Are Stock Market Results Random?

Statistics are great but you can’t be sure they matter without some thought.  

If a pro hockey player has a big first year and it is followed by a mediocre or worse second season, the sophomore jinx, people bring up the idea of reversion to the mean. Is that reasonable?

Wolfram Alpha says this:

“Reversion to the mean  is the statistical phenomenon stating that the greater the deviation of a random variate from its mean, the greater the probability that the next measured variate will deviate less far.”

So, if the stock market is up more than the average has been or possibly will be, for a long time, it must be below the average later in order to make the average work.  That seems reasonable and if we examine the history of the market, it seems to work out.  Average market returns are amazingly stable over long periods. Given that, I suppose we should become defensive after a series of good years and optimist after a series of poor ones.

Similarly in my hockey fantasy pool, I should pick players in their second year who had a bad first year. That might work except most of the ones who had a bad first year are not there to pick in the second year. Survivor bias. Maybe only the ones who had a good first year can ever have a bad second year. Makes me suspicious.

Go back and look at the definition above. Notice “Random Variate,” Notice “Greater the probability” It is likely that the performance of hockey players is not random so the idea does not apply.  More likely defenders learn their tendencies and minimize their effects. Possibly stock market returns are not random after all. Pseudo-random maybe.  In any case the idea is one of probability not guarantees.

If you are not yet convinced notice this similar idea. Wikipedia on “The Gambler’s Fallacy.

The gambler’s fallacy, also known as the Monte Carlo fallacy or the fallacy of the maturity of chances, is the mistaken belief that, if something happens more frequently than normal during some period, it will happen less frequently in the future, or that, if something happens less frequently than normal during some period, it will happen more frequently in the future (presumably as a means of balancing nature). In situations where what is being observed is truly random (i.e., independent trials of a random process), this belief, though appealing to the human mind, is false.

The Gambler’s Fallacy belief looks much like reversion to the mean but is false.

Reversion to the mean in the stock market cannot be both true and false so we must assume that the condition precedent, “independent trials of a random process” must not be present.

If the stock market is not a random walk or if the results are not independent, how much of the statistics remain valid?  

We should look for correlations. Know what things mean not what they look like.

You might prefer to use common sense rather than some mystical trading system based on historic data assumed to be nearly normally distributed. Results matter. It is like the old good news bad news joke. The bad news is you don’t have enough money to retire. The good news is your portfolio has an excellent Sharpe ratio. 

In Las Vegas, a casino will send a Gulfstream to New York for you if you have both a system and money.

Be wary of statistical analysis. 

Don Shaughnessy arranges life insurance for people who understand the value of a life insured estate. He can be reached at The Protectors Group, a large insurance, employee benefits, and investment agency in Peterborough, Ontario.  In previous careers, he has been a partner in a large international public accounting firm, CEO of a software start-up, a partner in an energy management system importer, and briefly in the restaurant business.

Please be in touch if I can help you.  866-285-7772

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