Value at Risk (VaR)

Value at Risk answers: “over the next day, with 95% confidence, I won’t lose more than X.” It compresses a whole loss distribution into one threshold, which is why risk desks love it as a limit and regulators mandate it.

The well-known weakness: VaR says nothing about the tail beyond the threshold. A 95% VaR of $4k is silent on whether the worst 5% loses $5k or $50k — and crypto tails are fat. It also assumes the recent past resembles the near future, which breaks precisely when a regime shifts. Complements like Expected Shortfall (the average loss in the tail) exist for this reason.

For an agent, VaR is a natural policy primitive: cap the portfolio’s estimated VaR, and refuse trades that would breach it. But because VaR under-weights tails, a robust envelope pairs it with a hard notional cap and a drawdown kill-switch — belt and suspenders, so a fat-tailed day can’t quietly exceed what the VaR limit implied was “safe.”