What are VaR and CVaR?
Value at Risk (VaR) and Conditional VaR (CVaR), also called Expected Shortfall, are downside risk measures that quantify potential losses in the tail of the return distribution.
Formula
"On 95% of days, your loss won't exceed this value."
CVaR (95%) = Average of all daily returns at or below the VaR
"When things go bad (worst 5% of days), how bad on average?"
We use the historical method - the actual percentile of observed returns. No normal distribution assumption (parametric VaR) is made, which is important because equity returns are typically not normally distributed.
Example
VaR and CVaR in Practice
VaR (95%) = −2.1% means: on the worst 5% of trading days, the fund lost at least 2.1%.
CVaR (95%) = −3.0% means: on those worst 5% of days, the average loss was 3.0%.
If a fund has 1,000 daily returns, VaR is the 50th worst return (5th percentile). CVaR is the average of those 50 worst returns.
How to Interpret
- Both values are in daily percentage terms and are negative numbers (representing losses).
- CVaR is always worse (more negative) than VaR - it captures the average severity of tail events, not just the threshold.
- Closer to zero = less tail risk. A fund with VaR of −1.5% has less daily downside than one with −2.5%.
- VaR tells you the "door" to the worst 5% of days. CVaR tells you what happens once you walk through it.
- CVaR is considered a more robust risk measure than VaR because it accounts for the shape of the tail, not just one point.
Important Notes
- Historical VaR depends entirely on the sample period - it cannot predict unprecedented events.
- A fund with few extreme losses will show VaR and CVaR close together. Large gaps between them indicate a long, fat tail.
- Minimum 60 daily observations required for meaningful percentile calculation.
- These are daily measures. To approximate monthly VaR, multiply by √21 (not exact, but directional).
Related metrics
More Advanced Risk methodology from the MFPRO analytics tool: