Behavioral finance FAQ / Glossary (CAPM)

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

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

CAPM /
   Capital Assets Pricing Model


00/6d,7i,8i,11i - 01/3i,4i,10i -
02/5i,8i - 04/3i - 05/12i
+
see risk, risk premium, beta,
APT

Shopping for risk and return among market stalls.

The mythical 50's - 60's produced not only Rock and Roll, but
also the CAPM / Capital Assets Pricing Model. 

It was a celebrated attempt, Nobel stuff, to give a rational and
highly mathematical model of financial asset markets.

The CAPM is supposed to describe how asset markets bring
optimal prices
.

Its main assumption is that the key criterion
that motivates investors and drive market prices
is a general mathematical relation
between all returns and risks.

A star theory

The CAPM and some of its relatives and friends, such as the
efficient market hypothesis
and the financial option theory,
are still largely the "pop theories" (see paradigm) in
finance, whatever their limitations.


For now half a century, without the rewarding jobs such
models made possible, many highly qualified scholars and
engineers might have wasted their precious time and brain
in devising robotized washing machines, energy efficient
transportation, or Mars mission rockets.

Definition

Considering returns and risks as a couple
and individual assets as the whole market's
obedient kids.

Said simply, the CAPM / Capital Assets Pricing Model is a

mathematical formula that relates


1) Generally

Financial assets returns
and as a consequence their
market
prices (*)

to


Statistical
risks 

2) More precisely:

Risks and expected

returns (*) of 

individual assets

to

 

Risks and expected
returns (*)
of  the 

whole market

(*) Taking into account:

that Asset returns include their price variations
   (price rises / falls)

Also that an asset price is normally linked to the asset
    expected returns.

What is the risk parameter that the CAPM uses?

An easy one: it starts with a B from old Greece...

Parameters Descriptions

The proxy for risk
    that this model uses is

The asset price

volatility 

(see that word).


Volatility (see the article)
is an indicator
of short term
price (or return) variations.

Its calculation assumes
that
those
variations follow
a random law.

It is a trait of assets  listed in
an organized
market, a major
stock exchange for example.

The price relation
   between
an individual

asset and the market
market
is given by:

The β beta
coefficient

The beta coefficient (see
the formula below
,
or the 
glossary article
)
is the
relation between

* An asset volatility and

* The whole market
   volatility
(*).


(*) In the case of unlisted assets, some extrapolation is needed
     to determine a beta coefficient.

Ok, but what is an "alpha"?

The CAPM equation, includes another return parameter called the alpha. It is
supposed
to be equal to zero except in case of market anomaly.

Therefore, money managers call an alpha the (positive or negative) portion of
a return that is not correlated to a risk.

Positive alphas are the Grail of money management.

Systematic and specific risk: A) Systematic risk

Every asset has its piece of the market (risk) cake

The CAPM states that the only risk that is priced (thus
rewarded) by rational (= risk averse) investors is the
systematic risk, in other words the risk correlated to
thewhole market risk (*).

That systematic risk can be reduced (but not eliminated)
by diversification.

(*) Careful here, words can create confusions.
      The whole market
risk can be called the "systemic
      risk"
,  to which an individual asset "systematic" risk is correlated.

Systemic / systemATic, see the difference?

If we try to interpret the not too clear statement in the box above,
we see in practice that the theory admits actually that the

systematic risk is rewarded / priced in two ways
:

By a general extra return for a risky asset market,

called the risk premium (see the related glossary article),

This additional return applies to the market in general,
or to a portfolio that mimics the general market,


And by the beta coefficient (see the related glossary article),

That coefficient differs from one individual asset to the other
asset and modulates indirectly the risk premium. It can
as well increase as lower the reward ...or the punishment.

More explicitly:

The risk premium is an extra return (or

price rebate) offered by the market for the whole class

of assets (stocks for example) traded on that market.

  It is a difference, normally positive, between the rate of return of
  riskless assets and the market rate of return for risky assets.

  It rewards the asset holder for its risk-taking.

The beta coefficient measures the impact of the systematic
    risk
on individual assets prices and returns.

The rationale is that:

The volatility of an individual asset - as well as its return
which is its price variation + other incomes such as dividends)

is correlated (1) to the whole market volatility
   (and return)

via the β (beta coefficient).

The β is thus also called a "sensitivity" coefficient (2).


(1) The normal reference for R(m) (the general market return, see

the formula below) is a diversified assets portfolio.

But there is no market index that reflects the combined
evolution of all classes of assets.

Thus, the usual - and quite imperfect - proxy is a large
     
stock market index.

(2) Additional note: The Arbitrage Pricing Theory (APT), which
     is a generalization
of the CAPM, uses several betas.

Systematic and specific risk: B) Specific risk

Vive la différence!

The CAPM defines the specific (or idiosyncratic) risk of an
individual
assets as the risk not correlated to market risks.

It is normally not rewarded, at least under the CAPM tenets, but can be
diversified.

Type of risks for an asset

Systematic

Specific

Is that risk rewarded?

yes

no

Can it be diversified?

yes

yes

How the CAPM formula
     uses
the beta coefficient

To the blackboard, please!

R(a) = R(f) + β.P(m)

In which:

R(a) = the expected return of the asset, for example a stock,

R(f) = the risk-free return : State bonds return usually, taking

as benchmark a country or institution with a top debt rating,

β = the beta coefficient, that relates the specific asset volatility
or return with the general market volatility or return.

P(m) = R(m) - R(j) = market "risk premium" (see that
phrase), the difference between the general market return R(m)
and the riskless return R(f).

  Example:

If we have

* Riskless return = 5% (=  .05),

* Risk premium = 4%  (=  .04),

* and β = 1,2,

The stock return should be

.05 + .04 x 1,2 = .098 (or 9,8%).

Consequence: to determine the stock normal price according
to the CAPM, we would use 0,098 as a discount rate applied
to the future incomes generally expected from that asset.

Does the CAPM reflect market realities?

Marshmallow-type correlation?

1) Time warp

Is the beta, which measures past relative returns, a good predictor
of future ones?

This is a crucial issue when trying to build an efficiently diversified portfolio.

The answer is that

For some capital assets, stocks for example, the future
beta might diverge from the past one
, which
makes that past one a poor predictor.

There are plenty of reasons for that, the first one is obviously that nobody
knows the future, only hypotheses can be made.

To take a practical example, market rotation (see that word) makes
      that some assets are leading or lagging in their correlation to the

overall market.

2) Behavioral warp


More generally, Behavioral finance, although it does not completely reject
the CAPM and the EMH in general, finds flaws in the concepts and parameters
on which they are based.

The three main flaws that make the CAPM, behind its apparent
sophistication, a reductive and primitive approach of market
realities, are that:

Measurable data and objective events,
    whether endogenous /
fundamental, or exogenous / technical,
    are not the only market pricing factors.

Investor perceptions are decisive also.

See for example the *alpha (coefficient)*. It measures anomalies in
risk / return correlations.


Probability laws, which are the basis of volatility calculation, cannot 
   apply fully in some dynamical systems.


This is the case of economics / finance, as well as other social areas,
which are driven more by uncertainty (see that
word)  than by measurable risk


The CAPM is exclusively focused on the monetary risk / reward
   criterion
.

It does not take into account that, in the real world, investors (*)
have a range of other motivations, either conscious
or unconscious, legitimate or biased.

(*) this diversity of motives is seen even among the most

professional and powerful players who are supposed - at
least if we follow the EMH (see that acronym) - to impose a
"rational pricing" via their arbitrages.

(*) 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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 vote on the glossary quality at BF polls

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This page last update: 26/08/15  

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