Loading...
Kurtosis measures the fatness of tails in a return distribution. A normal distribution has kurtosis of 3 (excess kurtosis of 0). Stock returns typically exhibit excess kurtosis of 3-10, meaning extreme moves occur far more often than a bell curve predicts.
⚡
Key takeawayHigh kurtosis means your short premium positions face larger tail losses than normal-distribution math suggests. Size positions assuming 3-4 standard deviation moves happen 5-10x more frequently than theoretical models predict.
💡 Why It Matters
Kurtosis quantifies the fat-tail risk that premium sellers face. With equity return kurtosis typically at 5-10 (versus 3 for normal), events that should happen once in 10,000 days actually occur every few hundred days. Ignoring kurtosis leads to catastrophic position sizing.
⚙ How It Works
Kurtosis is the fourth moment of the return distribution. Excess kurtosis (kurtosis minus 3) measures how much fatter the tails are versus a normal distribution. Stock returns typically have excess kurtosis of 3-7 for daily data, meaning 3-4 sigma events are 5-10x more common than normal distribution tables suggest.
📋 Example
Under a normal distribution, a 4-sigma daily SPX move (roughly 4%) should happen once every 126 years. With kurtosis of 6 (excess kurtosis 3), this event occurs roughly every 2-3 years. A premium seller sizing for normal-distribution tail risk will experience a portfolio-threatening drawdown far sooner than expected.
⚠ Common Mistakes
Traders use probability calculators that assume normal distributions to set strike prices. A 5-delta put appears to have a 5% chance of expiring ITM under normality, but with fat tails, the real probability is 8-12%. Adjust your position sizing for the real probability, not the theoretical one.
❓ FAQ
What is Kurtosis?
Kurtosis measures the fatness of tails in a return distribution. A normal distribution has kurtosis of 3 (excess kurtosis of 0). Stock returns typically exhibit excess kurtosis of 3-10, meaning extreme moves occur far more often than a bell curve predicts.
Why does Kurtosis matter for premium sellers?
High kurtosis means your short premium positions face larger tail losses than normal-distribution math suggests. Size positions assuming 3-4 standard deviation moves happen 5-10x more frequently than theoretical models predict.
How does Kurtosis work?
Kurtosis is the fourth moment of the return distribution. Excess kurtosis (kurtosis minus 3) measures how much fatter the tails are versus a normal distribution. Stock returns typically have excess kurtosis of 3-7 for daily data, meaning 3-4 sigma events are 5-10x more common than normal distribution tables suggest.
What are common mistakes with Kurtosis?
Traders use probability calculators that assume normal distributions to set strike prices. A 5-delta put appears to have a 5% chance of expiring ITM under normality, but with fat tails, the real probability is 8-12%. Adjust your position sizing for the real probability, not the theoretical one.
Related Terms
Close-to-Close Volatility
A basic volatility estimator using only daily closing prices.
Corridor Variance Swap
A corridor variance swap pays realized variance only when the underlying trades within a specified price range (corridor).
CPI Print
The CPI print is the monthly Consumer Price Index release by the Bureau of Labor Statistics, typically at 8:30 AM ET.
Dispersion Trading
Dispersion trading exploits the persistent premium of index implied volatility over the weighted average of its component implied volatilities.
This is not financial advice. Read our full investment disclaimer.