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

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Beta coefficient01/9i,11i - 02/7i - 03/9i - 04/5i

+ see CAPM, volatility, risk

Speed detector

for assets that lead the asset crowd,

and for assets that tail it.

DefinitionAsset return accelerator or moderator.

A beta coefficient, a quite popular parameter for market traders, is a

mathematical factor computed by market statisticians based on

volatility (see that word), in other words on average asset

price variations in a given period.

Hmm, is it about prices or returns?

The beta (

β) is a coefficient that measures

the relationship between:

The (expected)

return (*)

of aspecific asset,

and

The (expected)

return (*)

of thewhole market.(*) Taking into account that

price variations

( rises andfalls)are a large portion of an asset return

and of the whole market return.

Often, investors, rightly or wrongly as regards the real prospects,

expect to obtain more than just dividends or rents when they buy

stocks or real estate.

For example, if the beta is1.2,

the stock price is supposed to rise or fall by12%

when the whole market rises or falls by10%Thus, all along the market highway, the beta compares

two price evolution speeds

* the speed of a specific asset price

* and the speed of the whole traffic flow.

It shows which assets lead the - uphill or downhill - price race in front

of the main group, and which others are lagging.

As detailed below, there issome ambiguityhere, something like

a time warp:

The market is supposed to quote assets according to their

prospect. Yes, to anticipate their future!

But the traditional way to compute the beta is on...past

statistics

Well, investors have to live with ambiguities / uncertainties.

But they better know where they hide!

The β is about the asset return and risk

A dual purpose tool, in the trader's holster.

Beta as an indicator of asset price risk.The β is said to measure how the

systematic risk(see risk)

impacts a

specificasset price and return.It measures therefore

the risk that is linked to the overall

market price variation.It is sometimes also called the

"elasticity" or "sensitivity"

of the individual asset.

Beta as an indicator of (expected) return.In short, the β boosts or moderates the expected return of an

asset.Or, more rightly said, it shows how return expectations for

an asset are higher or lower than return expectations for the

whole market.The β, as it applies to an individual asset, is

a coefficient that(see the related article).

modulates the "risk premium"That premium is a general

"extra return"of the whole class

of assets (stocks for example) traded in a market.

The expected return mathematical formula, using

the beta coefficient, is given in the "CAPM"glossaryarticle.

Careful, here, remember that the expected return is the

anticipated asset price variationplus other incomes, such

as those little goodies called dividends in the case of stocks.

The beta calculation focuses on volatility as seen below,

thus often omits that return component.

Calculating the beta coefficient, as the relative

risk and returnof a capital asset.

A few statistical math, if you want

to weigh betas in your kitchen.

Now, let us define formally the beta.It is a coefficient based on the

correlation of volatilitiesin assets

markets.It is supposed to measure the

relative risk(or at least therelative) of an asset compared to the risk (volatility) of a diversified

volatility

asset portfolio that mirrors the whole market.To find the beta coefficient, statisticians use mathematical time-series

"regressions" from which they calculate:The "volatility" glossary article tells more about the variance.

1)Thevariance (Var)

of the overall return

r_{m }of thewhole

capital asset market

2)Thecovariance

between:(Cov)* the individual

asset returnr_{i}

* the generalr_{m}

market return,

3)And then the

β=

Cov (r_{i }, r_{m })

/

Var (r_{m)}

Expected or past?We see here that although the β is normally linked to expectations, its

traditional calculationtakes into account past dataon volatility (as a

proxy for risk) and returns.To be fair, this myopic focus on past data can be avoided by using

"implied betas", but this can be done only for assets which derivatives

are traded in an option market.

Levels and role of this parameter

Relative behavior and relative speed on the market highway

The average beta coefficient for all assets is by definition, which is the beta of the whole market .

equal to 1Its value differs largely from one individual asset to another.

Beta level

of a stock

Related stock price evolution

Above or

well above 1

This stock is acyclicalandvolatileracer,

alternatively fast climber or fast diver.

Close to 1

Foot soldier marching in sync.: its price

movelike the whole group average price.

Under or

well under 1

Adefensivestock: dull, not too profitable,

but (relatively) safe investment.

Equal to

zero

Might be a riskless - but theoretically

return-less- asset, a banknote maybe...

Negative

beta

A dissident stock which prices isinversely

correlatedto the whole market:

When the index makes a zig its price

makes a zag, and conversely.The beta coefficient is a

key parameter in various

standardmathematical financial models.

It is a basis of theCAPM(mentioned above), and is also is present in the

Arbitrage Pricing Theory (APT), see below, that generalizes the CAPM

by using several betas.

How does this coefficient work for a stock?

Assets are like people,

some are hypersensitive to what moves around,

others are cool and indifferent.

The stock market is a typical place where to apply the beta coefficient.Therefore, before defining more formally what is the beta coefficient,

better showhow it works in the case of a stock, by answering the

question:

"What does a high or low beta mean for a stock (or more

generally for any financial asset)?"

In theory,

for a stock, the highest its betais,The highest its

riskis, as well as itsreturn.The more its

pricewill move when the general stock

index moves (normally in the same direction).

To take the example above, if the beta is 1.2,

the stock price is supposed to rise or fall by

12% when the whole market rise or fall by 10%.

This is why that coefficient is also called

price (or return) "elasticity" or "sensitivity".The beta is applied mainly to individual stocks.

But it is sometimes

also applied to a grouping of stocks of an economiccompared to the whole stock market.

sector (or industry),In other words, there are

"sector betas".

Practical limitations of the beta coefficient

as a capital asset pricing parameter

A friendly pricing companion.

But should you take it as a pet you can fully trust?

See - in the "CAPM" article of the glossary -

the beta-based pricing calculation formula and an example.

There are at least two practical limitations:

There is no market index available that would measure the

combined price evolution ofall classes of assets.=> Thus the usual - and quite imperfect - proxy is a large stock market

index.

Also, the beta is usually calculated on the basis of the previous

12 month data, by using a linear regression.

It is an

historical statistical parameter.Therefore, it

cannot fully be a predictorof future

evolutions.

All the more in chaotic periods in which frenzies, panics or general

market liquidity overflows or on the contrary gets squeezed, can

send correlations to the dogs.On the other hand, the observation of option markets can give an idea

of implied volatilities, and thus of.implied betasBut implied volatility might also be a wrong predictor of future volatility.

Disruptive extreme events, unexpected by option players, might occur

(see extreme, fat tails...).

Related, but somewhat diverging,

concepts and parameters

A multi beta theory, the APT

Baby betas?The

APT / Arbitrage Pricing Theorygoes a little further than

the CAPM.It

splits the beta in several coefficients β1, β2, β3 ....Every one of those baby betas is linked to a

specific effect / anomaly

(see "PER effect" or "size effect" for example).According to that theory, any one of those discrepancies would

offzr an arbitrage opportunity (see that phrase), whence the name.

Stock Beta vs. stock Image

(see "image" and image vs. beta)

Zigzagging images?As β = stock price variation / market index variation,

and as stock images vary together with market variations,

some could say that:

β = var. stock image / var. whole market image.It is only

half-true, because:

Variations are

not completely simultaneousbetween a given stock image and the whole market.

Stock price variations are related not only to image

evolutions but also the evolutions ofthe stock

fundamentals.

Adaptation of the Beta in economics

and in project funding

Any project? Your beta is your karma!The beta has also been adapted as an "

economic beta" to appraise

project financing.It takes into account that a part of the project is financed with equity and

the other part with loans.The economic beta is thus a

weighed average coefficientwhich combines.The stock market beta of the

economic sector stock index

for the equity portion of the financing package,And a beta - that is considered equal to 1 (if the borrower is fully

solvent) -fortheloan portion.

Ok, but what is an "alpha"?

The CAPM equation, from which the beta originates, includes another

return parameter called the alpha that is supposed equal to zero except in

case of market anomaly.Therefore, money managers call an alpha a return that is not correlated to

a risk.

Positive alphas are the Grail of money management.

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