Behavioral finance FAQ / Glossary (Asymmetry, skew)

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Dates of related message(s) in the
Behavioral-Finance group (*):

Year/month, d: developed / discussed,
i: incidental

Asymmetry / skew / skewness



00/8i - 01/2i,9d - 02/9i,12i -
03/11i - 06/1i,8d
+ see skew,
semi-volatility, distribution,
style + bfdef3

One side of the financial playing ground
is in the sun, the other in the shade.

Better be on the good side.
Anyway, wear sunglasses!

Definitions

1) Generally, to put it simply, an asymmetry / dissymmetry) is what is seen
     when

One side is higher, bigger, nicer, faster or weigh
more
than another

(in kilograms, in Euros, or under whatever other
measuring criteria).

Such cases are rather frequent and natural:

many systems or situations tend to get imbalanced
and tilted, either occasionally or continuously / repeatedly, either
slightly or massively,

Hold the wheel tight to keep on the good side, or ...jump out!


2) In statistical distributions, an asymmetry occurs
     when data in one side (*) do not perfectly mirror those in the
     other

(*) when taking the mathematical mean as the middle of the scale or the

graph, as such traits are better seen on a picture.

This data distortion, skew, bias, tilting is one of the aspects showing that
a series of events strays from pure random laws (see
random walk).

This distortion can hardly be called an anomaly, as
* reality has not to fit always
and fully a theoretical law,
* also some areas or types of situations show "normal"
   statistical asymmetries.

For example, some asymmetries match a "Pareto
distribution"
aka the "L curve" or "20/80 law"
(20% of events / cases make 80% of the volume at play)

This article is more about distortions that are less "normal", as
seen in some
time-series, such as market prices and return
evolutions that are supposed to obey the "Gaussian"random
walk (see distribution)

3) In social fields (politics, economics...)
    there are asymmetries between players.

Some are abler than others to take advantage of situations, whatever the
source of their "power".


1. Asymmetry / skew in asset markets

  returns and prices evolutions

Right-handed or left-handed markets?

This article focuses on financial markets asymmetries.
They affect the time-distributions of returns, risks and volatilities.

Markets, and typically asset markets, are supposed to
"walk at random"
and follow the "normal law" of
randomness
,
the bell-shaped "Gaussian" symmetric
curve (see "distribution").

But that purported well balanced randomness is actually rather
tilted.

=> Markets are submitted to various asymmetries.

The past frequency of prices and returns,

and whence their future probabilities,
do not always follows this balanced random law.

  Incidences on financial models

Divorce between reality and theory?
Or just dents in the models?

Better make those models flexible!

Asymmetries, among other market discrepancies (see leptokurtosis, fat tails,
clusters...), belong to so-called "anomalies" between theory and realities.

Those deviations are

Small and negligible, or large and decisive.

Too much weight on one side of the boat sends it down.

Temporary or permanent, occasional or repetitive.

Those distortions create doubts about the full relevancy
of many standard financial models built on "random"
probabilities.

At least, those deviations have to be taken into account in
the financial / econonomic models
.

* The equations have to be adjusted (see "tilting").

* More important, some flexible criteria / parameters, yes,
   tinkering possibilities
might be inserted.

As seen in this glossary, the "stock image" and also the
"underreaction-overreaction"
time sequence might be recognised
among those flexible adapters.

Of course, theoretical models can keep their usefulness, for example when
the distortion
between short term occurrences and the model signals that:

Either new phenomena are at play, which have to be entered in
   the model,

Or some long term adjustment / convergence is in sight in the real world

that will make theory and reality friends again.

  Some examples of discrepancies

Melting an ice cream cone

Often, in a daily returns curve that is supposed to be "bell shaped" as
following a normal random distribution law (see distribution):


The top of the bell (it shows the daily moves, which are

the most frequent) does not match exactly the mathematical
mean, like when an ice cream cone starts to melt.

Or   one tail is fatter than the other (see fat tails).

For example, in the stock market

* there might be more days of violent market rises than days of violent
   market falls or the reverse.

* also short term volatility seems more "violent" in panic periods

(crashes are the extreme examples) than in buoyant times.

Even if we do not focus on exceptional events, it happens more generally
that prices evolve differently on the downside than on the upside.

Using technical words, the downside price volatility often differs from
the upside one (see semi-volatility).

 A bit of mathematics:

 Normally, a logarithmic scale, reflecting the "geometric / hyperbolic progression" /
 log-normal law
, would erase the distortions. But even so, they seem to persist,
 or to become even more salient on the chart.

 
Not only price rises might differ from price falls in size, length, frequency,
 speed
(usually, uptrends last longer and are larger than downtrends), but the
 sub variations
also might differ in frequency and amplitude between the
 downward trend and the upward trend.

  Why those market asymmetries?

Nature-made or man-made?

Several factors might play a part in the price evolution asymmetry,
here are some:

The general trends that affects:

Fundamentals:

For example an upward trend showing a continuous economic
growth and / or inflation (*)

(*) Inflation creates "money illusion" (see that word).
     The value of one dollar or one euro varies from one year to
     the other.

Or their variations (accelerating or decelerating economic
   growth).


An asymmetry might signal some critical mass / threshold (of 

buyers / sellers) is at work, like in most dynamical system:

Here, usually, the price trend

* either crosses the threshold and accelerates,

* or is not strong enough to cross it and might revert.


Some common cautious practices such as "cut your loss / let

your profit run" can have an effect on price variations.


The main explanation seems to lie in collective
   behavioral biases
that distort evolutions,

For example: anchoring, stereotypesl, loss aversion, herding, and
obviously hope and fear...


2. Asymmetries between investors

As the saying goes,
some people are more equal than others.

 At least four factors differentiate categories of investors, and their impact on
 the market:

* Financial strength,

* Level of information,

* Cognitive and cultural abilities,

* Control of emotions and reflexes.

2a. Financial strength asymmetry

Asymmetric pockets and weaponry?

Big hands (professional investors with
access to large pools of money) can have more effect
on market prices than the small guy
s, even as a group.

It gives them sometimes an advantage (big players can
   create a
short term trend in their benefit, and if the situation

allows, start a long term one).

At other times it is a disadvantage: they have problems
   to find counterparties
ready to buy or sell large holdings.

In shallow markets, unless the big hand finds another big hand as
a counterpart,
a big mass of money cannot enter or leave easily
an asset as this would have a too strong impact on its price.


Another thing is that trading operations are now made at the
   speed
of light between computers by big banks and other
  
financial institutions, bringing new risks  (computer herding)
  
and a "speed asymmetry" between small and big traders)

The "asymmetric war" metaphor comes to mind if we compare investor
strategy with military strategy.

Imbalance on the battle field!

  2b. Asymmetry of information

Asymmetric phones?


There is a difference, no surprise here, between
private 
information (insiders...) and
public information
(see that word).


Also some professionals normally gather more (and more reliable)
information than the general public, and are more apt at sorting it by
relevance and at using it.

As they are better (and faster) informed, they are in a better position

to take advantage of market opportunities.

Those people "in the know" might include:

1) Company insiders (the managers, but also some employees, for

example those who sell the company's goods and services),

2) Market analysts and intermediaries.

3) Not to forget some dubious scheme builders (see the "deception"
    article).

To grasp the macroeconomics consequence of the asymmetry of information,

let us have a look at the Ackerlof's "lemon" parable:

Normally, the guy who sells you his used car knows it better
than you do.

This asymmetry makes people wary of second hand cars.

They are thus underpriced.

=> Therefore, owners of good cars don't put them on the market.

At the end, the market offers only bad cars (lemons).


Another case of information asymmetry is given by the "agency theory" (see
that phrase), which for example can make company's executives in a more
favorable situation than their shareholders.

2c. Knowledge asymmetry / cognitive
         
asymmetry / cultural asymmetry

Asymmetric books?


Whatever its access to information, each individual has its own way to
process it and to acquire its basic knowledge (see knowledge
acquisition).

Thus, general culture as well as specialized knowledge (and
    also reasoning abilities) differs largely between people.

  On the other hand, imitation can make emerge some consensual "
     common knowledge", that is true or flawed, adapted or not to the
     real situations.

In asset markets, one of the mispricing factors can be a

widespread knowledge deficiency by investors.

This tends to happen massively when market playing becomes a

craze and attracts many inexperienced and uninformed players.

2d. Emotional asymmetry

Asymmetric hearts and nerves?

Between categories of investors (see style, profile...), there are

Differences of "nerves": confidence, self-control, sense of timing,

vs. impulsions, hyperactivity (or on the contrary fear of action),

Differences of risk aversion (*),

Differences of any other feeling / emotion and affective tendency
    that
impact their decisions,

And also inner feeling asymmetries (*)


     (*) The prospect theory (see that article) shows some inner conflict

            and asymmetry
inside investor minds in their attitudes towards

            prospective gains vs. prospective losses.

(*) To find those messages: reach that BF group and, once there,
      1) click "messages", 2) enter your query in "search archives".

Members of the BF Group, please
 vote on the glossary quality at
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