This histogram shows the frequency of various run lengths of the history of H&R Block, Inc..
The length of a run would appear to indicate something about over-bought or oversold conditions, and so it might be of value as a sentiment indicator. The transformation from a price series to a run series eliminates the magnitude of the price change, and simplifies the prediction problem to a simple binary process. That is, the next price in the series either will be up or down, so the problem of predicting the end of the run can be expressed in terms similar to those we might use to describe the probabilities of heads or tails when flipping a coin.
This is a good time to raise the question of the “Monte Carlo Fallacy” or “Gambler’s Ruin” as it might be applied to stock price prediction. A naïve gambler might notice that “heads” had been flipped 5 times in a row on a coin that was known to give a fair toss. He might reason like this: He knows that six heads in a row would be extremely rare, (assuming that no cheating was going on). So, not wishing to bet on an extremely unlikely event, he bets against it by calling “tails”.
He assumes the probability of heads in one toss is 1 out of 2, the probability of all heads in 2 tosses is 1 out of 4, and so on. By this logic, the probability of the sixth toss coming up heads would only be 1 out of 64.
The fallacy assumes that the coin somehow remembers that it has already come up heads 5 times, causing the probability on the next toss to be something different than the normal 1 out of 2. But so long as the toss is fair, the probability of the next will always be the same, regardless of history. Flipping a coin is a Bernoulli Process, because each flip is completely independent of what happened before.
So, if the Monte Carlo Fallacy applies, it would be useless to attempt to predict the length of a price movement run, because the probability of the next day’s price being up or down would always be very close to 1 out of 2, no matter what. However, are stock price runs comparable to Bernoulli processes? Coins don’t have memory, but speculators do, so the price behavior is not completely independent from price history.
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