Suzi Quant

Quant Alphabet

November 24, 2007

practitioners of quantitative analysis construct mathematical models
in attempts to mathematically model the actions within a stock market environment

Nobel prize winner (1963) William S. Sharp
was one of the first mathematicians to utilize a factor model
(each market variable being quantified by mathematical factors in equations)

quantitative analysis tries to mathematically describe the
interactive effects of stock prices

my understanding is that
when IBM tried to program a supercomputer to play chess
IBM - Deep Blue supercomputer
it was realized that because of processing and memory limitations
it would be physically impossible to build a computer which would contain
every possible move, for every square, for every combination of chess pieces.
instead, a practical system was implemented which was
programmed with the most likely (useful) chess move strategies

well, in the stock market a similar problem arises
if one tries to quantify every correlation, between every stock price.

the most popular quant solution for stock market applications
is to quantifiy only how every stock moves relative to a "proxy" for the market,
the "proxy" usually being some standard market index (such as: S&P 500)

if one is thus able to quantify the characteristcs of
how each stock moves relative to the market as a whole,
well then patterns can be found which
quantify which stocks seem to move together

such a quant model is called a "Single-Index Model"

such models quantify "systematic" risk,
id est: risks effecting the entire market,
which are expected to show up as effects to the entire market index;

and company specific risks,
which in theory would account for
specific characteristics of individual company stocks;

of course, although mathematics itself is quite predictible,
those with experience in the stock market would most likely tell you that
the stock market is not as reliably predictable
example: in math: 2 + 2 = 4
in the stock market: price is whatever the most powerful trading force says that it is;
such theory being based upon the herd type characteristics
of a significant percentage of market participants

"quants", being quite mathematical,
communicate with a mathematical alphabet
symbolically representing the factors of their mathematical equations

Alpha Alpha and Beta Beta
are the most basic quant symbols,
(the word "alphabet" itself is a contraction
of the first 2 ancient symbols: alpha and beta)
and are shown in the following equation:


Excess Return Equation


Quant Alphabet

in practical application: a stock's beta Beta
mathematically quantifies the direct correlation of
how much the price of a stock is expected to move (up or down)
based upon how much the market index moves (up or down)
(notice in the equation above, it multiplies the Market return)

also notice however that alpha factor Alpha stock price movements
are not correlated to entire market index price movements
(no multiplicative (direct) connection to index price movements)

an example of a stock with a beta of exactly 1
is mathematically expected to move by
the same percentage (100%) as the index does

the beta factors for each individual stock
being mathematically derived by statistical regression;
id est: for anyone who remembers some geometry:
beta is the slope of the stock price line graph,
statistical regression obtains the mathematical factors for that line
from statistical analysis of the observed cloud of stock prices

negative beta indicates a stock which tends to
have price movements opposite to the direction of the index;
short funds are expected to have such negative beta

a beta of less then 1 exhibit less stock price volatility
relative the whatever volatility the entire market is exhibiting

betas of more then 1 indicate stocks which exhibit price changes
which tend to be more then what the entire market experiences

example: an ultra-bear short fund with beta of -2.5
would be expected to go up 5% if the market declines by 2%
the high negative beta exhibiting magnification (leverage)

well, the point is that during bull market environments
high beta stocks are nice in that they tend to
provide investors with higher yield then the market index;

however if the market trend turns into a bear market environment
high beta stocks are expected to have greater losses then the market


information contained in this website is NOT intended to be investment advise;

if you find anything interesting here,
it is suggested that you follow up with your own research

any investment decisions should only be
with consultation of professional financial advisors.

this webpage was last updated on: November 23, 2007