Value at risk (VaR) explained: understanding tail risk in your portfolio
Value at risk (VaR) estimates the minimum loss a portfolio could be expected to experience over a given period at a specified level of confidence. It translates tail risk into a single number that is directly comparable across portfolios and asset classes.
What VaR measures
VaR answers a specific question: what is the minimum loss I should expect to experience in the worst x% of outcomes? At a 95% confidence level, a daily VaR of −2% means that on 95% of trading days the loss will be smaller than 2%—and on 5% of days it will be larger. VaR is not a measure of the average outcome; it is a threshold defining the boundary of the tail.
The metric takes a return series and produces a negative decimal (or zero). A VaR of −0.03 at 95% confidence means a 3% threshold: losses exceeding this are expected to occur on roughly 5% of days. In pfolio, VaR is presented as a 'higher is better' metric, where 'higher' means closer to zero—a VaR of −1% is preferable to −5%.
A critical point: VaR tells you where the tail begins. It does not tell you how bad things get once the threshold is crossed. Two portfolios can have identical VaR while one experiences occasional small losses just beyond the threshold and the other experiences catastrophic losses. For the severity of losses beyond the VaR threshold, expected shortfall is the relevant complement.
The formula
VaRα = μ̄ + z₁₋α · σ
Where:
- μ̄ = annualised mean return
- z₁₋α = quantile of the standard normal distribution at confidence level 1 − α
- σ = annualised volatility
- α = confidence level (e.g., 0.95 for 95%)
pfolio uses the parametric (Gaussian) method. This assumes that returns are normally distributed and uses the mean and standard deviation of the return series to compute the VaR threshold analytically. At a 95% confidence level, the relevant normal distribution quantile is approximately −1.645 standard deviations from the mean. At 99% confidence, it is approximately −2.326.
How to interpret VaR
VaR is most useful as a comparative tool and as a standardised risk communication device. A portfolio with a 95% daily VaR of −1.5% can be compared directly against another with a VaR of −3.2%—the first has materially lower tail risk on this measure.
As a concrete example: a portfolio with an annualised mean return of 8% and annualised volatility of 12% has an annual 95% VaR of approximately 8% + (−1.645 × 12%) = −11.7%. This means that in the worst 5% of annual outcomes, the loss is expected to exceed 11.7%.
VaR becomes less reliable for assets with fat-tailed or skewed return distributions—which includes most real-world financial assets, particularly equities and cryptocurrencies. In such cases, the parametric method systematically underestimates tail losses. This limitation should inform how VaR figures are used and communicated.
Rolling VaR
The scalar VaR summarises the tail risk of the full return history. Rolling VaR computes the same metric over a sliding window, producing a time series that shows how tail risk has evolved. Each point answers the question: what was the VaR over the return series ending on this date?
Rolling 12 M value at risk: S&P-500 vs. ACWI
This view is useful for identifying periods of elevated tail risk. When rolling VaR spikes—becoming more negative—it typically reflects an increase in both mean return volatility and the width of the return distribution. During market stress periods, tail risk tends to rise sharply and persist for some time before normalising.
Rolling VaR is available in pfolio Insights alongside the scalar figure.
Limitations
pfolio's VaR implementation uses the parametric (Gaussian) method, which assumes normally distributed returns. This is a significant limitation for most financial assets. Real return distributions tend to have fatter tails than the normal distribution predicts—extreme events occur more frequently than the model expects. As a result, parametric VaR systematically underestimates tail risk for assets with skewed or fat-tailed returns, including equities, commodities, and cryptocurrencies.
VaR does not describe the size of losses beyond the threshold. Knowing that losses will exceed a given level on 5% of days provides no information about whether those losses will be 0.1% above the threshold or 20% above it. For a measure that addresses this gap, see expected shortfall.
VaR is also sensitive to the confidence level chosen. A 95% VaR and a 99% VaR for the same portfolio can look very different, and the choice of confidence level is often somewhat arbitrary. When comparing VaR figures across sources, always verify that the same confidence level was used.
Value at risk in pfolio
In pfolio, VaR is calculated from the return series derived from the price data. Whether those returns are computed from the close price or the adjusted close price can be configured via advanced settings—a distinction that matters for dividend-paying assets.
VaR and rolling VaR are available in pfolio Insights. pfolio uses the parametric method at a default confidence level of 95%. For a full description of how pfolio calculates this and all other metrics, see the metrics we use.
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