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 and 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:

in practical application: a stock's 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 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

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this webpage was last updated on: November 23, 2007