Behavioral finance FAQ / Glossary (Probability) 

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

Probability / Probabilities
   (objective, subjective, conditional)



00/9i,10i - 01/2i,4i - 02/2i,5i,8i,9i
- 03/1i,5i,12i - 04/1i,4i,9i
- 05/5i
- 06/10i - 08/9i + see Bayesian,
distribution, model, risk, uncertainty,
utility, random, stochastic, base rate
fallacy + probabilities site link

Roulette mathematics.

Better know the odds!

Definition:

The probability of an event that happens randomly (see
random)
is a ratio that expresses the expected likelihood and frequency
of its occurrence.

To put it simply, it is

How many times - in average - that event will happen
if there are 100 draws.
For example, when throwing a coin, the probability is
50% that heads
come out (*).

The words "probabilities" and "odds" are most of the times used as
synonyms.

If we define more precisely the odds as the probability of non
occurrence vs. the probability of occurrence, the odds are 1 to 1
in the example above.

(*) Of course this cannot be verified with just a sequence of 100
      draw
s,but if on a rainy Sunday you spend your time making 100

sequences of 100 draws, you will see that the 10,000 occurrences
will closely match that ratio.

How to find probabilities and what for

Not forgetting the past when imagining the future?

This ratio most often derives from statistical distributions (see distribution)
that show the past frequencies of random events.

When those statistics are reliable and relevant to the situation, they
give what is called objective probabilities.

If probabilities are available (and relevant), which is a big "if",
to apply them to previsions and then to decisions
is seenas the most rational way to manage risk and to optimize
outcomes.

It can be highly dangerous to neglect them (see base rate neglect)

Applying probabilities to economic
     and financial decisions

Risk valuation is normally a key factor
in money matters.

But are people really walking computers?

As applied to asset markets, the classical "rational choice / rational
expectation" theory considers that, when people decide
either to invest in an asset, or to keep it, or to sell it,
those investors are supposed to


1)
Take into account, more or less consciously and
    mathematically, the risks / rewards
    probabilitie
s.

Those projections are supposed to give them a rather objective

 value: see (fair) value,

2) Adjust this expected value according to their attitude to risk, which 

gives their "expected utility": see that phrase.

What is called "financial quantitative analysis" uses market-
based mathematic models that are largely based on probabilistic
tools (see stochastic calculation).

They at least might help to detect discrepancies in the price and return
distributions.

Is to apply statistical probabilities always wise?

Choosing the right tool for the right work.


The pros:

Historical probabilities give precious information.

To ignore them (see base rate fallacy) is a common
error
that can put deciders into trouble.

.

Careful, the probability police is watching!


The limits:

Probabilities are sometimes overused / misused in
markets.

It can be dangerous to see them as pure / intangible "lotteries"
that offer well known and stable odds.
In markets, always complete them with a range of potential errors!

Actually, in this dield, applying probabilities based on known
frequencies is

* neither always possible

* nor fully reliable.


This is because uncertainty (see that word) often overcomes
measurable risk /
probability and therefore some misleading
factors can intervene:

Known data might be irrelevant

For completely new situations, past statistics don't exist,
    obviously,
    In times of upheaval, which the world experiences
    often
(such
as nowadays) historical references are
    poor predictors
.

In situations for which statistics exist, the data could be too

scarce or too short (for time series), or the sample too
small
(see small numbers, rare
events) to give a right
picture. It can even show the contrary of the real situation
/evolution

Even close-looking past situations can have hidden
    differences
.

Things change, there is no certainty that
past statistics  on apparently similar events/situations
reflect what will happen in the future.

All the more in social science phenomena, in which people can
change their usual behavior.


Standard distribution laws might be irrelevant

Events, even if they look so, various data distributions might not
be fully random.

They might not exactly fit like a glove a standard stochastic law
(see distribution).

This creates specific dangers (rare events / fast tails, asymmetries,
clusters: see those phrases).

The standard law might thus be applied wrongly to some situations.

Clear examples in economics / finance are
sudden illiquidity phases which rare precedents
did not show in recent statistics.

=> The famous "normal law" of randomness leads to a gross
      undervaluation
of risks.

To face uncertainty needs other types of
    
probability or even alternative tools

Uncertain does not mean improbable!


In cases in which statistics cannot be applied, we have

a situation of uncertainty, defined as a non
measurable risk
, (see the related glossary article).

This opaque mist tends to strike occasionally or frequently many
dynamical systems (see that phrase), for example financial and
economic activities are prone to such foggy periods.

Here we have to:

Use guesswork (subjective probabilities) and build a 

range of tentative scenarios (including extreme
ones),

by using deductions à la Sherlock, or analogies with other situations
.

It might help ...if done with a lot of precautions.

Adjust those projections after every new event (conditional
   probability
:
see  Bayesian).

See also the article on another alternative method called fuzzy logic,
that might be labeled "vague probabilities".

It was devised for situations that lack precisions, which is often the case in
dynamical systems.


But good reasons are needed to override
    objective probabilities
with subjective ones.


Often, even in cases when they are known and relevant, people tend to
neglect
historical probabilities (see base rate fallacy),
which is a common source of decision mistakes.

For example they often consider the odds as not too far from a
50/50 "heads or tails"
average, and therefore:

They overestimate low probabilities,

They underestimate high ones.

On the other hand, historical probabilities cannot be trusted fully either.

As seen above, they can get irrelevant in really new or very rare situations.

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

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This page last update: 12/09/15

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