Behavioral finance FAQ / Glossary (Cluster)

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Dates of related message(s) in the
Behavioral-Finance group (*):
Year/month, d: developed / discussed,
i: incidental

(price, volatility) Cluster / Clustering

00/6i,8i - 03/12i - 04/5i,10i +
see distribution curve,
round number, congestion,
accumulation, percolation, TA,
heteroskedasticity, stickiness
+ bfdef3

Just pour flour into a sauce to see the devilish tendency of
nature to make lumps

Or leave a string in a drawer to discover later that it
mutated into a mess of knots


In statistical series, a data cluster is a grouping of values (numbers)
that are close to one another
(for example similar daily returns in an
asset market)

Those closely similar numbers stick together in the distribution chart like gulls on
the same cliff.

Numbers that have a herding tendency?

That grouping makes a data "lump", an irregularity  in 
an otherwise linear or random distribution of events.

Markets and clusters

Little molehills on the market pasture.

In asset markets, price distribution clusters happen when prices:

stay frozen for a time more or less at the
    same level

cluster /

Or are caught in a trend that rises and 
falls for a time, creating then positive or negative
returns for the owner.


Or stick for a time in a  volatilility
that is higher or lower than usual.


Data clusters. Anomalies? Or not?

Meeting together by chance at a street corner?

Such distortion in the harmony of the distribution curve can be called
an "anomaly", if we define anomaly as a divergence from generally accepted
probability laws.

The questions are thus: are clusters normal traits in random series?

Or do they show that the data distribution does not obey a random law?

Here, economists use their two hands (on the one hand..., on the other
hand...) as the saying goes:

Clusters can happen even in completely random
    series (see cluster illusion). Randomness does not 

mean absolute regularity.

When throwing dices you might draw the same number
twice in a row just by coincidence.

It is only in the long run (law of large numbers) that true
probabilities appear.

If there was full regularity in random events, it would be easy to
predict the next occurrence (or next cluster), or at least the
mythical "reversion to the mean" (see gambler's fallacy), or
whatever other behavior.

Thus those events ...would not be random.

But un some cases clusters of similar events or numbers

occur above a "normal" frequency and amplitude.

In other words they deviate from a classical
distribution law,
for example the "normal law": see

Here we have real stickiness that alters randomness

Clusters are just an example of such statistical deviations from

They can even combine with other distortions, such as
asymmetries, fat tails and others
(see those phrases).

Clusters are even more conspicuous and "anomalous",
when they are asymmetric compared to the rest of the
distribution curve, as located on one of its side only.

Price / return / volatility clusters
     in asset markets

Sticking together in the money pool.

As seen above, occasional clusters are usually just kinds of traffic jams
happening as "accidents" that still fit the random law.

They are run of the mill events in market price evolutions.

Thus, to see clusters as significant patterns in such occasional cases

is probably a clustering illusion (see below the related article).

     On the other hand, again in capital asset markets, clusters that really

distort the randomnes scan be rather frequent.

 This is another dent in the "RWH / random walk hypothesis" (see that


Asset market clusters relate to price moves affected by complementary
parameters that show three types of rather frequent clusters:

Price cluster

(or neutral return
trend): when the
market stalls
for some
, as if





Sometimes, prices, after following an uptrend
or downtrend, stick (cluster / congest) for a
rather long period around some value.

There is a "stasis" something like an "hesitation"
or a lack of decisive evolution factors.

That price stickiness might even
signal some investor disinterest.

Boredom might make prices sticky.

After that phase, prices "decide" to rise or fall
until they percolate (see dynamical system) into
a new marrket life phase.

In a price curve resulting from an historical
data series charts (time-distribution), such a
roughly stable prices period appears as a cluster.


when prices
move for a
long time in
the same

Here we have persistent trends in which prices
rise or fall for several months
in a row
result in periods of higher / lower returns.

As price fluctuation are a major part of asset
returns, distorted price fluctuations make
distorted returns.

This cluster of high or low returns lasts until
the "reversion" is overdue.


When vibrancy
is low or high

Those are short periods when price changes
are larger / smaller than
usual, independently
of the long term trends described in the boxes

See also heteroskedasticity

How to explain the existence of such clusters
     in asset markets?

Declaration of dependence.

See "trend" for the explanation of the positive and negative return clusters.

It can signal that players are not fully independent of one another
in their behaviors.

The market is then subjected to:

Either a widespread collective mental anchoring (see that

definition) on past prices, or on round numbers,

Or - albeit less frequently - an asset accumulation or distribution

(see those definitions) by financially strong buyers or sellers.

Or even a market manipulation by those "big hands" who "exploit"

the anchoring of the poor small naive players proletariat.
Aaargh, kamarades!

TA (see technical analysis) fans see those barriers / congestions as
"signals" about the future market prices orientation (zones of support,
of resistance

They can be interpreted as minor percolation thresholds, around which the
market hesitates
between two directions:

* either jumping the barrier to follow the previous momentum,

* or going back (reverting the trend).

Cluster illusion

See cluster, superstition,

A cloud or a flying saucer?

Bring your plane closer to avoid optical confusion!

A cluster illusion is a representativeness heuristic
(see heuristic) by which people see patterns in
data series although occurrences are perfectly random.

For example investors or technical analysts might:

Perceive price or return clusters that do not exist, a kind of optical
   or mental illusion

Or interpret as durable or repetitive patterns some clusters that are real
   but are just occasional coincidences which always exist in

They are more salient (and more illusory) when the data series are small or
limited in duration, as things do not have time to average out.

Extreme cluster illusions can be found in superstitions when coincidences
are taken as signs from the sky.

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