Crowd sourcing, mass psychology, and the market

Once upon a time I was teaching a math class, and posed a famous problem to the students that went something like this.

You are boarding a plane, which seats 500 passengers. Every passenger has been assigned a seat. All seats are booked. The first passenger boarding the plane misplaces his boarding pass, and so he chooses a random seat. Every other passenger sits in their designated seat, unless it is full, in which case they select a random (presumably unoccupied) seat. What is the probability that you, the last passenger in line, will arrive at your designated seat to find it unoccupied?

It happened to be one of those days when everyone was feeling lazy and uninspired, and nobody had any ideas on how to approach the problem, so I decided to try an experiment in crowd-sourcing. I asked each student to guess the answer, wrote them all down, and calculated the average. Surprisingly, it was very close to the correct answer (which appears at the bottom of the post).

What I found very surprising was that no guesses were particularly close to the correct answer. There were also a couple of idiots who guessed numbers larger than 1. My conclusions were that crowd-sourcing does seem to work--but requires a few idiots among the crowd to work properly.

Which brings me to the market.

In some past articles I discussed the topological equivalence between some common methods of technical analysis and the sort of dynamical analytical techniques I have written about in numerous other postings. The reason that TA can be used at all has to do with the importance of mass psychology in setting share prices, as opposed to economic fundamentals.

An area of stability in a phase space reconstructed from a time series tells us that the system is dominated by negative feedbacks, which tend to stabilize values in the time series within a relatively narrow range of values. A crowd-sourced price for a stock could be such a value--if the majority of market participants believe that $1 is the correct price for shares in a certain company, they will tend to sell when the price is higher and buy when the price is lower.

No matter how long the game plays, the price may remains a crowd-sourced number. It can change in response to fundamentals--for instance, when Atna recently placed the Pinson mine on care-and-maintenance, the crowd decided on a dramatically lower price for a share of Atna.

As in all crowds, there are a number of idiots who influence the price so much that they can temporarily overwhelm the fundamental case, until they either suddenly realize they have made a mistake or run out of money. If the crowd-sourced price is a mean of a population, that value can be exaggerated by a few idiots greatly overestimating (or perhaps underestimating) the real value of a stock or commodity.

For example:

Huldra Silver Inc., one year chart. I plead innocent--I never owned it.

Atna Resources Ltd., one year chart. I was one of the idiots who overvalued this one. 
Both charts from TSX site.

I tend to reject the efficient-market hypothesis. I think the market is almost always wrong, mostly because the majority of market players are missing some information. Sometimes the idiots are too high; sometimes they are too low.

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The solution is 0.5. Explanation.

Information flow in price selection, part 2: stock charting and insider trading

In our last installment, we looked at creating higher dimensional phase space diagrams from a single time series. This technique is useful for inferring the dynamics of complex systems from individual time series. In the phase space, the system at each instant of time is represented by a single point in a 2- or higher-dimensional graph. A sequence of points describes the evolution of the system through time. Traditionally we draw a smooth curve through the sequential points, which is described as the trajectory of the system.

Today I would like to look at reconstructing the phase space of some idealized stock chart patterns.

Let's look at a simple one: the symmetrical triangle. I have digitized an hypothetical stock price series in excel and plotted the series. I made the limbs of the formation approximately linear, but rounded the edges, as the reconstructed phase space plot will look better if the limbs aren't perfectly linear.

Wedge pattern in a hypothetical stock. Breakout is circled.








The figure above represents a wedge--though not a falling one. Like all time series, the data are one-dimensional. We can use excel to create a 2-dimensional phase space portrait by lagging the price data by a time that is roughly half the time taken to move from a short-term low to a short-term high (this may seem vague but it is because I have not presented a time scale on the above graph).

Two-dimensional phase space portrait of the above stock price. The two dimensions are the price, and the lagged price. The flow of the system is in the direction of the arrow. As time advances, the system follows the trajectory around first the outer loop, then the smaller inner loop, and after the breakout, towards the upper right corner of the graph.



In the first part of this essay, we looked at a simple chaotic function to see the relationship between the one-dimensional and two dimensional projections. The Lorenz equations give us a function that exhibits simple chaotic behaviour, which is believed to be characteristic of many natural systems. We saw that complicated looking butterfly function. Now let's look at a smaller portion of it--say 501 points (the ones I have selected are points 100-600) from the excel file generated last time.

Lorenz calculations showing x-values only from point 100 (at left) to 600. Looks a little familiar. . .





The above does look rather suspiciously like the wedge pattern in the stock price shown above. Except for one thing--time is flowing from left to right. So the wedge is actually running backwards when compared to the stock price pattern.

The 2-D reconstructed phase space portrait from the above graph, using a lag of 12 points. The abscissa is price (higher to the right), and the ordinate is lagged price (higher towards the top). At first glance, this looks a little familiar. We see what appears to be the same flow starting from the larger loop, spiralling inwards until Pow! Moonshot!








We wish all investing was this easy. But there is something wrong. Unfortunately, this trajectory starts at the upper right and moves to the region of low prices at the bottom left. Not such a good investment after all!

The characteristic feature of stock price charts is the apparent time reversal--the dynamics of stock prices flows through time backwards in comparison to those of natural systems. The dynamics of the natural system is driven by the flow of energy, with consequences following from causes. We see a rapid evolution towards a new area of phase space, and subsequent fluctuations represent instabilities which grow until the system rapidly shoots over to a new region of phase space.

So how do we explain the reversal in time observed in the stock chart patterns?

As my background is science, you will forgive me if I insist that the natural systems are going the "right" way through time and the economic systems are moving backwards.

Stock prices we normally consider to be driven by greed and fear. But what does this really mean? They are driven by flows of money, which represents information in the economic system (it is not the only information in the system). That the dynamics of the stock prices evolve through time in the opposite direction relative to natural systems suggests that players with foreknowledge of some forthcoming announcement (what we call "insider" information) are making good use of their information.

In the absence of potential profit, that "insider" information would not flow out into the market, but rather the market would learn the information at the time that some announcement is made by the company in question. The profit margin actually causes the information to flow out into the market more rapidly than it would flow otherwise. Furthermore, the very existence of such an opportunity argues against the efficient-market hypothesis.

In conclusion, it appears that stock charting gives us some limited forecasting ability in stock prices because trading on insider information is endemic in the markets.