Skewness and Kurtosis
Skewness measures how lopsided a return distribution is; kurtosis measures how heavy its tails are compared with a normal distribution. Together they show the risk of rare, extreme outcomes that standard deviation alone misses.
Two strategies can have the same average return and the same volatility yet behave completely differently: one makes small gains and occasionally crashes, the other loses small amounts and occasionally soars. Skewness and kurtosis describe that hidden shape. This entry explains both measures, what they mean for traders and why markets have "fat tails".
- Category
- Risk Management
- Reading time
- 3 min
- Also called
- Skewness, Kurtosis, Fat tails
- Updated
Skewness and kurtosis in plain words
Skewness measures the asymmetry of a distribution; a normal distribution is symmetrical and has none.1
Kurtosis measures how heavily a distribution's tails differ from those of a normal distribution — whether extreme values are common.2
Excess kurtosis is kurtosis minus 3, the kurtosis of a normal distribution.2
How to use them, step by step
Collect returns
Daily or monthly, over a long period.
Check the average and spread
Mean and standard deviation. See Standard Deviation.
Measure skewness
Positive: long right tail; negative: long left tail.
Measure kurtosis
High: more extreme outcomes than normal.
Stress-test
Assume bigger moves than a normal curve suggests. See Black Swan.
Size accordingly
Negative skew and fat tails need smaller positions. See Position Sizing.
Worked examples
Example 1 — Positive skew
Right tailA trend strategy loses 1% on most trades but sometimes gains 15%.
| Typical trade | −1% |
| Occasional trade | +15% |
| Mean vs median | Mean above median |
In a positively skewed distribution the tail is on the right and the mean is above the median.1
Example 2 — Negative skew
Left tailAn option-selling strategy earns +1% most months but loses −20% in a crash.
| Typical month | +1% |
| Crash month | −20% |
A long left tail is negative skew — steady small gains with rare large losses. See Naked Options.
Example 3 — Excess kurtosis
Fat tailsA return series has kurtosis of 6.
| Excess kurtosis | 6 − 3 = 3 |
| Meaning | Fat tails, more extremes |
Positive excess kurtosis means more extreme values than a normal distribution would produce.2
Skewness vs kurtosis
| Aspect | Skewness | Kurtosis |
|---|---|---|
| Describes | Asymmetry | Tail heaviness |
| Normal value | 0 | 3 (excess 0) |
| Risk signal | Negative skew: crash risk | High: frequent extremes |
| See also | Mean vs median | Normal Distribution |
Where traders use these measures
Strategy evaluation
Hidden crash risk in backtests. See Backtesting.
Risk models
Adjusting value-at-risk for fat tails. See Value at Risk.
Options pricing
Skew in implied volatility. See Implied Volatility.
Portfolio design
Balancing positive and negative skew.
Advantages and disadvantages
Advantages
- Reveal risks standard deviation hides.
- Help compare strategy profiles.
- Improve stress testing.
Disadvantages
- Need lots of data to estimate.
- Very sensitive to outliers.
- Past shape may not repeat.
Going deeper
Read as far as you need. Each level builds on the one before it.
Why investors care
Beginner
Investors look at skewness because it accounts for extreme data points in a return distribution.1
Three kurtosis types
Intermediate
Distributions with excess kurtosis near zero are mesokurtic, like the normal; positive is leptokurtic (fat tails), negative platykurtic (thin tails).2
Markets are fat-tailed
Advanced
Daily stock returns typically show excess kurtosis and often negative skew, so normal-based risk models understate crash risk. See Black Swan.
Common mistakes
Relying on standard deviation alone
It ignores shape.
Mixing kurtosis and excess kurtosis
Check which one is reported.
Short samples
Rare events may not appear yet.
Chasing negative-skew income
Steady gains can hide crash risk.
Check your understanding
Test yourself before moving on. Each answer comes with an explanation.
Key points to remember
- Skewness measures asymmetry.
- Kurtosis measures tail heaviness.
- Normal distributions have zero skew and kurtosis of 3.
- Market returns usually have fat tails.
- Negative skew hides crash risk.
Frequently asked questions
Is positive skew good?
What does high kurtosis mean for risk?
Do stock returns follow a normal distribution?
Further learning
- Standard Deviation
The spread measure.
- Black Swan
Extreme events in the tails.
- Value at Risk
A risk model affected by fat tails.
Sources
This article is written in our own words. The sources below support the specific facts, rules and figures marked with a number in the text. Links open the original publisher’s page.
- Corporate Finance Institute. Skewness (opens in a new tab) Checked .
- Corporate Finance Institute. Kurtosis (opens in a new tab) Checked .
Educational content, not financial advice. Examples use hypothetical prices and simplified costs; actual fees, margin rules and regulations vary by broker, market and country. We are not affiliated with any publisher linked above. Last reviewed . Report an error or request a source credit.