Value at Risk

Value at Risk, VaR, is the maximum expected loss on a portfolio over a time horizon at a stated confidence level, compressed into one number. A 1-day 95% VaR of $10,000 means a 95% chance of losing less than $10,000 in a day, and a 5% chance of losing more. Banks and funds use it for capital, trader limits, and regulator reports.

Calculation needs a return distribution. Historical simulation uses past returns. Parametric methods assume a normal distribution. Monte Carlo draws thousands of scenarios. Each method fits different books. The 2008 crisis showed the holes. VaR is silent on the worst 5%. Tail loss can be huge. It treats the past as a guide, which fails when the regime changes.

It can be gamed by positions that look safe under VaR and hide tail risk. Conditional VaR, CVaR or Expected Shortfall, measures expected loss given that you are already in that worst percentile. In crypto, fat tails and regime shifts make naive VaR easy to misread.

A portfolio with 1-day 95% VaR of $10,000 means there's a 95% probability of losing less than $10,000 in a single day, equivalently, a 5% probability of losing more. The metric originated in traditional finance risk management, where banks and funds use it to set capital reserves, measure trader risk limits, and report to regulators.

Calculating VaR requires modeling the distribution of portfolio returns. VaR is a loss quantile: with probability p, you do not lose more than X over a horizon. It is not the worst case. Tails still break it.