It has been several days since our previous installment, where we laid out our basic hypothesis for how stock prices behave in response to changing expectations for the future in explaining why stock prices fell from the level they were on 22 January 2014 to the level they reached on 29 January 2014.

Today, we have enough additional data to tell how investors are behaving going forward in time from that data. And what that additional data tells us is that the change in U.S. stock prices from 22 January 2014 to 29 January 2014 was itself a noise event.

This outcome brings up a curious situation where we can directly challenge the theories of two of the three most recent recipients of the Nobel Prize in economics: Eugene Fama and Robert Shiller.

Starting with Shiller first, Chris Dillow recently provided a great description of Shiller's work and how it led to progress in the field of economics:

Back in 1936 Maynard Keynes said that share prices were more volatile than they should be. “Day-to-day fluctuations in the profits of existing investments, which are obviously of an ephemeral and non-significant character, tend to have an altogether excessive, and even an absurd, influence on the market,” he wrote. Prices, he continued, are “liable to change violently as the result of a sudden fluctuation of opinion.”

This, though, was no more than an idle claim. He offered no evidence to support it, other than a passing reference to American ice manufacturers and UK railway shares. It was a mere hypothesis.

Then in 1981 Robert Shiller – in work which was to win a Nobel prize – provided some solid support for this. He calculated that between 1871 and 1971 the S&P 500 was between five and 13 times more volatile than could be justified by changes in expected dividends.

This work represented genuine progress. An uncorroborated claim became an accepted empirical finding.

But our story doesn’t end there. Why are shares more volatile than dividends? The inference which Shiller invited was that investors were simply irrational. But he didn’t provide direct evidence for this. And this invited another interpretation of his result. If investors attach reasonable and varying probabilities to events which could have happened but did not, then prices will seem excessively volatile in hindsight even though they are reasonable at the time.

Take a moment, if you would, and read through the portion of our previous installment where we described how investors behaved through the end of 29 January 2014 (before we embarked on a "what-if" scenario).

It occurs to us that we now have a means by which we can quantify how investors might rationally and reasonably respond to risks in real time by assigning probabilities to events as they develop. For those events where the risk that investors face cause them to shift their forward-looking focus from one period of time to another, we can estimate the probability that they have assigned to the event in question by calculating how much the change in the growth rate of stock prices has deviated from the expectations associated from the level they were to the level associated with the expectations that go along with the event.

The level of expectations for each event is given by the change in the expected growth rates for dividends in future quarters.

Here, stock prices that match up with the perception of investors of the likelihood of a given event would be set at 100%, while the probability of it not occurring would be set at 0%. The varying probability would be represented by the percentage between these levels that stock prices are.

With that in mind, let's do that now with stock prices immediately before and after the 22 to 29 January 2014 noise event:

If all this sounds or looks somewhat familiar, it's because this isn't the first time that we've demonstrated this phenomenon with respect to expectations of the Federal Reserve's QE tapering policy.

Meanwhile, Eugene Fama's main contribution to the understanding of how markets work is the idea that markets are efficient - that asset prices reflect all known information because the market almost instantly incorporates information as it becomes known.

But if that's completely true, why wouldn't stock prices have instantly fallen to the level they reached on 29 January 2014? It's not like there were ever high odds in favor of the Fed not continuing its tapering of its QE bond buys.

In practice, this is an example of the market being inefficient, where the rational response of investors to risks associated with the Fed's QE tapering policy, something that Shiller's Nobel prize-winning theory says could never happen, actually created an inefficiency in the market, something that Fama's Nobel prize-winning theory says could never happen.

While that's bad news for current state of Nobel prize-winning economic theory, the good news is that if these kind of inefficiencies exist, it means that a sharp investor could take advantage of the resulting opportunities to profit, provided they could recognize and act upon them in real time.

This is not to say that either Shiller's or Fama's theories are completely wrong, since our own work in this space wouldn't be possible without very large portions of their preceding accomplishments, for which they have deservedly earned Nobel prizes. We would instead observe that there's more in markets to discover than what either Shiller or Fama have found.