# Do stock prices really tend towards a fair valuation?

I recently started working myself into the concepts of valuation. While I find the concept of fair value very interesting and intuitive, I wonder if prices are actually empirically driven by value in the long run.

For convenience, let me summarize my understanding of the concept (please correct me at any point if I am wrong) and the problem:

Typically, assuming an infinite lifetime, the fair value of a publicly listed company (the fair value of the firm) can be determined by the expected future cashflows discounted back to their current value. Additionally, one should add cash and subtract debt.

That is, the fair value $$FV$$ is given by the future cash flows to the firm $$FCFF$$, the discount rate $$DR$$, the cash $$C$$ and debt $$D$$ as $$FV =C-D+\sum_{n=1}^\infty\frac{FCFF_n}{(1+DR)^n}$$ While we can take $$C$$ and $$D$$ from the balance sheet, the discount rate $$DR$$ can be calculated from the weighted averaged cost of capital. Therefore the only unknown parameters are the future cashflows. Future cashflows are in general hard to predict and the predictions become more uncertain the further into the future they go. Therefore most valuations attach a growth period to a stock of 5-10 years with the company falling into a state of stable growth afterwards. A reasonable estimate of the stable growth is usually the risk free part of the discount rate. Therefore we are left with estimating the cashflows of the next 10 years.

Now, while future cashflows are hard to estimate, we can look back in time and compare the prices of stocks e.g. 10 years ago to the fair valuation resulting from the real cashflows of the past 10 years.

This raises the question: Do stock prices really tend towards their fair value (as calculated exactly for the past)?

Or in other words: How good is the stock market at estimating future cashflows?

Edit:

Comparison to the efficient market hypothesis (Again please correct me if I missunderstood stuff)

As far as I understand it, the EMH states that at any given time the price of an asset reflects all available information about it. That is, at any given time the price of a stock reflects the expectations of future cashflows that can be extracted from publicly available information.

While one can argue about the truth of this hypothesis it does not cover my question. My question is about the intrinsic value that one would have assigned to a company in hindsight, knowing the future cashflows.

Example: lets assume a growth period of 10 years with a stable growth period afterwards. Then the fair value is given by $$FV=C-D+\sum_{n=1}^{10}\frac{FCFF_n}{(1+DR)^n}+\frac{1}{(1+DR)^{10}}\sum_{n=1}^\infty\frac{FCFF_{10}{(1+G)^n}}{(1+DR)^{n}}\\ =C-D+\sum_{n=1}^{10}\frac{FCFF_n}{(1+DR)^n}+\frac{FCFF_{10}}{(1+DR)^{10}}\frac{1+G}{DR-G}\\=C-D+\sum_{n=1}^{10}\frac{FCFF_n}{(1+DR)^n}+\frac{1}{(1+DR)^{10}}\frac{FCFF_{11}}{DR-G}$$ where we can simply put the stable growth rate $$G$$ to be equal to the risk free part of the discount rate. (I know there are different models to determine the terminal value and one can argue about this choice but let's stick with it).

Now if we want to estimate a stocks intrinsic value today, we have to estimate $$FCFF_1...FCFF_{10}$$. The statement of the efficient market hypothesis is that the price of a stock always reflects the best possible estimate of the future cashflows based on currently available information.

The EMH does, however, not make any statement about how good this estimate actually is.

What we can do to answer this question is to go back 10 years in time, plug in $$FCFF_1...FCFF_{10}$$ into the equation and compare the fair value we get from the calculation to the price the stock had 10 years ago. (Maybe 5 years would be a better estimate but one can of course vary this and ask the question for a different number of years forecasted)

Comment: I know this model is quite simplified (Assuming constant discount rates for example) and that there are other ways to determine the terminal value. Still, I think the simplifications should not lead to large deviations from more sophisticated approaches and the stable growth model seems to be the best fit for a general approach.

• This seems to be better fit for quantitative finance stack than economics.se. If you want you can keep it here as it would still be on topic since its not just about personal finance but general workings of the market, but I think you will get answers of higher quality on quantitative finance stack. – 1muflon1 Feb 5 at 17:22
• I am not quite sure where it fits better as I don't know the communities very well. If you think it fits better then I will post it there too. Thank you – Katermickie Feb 5 at 17:33
• You might be interested in the work of Robert Shiller who (working with the stock market as a whole, not individual companies) compared the "perfect foresight" future discounted cash flows with the market valuation. He found rather large errors, or equivalently that DR is not constant but changes very substantially over time. – noob2 Feb 5 at 19:43
• His 1st book was called Market Volatility (1990) and was initially quite controversial. There has been much additional research since then, of course. – noob2 Feb 5 at 19:48
• For a more recent overview of his work you might like this 2013 lecture nobelprize.org/prizes/economic-sciences/2013/shiller/lecture – noob2 Feb 5 at 20:25

Discounted cashflow is a framework. For a stable company with years of track record and predictable cash flows, it should give you a framework to conduct your analysis and form some opinion (or revise them). As you may have realized, it is extremely hard to predict cashflows and these predictions can depend on extraneous things as well. But DCF framework will give you a starting point. You can do this analysis and compare DCF value to stock price. If you see glaring difference then you can ask yourself questions as to why market is pricing different from what you are valuing. May be market believes future cashflow will be a lot more due to growth and therefore stock price is higher etc etc

However, please keep in mind that it is just a framework. And it fails miserably when dealing with new companies, new sectors, economic stress etc. Take a look at Amazon stock. why did price move up exponentially in last few years and why market didnt price it correctly when it was issued? There is no way for you to know what was market expectation of cashflow in the past really. Observable metric at any given point is stock price only. However, faith of market paid off and finally amazon (atleast aws) is producing a lot of cash and is expected to make much more cash in future.

The market price for any stock is a market estimate of that stock's intrinsic value. Assuming you do not have an exogenous belief that the market is either completely over/under-valued across the board, it then follows that half of the market is then overvalued and half undervalued. Whatever your belief thus, half the market will be relatively overvaued and half undervalued. The market had to guess about everything all of the time... and half of those guesses will be over, while half will be under.

The logic of "value investing" is precisely that a passive market strategy will thus always overweight the overvalued, while underweighting the undervalued. Over the last decade, this philosophy has consistently destroyed wealth, even more than the paranoid ranting of the gold/silver-bugs!

So if the logic of Value is mean-reversion, the logic of Growth/Momentum isn't necessarily explosive. It's best put in a word "convexity". If we're in a Depression and growth is stuck at zero (and so are interest rates, with a cap and the possibility of sub-zero like Japan or Europe), then ANY growth can trade at stupid prices IF it can be sustained.

That's the real problem here. Your model doesn't model the distribution of future discount rates... which is the essence of investors' dilemmas here ;-)

best, DEM

The market is actually very good at estimating future cash flows. I’ve done OLS regressions on time series estimate consensus provided by sell-side analysts, and for the next period earnings, r-squared hovers around .95. The problem is that most of a stock’s value comes from cash flows more than 5 years out. In that case, no one will be “good” at estimating company earnings, but in theory, the market gives the “best” prediction using all publicly available information at the time of the estimate.

Most factor models like CAPM and the Fama and French 3 and 5 factor model use ex-post returns in their factor estimation. The underlying assumption there is that realized market returns are equivalent to expected future returns on average.

In summary, stocks don’t just “trend” to their fair value. By the time you see them, banks, market makers, and Warren Buffet have all taken their slice, and the prices are re already at their fair market value. This is called Efficient Market Hypothesis.

• I understand that estimating company earnings many years into the future is vague to say the least. In that sense I view the efficient market hypothesis as kind of a redundant statement as of course nobody can at any point in time predict the future and the market just resembles the sum of all peoples knowledge. In that sense the efficient market hypothesis is a statement about a different kind of "fair value" than a typical intrinsic valuation. It is interesting to know though that next period earnings estimates are usually quite good. – Katermickie Feb 6 at 12:16
• The kind of fair value described by EMH is fair value or intrinsic value. There is no other type. Check out the Wikipedia page: en.m.wikipedia.org/wiki/Intrinsic_value_(finance) – Mild_Thornberry Feb 6 at 13:28
• @ Mild_Thornberry I edited the question. – Katermickie Feb 6 at 18:11