Value at Risk (VaR) & CVaR Calculator

VaR at confidence level c is a dollar loss threshold: over the chosen horizon, there is a (1−c) chance the portfolio loses more than the VaR figure. A 95% one-day VaR of $10,000 means a loss bigger than $10,000 is expected on roughly 5% of days, based on the return series or distributional assumption used to compute it. VaR says nothing about how much worse that 5% of outcomes could get — that is what CVaR is for.

CVaR is the average loss in exactly the scenarios where VaR is already breached — the mean of the tail beyond the VaR threshold, not just the threshold itself. CVaR is always at least as large as VaR at the same confidence level. Two return series can share an identical VaR while having very different CVaR, if one has a hard cutoff past the threshold and the other has a long, thin tail of much larger losses — CVaR is what distinguishes them, and it's the metric Basel III capital rules moved toward for exactly this reason.

Parametric VaR assumes returns are normally distributed and derives VaR from just the mean and standard deviation of the series in closed form. Historical VaR makes no distributional assumption at all — it reads the actual empirical quantile out of the returns you pasted. Real return series are usually fatter-tailed than a normal distribution (more frequent large moves than a bell curve predicts), so historical VaR often comes out larger than parametric VaR. When it does, that gap is the finding: it means the parametric number is understating real tail risk, and the historical estimate — despite being noisier at small sample sizes — is the more trustworthy one for this data.

A 99% VaR is, by definition, about the worst ~1% of outcomes. With 50 observations, that is half of one data point — the calculator is extrapolating a tail estimate from essentially the single worst return in your sample. This calculator surfaces the expected number of tail observations (n × (1−c)) directly and flags it explicitly when it drops below 1, rather than presenting a falsely precise percentile. More data — or a lower confidence level — narrows this.

The Sharpe/Sortino/Calmar calculator (risk-adjusted-return) measures realized, backward-looking performance per unit of risk already taken. This calculator instead asks a forward-looking question: given this return history, how large a loss should the portfolio be prepared for over the next period, at a stated confidence level? Both read the same kind of input — a pasted return series — but answer different questions.

Parametric VaR/CVaR assume returns are i.i.d. and normally distributed — real markets exhibit volatility clustering, fat tails, and skew that this understates, which is exactly why the historical method is shown alongside it. Historical VaR/CVaR assume the future resembles the exact sample pasted in, with no adjustment for regime change, and are estimated from very few points at high confidence levels or small samples. Neither method accounts for intra-horizon rebalancing, changing position sizes, or tail correlation across a multi-asset book beyond what's already embedded in a single return series. Treat the output as a risk-communication figure, not a guarantee of maximum loss.