The Gambler's Fallacy

If there is a 50-50 chance that something can go wrong, then nine times out of ten it will. - Paul Harvey News

The gambler's fallacy is a basic misunderstanding of probability theory. In a fair coin flipping contest the chances are always 50% that the next throw will be a head, and 50% that the next throw will be a tail. The coin has no memory, and those that keep track of lotto numbers trying to identify which numbers are soon to have their "turn" fall into the same trap.

Stocks and commodities do have trends. Some of these can even be traded. Most of the time though, it moves about in a more-or-less random fashion. Ignoring Elliott Wave and Gann and other forecasting methods that may or may not (probably not) have any usefulness for most traders, there isn't really any way to tell which way the coin will land.

Those that pick on trends, ready to sell at tops and fish for the bottoms are falling victim to the gambler's fallacy. Just because the coin, or the market, has had ten straight up days doesn't mean anything about the 11th day, the chances of a fair coin landing on heads are still 50% for the next trade, there is no diminishing probability that increases the chances of the coin landing on tails on the next toss.

In trading, there is no such thing as too high or too low. There are no overbought or oversold markets. Value, in the Ben Graham context, means nothing to someone that trades a squiggly line. A long term investor knew all along that the Internet bubble wouldn't last, and the whole market was quite obviously overpriced in 1987, 1929 and the end of the 60s. Hundreds of traders went broke shorting stocks in the middle of those booms, trying to pick the moment of reversal. It just didn't work. Jesse Livermore himself was bankrupted for the last time when he went short stocks a few months before the crash of 1929.

Traders do of course believe in trends, and fundamental analysts believe in oversupply and undersupply. These are all very well for giving you a view of the likely risks and potential in either direction, but it is the gambler's fallacy to believe that in the short term the market is anything but a random walk. The market may go up if supply is tight, but it could well go down as people start to realise that the market consensus is so well established that prices already reflect that situation, or on another level, as traders take their profits, starting a quick retracement in the price.

When the market really does break, the trader should be ready for it, though don't assume that a stop-loss will save your skin, someone actually has to buy your stocks or go long against your short for this to pay. In extreme situations the market will have practically no buyers and thousands of sellers. The price is purely theoretical because the only volume is coming from arbitrageurs or a few bottom pickers and when you want out there will be millions of shares ahead of you.

If you think you will be clever enough to trade successfully with a "stop loss" order, you should probably read such books as "The Market Wizards" by Jack Schwager, it is clear that a stop-loss order won't help in all occasions. Even the best traders in those books have been forced to take harrowing losses with absolutely no chance of exit when sudden action has caused the market to move against them. In stocks and in futures the price is set only by what someone is offering you to take your position off you. If there are no takers, then you might as well consider the trade as a total loss. Until someone is willing to take the opposite side of the trade you will be unable to close the trade, and losses may be unlimited.

A consequence of the gambler's fallacy is that even in the long term, there is no guarantee that a series of random events will have a frequency in line with their expected odds. There is no rubber band that is going to move future outcomes toward the average. If you flip 10 heads in a row, nothing says that tails will be overly represented in the future. Probability does not say that the more flips the more likely you are to see an equal number of heads and tails come up.

The law of large numbers, as described by James Bernoulli in 1713, tells us that the difference between the probability of an event and the frequency of an event become arbitrarily close to zero as the number of attempts approaches infinity. This means that the fraction of heads (or tails) in a series of coin flips will approach 0.5, which is the probability of getting a head (or a tail) in a coin flip.

What it does not mean is that after a million flips there will be exactly half a million heads and half a million tails, as a matter of fact it is quite likely that there will be quite a difference between the number of heads and the number of tails. And don't assume that because the first thousand flips turned out an unexpectedly large number of heads that the second will turn up a similarly large number of tails to even things out, all the law says is that the ratio of heads to tails will become closer and closer to one with some vast number of flips, not that tails become more likely after a series of heads. A tail is not more likely on the next flip just because you have just thrown 15 straight heads, the probability of getting another tail is still 50%.

In trading you should bear this in mind because some money management techniques are based on the gambler's fallacy. Martingale and other "improper" methods of money management make the assumption that a lucky or unlucky streak will end. It will, eventually, but quite possibly not before an "impossible" 50 consecutive losing trades have completely wiped out your equity.

... not to be confused with regression to the mean

Regression to the mean is something entirely different. Unlike coin flips or the short term signals of a technical "indicator", in the longer term there is a definite bias to the outcome of each "trial".

Shares as a whole drift upward in value over the long term because most companies don't pay out 100% of their profits as dividends, instead they retain some of this money for the purposes of expanding the business. As long as the management is reasonably competent they should be able to create at least some enduring positive benefit out of this accumulation, and hence the value of the business will increase in line with this capital retained and reinvested.

Similarly, property has a general upward bias. As inflation pushes up people's income, they can afford larger mortgages. To date I have seen no tendency for "cheap" suburbs to be left for the desert to reclaim, and I haven't seen the entire population congregate in a few glitzy suburbs. The system tends to stabilise after a while, and despite it not necessarily being a smooth process higher prices do move their way through the whole market and in a relative sense most suburbs tend to retain their socioeconomic status.

So shares and property do tend to move up, over the long term anyway. The factors that drive this appreciation are very different, but over the last 50 years or so it appears that they are in fact quite similar, giving long term increases of around 7%pa or more.

Unlike coins, where there is no force that biases any particular outcome, each downward movement the shares or property market makes increases the subsequent probability of a gain. By the same token, when gains are made in prices at a rate that is much higher than the underlying factors would seem to justify, a subsequent fall, also known as a correction becomes more likely.

If corporate profits and inflation have averaged an annual 7% increase over the long term, this means that when the markets have driven prices down very low, below what a 7% trend-line would indicate, the subsequent movements have greatly exceeded 7% in order to reestablish the market at price levels justified by the growth trend. This is a fairly important concept to realise. In the long term, most extreme movements in markets that have an intrinsic value are reversed at a later time, such that overall price levels "correct" to an appropriate mean level.

The shorter your time frame, the more random events become and the less regression to the mean becomes important. If events are random then actually most money management techniques are probably going to fail to make money after you take into account trading expenses. This is as good an argument as any not to be a short term trader.