# Volatility and Beta coefficient

## Zigzagging in sync.

Volatility shows the average dispersion of market price fluctuations.
The average size of its zigzags in other words.

As for the beta coefficient, it is the relation between the volatility
of a financial asset and the volatility of the whole market.

Those parameters are found by calculating the statistical
"standard deviation", itself a Gaussian probability law parameter.

Using mathematical horses to ride market zigzags

Couurtesy of market statisticians, and quite popular among traders,
volatility and beta coefficient are two statistical tools / parameters

usually used to measure  financial market fluctuations.

They are based on a standard law of probabilities, the Gaussian "normal
law", see below
.

## Volatility

Ripples or storm on the ocean of financial assets

To simplify things:
A
financial asset volatility is the
average size of the asset price
zigzags, or more precisely the average statistical dispersion of its market price (*) fluctuations.
(*) also the dispersion of returns, as price rises or falls, are elements
of an asset return.
This average dispersion applies for example (there are several sizes in
store to fit your needs), to:
• (short term volatility):
Its daily fluctuations during three months, whatever the direction
(rise or fall)
of those variations
• (long term volatility ):
Its annual fluctuations during 10 years
Probabilistic aspect:
the Standard deviation

If - a big if - we suppose that the statistical distribution of market
prices follows a "normal law of probability" (aka Gaussian
probability law) then the volatility can be measured with mathematical
values such as the "standard deviation" or the "variance".

Beware of this Christmas present by Gauss and Laplace, check the
directions for use as there are limitations. Markets often stray from
such a perfect law.How many toasters have blown the fuses when
used as coffee machines!
To simplify again, if, to take an example:

* 68% of the daily fluctuations are
* in a symmetric way,
* in a - 1% to + 1% range,
=> their standard deviation is 1%
Thus, obviously, if we take waves as examples,
• A .05% standard deviation
(thus 68 % of fluctuations in the +.05% / -.05% range)
relates to a farmyard pond with frolicking ducks
• And a 5% one describes a (financial) surfer paradise,
but a bit more becomes a killer wave

A high volatility is supposed to signal a lack of confidence / visibility on future evolutions by market operators
(fear index)

## Beta coefficient

The ( β ) beta coefficient (or elasticity / sensitivity)
is the mathematical relation between:
• The volatility of a specific asset
(for example a stock)
• vs. the volatility of the whole market
(for example based on a broad enough stock market index)
For example, if in average,

* The prices of an asset move by 12 % (in a direction or another)
in a period,

* While the general market prices move by 10% in the same
period;

=> the asset's beta coefficient is 1,2.

Obviously a stock with a beta of .8% is less volatile than one with 1.2%
It is said that the beta measures an asset's "systematic risk".

## OK, but what is an "alpha"?

The CAPM (Capital Assets Pricing Model) equation, from
which the beta coefficient originates,
includes another return
parameter, the alpha.
It is supposed equal to zero ...except in case of
market anomaly (the
Achilles' heel that perturbs the beta coefficient).

Therefore, money managers call an alpha a return (or the portion
of a return) that is not correlated to a risk.
=> Positive alphas are the Grail of money management.

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