Cosmo, for a man with more degrees than a thermometer you must have somehow missed statistics and probability theory. Your comment to Pruguy on the simplicity of investing is, ... well, simple.
So, at this risk of being complicated, here is a lesson in probability theory for you. Suppose you have an honest coin. That means that the probability is equal that it comes up heads and tails are equal, and has nothing to do with the results of the previous throw. That is what is called statistical independence.
The probability that a coin will come up with 5 identical results (either heads or tails) is 0.5^4, or 0.0625%, or 1 time in 16. So what is the probability of achieving at least 1 of those runs in a simplified market setting where we would say there are 250 trading days in a year, and we are asking for the probability that any particular stock will move up or down ten days in a row.
There are 246 consecutive 5 day periods in a year, and given the assumption of statistical independence, the probability of seeing at least 1 five day run is calculated as follows:
1. The probability that any particular run does not contain all of the same results is 1-0.5^4 = 0.9375
2. Therefore, the probability that none of the 241 contains a run of ten identical results is 0.9375^246 is .0000001, or 1 chance in 10 million.
Now let's repeat that exercise with 8 consecutive results. We have a chance of 1-(1-0.5^7))^244 = 85.25%
These results ought to demonstrate some very important lessons. First, runs are to be expected in a stochastic system. In fact, some rather sophisticated techniques for discerning non-random patterns are based on the absence of runs. Second, given the upward bias of the market, the runs probability is actually greater than predicted in my example (i.e., the coin is biased).
Remember, as Mark Twain said (I believe, or it could have been H.L. Mencken):
For every difficult and complex problem there is an easy answer ...
and it is always wrong.
TTFN,
CTC (who has a real Ph.D) |
