There are some things that we seem to take on faith as self-evidently true. "Everybody knows that over the long term (whatever that means) the stock market goes up" is a good example. Even when the data support an assertion, absent at least a working theory of why, it's just an article of faith that past patterns won't change.
One could explain that stocks go up because pricing could represent discounted future earnings, and as time progresses, those projections improve (e.g. due to overall GDP growth). There are other factors and theories as well; the point is that there are rational theories that go beyond both faith and raw data. (Obviously I'll never be a chartist.)
Another belief many people seem to hold is in "mean regression" (as used in the popular press). But only for some things and not others. For example, for annual market returns, but not for stock prices that tend to rise without reverting to their past mean. Used in this popular sense, what exactly does "mean regression" really mean?
Consider coin flips. Say you get ten heads in a row. Does the fact that you had an abundance of heads mean that you should expect a dearth going forward ("mean regression")? Of course not. As you flip more and more times, the average will tend back to 50%, but not because you got more tails than heads. Rather because 100% of heads (10:0) becomes 55% (55:45) after another 90 tosses that split evenly, and becomes 50.5% after another 990 tosses (505:495). The small original anomaly simply gets swamped.
On the other hand, some things really are cyclical. Past is prologue and affects results going forward. Over a cycle things average out (give or take random noise); there's real "mean regression."
Sometimes though there's so much random noise that people don't see the cycle - missing the forest for the trees. See image below. There is a cyclic pattern in the very noisy data of the upper line, as shown by the lower graph indicating a natural frequency. But all that noise may lead one to mistakenly believe that there is no pattern and each data point is independent of the ones before.
ISTM that there can be "mean regression" or each data point can be independent, but not both. If you posit that a market has a "natural" rate of return (so if you've had seven fat years, it's more likely than not you'll experience some lean years soon), then you're saying that next year's returns are not independent. Even if there's so much noise that each year looks independent.
That's the problem with models that use the same probability distribution for each year. Those models assume that what happened in the past has no influence on next year's results. How good is a model that says each year in the past decade was not influenced by 2008 (with its global recession and
stock market collapses)?
Does starting from such a low point not count for something? If so, then each year is not independent and the model is built on a fundamentally flawed assumption. If not, and so each year is independent, then how can one believe that bad years should be followed by good years ("mean regression")?
