Behavioral finance FAQ / Glossary (Beta)

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Year/month, d: developed/ discussed,
i: incidental

Beta coefficient

01/9i,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.

Definition

Asset 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 a specific asset,

 and

The (expected)
return (*)

of the whole market.

(*) Taking into account that price variations
      ( rises and
falls) 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 is 1.2,

the stock price is supposed to rise or fall by 12%

when the whole market rises or falls by 10%

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 is some ambiguity here, 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 specific asset 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
modulates the "risk premium"
(see the related article).

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"
glossary article.

Careful, here, remember that the expected return is the
anticipated asset price variation plus 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 return of 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 volatilities in assets
markets.

It is supposed to measure the relative risk (or at least the relative
volatility
) of an asset compared to the risk (volatility) of a diversified
asset portfolio that mirrors the whole market.

To find the beta coefficient, statisticians use mathematical time-series
"regressions" from which they calculate:

1) The variance (Var)

of the overall return
rof the whole
capital asset market


2) The covariance 
     (Cov) between:

* the individual
   asset return ri

* the general rm
   market return
,

3) And then the

β =

Cov (ri , rm )
/
Var (rm)

The "volatility" glossary article tells more about the variance.

Expected or past?

We see here that although the β is normally linked to expectations, its
traditional calculation takes into account past data on 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
equal to 1
, which is the beta of the
whole market .

Its 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 a cyclical and volatile racer,
      alternatively fast climber or fast diver.

Close to 1

Foot soldier marching in sync.: its price
     
move  like the whole group average price.

Under or
    well under 1

A defensive stock: 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 is inversely
     
correlated to 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

standard mathematical financial models.


It is a basis of the CAPM (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 show how 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 beta is,

The highest its risk is, as well as its return.

The more its price will 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 economic
sector (or industry),
compared to the whole stock market.

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 of all 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 predictor of 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 betas.

But 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 Theory goes 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 simultaneous 

between a given stock image and the whole market.

Stock price variations are related not only to image
   evolutions
but also the evolutions of the 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 coefficient which 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) - for the loan 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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This page last update: 10/09/15  

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