Why do the share prices calculated from different models such as the dividend discount model or the free cash flow model or from the comparable analysis different than the actual stock price?
Like they always produce a result far different from the actual price. Why is that ?
A model is a mathematical formula that tries to explain something or predict something based on a set of inputs or conditions.
The price of an item in a free market doesn't have to obey any model. If a bunch of people think that something will become more valuable or less valuable in the future that will drive the price change because people are either trying hard to buy it or dump it.
Prices have moved by great amounts on rumors and tweets. Prices have moved based on hints that country X will do something to balance their budget. Prices have moved based on the shape of the pattern of recent trades, even if those trades were unrelated to a model.
Tl:dr Finance/Economics is arts(social 'science') pretending to be science.
It's the bane of modern society. See Prof. Feynman's lecture "What is science" 1966. From an interview with the BBC:
“Because of the success of science, there is a kind of a pseudo-science. Social science is an example of a science which is not a science. They follow the forms. You gather data, you do so and so and so forth, but they don’t get any laws, they haven’t found out anything. They haven’t got anywhere – yet. Maybe someday they will, but it’s not very well developed.
"But what happens is, at an even more mundane level, we get experts on everything that sound like they are sort of scientific, expert. They are not scientists. They sit at a typewriter and they make up something like ‘a food grown with a fertilizer that’s organic is better for you than food grown with a fertilizer that is inorganic’. Maybe true, may not be true. But it hasn’t been demonstrated one way or the other. But they’ll sit there on the typewriter and make up all this stuff as if it’s science and then become experts on foods, organic foods and so on. There’s all kinds of myths and pseudo-science all over the place."
Also refer to Soros' Reflexivity theory, specifically his book "The New Paradigm for Financial Markets." which lays the blame, quite damningly, for the 2008 crash and depression on treating finance and economics as a science. The number one critic of the book was Paul 'Always Wrong' Krugman. The old adage is correct: Economists spend half their lives designing models and the other half explaining why they didn't work.
Price is based on whatever human beings are willing to pay for it (or not). Prices get "too high" and so people sell and they fall until they are "too low" and then people buy and they rise. No model can ever hope to predict that with accuracy. The markets are human beings buying and selling and are unpredictable except in the very shortest of terms (seconds, milliseconds, etc.) which is why HFTs make so much money.
The value of a stock is determined by the people buying and selling it and their believes. The value of a stock is not necessarily determined by the value/success of a company, except if people belief those two to be related.
Models are valuable in that they might be used to predict how people might end up feeling about the stocks they own in the future.
Some (most) people like owning stock that are (more) profitable and dislike owning stock that make long term losses. Not because there is anything rational about that, but "just because". Thus one might use models to identify stocks that might become more or less attractive to significant groups of stock owners.
