the portfolio

Average daily return as a decimal (e.g. 0.0003 ≈ 0.03%/day)

Daily standard deviation as a decimal (e.g. 0.01 = 1%/day)

0.95 = 95%, 0.99 = 99%

1-Day VaR

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Not investment advice.

How to Interpret Value at Risk

< 10000
< $10K — low absolute loss exposure for $1M portfolio
10000 – 25000
$10K–$25K — moderate; typical equity market conditions
25000 – 50000
$25K–$50K — elevated; high-volatility period
> 50000
> $50K — severe; consider reducing risk exposure

📚 Advanced Risk — Complete the path

  1. Value at Risk
  2. Max Drawdown
  3. Calmar Ratio
  4. Capture Ratios
  5. Kelly Criterion
Sources
  1. CFA Institute — Risk Management, 2nd ed., Ch. 3
  2. BIS — Basel III: A Global Regulatory Framework
  3. Investopedia — Value at Risk (VaR)