Value at Risk (VaR) Calculator

What is Value at Risk? Value at Risk answers a precise probabilistic question: "What is the maximum loss my portfolio can sustain over the next N days, such that this loss is not exceeded X% of the time?" For example, a 1-day 95% VaR of $50,000 means that on any given day, there is only a 5% chance the portfolio will lose more than $50,000. This makes VaR an intuitive loss threshold rather than an average or worst-case figure, which is why it has become the standard language of risk across banks, hedge funds, and asset managers globally.

The Parametric (Variance-Covariance) Method: This calculator uses the parametric VaR method, also called the variance-covariance approach. It assumes portfolio returns follow a normal distribution, which allows risk to be fully characterised by two parameters: the mean (μ) and standard deviation (σ). The formula is VaR = (μ·t − z_α · σ · √t) · P, where P is the portfolio value, μ is the expected daily return expressed as a decimal, σ is the daily volatility (standard deviation of daily returns), t is the holding period in days, z_α is the critical z-score for the chosen confidence level (1.645 for 95%, 2.326 for 99%), and the holding period scaling uses the square-root-of-time rule — a standard approximation derived from the random walk assumption. The result is multiplied by negative one to express VaR as a positive loss figure, consistent with industry convention.

Practical Context and Regulatory Use: Under the Basel II and Basel III accords, banks are required to compute a 10-day, 99% VaR daily and hold regulatory capital as a multiple of this figure. The choice of confidence level matters greatly: a 99% VaR is more conservative than a 95% VaR and captures more extreme scenarios. In practice, risk managers often compute VaR at multiple confidence levels and time horizons simultaneously. VaR is also used for position limits, stop-loss calibration, margin requirements on derivatives, and performance attribution. When combined with Expected Shortfall (CVaR), it provides a more complete picture of tail risk that goes beyond the VaR threshold.

Normality assumption: The parametric VaR method assumes returns are normally distributed. In reality, financial returns exhibit fat tails (leptokurtosis) and negative skewness, meaning extreme losses occur more frequently than the normal distribution predicts. This was starkly illustrated during the 2008 financial crisis when observed losses far exceeded parametric VaR estimates. For portfolios with significant exposure to options or illiquid assets, historical simulation or Monte Carlo VaR are more appropriate.

Square-root-of-time scaling: Scaling daily VaR to a multi-day horizon using √t assumes returns are independently and identically distributed (i.i.d.), which breaks down during market stress when autocorrelation and volatility clustering are present. For horizons beyond a few days, this approximation introduces meaningful error.

VaR does not measure tail losses: VaR only tells you the threshold loss at a confidence level — it says nothing about how bad losses can be beyond that threshold. A 99% VaR of $100,000 is consistent with losses of $101,000 or $10,000,000 in the remaining 1% of scenarios. Expected Shortfall (ES or CVaR), which averages losses beyond the VaR threshold, is a more complete tail risk measure and is now preferred by the Basel Committee under FRTB.

Single-asset approximation: This calculator computes VaR for a single portfolio treated as one asset with aggregate volatility. For multi-asset portfolios, full VaR requires a covariance matrix across all positions. Diversification benefits are captured only implicitly through the aggregate portfolio volatility input.