Misconceptions of Regression

Forgive me as this is an usually long post (even for me!) It is a passage from a book I've just started reading called "Judgement under uncertainty: Heuristics and biases" by Daniel Kahneman, Paul Slovic and Amos Tversky.

Suppose a large group of children has been examined on two equivalent versions of an aptitude test. If one selects ten children from among those who did best on one of the two versions, he will usually find their performance on the second version to be somewhat disappointing. Conversely, if one selects ten children from among those who did worst on one version, they will be found, on average, to do somewhat better on the other version. More generally, consider two variables X and Y which have the same distribution. If one selects individuals whose average X score deviates from the mean of X by k units, then the average of their Y scores will usually deviate from the mean by Y by less than k units. These observations illustrate a general phenomenon known as regression toward the mean, which was first documented by Galton more than 100 years ago.

In the normal course of life, one encounters many instances of regression toward the mean, in the comparison of the height of fathers and sons, of the intelligence of husbands and wives, or of the performance of individuals on consecutive examinations. Nevertheless, people do not develop correct intuitions about this phenomenon. First, they usually do not expect regression in many contexts where it is bound to occur. Second, when they recognise the occurrence of regression, they often invent spurious causal explanations for it. We suggest that the phenomenon of regression remains elusive because it is incompatible with the belief that the predicted outcome should be maximally representative of the input, and, hence, that the value of the outcome variable should be as extreme as the value of the input variable.

The failure to recognise the import of regression can have pernicious consequences, as illustrated by the following observation. In a discussion of flight training, experienced instructors noted that praise for an exceptionally smooth landing is typically followed by a poorer landing on the next try, while harsh criticism after a rough landing is usually followed by an improvement on the next try. The instructors concluded that verbal rewards are detrimental to learning while verbal punishments are beneficial, contrary to accepted psychological doctrine. This conclusion is unwarranted because of the presence of regression toward the mean. As in other cases of repeated examination, an improvement will generally follow an outstanding performance, even if the instructor does not respond to the trainee's achievement on the first attempt.

Because the instructors had praised their trainees after good landings and admonished them after poor ones, they reached the erroneous and potentially harmful conclusion that punishment is more effective than reward.

Thus, the failure to understand the effect of regression leads one to overestimate the effectiveness of punishment and to underestimate the effectiveness of reward. In social interaction, as well as in training, rewards are typically administered when performance is good, and punishments are typically administered when performance is poor. By regression alone, therefore, behaviour is most likely to improve after punishment and most likely to deteriorate after reward. Consequently, the human condition is such that, by chance alone, one is more often rewarded for punishing others and most often punished for rewarding them. People are generally note aware of this contingency. In fact, the elusive role of regression in determining the apparent consequences of reward and punishment seem to have escaped the notice of students in this area.

Forecast like a politician

I'm still reading a collection of Bertrand Russell's sceptical essays and today came across the quote below.

As I read the words "forecasting opinion" it struck me how closely an analogy might be drawn between democratic political process and the operation of financial markets. As a preference processing system, financial markets are just another voting machine and an obvious manifestation of liberal democratic ideology.

My question is, could the intuitive forecasting processes used by politicians be adapted for prediction of financial market behaviour? How might such an approach overcome the limitations inherent in "expert" approaches that tend narrowly to focus on how participants ought to behave rather than how they are actually behaving?

I was particularly attracted by the line "It is useless to urge that politicians ought to be high-minded enough to advocate what enlightened opinion considers good, because if they do they are swept aside for others." With financial markets, the clear parallel is with making a bet against the prevailing view. Even if the crowd are acting in a way that is unsupported by fundamentals, fading their move may still see you swept aside and your capital much diminished.

Here's the passage in full with emphasis added:

"There are at present two very different kinds of specialists in political questions. One the one hand there are the practical politicians of all parties; on the other hand there are the experts, mainly civil servants, but also economists, financiers, scientific medical men, etc. Each of these two classes has a special kind of skill. The skill of the politician consists in guessing what people can be brought to think advantageous to themselves; the skill of the expert consists in calculating what really is advantageous, provided people can be brought to think so. (The proviso is essential, because measures which arouse serious resentment are seldom advantageous, whatever merits they may have otherwise.) The power of the politician, in a democracy, depends upon his adopting the opinion which seem right to the average man. It is useless to urge that politicians ought to be high-minded enough to advocate what enlightened opinion considers good, because if they do they are swept aside for others. Moreover, the intuitive skill that they require in forecasting opinion does not imply any skill whatever in forming their own opinions, so that many of the ablest (from a party-political point of view) will be in a position to advocate, quite honestly, measures which the majority thing good, but which experts know to be bad. There is therefore no point in moral exhortations to politicians be disinterested, except in the crude sense of not taking bribes."

On philosophical pragmatism...

Some thoughts on philosophical pragmatism from one of Bertrand Russell's "Sceptical Essays":

"Although pragmatism may not contain ultimate philosophical truth, it has certain important merits. First, it realises that the truth that we can attain is merely human truth, fallible and changeable like everything human. What lies outside the cycle of human occurrences is not truth, but fact (of certain kinds).

Truth is a property of beliefs, and beliefs are psychical events. Moreover their relation to facts does not have the schematic simplicity which logic assumes; to have pointed this out is a second merit in pragmatism.

Beliefs are vague and complex, pointing not to one precise fact, but to several vague regions of fact. Beliefs, therefore, unlike the schematic propositions of logic, are not sharply opposed as true or false, but are a blur of truth and falsehood; they are of varying shades of grey, never white or black.

People who speak with reverence of the 'Truth' would do better to speak about Fact, and to realise that the reverend qualities to which they pay homage are not to be found in human beliefs. There are practical as well as theoretical advantages in this, since people persecute each other because they believe the know the 'Truth'. Speaking psycho-analytically, it may be laid down that any 'great ideal' which people mention with awe is really an excuse for inflicting pain on their enemies. Good wine needs no bush, and good morals need no bated breath."

The sinister side to this philosophy is the idea that "Truth ... is what pays in the way of beliefs. Now a belief may be made to pay through the operation the criminal law. In the seventeenth century, Catholicism paid in Catholic countries and Protestantism in Protestant countries. Energetic people can manufacture 'truth' by getting hold of Government and persecuting opinions other than their own."

Russell goes on to critique what he believes are the the exaggerations latent in this view. Let me know if you'd like me to post more on the topic. Otherwise, the book is called "Sceptical Essays" and it is Routeledge Classic.

Derren Brown explains the art of "Cold Reading" to Richard Dawkins

From Dawkin's two-part documentary "The Enemies of Reason"

Part 1

Part 2

Part 3

Part 4

Part 5

Part 6

Some interesting videos on the falliability of our perceptions

Two part series by Derren Brown: "Can NLP be weaponised?"
http://www.youtube.com/watch?v=dU10LTfF9UQ
http://www.youtube.com/watch?v=eyl22X2v6zg

Reponse to The Falcon on the matter of independent betting markets. Also, how Warren Buffet unwittingly changed the world.

You know Falcon, you've brought us full circle and back to the crux of the market conundrum.

I know we've talked of this before, but the mispricing in the horse racing situation does not influence the outcome because it is independent of the bettors expectations. This means that if you know the real factors that influence the outcome of the race you can take advantage of that mispricing, much like the quantitative horse racing model Thor sent a while back that used an algorithm that balanced approximately 120 weighted factors.

(quantitative horse model: http://www.contingenciesonline.com/contingenciesonline/20090506/?sub_id=qxyLfphSqUiJ)

As we know that is not the case with financial markets owing to feedback between expectations and outcomes. Those feedback loops are deep, varied and I'd imagine nearly impossible to quantify in a non-stationary way.

For example, the present sharp rally in equities might reflect the most optimistic recovery themes. Without an objective metric we'll never actually know. But what we can strongly suggest is that the rise has allowed many firms to raise additional capital where they would have otherwise been unable. This has undoubtedly changed the future path of their businesses in an unknowable and unalterable way. In addition there will have resulted certain less tangible elements that stem from prices acting a signal, e.g. of broader sentiment and the perceived wealth effects. In other words, do the higher equity prices encourage consumers to spend, employers to hire, etc?

This isn't just abstract Kantianism. This is a fact.

Warren Buffet once remarked that in the short run markets were a "voting machine" but in the long run a "weighing machine". But I doubt strongly whether the market machine serves two masters. Instead, I suspect that Buffet has been unusually lucky in the sense that the voting machine has always tended to eventually validate his weighing process.

And why wouldn't it? In the same way Smith's work cemented our belief in the "laws" of supply and demand, Graham's Security Analysis has had a profound influence on beliefs about valuation. As just another belief, this is liable to change with time. However, at the present time it appears that while price might deviate substantially from "value" in the Graham/Dodd sense, eventually price and value converge and reward those with the time, liquidity and patience to wait for it to do so.

And this is where Buffet has been genius. He has always ensured that any acquisition has provided him with "float". These invaluable free cash flows have funded his speculation while waiting for the voting machine to catch up. Stripped of all the narrative it is just another convergence bet, not too dissimilar to the ones made by Long Term, with the exception that Buffet due to his fear of leverage and use of "float" has always been in a position to withstand the liquidity risks associated with convergence bets.

I also think it is interesting to ponder how Buffet has played a hand in spreading the Graham and Dodd gospel upon which he relies to make a profit. What would the world now be like without Security Analysis, and without Warren Buffet?

So finance guru's, the question is how then to create a model which can account quantitatively for exogenous and endogenous factors?

Finally, one thing to note with that quantitative horse betting model is that their experience working solely off the 120 factors was relatively mixed. Their performance didn't' really improve until they incorporated market generated prices into the model.

Copy and Paste : The Falcon's response to my post on the role of belief's in markets

In response to the prior musing, my friend "The Falcon" added

The Melbourne Cup reference is an interesting one - and for this reason:

" Imagine if every single punter at the Melbourne Cup this year placed
their bet on the apparently irrefutable communal belief that only even
numbered horses win races... it would considerably alter the market's
pricing dynamics. "

The result would be mis-pricing in betting markets - however, the result
of the race itself would remain unaffected.

The scary thing is - if the same latent human desires create misguided
human beliefes in the market place then the result is a grave
misallocation of so called scarce resources.

Then again - maybe my desire to have resources optimally allocated is
feeding some evolutionary drive that has been with me since I first
climbed out of the slime millions and millions of years ago....