Value at Risk (VaR) is finance’s most-used and most-criticized risk number. It compresses the question “how much could this portfolio lose tomorrow?” into a single dollar figure tied to a confidence level. Every major bank reports it, every Basel and SEC rule references it, and every textbook teaches it – which makes its blind spot (it cannot tell you anything about losses beyond the threshold) one of the most important things to understand about modern risk management.
TL;DR: The 1-day 99% VaR of a $10 million portfolio is the loss level that should be exceeded only about 1 trading day in 100. If the number is $230,000, you are saying: “In a normal day, our worst credible loss is around $230k; on the 1% of days that are not normal, we have no idea how bad it gets.” That last clause is why regulators have shifted toward Expected Shortfall, which averages the size of losses beyond the VaR cutoff.
The formal definition
For a portfolio with random loss L over a chosen horizon, the Value at Risk at confidence level α (for example 95% or 99%) is the smallest threshold the loss is unlikely to exceed:
VaRα(L) = inf { x : P(L > x) ≤ 1 − α }
Plain English: pick a horizon (1 day, 10 days), pick a confidence level (95%, 99%, 99.5%), and find the loss number such that the probability of doing worse is only (1 − α). The three pieces of any VaR quote are therefore horizon, confidence, and the resulting dollar (or percentage) loss. A VaR with no horizon or no confidence attached is meaningless.
Three things VaR does not tell you, no matter how it is computed:
- How bad the bad days are. VaR is the threshold of the tail, not the average of the tail.
- Anything about the diversification. VaR is not subadditive, which means the VaR of a combined portfolio can be larger than the sum of the parts’ VaRs. That violates a basic property risk theorists want from a coherent risk measure.
- Anything about regimes. A VaR calibrated to calm markets will systematically understate risk going into a crisis.
The three ways to compute VaR
Banks and funds use one (or all three) of these methods. The BIS’s overview of the regulatory framework groups VaR techniques into the same three families, and the McKinsey-Risk industry survey cited in academic reviews of VaR practice has long shown historical simulation dominating large banks’ usage with Monte Carlo a distant second.
| Method | How it works | Strengths | Weaknesses |
|---|---|---|---|
| Historical simulation | Re-price today’s portfolio under the last N days of observed market moves. Sort the resulting P&Ls; the (1 − α) quantile is the VaR. | No distributional assumptions. Captures real, fat-tailed history. Easy to explain to non-quants. | Past 1-3 years rarely contain the worst-case move. Sensitive to the window chosen. |
| Variance-covariance (parametric) | Assume returns are normally distributed. VaR = zα × σ × portfolio value, where zα is the standard-normal quantile. | Closed-form and fast. Works as a sanity check. | Normality assumption fails in real markets – actual return distributions are fat-tailed and skewed. Systematically understates extreme losses. |
| Monte Carlo simulation | Draw thousands of synthetic market-move paths from a calibrated multivariate distribution; re-price the portfolio under each; take the quantile of simulated losses. | Handles non-linear positions (options, convex bonds) and arbitrary distributions. The only practical option for complex derivative books. | Expensive. Result is only as good as the assumed joint distribution. Garbage in, garbage out. |
The standard analogy: historical simulation says “yesterday’s worst day is roughly our worst day.” Parametric VaR says “if returns were a clean bell curve, here is the cutoff.” Monte Carlo says “let us write down a richer model and roll the dice ten million times.” Each is a different bet on which lie about the world is least harmful.
A worked example with real numbers
Suppose you hold a $10 million S&P 500 ETF position and want a 1-day 99% VaR. Use the parametric method as the textbook starting point. The S&P 500’s daily return standard deviation in a typical year sits near 1.0% (it spent most of 2024-2026 between 0.7% and 1.2%; in crisis weeks it spiked above 4%). The standard normal quantile at 99% is z0.99 ≈ 2.326.
1-day 99% VaR ≈ 2.326 × 0.010 × $10,000,000 = $232,600
Drop the confidence to 95% and z falls to 1.645, so the VaR drops to about $164,500. Extend the horizon to 10 trading days under the square-root-of-time rule used in Basel’s traffic-light backtest, and the 99% number grows by √10 to roughly $735,500. Already you can see two of the dangers of parametric VaR: the number is highly sensitive to the σ you plug in (real volatility moves a lot), and the square-root-of-time scaling assumes returns are independent across days, which they are not when markets trend or crash.
Real history overflows the parametric numbers
The parametric VaR above implies the S&P 500 should drop more than 2.33 standard deviations only about 1 day in 100. Reality has many days well outside that boundary:
| Date | Event | S&P 500 1-day return | Std devs from zero (σ = 1.0%) |
|---|---|---|---|
| Oct 19, 1987 | Black Monday | −20.5% | ~20σ |
| Oct 15, 2008 | Great Financial Crisis | −9.0% | ~9σ |
| Mar 16, 2020 | COVID shock | −12.0% | ~12σ |
| Aug 8, 2011 | US debt downgrade | −6.7% | ~7σ |
A 20-sigma event under a normal distribution should not occur once in the age of the universe. The S&P 500 has produced several of them inside a single lifetime. This is the well-known fat-tail problem, and it is why a parametric 99% VaR can pass 99 days out of 100 and still be wrong about the loss that actually matters.
Why VaR cannot tell you about the tail
Set aside method choice for a moment. VaR has a structural blind spot baked into its definition. By construction it is the threshold of the tail, not the depth. Two portfolios can have identical 99% VaRs and very different consequences if the worst 1% of days actually arrives.
The famous David Einhorn quote cited in the Wikipedia article on VaR puts it bluntly: VaR “focused on the manageable risks near the center of the distribution and ignored the tails.” That is not a complaint about a particular calculation method – it is a complaint about the metric itself. Even a perfect 99% VaR by construction says nothing about the size of the worst 1%.
How regulators responded: from VaR to Expected Shortfall
The 2008 crisis embarrassed the parametric, calm-market-calibrated VaR numbers banks had been reporting. The Basel Committee’s 2019 Minimum Capital Requirements for Market Risk (the final standard from the Fundamental Review of the Trading Book, or FRTB) replaced the old VaR-based internal-models approach with an Expected-Shortfall-based one and added a stressed calibration so capital charges no longer collapse during a quiet year. The Fed and other supervisors followed with national implementations. The headline change for risk officers: the IMA capital charge is now anchored to the average of the bad tail, not its threshold.
Common mistakes when reading or quoting VaR
- Quoting it without horizon or confidence. “Our VaR is $5M” is meaningless. “Our 1-day 99% VaR is $5M” is a claim.
- Treating the quantile as the worst case. A 99% VaR is exceeded on about 2-3 trading days a year. That is not the worst case; it is the merely-bad case.
- Trusting parametric numbers for option-heavy books. Options have non-linear, asymmetric payoffs. A normal-distribution VaR badly misrepresents the loss distribution of even a simple short-put position.
- Forgetting backtesting. Basel’s traffic-light system (green / yellow / red zones) is a count of exceptions per 250 trading days. A green model can still understate severity – which is partly why FRTB moved past it.
- Mistaking VaR for diversification math. VaR is not subadditive. Combining two desks can produce a VaR larger than the sum of the individual VaRs.
Where this leaves a working investor
VaR remains the dominant industry shorthand because it is simple to quote and easy to map to a capital number. Treat it as a useful summary in normal conditions and a misleading one in tail conditions. If the only number on a fund’s risk page is a VaR, the next questions are: which method, which window, which confidence level, what was the most recent backtest, and what does the Expected Shortfall look like alongside it? Pair VaR with at least one tail-aware measure and one drawdown-aware measure, and the resulting picture is far more honest than the headline number alone.
Related concepts and what to learn next
- Expected Shortfall / CVaR / Conditional VaR – the average loss conditional on being in the tail. Coherent (subadditive). The Basel FRTB metric.
- Stress testing – scenario-based losses (1987, 2008, COVID, hypothetical rates spike). Complements statistical VaR with named, plausible disasters. The Fed’s CCAR/DFAST framework for large banks is the most visible US example.
- Backtesting – count actual exceptions versus expected. Required by regulators; useful in-house for catching model drift.
- Maximum drawdown – the realized worst peak-to-trough loss. See the explainer. A complementary, path-dependent risk number.
- Sharpe ratio – return per unit of volatility. See the explainer. What VaR-aware investors pair with a tail measure.
The short version
Value at Risk turns the question “how much could we lose?” into a one-number answer at a chosen horizon and confidence. Compute it three ways – historical, parametric, or Monte Carlo – knowing each is a different bet on the world. Quote it with horizon and confidence or do not quote it. And remember the structural blind spot: VaR is the threshold of the tail, not its depth. The Basel response to 2008 was to move regulatory capital from VaR to Expected Shortfall, and that move tells you everything about how to use VaR in practice – as a useful summary, never as a guarantee.
Sources & further reading
- BIS BCBS – Minimum capital requirements for market risk (final standard, January 2019). The FRTB document that replaces VaR with Expected Shortfall in the internal models approach.
- Wikipedia – Value at risk. Definition, history of JPMorgan’s RiskMetrics (1994), three calculation families, and the subadditivity counter-example.
- Wikipedia – Expected shortfall. Definition, coherence properties, relationship to VaR.
- Federal Reserve – Stress Tests and Capital Planning. CCAR and DFAST framework for the largest US bank holding companies.
- FRED – S&P 500 (daily). The Federal Reserve Economic Data series used to verify daily closing prices and the realized losses in the historical table.
- Federal Reserve History – Stock Market Crash of 1987. Source for the Black Monday return.
- Artzner, Delbaen, Eber, Heath. Coherent Measures of Risk, Mathematical Finance, 1999. The original paper proving VaR is not coherent and proposing the four axioms a risk measure should satisfy.
- Related on ECMSource: Maximum drawdown, Sharpe ratio, VIX, bond duration, bank capital ratios.
Disclosure: This article was produced with AI assistance and reviewed before publication. It is for informational purposes only and is not investment advice.