Tail risk
VaR and CVaR calculator the loss in the tail
Empirical value at risk and conditional value at risk from the closes you paste. VaR is the loss you only breach on the bad days. CVaR is the average loss on those days.
BTC
95% VaR 2.8%
On the days past the 95% line, the average loss was 3.1%. The gap above VaR is 0.3%.
- 95% VaR
- 2.8%
- 95% CVaR
- 3.1%
- Tail gap
- 0.3%
- Closes
- 90
Empirical one-period loss
Average loss beyond VaR
CVaR minus VaR
Sample behind the quantile
- Each row is daily, 365 periods a year. Annualized figures use 365 periods.
- 90 closes in the series. Computed by Thrive's portfolio engine. Rounded to the digit shown.
- Empirical estimator. Not a normal formula, and not a multi-day regulatory VaR.
VaR is a line. CVaR is the hole past it.
A 95% one-period VaR of 4% means about one period in twenty lost more than 4%. It does not say whether those losses were 4.1% or 20%.
CVaR, also called expected shortfall, averages the losses beyond that line. For crypto, the gap between VaR and CVaR is the number that matters. The tail is fatter than a bell curve.
How this page runs it
Both figures are empirical, from the portfolio values you send, not from a normal formula. You pick 90%, 95%, or 99%. The engine returns the loss as a fraction of value.
This is a historical one-period loss, not a 10-day regulatory VaR. Scale it yourself if you need a longer horizon, and do not pretend the square-root-of-time rule holds in a crash.
How to run it
- Paste closes.
- Pick a confidence level. 95% is the usual desk default.
- Read VaR and CVaR as losses, so both print as positive percents.
- If CVaR is far above VaR, size off CVaR.
FAQ
People also ask
VaR is a quantile of the loss distribution. CVaR is the mean loss on the days that breach that quantile. CVaR is always at least as large as VaR.
Crypto returns are skewed and fat-tailed. A normal VaR understates the days that actually showed up in the series. The empirical estimator uses those days.
It is a fraction of portfolio value over one period. Multiply by the account you care about. A 5% CVaR on a $20,000 book is $1,000 on the average bad day at that confidence.
At 95%, a 90-close window has only a handful of tail days. Treat the number as a description of this window, not a law. Longer series make the tail less jumpy.
Related
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Peak to trough, the ulcer index, the pain index, and the worst drawdowns in the window. One close series, four ways the path hurt.
Monte Carlo portfolio simulator
The engine draws multivariate normal returns from your sample, then Thrive compounds your weights into a fan: 5th, 50th, and 95th percentile wealth.
Volatility calculator
Close-to-close realized volatility from the closes you paste, de-meaned, then annualized with the calendar you pick. One asset or a whole list.
Position size calculator
Vol and drawdown tell you the path. Size tells you what you can hold.
Trading journal
The ratio on a pasted series is a lab result. The journal is the book you actually traded.
Bitcoin volatility
The live 90-close vol print for the BTC sample.
Size the tail you can survive.
VaR on a chart is a statistic. VaR on your account is a stop you either have or do not. Thrive keeps the size next to the fills.