Suzi Quant Photo by Glamourzons.com


 
Quant Funds

August 17, 2007

here's more information about
what Wall Street Gecko said about Hedge Funds

there exists Wall Street folklore
about some hedge funds having had amazing returns.

my understanding is that George Sorosís Quantum Fund
made more than $1 billion betting against the Brittish pound
in the European exchange-rate crisis of September 1992.

however there has been a lot of recent headline news
reporting that some of the top (and/or largest) hedge funds,
(such as Goldman Sachs 9 billion dollar Global Alpha Fund)
had been experiencing significant difficulties recently.

hedge funds are private investment funds
which often obtain large profits by leverage
(borrowing money to invest more than the money actually invested in the fund)
small profits from statistical arbitrage investments can thereby be magnified;
which works very nicely, as long as the market remains favorable;

however, leverage also magnifies losses if the market turns unfavorable;
such downside risk is not always obvious during favorable periods

the recent problems with subprime mortgage loans
exposed the underlying risk of the financially engineered derivitive products
which re-packaged (and redistributed) the risk involved in such loans.
CDO's (Collateralized Debt Obligations)

one of the most dramatic hedge fund incidents in recent history was
Long-Term Capital Management (LTCM),
which was a hedge fund put together in 1994
by some of the top people on Wall Street and academia, including:
John Meriwether (formerly the vice-chairman and head of bond trading at Salomon Brothers), and
Myron Scholes and Robert C. Merton,
who were awarded the 1997 Nobel Memorial Prize in Economics.

initially, LTCM began with impressive annualized returns of over 40% for its first years,

however in July 1998 the Russian government devalued the ruble
and declared a moratorium on future debt repayments.

in 1998 LTCM lost $4.6 billion in less than four months.

along with such losses equity capital declined by 50%
causing LTCM leverage ratio to climb to over 45 to 1
with that high leverage ratio being during a period of high volatility.

by September 19, 1998 LTCM capital was down to only $600 million in the fund,
however the fund had an asset base of $80 billion at that point.
October 1, 1998 SEC testimony to the House Committee on Banking and Financial Services

well, in September 1998 the Federal Reserve rescued Long-Term Capital Management

the title of "hedge" fund implies there they are hedged against risk.

some hedge funds utilize computers and databases
to invest in arbitrage opportunities which might arise
from perceived deviances from normal patterns,
which are expected to return to normal patterns;

simultaneously taking offsetting positions
are expected to hedge against any risks involved.

such arbitrage opportunity pricing differentials are often rather small,
however financial leverage makes the effort worth while;

Myron Scholes explained the functioning of LTCM
with a simile of a giant vacuum cleaner
picking up nickles that everyone else had overlooked.

however Nassim Taleb compared the LTCM strategies as:
"picking up pennies in front of a steamroller"

economist John Maynard Keynes, is said to have warned investors that
although markets do tend toward rational positions in the long run,
"the market can stay irrational longer than you can stay solvent."

mathematical covariance matrices quantify
the relative price movements of stocks,
more specifically, which stocks are likely to have
price movement in opposite directions;

problem is that such covariance matrices
(upon which the risk hedges are based)
are not static,
and can dramatically change quite rapidly.

there also exists some skepticism as to whether all "hedge" funds
are actually hedged against risk.

in the United States, financial securities are regulated by
the Securities Act of 1933
the Securities Exchange Act of 1934, and the
Investment Company Act of 1940.

however hedge funds with fewer than 100 shareholders are exempt from regulation

some "hedge" funds might be nothing much more then
over-leveraged long funds.

anyone remember the accounting issues
which arose in the Enron/WorldComm era of the previous decade?

 



 
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

 


the 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: December 5, 2007

SuziQuant.com