Value at Risk (VaR): A 5-Minute Guide for Investors

Value at Risk (VaR) is a single number that summarizes the worst expected loss over a given horizon at a given confidence level. "The 1-day 95% VaR of my portfolio is $10,000" means: "On 95% of days, I expect my portfolio not to lose more than $10,000." It is the most widely-used risk metric in institutional finance, and it is also one of the most widely-misunderstood. This guide explains what it measures, how it is computed, where it breaks, and what to use instead.

What VaR actually says

A 1-day 95% VaR of $10,000 means: on 5% of days (one in twenty), your loss is expected to exceed $10,000. It says nothing about how much you might lose on those bad days. VaR is a threshold; it is not a worst case. The most common mistake in interpreting VaR is treating it as a maximum possible loss, it is not. On a day where the VaR threshold is breached, you might lose $11,000 or you might lose $100,000. VaR is silent on the magnitude of breaches.

This single property is the source of most VaR controversy. Nassim Taleb and others have argued that VaR is dangerous precisely because it gives users a false sense of bounded loss. The 2008 financial crisis is often cited as an example: banks reported VaR numbers that were technically accurate on a daily basis but completely failed to capture the tail risk that ultimately materialized.

Three ways to compute VaR

There are three standard methods for computing VaR, each with different strengths and weaknesses.

1. Historical VaR

Take the last N days of portfolio returns (typically 250-500 days). Sort them. The 95% VaR is the 5th percentile of that sorted list. If the 5th percentile is -1.8%, the 95% VaR is 1.8% of portfolio value.

Pros: makes no assumptions about the return distribution. Easy to understand and explain.

Cons: depends entirely on the historical window. A window that does not include a crisis will systematically underestimate VaR. A window that includes a recent crisis will overestimate it for years afterward.

2. Parametric VaR

Assume returns are normally distributed with mean μ and standard deviation σ. The 95% VaR is approximately 1.645σ; the 99% VaR is approximately 2.326σ. Parametric VaR is the fastest to compute and the easiest to extend to multi-asset portfolios using a covariance matrix.

Pros: fast, scalable, analytically tractable.

Cons: assumes normality, which is empirically false for almost every financial asset. Parametric VaR systematically underestimates the probability of extreme losses, which is the case where you most need accurate numbers. See our Monte Carlo article for an explanation of why normality fails.

3. Monte Carlo VaR

Simulate 10,000 paths of portfolio returns using a chosen model (t-distributed GBM with GARCH volatility, for example). The 95% VaR is the 5th percentile of the simulated ending values. ARIA computes Monte Carlo VaR for every portfolio analysis.

Pros: can use realistic return distributions (fat tails, autocorrelation, volatility clustering). Handles non-linear instruments (options, structured products) cleanly.

Cons: computationally expensive. Depends on the model, garbage in, garbage out.

95% vs 99% confidence: the trade-off

Higher confidence levels (99%, 99.9%) measure deeper tails. The trade-off is statistical: estimating the 95% VaR from 250 days of data uses 12-13 observations from the bad tail; estimating the 99% VaR uses 2-3 observations; estimating the 99.9% VaR uses essentially zero. The deeper the tail, the noisier the estimate.

Banks under Basel III regulation are required to compute 99% 10-day VaR. This is a deep-tail measure on a long horizon. The estimation noise is significant; banks typically use multi-year windows and bootstrapping to stabilize the estimates.

For retail and pro investor use, 95% 1-day or 95% 10-day VaR is the sweet spot. The estimate is stable enough to be meaningful, and the horizon is short enough to be actionable.

CVaR (Expected Shortfall): the better metric

Conditional VaR (CVaR), also called Expected Shortfall (ES), is the average loss in the worst (1 − α) of cases. The 95% CVaR is the average loss on the days where loss exceeds 95% VaR. Where VaR says "5% of days, loss exceeds $10,000," CVaR says "and on those days, the average loss is $15,000."

CVaR is strictly more informative than VaR. It tells you not just where the bad tail starts but how bad it gets on average. For fat-tailed distributions, CVaR can be 50-100% higher than VaR at the same confidence level. For thin-tailed (normal) distributions, the gap is much smaller (about 25% higher).

CVaR is also a "coherent risk measure", a technical property meaning it behaves well under portfolio aggregation. VaR famously violates this property: adding two assets can produce a portfolio VaR higher than the sum of the individual VaRs, which is paradoxical. CVaR does not have this problem.

Basel III is gradually shifting bank capital requirements from VaR to CVaR for exactly these reasons. For retail investors evaluating portfolios, CVaR is the better default. ARIA shows both.

A worked example

Suppose your portfolio is worth $100,000 and consists of 60% S&P 500 ETF, 40% intermediate Treasury ETF. Annualized portfolio volatility: roughly 9%. Daily volatility: about 0.57%.

• Parametric 95% 1-day VaR ≈ 1.645 × 0.57% × $100,000 = $938. That is, on 5% of days, you expect to lose more than $938.
• Historical 95% 1-day VaR (computed over the last 252 days) ≈ $850 in a calm year, $1,400 in a year that includes a sell-off.
• Monte Carlo 95% 1-day VaR with t-distributed shocks (ν=5) ≈ $1,050. Higher than parametric because fat tails matter.
• 95% 1-day CVaR (Monte Carlo) ≈ $1,750. The average loss on the worst 5% of days is $1,750, well above the $938 parametric VaR.

Notice that the parametric VaR ($938) understates the actual tail risk by almost half compared to the Monte Carlo CVaR ($1,750). For a small portfolio this is a $800 difference and easy to dismiss. For a $1B institutional book the same proportions become an $8M difference, which is the kind of thing that ends careers when a black swan day arrives.

Common VaR misuses

• Treating VaR as a maximum loss. It is not. It is a threshold, and beyond the threshold the loss can be much larger.
• Using parametric VaR for fat-tailed assets. Most equity and all crypto portfolios have fat tails. Parametric VaR systematically underestimates risk.
• Comparing VaR across portfolios with different liquidity. A 1-day VaR for a portfolio of microcap stocks is meaningless because you cannot actually trade out of those positions in a day.
• Reporting VaR without horizon. "VaR is $10,000" without specifying 1-day, 10-day, or 1-month is uninterpretable.
• Aggregating VaRs additively across asset classes. VaR is not subadditive, the portfolio VaR is not the sum of component VaRs in general. Use a model that captures correlations.

Conclusion

VaR is useful as a starting point for risk discussion but should never be the only risk metric you look at. The 95% confidence threshold is more stable than 99% for typical retail data sizes. Monte Carlo VaR with fat-tailed shocks is the most realistic. CVaR is the more honest cousin and should be reported alongside VaR.

ARIA computes historical, parametric, and Monte Carlo VaR plus CVaR for every analysis. Start free to see VaR on individual positions, or upgrade to Premium for portfolio-level risk decomposition.