Value at Risk (VaR) and Conditional VaR: quantifying tail risk
Value at Risk (VaR) and Conditional VaR: quantifying tail risk
Value at Risk answers a specific, bounded question: over a given period, at a given confidence level, what's the most a portfolio should lose under normal conditions. Conditional VaR answers the harder follow-up: and when it's worse than that, how bad does it get. Together they're the standard vocabulary for putting a number on tail risk.
How it works
Value at Risk (VaR) is a threshold loss at a confidence level. A one-day 99% VaR of $2 million means: on 99 out of 100 normal days, losses should not exceed $2 million. It's a way of compressing an entire distribution of possible outcomes into a single, communicable figure that a risk committee can actually act on. VaR is estimated three common ways: from historical data (how did this portfolio's losses actually distribute in the past), from a parametric model (assume a distribution and calculate), or from Monte Carlo simulation (generate thousands of possible scenarios and observe the outcomes).
VaR has a well-known blind spot, and it's exactly where it hurts most. It tells you the threshold, not what's beyond it. A 99% VaR says nothing about how bad the worst 1% of days actually are; a portfolio could breach its VaR by a little or by a catastrophic amount, and the VaR figure looks identical either way.
Conditional VaR (CVaR, also called Expected Shortfall) closes that gap. It measures the average loss in those tail scenarios, the expected loss given that you're already past the VaR threshold. If the 99% VaR is $2 million, the 99% CVaR might be $3.5 million, telling you that on the worst 1% of days, the average loss isn't $2 million but $3.5 million. CVaR is the more honest number for anything where the shape of the tail matters, which for a credit portfolio, it always does.
Why it matters
The distinction between VaR and CVaR is the distinction between knowing where the cliff edge is and knowing how far the drop goes. Risk frameworks that stop at VaR systematically understate tail risk, because they treat every breach of the threshold as equivalent when the whole point of tail risk is that some breaches are far worse than others. This is precisely why post-2008 regulatory frameworks shifted emphasis from VaR toward Expected Shortfall.
For credit portfolios specifically, where losses are asymmetric (you can lose the whole principal but only ever earn a capped return), the tail is where the real danger lives, and CVaR is the tool built to measure it. A portfolio can look safe on VaR while carrying a fat, dangerous tail that only CVaR reveals.
Where this shows up in Rekord
Rekord's portfolio risk monitoring uses tail-focused measures, not just threshold VaR, because a credit book's asymmetric loss profile makes the shape of the tail the number that actually matters. For the concentration factors that shape that tail, see Portfolio correlation, concentration, and the HHI index.