# Skewness and Kurtosis

The asymmetry and fat tails of a fund’s return distribution.

Source data: AMFI daily NAV (17,900+ schemes) + Nifty benchmark indices. Last updated: 2026-07-02. Interactive tool: https://mfpro.tigzig.com

## What are Skewness and Excess Kurtosis?



Skewness and kurtosis describe the **shape** of the return distribution beyond what
 mean and standard deviation capture. They reveal asymmetry and tail thickness - critical for
 understanding risks that standard deviation alone misses.

 


## Skewness


 
 Skewness measures asymmetry of the return distribution:

Negative skew = longer left tail (more extreme losses than gains)
Positive skew = longer right tail (more extreme gains than losses)
Zero = symmetric (like a normal distribution)
 

Most equity funds exhibit **negative skewness** - they have occasional large drawdowns
 that are more extreme than their best up days. This means the "average" return overstates how
 often you actually experience good outcomes.

 


## Excess Kurtosis


 
 Excess Kurtosis measures fat tails relative to a normal distribution:

Normal distribution = excess kurtosis of 0
Positive = fatter tails than normal (more extreme events in both directions)
Negative = thinner tails than normal (fewer extreme events)
 

Most equity funds show **positive excess kurtosis** - more crashes and rallies than a
 normal distribution would predict. This means standard deviation **underestimates** the
 probability of extreme moves.

 


## Example



Interpreting Shape Metrics


Fund A: Skewness = −0.45, Excess Kurtosis = 2.1
Interpretation: Moderately left-skewed (losses are more extreme than gains) with fat tails
 (extreme events happen more often than normal distribution predicts).


Fund B: Skewness = 0.10, Excess Kurtosis = 0.3
Interpretation: Nearly symmetric with tails close to normal - a "well-behaved" return distribution.

 
 


## How to Interpret





- **Skewness closer to zero** is generally preferred - symmetric distributions have no directional tail bias.

- **Negative skew is worse** for investors - it means the downside surprises are larger than upside surprises.

- **Higher kurtosis = more tail risk** - extreme events (both good and bad) occur more frequently than standard deviation implies.

- A fund with high kurtosis and negative skew has the worst combination: fat tails biased toward losses.


 


## Important Notes





- Both computed using DuckDB's built-in **SKEWNESS()** and **KURTOSIS()** functions on daily returns.

- DuckDB's KURTOSIS() returns **excess** kurtosis (already subtracts 3), so 0 = normal distribution.

- These metrics require a reasonable sample size (60+ observations) to be stable.

- Skewness and kurtosis complement VaR/CVaR - they explain *why* the tails look the way they do.

## Related metrics

More Advanced Risk methodology from the MFPRO analytics tool:

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

- [Value at Risk (VaR) and CVaR](/mfpro/value-at-risk-cvar)

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

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

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

---
Source: https://www.tigzig.com/mfpro/skewness-and-kurtosis