VaR and CVaR (also called expected shortfall) are both "downside summary statistics," but they summarize different parts of the loss distribution.

VaR: a threshold, not a story

Value at Risk answers:

"What loss level is exceeded only X% of the time, under my chosen model?"

That is useful for simple limits and communication. It is also dangerously incomplete when the tail is thick: the rare events beyond the VaR line can still destroy you.

CVaR: the average of the bad tail

Conditional VaR averages losses in the worst tail beyond the VaR threshold. Intuitively:

VaR tells you where the fire starts
CVaR tells you how hot the fire gets

Two strategies can share VaR but differ sharply in CVaR when one has catastrophic tail events.

Why this matters more in crypto

Crypto returns often show fat tails, gap risk, and regime shifts. Tail averages are noisy on short samples, but ignoring tails is worse than noisy estimation.

Treat tail metrics as directional evidence, not precise oracle values.

Model risk is still the boss

Both VaR and CVaR depend on:

return sampling frequency
distribution assumptions (historical simulation vs parametric)
window length and regime mixing

If your model is toy-like, your tail number is toy-like.

Pair tail metrics with trader-real outcomes

Use CVaR alongside:

max drawdown and recovery time
stress tests with harsher slippage
walk-forward stability of the tail metric itself (does CVaR explode in some OOS windows?)

A practical workflow

Compute VaR and CVaR on the same return series and same confidence level.
Stress the return series with higher costs and wider spreads.
Recompute and check whether rankings change.
If rankings flip, your edge was partly a liquidity illusion.