VaR is not the maximum loss, because its definition never promises a "maximum." VaR answers the question: "At a given confidence level and time horizon, there is an X% probability your loss will not exceed a certain number." It does not answer: "How much can you lose at most?" It cuts off the entire tail risk beyond that threshold. For crypto portfolios, whose return distributions are clearly heavy-tailed, the part that gets cut off is exactly what needs the most attention.
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What VaR Actually Says
The European Central Bank explained the logic of VaR clearly in an analysis of risk measurement: if a portfolio's one-week VaR is 1.5% of assets at the 95% confidence level, it means "there is a 5% probability that the loss will exceed this number." Notice the wording: exceed. VaR only tells you where the threshold is. It does not tell you how deep the fall will be once you cross that threshold.
There is nothing wrong with the definition itself. The problem is how people interpret it. Treating VaR as the "maximum loss" means misreading "on 95% of days it will not be worse than this" as "under no circumstances will it be worse than this." VaR is not responsible for answering what hides in the remaining 5%.
Crypto Portfolios Make This Flaw Especially Dangerous
Traditional assets, such as major currency pairs or stock indices, deviate from a normal distribution only moderately. Crypto assets are different. A study covering ten major crypto assets from 2014 to 2026 confirmed that crypto returns are "sharply non-Gaussian and heavy-tailed," and it quantified how much Gaussian models underestimate Bitcoin's 99% VaR. Another study using historical simulation gave specific numbers: BTC's one-day VaR at the 1% confidence level was -10.87%, but the expected shortfall at the same confidence level, meaning the average loss when the loss exceeds VaR, was -13.92%. ETH's VaR was -14.92%, while its expected shortfall was -19.81%.
In other words, on the worst 1% of days, BTC lost close to 14% on average, and ETH lost close to 20% on average. You cannot see these numbers in VaR. If you use VaR to size positions or set stop losses, you will systematically underestimate the damage caused by the truly bad days.
The Cut-Off Tail Is Not an Abstract Concept in Crypto Markets
In traditional finance, VaR's tail weakness has been discussed for thirty years. The European Central Bank pointed out that a key limitation of VaR is that it "cannot tell investors how much they will lose when a tail event occurs." Two positions with the same VaR may have completely different risk exposures in the tail. The Basel Committee on Banking Supervision later pushed for expected shortfall to replace or supplement VaR, precisely because expected shortfall is a "coherent risk measure" that satisfies subadditivity, while VaR does not.
This theoretical problem becomes a practical problem for crypto portfolios. Crypto markets are characterized by high volatility, low depth, and event-driven crashes. That means the "1% or 5% beyond VaR" is not a theoretical tail, but a reality that keeps reappearing. Data through 2026 has recorded many single-day drops far exceeding normal VaR estimates. If your portfolio holds multiple highly correlated assets, such as several major coins, diversification looks effective in normal times, but correlations move toward 1 during crashes. The portfolio's actual loss can far exceed the VaR calculated from historical correlations.
What to Look At Instead
If you use VaR for risk management, treat it as a lower-bound style of risk warning, not an upper bound. VaR tells you that "normal fluctuations are roughly in this range," but it has nothing to say about abnormal days.
Expected shortfall, or conditional VaR, is the metric that directly fills this hole. It answers the question: on the days when losses exceed VaR, how much will you lose on average? In the data cited above, BTC's expected shortfall was about 3 percentage points deeper than its VaR, and ETH's was about 5 percentage points deeper. That gap is the part VaR cuts off.
For a crypto portfolio, a practical approach is to look at both numbers at the same time: use VaR to understand the normal fluctuation range, and use expected shortfall to understand the size of tail risk. If expected shortfall is much larger than VaR, the portfolio's loss distribution has a long left tail, and position sizes should be considered based on expected shortfall, not VaR. Another useful supplement is stress testing: ignore probabilities and directly ask, "If the market drops 30% tomorrow, what happens to the portfolio?" No matter how high the VaR confidence level is, such as 99%, it cannot cover a "once in a hundred years" shock. In crypto market history, "once in a hundred years" events appear far more often than in traditional finance.
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