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The maximum loss expected at a given confidence level. The regulator's favorite, despite its flaws.
Value at Risk (VaR) is the maximum loss expected over a given time horizon at a given confidence level, under normal market conditions. A 1-day 95% VaR of −$3,000 means there is a 95% chance daily losses will be no worse than $3,000 (and a 5% chance they will be worse). VaR is the dominant regulatory risk measure but has known weaknesses.
P(Loss > VaR_α) = 1 − αP(Loss > VaRα) = 1 − αVaR is the threshold loss such that the probability of exceeding it is 1 − α. Computed via historical simulation, parametric (Gaussian), or Monte Carlo methods.
VaR is widely criticized for two reasons. First, it does not tell you how bad the bad days are — only their threshold. Two portfolios with identical VaR can have very different Expected Shortfall (CVaR) in the tail. Second, VaR is not "subadditive" — combining two portfolios can in theory increase total VaR, which is mathematically incoherent. Most modern risk frameworks (Basel III for banks) prefer CVaR.
Your portfolio's daily returns over the past 1000 days, sorted from worst to best, have the 50th worst at −2.3%.
Daily 95% VaR (historical method) = −2.3%. With a $100k portfolio, that translates to −$2,300.
Meaning: 5% of days (50 of 1000) had losses worse than −2.3%, but we cannot tell from VaR alone how much worse.
VaR is asset-class-dependent. Daily 95% VaR for the S&P 500 is roughly −1.5% to −2%; for crypto it can exceed −5%; for cash it is essentially 0.
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Open the Value at Risk Calculator →CVaR (Conditional Value at Risk) · Expected Shortfall · Kurtosis · CDaR (Conditional Drawdown at Risk) · Standard Deviation
95% is standard for daily VaR. 99% for stress scenarios. 99.9% for tail-event modeling. Lower confidence (90%) is rarely used in practice.
Three methods: historical (sort actual returns), parametric (assume normal distribution), or Monte Carlo. Foliolytic uses historical by default and provides parametric as comparison.
VaR does not tell you how bad the tail is. CVaR (Expected Shortfall) averages losses beyond VaR — capturing severity. Basel III favors CVaR.
Yes — at 95%, 99%, and 99.9% confidence in the tail risk section.
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