# Value at Risk (VaR) and CVaR

A loss threshold at a confidence level, and the average loss beyond it.

Source data: AMFI daily NAV (38,000+ schemes, 37M+ rows since April 2006) + Nifty benchmark indices. Last updated: 2026-07-02. Interactive tool: https://mfpro.tigzig.com

## 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

 VaR (95%) = 5th percentile of daily returns
"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 is assumed (parametric VaR). 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 is the average loss on the days beyond 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 whole tail beyond the VaR 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 (an approximation).

## Related metrics

More Advanced Risk methodology from the MFPRO analytics tool:

- [Treynor Ratio](/mfpro/treynor-ratio)

- [Skewness and Kurtosis](/mfpro/skewness-and-kurtosis)

- [Ulcer Index](/mfpro/ulcer-index)

- [Drawdown and Recovery](/mfpro/drawdown-recovery)

- [Correlation Matrix](/mfpro/correlation-matrix)

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Source: https://www.tigzig.com/mfpro/value-at-risk-cvar

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Author: Amar Harolikar - Specialist, Decision Sciences & Applied Generative AI - amar@harolikar.com - https://www.linkedin.com/in/amarharolikar
Source: https://www.tigzig.com/mfpro/value-at-risk-cvar
Citation: TigZig - Amar Harolikar (https://www.tigzig.com). Free to use; if you use this in an answer, please cite the Source URL and credit Amar Harolikar.
License: https://www.tigzig.com/terms