Behavioral finance FAQ / Glossary (Random walk)

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

Random, randomness

See distribution,
random walk hypothesis

Random walk hypothesis / RWH




00/8d,12i - 01/1i,9i,11i

- 02/1i,2i,4i,8i,10i - 03/12i
-
04/3i,5d,10i - 06/7i + see
arbitrage, distribution, risk,
persistence, probability
+ bfdef

Strolling in the Stock Mall to buy a stock?

Are all of them equally worth their price?
Can they be picked at random?

Definition:

The random walk hypothesis / RWH states that

in perfectly competitive and well informed
financial marketsthe upwards and downwards price
variations occur "randomly".

Here a definition of randomness / random walk is
needed.

To put it simply, in finance (and in some other fields, such as physics...),
when things (prices, returns...) move in a random walk:

You cannot predict the next event (here, the next price
    move
)

Whether to find a gold coin or get mugged at a street
corner.

But its occurrence fits a precise
   probability aw
(law of large numbers)
   you can observe when you
look at the broad picture

(= after you have seen many draws).

If that hypothesis was valid, you might conclude, as you could not
predicthow asset market prices will evolve , that:

The current prices are based on current information,

They are the "right" prices at the moment,

They would change only when new decisive and unexpected events
   surge
(for example a massive loss by some bellweather corporation).

Those are the (debatable) assumptions the EMH (see that acronym)
claims, seemingly confusing market traders with regulation robots.

When prices walk (randomly),
    returns also walk (randomly).

When an asset, such as a stock, is listed in a public market, its return depends
largely (if dividends are not taken into account) on market price
variations.

Those variations bring capital gains or losses, which are crucial return
components
.

When prices walk, returns walk. Thus if prices walk randomly, returns
follow like shadows in their random steps.

Thus, are asset markets pure lotteries?

Is it like throwing dice?
Or is it another species of randomness?

Flat? Or bell shaped?

As said above, market price rises and falls are usually the main components
that make asset returns.

A random evolution of those moves does not mean that returns follow a
"flat" lottery distribution
, in which each event, each move (daily
returns for examples) would have the same frequency of drawing.

So, if frequencies are not the same, how are they "distributed"?

What the random walk hypothesis supporters claim is
that market price moves are distributed in a symmetric
"Gaussian distribution"
(aka normal law, or log-
normal
law, or bell curve).
See "distribution".

If such a standard distribution is at play in past moves, it is deemed possible
to apply it to future moves, thus to measure probabilities
and therefore risk
(see those words)

Smooth and regular? Or wild and stormy?

Another - maybe more important - difference with a lottery, is that
there  is always a part played by:

Non random elements, often in the form of stickiness
   (price or return
clusters), as statistical distribution

   anomalies (see below).


The unquantifiable uncertainties of markets.

When events are totally new and thus did not appear in
past statistics,
their frequency is not
measurable.

As a consequence, their future probabilities, thus their 
risks, are unknown
and can only be estimated.

Whatever the clues, it is a matter of guesswork.

What could cause
     market price / return randomness?
 

Is the randomness in the market or in the world around?

This price / return randomness, when effective, would result from
two effects: 1) endogenous and 2) exogenous

The players

1) The endogenous (*) randomness

is the one that financial  market
players create.

The players behaviors
are unpredictable
.

Thus, the financial tail
might
wag in a different
way than
the economic
dog.

The theater

2) The exogenous (*) randomness

is the random occurrence of new
events
and information with

economic impacts.



Random events that
affect fundamentals
influence
in their turn
financial market prices.

The economic dog
wags
the financial
tail.

This randomness is
consistent with the
EMH.

(*) This is the vocabulary for financial market analysts.

An economist might use the semantic in the opposite way,
seeing the economy as the endogenous world and the financial
market as the exogenous one.

Everybody can choose its side on that matter :-)

Is randomness always present,
     and linked to the EMH?

Efficient randomness? Random efficiency?

The RWH is a concept often associated with the EMH / efficient market
hypothesis.

But the twining is not perfect, the two notions are not fully identical.

The RWH just states that most prices move at random, or at
    least unpredictably.

It does not infer that markets always find the right

balance that makes assets always fairly priced
with prices that reflect efficiently the information flow.

If the market is efficient, prices should move exclusively by following the
exogenous randomness.

But we have just seen above that price moves take place even in the lack 
of new fundamental events, or in contradiction to them.

Therefore:

Nothing proves that a random price evolution - for an

asset or asset class - signals that it is priced efficiently.

Even "inefficient" or fully crazy prices might

move randomly in some circumstances.

Behavioral finance, which brings a reserved attitude towards the EMH,

accepts its brother, the RWH only in some degree.

It recognizes some random phenomena in markets, or at least a large

unpredictability of prices / returns evolution.

On the other hand, BF stresses the existence of phenomena that

are not fully consistent with randomness.

Those phenomena are distribution "anomalies", which are not just optical
illusions when reading statistics.

Those discrepancies are developed in this site.

Salient examples are trends, clusters, fat tails, leptokurtosis, skews,
and other
"sticking" effects.

Does randomness preclude arbitrage?

Choosing our horses at random?


This large unpredictability linked to the random hypothesis is said to entail
another concept,
the "absence of arbitrage opportunity" (see the
"arbitrage" glossary article).

Under that theory, if evolutions are random and cannot be predicted, there
would be no reason to buy or sell
a specific asset preferably to another, or
even to buy or sell it at all.

This "better stay at home and sleep" theory has some
analogy with a traffic jam, in which you are not sure to advance
faster if you take another lane, or even if you change your itinerary.

Anyway, various financial models (see model) that try to find ...arbitrage
opportunities from slight random variations around that rule.

Actually, it seems that arbitrages might still be opportune in some
cases
:

Some repetitive distortions take place rather often (see
   "persistence" or "percolation" for example)
.

They make the financial evolutions not completely random.

Some price moves might even get predictable in some (rare) situations.

Some so-called "rare events" seem more frequent than
   the
standard laws of probabilities (i.e. the Gaussian distribution)
   predicts (see clusters, fat tails...).

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

Members of the Behavioral Finance Group,
please vote on the glossary quality at
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