This falls under value investing, and value investing has only recently picked up study by academia, say, at the turn of the millennium; therefore, there isn't much rigorous on value investing in academia, but it has started.
However, we can describe valuations:
- Valuations tend to be log-Variance Gamma distributed This is a special kind of probability distribution that allows one to set mean, variance, skew, and kurtosis, the building blocks of a good distribution.
- P/Es are larger for higher growth The market is not quite as inefficient as Buffett says. Companies that do well are rewarded with higher valuations; those that do not get less. It starts to get a little out of hand when tiny technology companies have 100 P/Ss simply because they have a biotech or computer tech name and business plan. We saw the worst of that before the tech collapse, or a loathed industry is selling for half the market valuation because of this or that dramatic narrative. Generally though, if a company is or has grown fast, it won't be cheap, and one that grows ever slowly like a utility can only enjoy not below average P/Es during a boom in their industry, like overprice oil in the utility's case.
In short, valuations are randomly distributed in a log-Variance Gamma fashion with some reason & nonsense mixed in.
You can check for yourself on finviz. You can basically download the entire US market and then some, with many financial and technical characteristics all in one spreadsheet.
Re Fisher: He was tied for the best monetary economist of the 20th century and created the best price index, but as for stocks, he said this famous quote 12 days before the 1929 crash:
"Stock prices have reached what looks like a permanently high plateau. I do not feel there will be soon if ever a 50 or 60 point break from present levels, such as (bears) have predicted. I expect to see the stock market a good deal higher within a few months."
- Irving Fisher, Ph.D. in economics, Oct. 17, 1929
Value investing has almost always been ignored by academia. Irving Fisher and other proponents of it before it was codified by Graham in the mid 20th century certainly didn't help with comments like the above. It was almost always believed that it was a sucker's game, "the bigger sucker" game to be more precise because value investors get destroyed during recession/collapses. So even though a recessionless economy would allow value investors and everyone never to suffer spontaneous collapses, value investors are looked down upon by academia because of the inevitable yet nearly always transitory collapse. This expresses that sentiment perfectly.
It didn't help that Benjamin Graham didn't care about money so never reached the heights of Buffett who frequently alternates with Bill Gates as the richest person on the planet. Buffett has given much credibility, and academia finally caught on around in 2000 or so after he was proven right about a pending tech collapse that nearly no one believed would happen; at least, that's where I begin seeing papers being published delving into value concepts. If one looks harder, academia's even taken the torch and discovered some very useful tools.
Yes, investment firms and fellow value investors kept up the information publishing, but they are not academics.
The days of professors throwing darts at the stock listings and beating active managers despite most active managers losing to the market anyways really held back this side of academia until Buffett entered the fray and embarrassed them all with his club's performance, culminating in the Superinvestors article which is still relatively ignored. Before that, it was the obsession with beta, the ratio of a security's variance to its covariance to the market, a now abandoned theory because it has been utterly discredited; the popularizers of beta have humorously embraced the P/B, not giving the satisfaction to Buffet by spurning the P/E.
Tiny technology firms receive ridiculous valuations because a long-surviving tiny tech firm usually doesn't stay small for long thus will grow at huge rates. This is why any solvent and many insolvent tech firms receive large valuations: risk-adjusted, they should pay out huge on average. Still, most fall by the wayside dead, and those 100 P/S valuations quickly crumble.
Valuations are influenced by growth. One can see this expressed more easily with a growing perpetuity:
P = i / (r - g)
P is price,
i is income,
r is the rate of return, and
g is the growth rate of
r looks like:
r = i / P - g
Here, one can see that a higher
P relative to
i will dull the expected rate of return while a higher
g will boost it.
It's fun for us value investor/traders to say that the market is totally inefficient. That's a stretch. It's not perfectly inefficient, but it's efficient. Valuations are clustered very tightly around the median, but there are mistakes that even us little guys can exploit and teach the smart money a lesson or two.
If one were to look at a distribution of
rs, one'd see that they're even more tightly packed. So while it looks like P/Es are all over the place industry to industry,
rs are much more well clustered.
Tech, finance, and discretionaries frequently have higher growth rates so higher P/Es yet average
rs. Utilities and non-discretionaries have lower growth rates so lower P/Es yet average