Lesson 6 of 8
Distributions
Every claim about a typical company assumes a shape. US price to earnings ratios are not normal, are not quite lognormal either, and the gap matters.
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.
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In one minute
- A distribution is the shape of a set of values, and every summary statistic is a compression of one.
- A normal distribution is symmetric, so its mean and median agree. Valuation ratios are not symmetric and theirs do not.
- Taking logarithms gets much closer to symmetry, which is why ratios are better compared as ranks than as levels.
Behind every sentence about a typical company sits an assumed shape. If the shape is wrong, the average, the standard deviation and the threshold built from them are all describing something that is not there.
Where US price to earnings ratios actually sit
- 5th percentile: 6.18x
- 10th percentile: 9.03x
- 25th percentile: 13.59x
- median: 20.37x
- 75th percentile: 34.50x
- 90th percentile: 68.18x
- 95th percentile: 121.14x
What symmetric would look like
In a normal distribution the mean and the median are the same number, the two halves are mirror images, and almost everything sits within three standard deviations of the centre. It is the shape most statistical intuition is built on, and it describes measurement errors and heights well.
It does not describe a price to earnings ratio. Across the 2,075 active US listings holding a positive ratio on 16 September 2026, the median was 20.85 and the mean was 64.33. A symmetric distribution cannot do that.
Why a ratio cannot be symmetric
The arithmetic forbids it. A P/E has a hard floor at zero and no ceiling at all, because the denominator can approach zero from above while the numerator stays put. Every ratio built this way inherits the same asymmetry.
So the interesting question is not whether the shape is normal. It is whether the logarithm of the ratio is, because a variable with a floor at zero and a long right tail often becomes symmetric once you take its log.
What follows for reading a ratio
Three things, all practical.
The median is the summary to use. It is the middle company, it does not move when one outlier triples, and it is what every distribution on this product publishes as the centre.
Percentiles beat levels. Saying a company sits at the 25th percentile of its cohort survives the shape. Saying it is "below average" does not: 1,839 of the 2,075 listings, which is 88.6 percent of them, sit at or below the mean. Beating this average is the ordinary case, not a distinction.
Standard deviations do not travel. A rule such as "flag anything two standard deviations above the mean" assumes symmetry. On this shape it flags almost nothing on the cheap side and a long tail on the expensive one, which is not what the rule was meant to do.
The shape is not the same in every cohort
A ratio is not one distribution. The same build put the technology cohort's median far above the financial services cohort's, and a threshold set on one reads as a different test on the other. Always ask which cohort a distribution describes before reading a company's place in it.
Check yourself
A set of values has a median of 20.85 and a mean of 64.33. What does that tell you?
- The values were measured incorrectly
- The distribution is right-skewed, with a long tail of high values
- The distribution is normal with a large standard deviation
Show the answer
Answer: B.
In a symmetric distribution the mean and median coincide. A mean three times the median means a small number of very large values are pulling the average up.Why can a price to earnings ratio never be symmetrically distributed?
- Because earnings are reported annually
- Because it has a floor at zero and no upper bound
- Because some companies have no earnings at all
Show the answer
Answer: B.
A bounded floor with an unbounded ceiling forces a right tail. Companies with no positive earnings are excluded from the ratio entirely, which is a separate selection problem.A screen flags any company more than two standard deviations above the mean P/E. What is wrong with it?
- Two standard deviations is too strict
- The rule assumes symmetry, and this distribution has none
- Standard deviation cannot be computed on ratios
Show the answer
Answer: B.
Standard-deviation thresholds are built for symmetric shapes. On a right-skewed distribution the same rule cuts the two sides at completely different percentiles, which is not the test anyone intended.Sources
GET /api/public/distribution/peon ValueScreener, build of 15 September 2026: 1,964 US companies with a computed ratio, one row per company, equity REITs excluded, winsorised at the 1st and 99th percentiles.- Log statistics computed across 2,075 active US equity listings with a positive ratio, read from this product's own store on 16 September 2026.
What this leaves out
- The published breakpoints are winsorised at the 1st and 99th percentiles, so the extremes of the real distribution are clamped rather than shown. The log statistics in the worked example are not winsorised, which is why the two sets of figures are labelled separately.
- Both readings are one date. Distributions are rebuilt on a schedule and will differ later.
- Listings are counted in the log table, deduplicated companies in the published distribution. The two counts are not interchangeable.
- Nothing here is advice about any security.