Behavioral finance FAQ / Glossary (Volatility)

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Dates of related message(s) in the
Behavioral-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 returns can mutate
into
sudden 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
      rises and falls
(*) something like x% a day or a month

...more academically, a statistical coefficient that measures the
       average amplitude of 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 the zigzagging measures 
       by seismographs of the earth crust moves.
You see then:

Usually, slow vibrations
Sometimes or for some assets stronger 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 on price 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 dividends
.

Although 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 called a volatile asset is an asset

which
prices,
and therefore returns, vary widely.

Therefore, in asset markets, volatility is usually
      considered as a risk indicator.

Volatility and randomness hypothesis

A lottery of zigzags?

Mathematically, volatility is the average size of the price
zigs and zag,
.under the 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" deviation is an indicator of the
        average distance from the mean

Now some math: in series of random phenomena that
obey the Gaussian "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
deviations 
from the statistical mean".

Yes,

1) You collect all those deviations,
2)
You square them,
3)
You make the sum of those results,
4)
You compute their average, and,
5) Fresh from the oven, you get the
    variance.
6)
You take its square root, and you get
     the standard 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
using 36 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 an indicator of the financial market risk


Of course this indicator gives only a limited information
ton he
real risk, as

Risk (see that word) is not just volatility

Also, volatility tells only the identified risk, the risk

shown  either 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
   
related glossary article).

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 imperfections

This 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-
liquidity
.

When 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
    sell
and buy orders cannot 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 mysterious market

"signals" they consider to have detected.


3) Whatever the traded assets, the general uncertainty /
ambiguity .

In human and social fields, as in any evolutionary field, new - and
sometimes unpredictable - phenomena
arise (see
"emergence", "rare events"...).

Here, statistical data,  based on previous frequencies of 
known events, 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) In stock markets more specifically, earnings
    uncertainty
.

Future financial results (earnings...) of corporations which 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 future
.

They 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
record of instability
(in other words which were volatile in the
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 some spicy, sticky, skewed,
fluctuatingand dramatically evolving
randomness.


To use historical standard deviation measurements as a reference takes for
granted that the phenomenon is random and stable
.

Yes, 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
phenomenon (pure "Brownian
    movement").

Behavioral aspects can distort fluctuations by creating
     "sticky" events:

* High volatility clusters in 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 law

Instead 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 

the upside volatility, is often a more important parameter
than full volatility (this data is used in the Sortino ratio, a
half brother of the Sharpe ratio)


3) Also, volatility changes at times (instability, regime switching).

Usually there is a flurry of excess volatility in 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 phase and back, like in many dynamic systems, do 
not follow a purely random law: see heteroskedasticity,
(volatility) clusters,
(volatility) cycles, (volatility) kurtosis,
(volatility) skew...


4) Statistics show only past 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 the
Behavioral-Finance group (*):
Year/month, d: developed / discussed,
i: incidental

(excess) Volatility


05/6i, 08/6i 
+ see heteroskedasticity,
(volatility) clusters,
(volatility)
cycles

Volatility cluster

See (volatility) cluster

Volatility smile

03/7i

Happy options?

The distribution of implied volatilities in financial options doesn'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 is higher than
the volatility of at-the-money (ATM) options
.

Thus, the graph of the implied volatilities of all the strike prices of all
options
having the same maturity
is approximately U-shaped like a
(volatile) smile.

downside) or (semi-) Volatility

See volatility,
semi (volatility)

Volatility puzzle

See volatility

What makes it moves?
What does it entail?
What is its amplitude?
Mysteries remain!

The problems about volatility are that:

What causes volatility, and how it evolves, has never be fully explained,
    as seen in the "volatility" article.

But its existence is not a surprise, as dynamical
systems
(see that phrase)
rarely 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 relevance as 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 an imperfect anticipation tool.

(*) 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: 27/07/15   

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