Which downside risk metric should I use?

For regulatory and reporting: VaR (it is the standard). For capital allocation decisions: CVaR or max drawdown — both capture tail risk that VaR misses. Best practice is to report all three because they answer different questions: "how often I might lose more than X" (VaR), "how bad it gets when I lose more than X" (CVaR), and "what is the worst it has actually been" (drawdown).

Why is VaR criticized?

VaR tells you the threshold but says nothing about what happens beyond it. A strategy with 95% VaR of -2% might lose -3% one day or -30% — VaR doesn't distinguish. Worse: VaR is not "subadditive", meaning combining two portfolios can have HIGHER VaR than the sum, which makes no sense for a risk measure. CVaR fixes both problems.

What is the relationship between VaR and CVaR?

CVaR (also called Expected Shortfall) is the EXPECTED VALUE of losses given that losses exceed VaR. Mathematically: CVaR_α = E[loss | loss > VaR_α]. CVaR is always at least as large as VaR — usually 20-50% larger for normal distributions, much larger for fat-tailed distributions. The ratio CVaR/VaR is itself a tail-fatness indicator.

How is max drawdown different from VaR/CVaR?

VaR and CVaR are quantile-based probability measures computed from a return distribution. Max drawdown is a path-dependent realized loss — it tracks the actual peak-to-trough decline of the equity curve. VaR/CVaR can be computed without any history (just inputs μ, σ, etc.); max drawdown requires an actual sequence of returns. Drawdown captures correlation across time that VaR/CVaR miss entirely.

What is the right confidence level — 95% or 99%?

95% is more common in trading/portfolio management. 99% is more common in bank capital regulation. The choice depends on your loss-tolerance horizon: 95% VaR is exceeded once every 20 periods (~12 days/year for daily VaR), 99% is exceeded once every 100. For position sizing, 95% is usually sufficient. For tail risk hedging or stress testing, 99% or even 99.5% is more relevant.

How do I compute these for a real strategy?

For VaR: either parametric (assume normal returns, multiply σ by z-score) or historical (rank returns, pick the 5th percentile). For CVaR: average all returns below VaR. For max drawdown: walk through the equity curve tracking the running peak and current value, record the largest (peak - current)/peak. The QuantOracle calculators do all three.

Why does my VaR look low but my drawdown look terrible?

VaR is per-period; drawdown is cumulative. A strategy that loses 0.5% on the bad 5% of days has tiny VaR — but if those bad days cluster (during a crisis, say) the cumulative drawdown can easily exceed 20%. This is the autocorrelation gap: VaR assumes independence across periods; drawdown captures the path. Most real market crises have strong autocorrelation — 2008, 2020, etc. are sequences of bad days clustered, not independent draws.

Which is best for retail position sizing?

Max drawdown. It is the metric that directly answers "how much would I lose if I held this strategy through the worst period?" For retail traders without sophisticated risk infrastructure, max drawdown + Calmar ratio (return / max drawdown) is more practically useful than VaR or CVaR. VaR/CVaR are valuable but operationally complex; max drawdown is just a number.

Are there calculators for all three?

Yes. The Value at Risk Calculator computes parametric and historical VaR + CVaR with skewness and kurtosis correction. The Drawdown Calculator gives max drawdown, average drawdown, and underwater periods. Each is free and backed by the same deterministic QuantOracle API.

What about Expected Shortfall — is that the same as CVaR?

Yes, Expected Shortfall (ES) = Conditional VaR (CVaR) = Expected Tail Loss (ETL) = Average VaR. These are four names for the same number. European regulators tend to say "Expected Shortfall"; US academics tend to say "CVaR"; risk management practitioners often say "ETL". Don't let the terminology fool you — they are mathematically identical.

VaR vs CVaR vs Max Drawdown: Three Ways to Measure Downside Risk

Metric	Answers	Misses
VaR	How often do I lose more than X in a single period?	How bad it gets when I exceed X. Cross-period clustering.
CVaR	How bad is the AVERAGE loss when I exceed VaR?	Cross-period correlation (still single-period). Worst case.
Max Drawdown	What is the worst peak-to-trough loss this has ACTUALLY had?	Probability of future drawdowns. Anchored on one data point.

What each metric actually measures

VaR: a quantile of the return distribution

VaR_α = −Q_α(returns) where Q_α is the α-quantile (e.g., 5th percentile)

Value at Risk asks: "what loss am I exceeding only α% of the time?" A 95% VaR of -2% means: on 95% of days, losses are within -2%; on the bad 5% of days, losses are larger than -2%. VaR is a single point on the distribution. It says nothing about the shape beyond that point.

CVaR: the expected loss beyond VaR

CVaR_α = E[loss | loss > VaR_α]

Conditional VaR (also called Expected Shortfall) is the AVERAGE loss given that a loss exceeds VaR. Where VaR tells you the threshold, CVaR tells you the average depth of the tail. CVaR is always at least as large as VaR — for normal distributions about 25% larger, for fat-tailed distributions 2-5x larger. CVaR satisfies the mathematical property of subadditivity (combining portfolios never increases risk), which makes it a "coherent risk measure" in the sense of Artzner et al. (1999). VaR is not.

Max Drawdown: the worst path-dependent realized loss

MaxDD = max over t of (peak_to_t − value_t) / peak_to_t

Maximum drawdown is the largest peak-to-trough decline ever observed in the equity curve. Unlike VaR and CVaR, drawdown is path-dependent — it requires an actual sequence of returns and captures correlation across time. A strategy that loses 1% per day for 30 straight days has a max drawdown of ~26% but a daily VaR of only ~1%. VaR is blind to that clustering.

A concrete example: three strategies, three rankings

Same expected return (10% annualized), same volatility (15%), but very different tail behaviors:

Strategy	Profile	VaR_95 (1-day)	CVaR_95 (1-day)	Max Drawdown
A. Normal returns	Symmetric, thin tails	-1.5%	-1.9%	-18%
B. Fat-tailed	Symmetric, kurtosis 8	-1.4%	-3.5%	-35%
C. Negative skew	Small wins, rare big losses	-1.1%	-4.2%	-42%

By VaR alone, Strategy C looks SAFER than A and B — it has the lowest VaR. That's wrong. CVaR immediately exposes the problem: when C goes bad, it goes much worse than A or B. Max drawdown confirms: C had a -42% drawdown. The single VaR number missed this entirely.

This is the canonical reason CVaR was developed and why drawdown is reported alongside VaR in every serious risk system. VaR alone systematically under-rates the risk of negatively-skewed and fat-tailed strategies — which is most real strategies.

When each one lies

VaR lies on fat tails and negative skew

VaR is just a quantile. It says nothing about distribution shape beyond the threshold. Worst cases:

Option-selling strategies have tiny daily VaR (small losses on most days) but enormous CVaR when the rare large loss arrives. VaR will make them look safer than long-only equity.
Crypto strategies have fat tails — parametric normal VaR routinely understates real loss potential by 2-3x. Use historical VaR or Cornish-Fisher VaR with skew and kurtosis corrections.
Carry trades classically have small VaR for years and catastrophic losses on the few bad days. VaR completely misses the structure.

CVaR lies less, but still single-period

CVaR fixes VaR's tail-blindness but is still computed per-period. It does not capture clustering of bad periods. A strategy can have CVaR_95 of -3% per day and still experience a -50% drawdown if the bad days cluster. CVaR & VaR together do not replace looking at drawdown.

Max Drawdown is anchored on one data point

The denominator of Calmar (max drawdown) is the single worst observed peak-to-trough. That makes it:

Sensitive to one bad period — a strategy can go from MDD -15% to MDD -35% overnight
Optimistic for short track records — a strategy that hasn't had a real drawdown yet shows artificially low MDD
Blind to frequency — one -30% drawdown and three years of recovery looks the same as five -30% drawdowns and consistent re-recoveries

Many shops report MDD alongside "average drawdown" (mean of all drawdowns) and "pain index" (time-weighted average of underwater values) for a fuller picture.

The Cornish-Fisher fix for VaR/CVaR on fat tails

Standard parametric VaR assumes normal returns. For real strategies with skew and excess kurtosis, this systematically understates VaR. The Cornish-Fisher expansion corrects the quantile estimate using the third and fourth moments of the return distribution:

z_CF = z + (z² − 1)·γ/6 + (z³ − 3z)·κ/24 − (2z³ − 5z)·γ²/36

Where z is the standard normal quantile, γ is skewness, and κ is excess kurtosis. The QuantOracle Value at Risk Calculator uses Cornish-Fisher by default for parametric VaR and CVaR.

What good values look like (rough ranges)

Annualized strategy with daily returns, 95% confidence:

Strategy class	Daily VaR_95	CVaR/VaR ratio	Max DD
Long-only equity	-1.5 to -2.5%	1.3 - 1.5x	-25 to -55%
60/40 balanced	-0.8 to -1.2%	1.3 - 1.4x	-15 to -30%
Market-neutral	-0.4 to -0.8%	1.5 - 2.0x	-5 to -15%
Trend-following CTA	-1.5 to -2.0%	1.2 - 1.4x	-15 to -25%
Crypto	-4 to -7%	1.8 - 3.0x	-50 to -85%
Option-selling	-0.5 to -1.0%	2.5 - 5.0x	-30 to -60%

The CVaR/VaR ratio is the most useful single tail-fatness indicator. Anything above 2.0 means VaR is dramatically understating the risk and you should NOT use VaR alone for decisions about that strategy.

The decision rule

Compute VaR_95 (historical and parametric) with the VaR calculator. Always include CVaR_95 in the same call — it costs nothing extra and immediately reveals tail fatness.
Check the CVaR/VaR ratio. Under 1.5: probably near-normal tails, VaR is reliable. Over 2.0: fat tails or negative skew, VaR systematically understates risk, prefer CVaR for decisions.
Compute max drawdown with the drawdown calculator. This catches cross-period clustering that VaR/CVaR miss.
For capital allocation, weight all three. A strategy that looks good on all three is rare and worth allocating to. A strategy that looks good on VaR but bad on CVaR or max drawdown is a tail-risk strategy in disguise.

Related calculators

Value at Risk Calculator — parametric and historical VaR + CVaR with Cornish-Fisher correction
Drawdown Calculator — max drawdown, average drawdown, underwater fraction
Sharpe Ratio Calculator — pair with VaR/CVaR for full risk picture
Monte Carlo Simulation Calculator — forward-projects drawdown distribution under different return / vol assumptions
Related: Sharpe vs Sortino vs Calmar — Calmar uses max drawdown as the denominator

References

J.P. Morgan/Reuters (1994). "RiskMetrics — Technical Document." — introduced parametric VaR as industry standard.
Artzner, P., Delbaen, F., Eber, J.-M., & Heath, D. (1999). "Coherent measures of risk." Mathematical Finance 9(3), 203-228. — formal VaR critique, CVaR motivation.
Rockafellar, R. T. & Uryasev, S. (2000). "Optimization of Conditional Value-at-Risk." Journal of Risk 2, 21-41. — CVaR computation.
Acerbi, C. & Tasche, D. (2002). "On the coherence of Expected Shortfall." Journal of Banking & Finance 26(7), 1487-1503. — CVaR = ES equivalence.
Magdon-Ismail, M. & Atiya, A. F. (2004). "Maximum drawdown." Risk Magazine, October.