Conditional VaR (95%) — Return

Average of the worst 5% of daily returns on the Return curve (low-to-low). Expected Shortfall — captures tail severity.

Computed from: Equity curve
Scope: Single report
Range: ≤ 0%
Direction: Higher is better

Basis

Computed on the low-to-low Return Series (money-weighted) — measured day-worst-point to day-worst-point, not close-to-close.

Conditional VaR (95%) is the average loss on your worst days — the average of the bottom 5% of daily results. In plain words: on a bad day (the worst 1 in 20), this is how bad it gets on average. It's called conditional because it looks only at the bad days — the average loss given that you're already having one of the worst 1-in-20 days. It's the companion to Value at Risk: VaR is the loss your worst-1-in-20 day at least reaches; CVaR is the average loss once you're past that point. It's a negative number, so a CVaR of −4% reads as "on the worst 1-in-20 days, you lose about 4% on average."

Key takeaways

What it is — the average of your worst 5% of daily returns: take every day worse than the VaR cutoff and average them. A negative percentage — also called Expected Shortfall (ES), Expected Tail Loss (ETL), or Average VaR (AVaR).
Read it as — on a bad day, this is how much you lose on average. Less negative (closer to zero) is better — a milder tail. Higher is better.
Why it matters — it sees the depth of the tail that VaR is blind to. Two accounts with the same −2% VaR can have a tame −2.4% CVaR or a fat-tailed −9% CVaR — and CVaR is the number that tells them apart. After the 2008 crisis exposed VaR's blind spot, the Basel FRTB framework replaced 99% VaR with 97.5% Expected Shortfall as the bank market-risk capital standard, for exactly this reason.
In EquityTruth — the historical average of the worst-5% tail: the mean of every daily return at or below the VaR cutoff (no bell-curve assumed), on the Return, P&L, and TWR curves.

How it's calculated

First find the VaR line — the 5th percentile of your daily returns. Then take every day at or below that line (your worst 5%) and average them. That average is your CVaR. Because it's the mean of everything past the threshold, CVaR is always at least as negative as VaR: CVaR ≤ VaR, always.

CVaR (95%) = average of all days worse than the VaR line

VaR line: the 5th percentile — the loss your worst 5% of days fall below
average: the mean of every daily return at or below that threshold

In this product: EquityTruth uses historical CVaR — the empirical mean of the observed worst-5% days (tail = arr[arr <= p5]; cvar = tail.mean()), not a parametric formula. It makes no bell-curve assumption: it reads the real shape of your worst days rather than assuming a tidy distribution. Computed on the daily low-to-low returns — one value per trading day, each day's lowest equity to the next day's lowest. VaR is the threshold; CVaR is the average past it. Reported as a (negative) percentage on the Return, P&L, and TWR curves.

On the Return and TWR curves CVaR is the average of the worst 5% of percentage daily returns. Return is money-weighted (deposits and withdrawals move it); TWR strips cashflows out for the cleanest read of the strategy's own tail.

What it tells you

These are losses, so a smaller loss — a number closer to 0 — is better: −1.5% beats −8%. The bands are calibrated for leveraged retail forex daily CVaR (more negative than the matching VaR bands, since CVaR averages deeper in the tail) — on a 1:100 account a −3% average bad day is ordinary, so read it relative to leverage. Always read CVaR alongside its VaR.

Value	Reading	Notes
> −2%	Mild tail	Even the worst days stay shallow — but check it isn’t simply barely trading.
−2% to −5%	Moderate	A typical band for an active forex account.
−5% to −10%	Heavy tail	Bad days bite hard on average — read with leverage and max drawdown.
−10% to −18%	Severe	The worst days average a serious dent. Aggressive sizing — pair with max drawdown.
< −18%	Blow-up profile	A fat-tailed bomb — typical of grid / martingale in its death throes. (Always deeper than the VaR line: if VaR is past −12%, CVaR is well past this.)

The shaded sliver is the worst 5% of days — VaR marks its right edge, CVaR is its average. CVaR sits left of the VaR line because the mean of the tail is deeper than the tail's starting edge.

Worked example

An account's VaR (95%) is −2% — about 1 day in 20 is worse than a 2% loss. But how much worse? Suppose the breach days came in at −2%, −3%, −5%, and −9%. Their average is −4.75% — that's the CVaR. So while VaR says "1 day in 20 breaches −2%," CVaR says "and when it does, you lose about 4.75% on average." The −9% day, invisible to VaR, is exactly what drags CVaR down.

Pitfalls

Pitfalls & caveats

It still only sees the bad days that already happened. Like VaR, historical CVaR is read off observed returns — but one level deeper. A young, quiet, or winning-streak record shows a benign CVaR not because it's safe but because its crisis day hasn't printed yet. A clean record and one that simply hasn't met its shock look identical.
Even more sample-hungry than VaR — put a number on it. CVaR averages only the worst 5%. On a 2-year daily record (~500 days) that's about 25 days; on six months, about 6 days — and a single new outlier can swing the average by a full percentage point. It's the least stable number on the page: treat short-record CVaR as indicative, not measured.
The 95% cutoff is a choice, and it trades against stability. A 97.5% or 99% CVaR (Basel uses 97.5%) sits deeper and reads more negative, but averages even fewer days, so it's noisier still. Compare like with like — always the same cutoff. Our 95% is the most stable of the common choices, not the most conservative.
It's an average, so one disaster pulls it hard. A single −40% day can dominate the mean of a small tail. That's the point — it's meant to feel the deep loss — but read it knowing a lone catastrophe is doing the work.
Daily, not per-trade. Measured day-to-day on the equity curve (low-to-low, one value per trading day), not per individual trade.
Still backward-looking. It describes the tail you've had, never guarantees the tail you'll get.

CVaR vs VaR

VaR and CVaR are two readings of the same tail. VaR is the threshold — the edge where the bad 5% begin. CVaR is the average beyond it — how deep that tail runs. Because it averages everything past the line, CVaR ≤ VaR always. Read them as a pair: VaR tells you how often (1 day in 20), CVaR tells you how bad (the average loss when it happens).

This pairing is the post-2008 standard. Basel's FRTB market-risk framework replaced 99% VaR with 97.5% Expected Shortfall (CVaR) for bank capital — precisely because VaR could not see the tail it was meant to guard. CVaR also has a property VaR lacks: it rewards spreading your risk — combine two books and their CVaR never looks riskier than adding them up separately (the formal term is sub-additive / coherent). VaR can violate this, even penalizing diversification, which is exactly why regulators stopped trusting it for capital. When you need a single tail number, CVaR is the one they use.

Value at Risk is the threshold CVaR averages beyond, Tail Ratio reads the same 5th percentile against the 95th, Max drawdown is the worst peak-to-valley fall the deep tail can build into, and Skewness measures whether your distribution leans toward that bad left tail in the first place.

Compare withValue at Risk (95%)

Variant ofValue at Risk (95%)