Changing Price Of Stock
Once Samuelson and his colleagues rediscovered Bachelier, they also had the great fortune of being able to harness his insights on a large scale with the advent of the computer age and the widespread availability at universities and research foundations of high-speed computers. Using those new technologies in the early 1960s, stock market researchers went to work with a vengeance exploring random processes in stock market.
One aspect of the investigation consisted of correlation tests that were used to determine whether specified data sequences move together to any degree. In the case of stock prices, price changes of a given stock are recorded over a specified time period—say, a number of days—and a subsequent period of the same length. These sequences (called time-series data) are then compared to determine whether they move together to any degree—whether they show any "correlation."
Robert Kiyosaki - Rich Dad, Poor Dad The comparison takes the form of a correlation coefficient, a number that reflects the degree to which the data are linearly related. In effect, the time series of data is tested for correlation by fitting a straight line to the data and then calculating that number. A correlation coefficient equal to zero provides evidence that the data in the series have the property of statistical independence; correlation coefficients that are close to zero (but not equal to zero) indicate that the data are uncorrelated. A time series of data is random if it is either independent or uncorrelated.
Consider televised lottery drawings in which winning lottery numbers are determined by selecting numbered balls from a bin containing numerous balls with different numbers painted on them. The auditor retrieves a ball, records its number, and replaces that ball. The auditor does this perhaps three times, each time retrieving, recording, and replacing. This process has the property of statistical independence because the number recorded after any retrieval indicates nothing about the numbers recorded either previously or subsequently.
Jim Cramers Real Money Sane Investing In An Insane World Outside of a controlled context such as a lottery bin, particularly in the context of time-series data such as stock prices, it is extremely difficult to prove statistically that a series of data has the property of statistical independence. The less restrictive property—that data are uncorrelated—is susceptible to statistical proof and allows for conclusions substantially similar to those which follow from the independence property.
The correlation tests of the 1960s all resulted in correlation coefficients that did not differ significantly from zero. This meant that various series of actual stock market data were indistinguishable from various series of numbers generated by a random number table, roulette wheel, lottery drawing, or another device of chance.
These findings had an important practical implication: Traders could not systematically make above-normal gains from trading because a statistical lack of correlation implies that the best estimate of the future price of a stock is its present price. In other words, if prices follow a random walk, the price change from one time to the next will not affect the probability that a particular price change will follow that one. Past prices cannot predict future prices.
Runs
A long known weakness of correlation tests is that the results can be skewed by a small number of extraordinary data in the time series. An alternative test that avoids this weakness is an analysis of runs in the data—an investigation of whether there is any persistence to the direction of successive changes.
A run is defined by an absence of directional change in a statistic in the series. Thus, a new run begins any time the direction changes (i.e., from negative to positive, from positive to negative, or from unchanged to either negative or positive).
Instead of testing the correlation of numerical changes in the data in the series, one investigates the relationship of the direction of those changes. If stock price changes follow the random walk model, the number of sequences and reversals in time-series data of stock prices will be roughly equal. If the same direction persists for a significantly longer period, the random walk model will be contradicted.
Among the numerous run studies conducted in the early 1960s, the University of Chicago economist Eugene Fama's is regarded as the most careful. 3 Fama found that the direction of price changes tended to persist but nevertheless concluded that no trading rule or strategy could be derived that outperformed the market consistently. Accordingly, almost everyone involved in the debate in the late 1960s agreed that the observed departures from randomness were negligible and believed that this constituted strong support for the random walk model.
