Lesson 7 of 8
Fat tails
Twenty-one US listings out of 2,075 carry 45 percent of the total of every P/E in the market. That is what a fat tail does to an average.
By Javier Sanz
Founder of ValueScreener. Built Ninety Nine, a securities services provider, and sold it to a tier-one global bank; ran operations and internationalization at Alpaca, the brokerage API.
Who writes thisEditorial processLinkedIn (opens in a new tab)X (opens in a new tab)
In one minute
- A fat-tailed distribution produces extreme values far more often than a normal one, and far more often than a lognormal one.
- Where the tail is fat, the mean is dominated by a handful of observations and stops describing anything typical.
- The practical defence is the median, a rank, or a winsorised cohort, and each of those choices has to be stated.
The last lesson showed a right-skewed distribution and a log transform that nearly straightened it. Nearly is the word that matters. What is left after the transform is a tail heavy enough to control every average built on top of it.
How much of the total sits in the top one percent
- The bottom 99 percent of listings54.7%
- The top 1 percent of listings45.3%
What the numbers do
Across 2,075 active US listings with a positive ratio on 16 September 2026, the median was 20.85 and the largest was 19,697.5. The mean was 64.33, three times the median. And 45.3 percent of the sum of every ratio in the market came from the 21 listings above the 99th percentile.
That is the definition of a fat tail in practice. One percent of the observations control nearly half of the total, so the mean is mostly a statement about those twenty-one rows.
Fatter than lognormal, not just fatter than normal
The last lesson found the logs had a mean of 3.1354 and a standard deviation of 1.0422. If the distribution were exactly lognormal, those two numbers imply a mean of 39.59 and a 99th percentile of about 260.
Why the tail is there
Most of it is arithmetic rather than mystery. A P/E is price divided by earnings, and a company whose earnings fall to almost nothing while its price does not produces an enormous ratio. Nothing dramatic happened to the business. A small denominator happened.
That is worth stating because the tail is often read as a list of the most expensive companies in the market. Some of it is. Much of it is companies whose earnings are near zero, which is a different fact needing a different figure.
What to do about it
Use the median. One observation cannot move it, and 1,037 listings sit on either side of it by construction.
Winsorise, and say so. The published distributions on this product clamp values to the observed 1st and 99th percentiles before computing breakpoints, and the response states the rule beside the numbers. Clamping is a defensible choice. Silently clamping is not.
Never average across a fat tail without checking what one row does. Remove the single largest value from this set and the mean falls from 64.33 to 54.87. One row out of 2,075 was carrying nine and a half points of the average. The median does not move at all.
Where else this bites
The same shape appears in market capitalisation, in trading volume, in drawdowns and in the distribution of returns across a portfolio's holdings. Anywhere a handful of observations can be orders of magnitude larger than the middle, the mean becomes a statement about the handful.
Check yourself
Twenty-one listings out of 2,075 supply 45 percent of the sum of all P/E values. What does that make the mean?
- A robust summary of the market
- Largely a statement about those twenty-one listings
- Equal to the median in a large enough sample
Show the answer
Answer: B.
When one percent of observations carry nearly half the total, the average describes that one percent rather than the typical case. Sample size does not fix this, because more data brings more tail.Sixteen listings have a P/E above 1,000. What is the most likely reason?
- They are the most expensive companies in the market
- Their earnings are close to zero, which makes the denominator tiny
- The ratio was computed incorrectly
Show the answer
Answer: B.
A ratio with a denominator approaching zero grows without limit. The extreme values say more about near-zero earnings than about what anyone paid for the shares.What does winsorising a cohort at the 1st and 99th percentiles do?
- Deletes the extreme observations
- Clamps them to the observed values at those percentiles, keeping the cohort size unchanged
- Converts the distribution to a normal one
Show the answer
Answer: B.
Values are clamped rather than dropped, so the cohort that produced the breakpoints is the whole cohort. It is a defensible treatment, and the rule has to be published beside the numbers.Sources
- P/E values across 2,075 active US equity listings with a positive ratio, read from this product's own store on 16 September 2026: median 20.85, mean 64.33, maximum 19,697.5, 99th percentile 744.7, 131 above 100 and 16 above 1,000.
GET /api/public/distribution/peon ValueScreener, build of 15 September 2026: the published winsorisation rule and its stated basis.
What this leaves out
- Every figure is a reading on one date. A fat tail is exactly the kind of statistic that moves most between readings, because a single new extreme value changes it.
- The lognormal comparison fits a model to this data and then measures the gap. It is a description of the shape, not a claim that any model should be used for a forecast.
- Listings are counted, not deduplicated companies, and only listings with a positive ratio are in the set at all.
- Nothing here is advice about any security.