**Behavioral finance FAQ / Glossary (Volatility)**

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

Year/month, d: developed / discussed,

i: incidental

Volatility

Many occurences, a standard

notion in financial theory+ see

random, semi-volatility,

heteroskedasticity, (volatility)

clusters, (volatility) cycles, risk,

volatility smile, volatility puzzle..

Gently vibrating returnscan mutate

intosudden hiccups that jolt prices.

The market road is rarely fully stable

and is sometimes really bumpy.

Use your safety belt and crash helmet.

Definition:In financial asset markets, volatility measures price or return

fluctuations.

As a popular market parameter calculated by market statisticians, it is......to simplify, the

average rate at which an asset price(*) something like x% a day or a month

rises and falls

...more academically, a

statistical coefficientthat measuresthe

average amplitudeof the asset returns(**),...even more precisely, the

average statistical dispersion(***)

of those returns in a given period.

(*) Some visual analogy in a chart is seen in theYou see then:zigzagging measures

by seismographs of the earth crust moves.

Usually,

slow vibrations

Sometimes or for some assetsstronger oscillations,in fact not too regular, as if investors drank a little too

much at the party.And in some cases

sudden jumps or dives.

(**) Actually, volatility is based onprice variations, which are

important components of returns.A price rise is a positive return, a price fall is a negative return.

Price variation returns

should normally be adjusted with additional.

incomes such as cash dividendsAlthough some stockmarkets adjust their index accordingly, most other

market statisticians do not bother too much about that. Why should they

stay late at the office?

(***) The dispersion of returns tells (see below and also the

"distribution"glossary article):1) what proportion of price variations are positive or negative,

2) what proportion of those variations are small or large.

To complete those definitions, what is calleda volatile assetis an assetand therefore returns, vary widely.

whichprices,

Therefore, in asset markets, volatility isusually

considered as a risk indicator.

Volatility and randomness hypothesis

A lottery of zigzags?

Mathematically, volatility is the

average size of the price.under the

zigs and zag,hypothesis that market evolutions

occur purely at random .

What is routinely applied to calculate it is

- as seen below -

the"standard deviation",

Actually some phenomena - which are analyzed also below - throw

some doubts about the hypothesis of a perfectly random phenomenon

that is behind this calculation

Calculation

Market wavelengths and tide coefficients

that tickle market toes.

1) Historical volatility

Here we have to mention some mathematical concepts related to

statistics.

The historical volatility of an asset is:

The

standard deviation()

of this asset's returns ( )

in a given period ().

(

) The"standard" deviationis an indicator of the

average distance from the mean

Now somemath:in series of random phenomena that

obey theGaussian "normal" law(see random, distribution),The "standard" deviation is the square root of the

dispertion variance.The dispersion variance (or said simply, the "variance") is:

"The arithmetical average of the squares of all

deviationsfromthestatistical mean".

Yes,

1)You collect all those deviations,You square them,

2)You make the sum of those results,

3)You compute their average, and,

4)

5)Fresh from the oven, you get the

variance.You take its square root, and you get

6)

thestandard deviation.

Piece of cake! ;-)

Obviously, if the standard deviation of the wave sizes is

2 centimeters, you are looking at a duck's wake in a

farmyard pond. If it is 5 meters,you are at the seaside

observing a surfer's paradise.

( )

Return = price evolution in that case.Speedy rise = high positive return.

Speedy fall = high negative return.

( ) The period can be one day, one month,

one quarter,one year..By convention the volatility is usually calculated by

using36 observations in one year.But we can consider that there are

several kind of

volatilities, according to their durations.Very long term "cycles" cannot be defined in the same

way than intraday vibrations.

2) Implied volatility

The implied volatility (a kind of anticipated volatility) is given by another type

ofcalculation,taken from financial option pricing models.Therefore it can be calculated only when there is an option market for the

asset.

What is the purpose of those calculations?

Something to do with (identified) risk.

Volatility is one of the key concepts of theoretical finance,

as anindicator of the financial market risk.

Of course this indicator gives only alimited information

ton he real risk, as

Risk(see that word)isnot just volatility

Also, volatility tellsonly the identified risk,the risk

showneither by the market history or by the current

situation.

The fact that volatility is a quite practical indicator

should not make decision-makers forget its limitations

This indicator is used in financial calculation, either directly, or via

two composite parameters:

Beta coefficient, a mythic financial parameter (see the

relatedglossaryarticle).

Sharpe ratio. It measures=/

the relation between the returns (the numerator) and the risks

(volatility, as the denominator) during a given period.

The causes of volatility

Why those ripples in the pond?Whether or not a purely random phenomenon, the volatility that affects a whole

market - or an individual asset - seems to be linked to:

1) Technical market imperfectionsThis regards situations in which prices that do not fit the law of

supply and demand in perfect competition.This is what happens for example in case of

under-.

liquidityWhen markets lack liquidity (very few buyers and/or sellers),

large price changes are needed to find counterparts for large

buying or selling orders.

2)The fact that, even in perfect markets, the timing of

selland buyorderscannot fully coincide.The market machine has always "vibrations", like

any dynamical system.

Even in quiet periods, there is not such thing as a fully

"stable equilibrium" (see equilibrium).

This is accentuated or moderated by the actions of market

players (noise traders, technical analysts, quants: see

those names) that are triggered by mysteriousmarket

"signals"they consider to have detected.

3)Whatever the traded assets, the generaluncertainty/

ambiguity .In human and social fields, as in any evolutionary field,

new - andarise (see

sometimes unpredictable - phenomena

"emergence", "rare events"...).

Here, statistical data, based on previous frequencies ofknownevents, can mislead about future probabilities, as

thoseunprecedented events might strike at any time.This uncertainty translates into

fluctuating

investor anticipations.

Their prices / returns predictions are unstable.This implies either cognitive reasons or emotional

mood variations:

contagious hope / greed today, doubt / fear of tomorrow.<

What makes you shiver today: fright or bliss?

Volatility is higher when uncertainty is higher, notably after a

hard to gauge "surprise".

4)Instock marketsmore specifically,earnings

uncertainty.

Future financial results (earnings...) of

corporationswhich stocks

are traded cannot be predicted with certainty.

Surprises are always possible!The less the firm's (or the whole economy) prospects have

visibility, the more investor opinions diverge and shift.=> Often, a high volatility means a

period in which investors.

are feeling less certain of the futureThey see assets as more risky which leads to a higher risk

premium.Also volatility is higher for stocks of firms that either have a

past(in other words which were volatile in the

record of instability

past), or prospects which are sensitive or far from predictable.Thus

high volatility often accompanies either a

general bear market or only stocks with uncertain

prospects.

Is volatility really random? Is it predictable?

Expecting vanilla randomness?

You might be served somespicy, sticky, skewed,

fluctuatingand dramatically evolvingrandomness.

To use historical standard deviation measurements as a referencetakes for.

granted that the phenomenon is random and stableYes, stable randomness, that would follow a "law of randomness"

(see distribution).There are several snags in this (or mental anchoring we could say,

in our behavioral finance jargon) as, on the contrary:

1)Volatility, in the broad sense of a degree of fluctuation,cannot be

labeled a purely random(pure "Brownianphenomenon

movement").Behavioral aspects can distort fluctuations by creating

"sticky" events:* High volatility

clustersin short periods, like when an

earthquake strikes.* Or

trend persistence, in the case of long term volatility.

2)Thus,often, volatility does not obey a Gaussian distribution lawInstead of a standard deviation around the mean (mean-

variance), the actual distribution shows often fat tails,

asymmetries / skew, clusters, diverging semi-

volatility, volatility smile...(see the related articles).

Thus,downside volatility,which can be higher or lower than

theupside volatility,is often a more important parameter

than full volatility (this data is used in theSortino ratio, a

half brother of the Sharpe ratio)

3)Also, volatilitychanges at times(instability, regime switching).Usually there is a flurry of

excess volatilityin periods of* either exuberance / overconfidence

* or panic /uncertainty.

They are followed by calmer periods, the "aftershocks" being milder

and milder.In other words, volatility itself is volatile. The dance changes its

tempo.

Volatility fluctuations,from a rather stable phase to a

chaotic phaseand back, likein many dynamic systems, donot follow apurely random law: see heteroskedasticity,

(volatility) clusters,(volatility)cycles, (volatility) kurtosis,

(volatility) skew...

4)Statistics show onlypast behaviors. And, as seen

below (volatility puzzle), the past volatility is not completely reliable

to predict the future one.

Here, calculations based on financial option prices are useful.

They help to measure the (expected) future volatility

(implied volatility).

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

Year/month, d: developed / discussed,

i: incidental

(excess) Volatility

05/6i, 08/6i

+ see heteroskedasticity,

(volatility) clusters, (volatility)

cycles

Volatility clusterSee (volatility) cluster

Volatility smile03/7i

Happy options?The distribution of

implied volatilities in financial optionsdoesn't fit

exactly the calculations given by the option theory.

In market reality the implied volatility of in-the-money (ITM)

or out-of-the-money (OTM) options ishigher than.

the volatility of at-the-money (ATM) optionsThus,

the graph of the implied volatilitiesof all the strike prices of all

options

having the same maturity is approximatelyU-shapedlike a

(volatile) smile.

downside) or (semi-) VolatilitySee volatility,

semi (volatility)

Volatility puzzleSee volatility

What makes it moves?

What does it entail?

What is its amplitude?

Mysteries remain!The problems about volatility are that:

What

causesvolatility, and how it evolves, has never be fully explained,

as seen in the "volatility" article.

But its existence is not a surprise, as

dynamical(see that phrase)

systemsrarely reach full

equilibrium .

There are always small "vibrations" and sometimes more

fundamental changes / disruptions.

There are

various kinds of volatilities,short term and long term to

cite the main ones.Actually that difference between the small vibrations and the more

radical changes makes wonder if they are related phenomena.

Its relevanceas a proxy for risk is disputed: see the "risk"

article.Volatility is based

past statistics

(or, as concerns the "implied volatility" on instant observations).

Thus, even if it is linked to some aspects of risks - those already seen

before -it gives an imperfect information about the future ones.In other words, there is always some uncertainty (see that word) left

and volatility is animperfect anticipation tool.

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1) click "messages", 2) enter your query in "search archives".

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