Taleb writes:
This applies to the height of individuals or the size of dogs. In the latter case, consider that two average sized parents produce a large litter. The largest dogs, if they diverge too much from the average, will tend to produce offspring of the smaller size than themselves, and vice versa. This "reversion" for the large outliers is what has been observed in history and explained as regression to the mean. Note that the larger the deviation, the more important the effect.I've long thought it obvious that "regression to the mean" of populations was a myth. After all, on an evolutionary time scale, the "tree of life" expands (into a tree) rather than reaches equilibrium, at a mean. If it were true, we'd all be the same size, and we are not, therefore it isn't true.
Let's assume that the population is normal, and hence whose distribution can be visualized as a bell curve. The two "large" parents must be over to the right of the bell curve. The offspring that the parents produce will also be a normal distribution, and hence visualize a smaller bell curve, centered around the mean of the two parents. So, most offspring will tend to be smaller than the larger of the two parents, which I suspect is the reason for the myth, however there is no "regression to the mean".
Not only that, but other factors such as modern health, survival of the fittest, will tend to change to the average height of the population over time. In some cases, this is larger and larger. There is no regression to the mean, as there is no constant mean.
The reason should be obvious, and it's got to do the causality. Does the population determine the mean, or does the mean determine the population? In the case of height, clearly, the population determines the mean. In 1000 years time, do you think that the mean height of people will be the same as it is today? No way! It's growing over time. Think back only 1000 years. The average height of a person was lower than it is today.
Regression to the mean occurs when there is a fundamental cause of the mean, that causes the mean to remain constant. That is, in another thousand or million years, the mean will still be the same as it is today.
Relating this back to investing, Leither often writes about long term averages of the markets, going back as far as he can, into the 1800's in some cases. I was wondering how relevant that information is. For the last 20 years, in Australia, interest rates have averaged 6%, but over the last 100 years, they have averaged 10%. Which is more relevant?
It seems logical to me, that the cost of capital is a constant over the long term. In 1000 years time, the cost of capital will be the same as it was 1000 years ago. It therefore follows that the regression to the mean will occur for the cost of capital, and that the last 20 years can (and will) be seen as an anomaly, rather than as a "new normal". Interest rates will, therefore, revert to the mean. By definition, this must include an overshoot. To back out the last 20 years, interest rates would need to be at 14% for the next 20 years. Unfortunately, this necessarily requires asset prices to fall by 60%.
The only question remains: When?
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regression to the mean is an observable phenomenon and is a fact. your thinking is jumbled on this subject. If Yao Ming and the tallest woman in the world had kids chances are very good that none of them would be as tall as either parent. if two parents that are very large have children, they will, on average be smaller. thats an observable fact and I don't know enough to explain to you why thats the case, I am sure the right biologist could.
ReplyDeleteAlso, a mean does not necessarily refer to one single measurement. So yes, the average height of a human has changed over time, but it has followed a steady change, and humans of extreme size within the population have had offspring that regress to the mean, here meaning that they usually fall closer to the curve representing the long term change in human size.
your thinking has a serious mixing of scales problem. the 'tree of life' picture you reference is on a vastly larger scale than regression to the mean over, say twenty generations. these are actually not conflicting ideas. also you have misinterpreted the tree of life as representing the nature of biodiversity. the diversity of extant creatures has waxed and waned through history and is itself subject to regression to the mean.
Lastly, there is no reason to think that the cost of capital is constant over the long term. As a society today, we have vastly more disposable income than 1000 years ago... There was a time when almost no one had disposable income and there was almost no such thing as borrowed capital. think of a feudal system. In that time, the cost of capital in the form of land and taxes to the lord was astronomical compared to 10%. The law of diminishing returns applies to all things. And like I said above, a regression to the mean does not require a single constant average value. also, the cost of capital (interest rates) is dependent on a variety of factors that are extremely important, like overall economic health, economic policy making, distribution of wealth, monetary policy, etc. which have such a great effect on interest rates, and can change so drastically that some kind of 1000 year average would be pretty much meaningless to investment considerations.
Obviously you are the one who has been fooled... by your self. Probably some humility would have prevented you from proclaiming that a greatly respected professional just 'didn't quite get it right', as evidenced by some misguided thought experiments you did in your head in five minutes. You have "long thought" wrong, my friend.
Regression to the mean is applicable in some situations and not applicable in others. A long term mean suggest applicability, and the lack of a long term mean suggests inapplicability.
DeleteIn biological evolution, I don't understand how you think it is possible to have regression to the mean over 20 generations, but not have regression to the mean over 1000 generations. In both of those situations, you have "regression to slightly above the mean", but it is more apparent over the longer time scale.
My best guess is that in 1000 years, the interest rate will be 10%. What is yours?
Say you plot out the points that represent humans on a graph where the x axis is time and the y axis is height. If the average height at any single moment is increasing, you can find a function (line) on the graph that follows the trend of the points. You can use mathematics to find the function that most closely matches the data, in fact. When biologists talk about regression to the mean, they are referring to this line as the 'mean' (any point on this line will also be very very close to the mean for that point in time). Now, if you choose a point (person) on the graph that falls quite far from this line, their offspring are extremely likely to fall closer to the line.
DeleteBeginning with an extreme case is the only way to observe regression to the mean. If you begin with an individual who is exactly at the mean, a human of perfectly average height, for example, her offspring are very likely to be more extreme, simply because it highly unlikely that they would be exactly the same size as their mother. But as soon as her offspring deviate from the mean, their offspring will be slightly more likely to be closer to the mean than them, and how far a parent deviates from the mean determines the probability that the next generation will be closer to the mean. If you think more about this you will discover that regression to the mean is the very mechanism that creates a trend in a set of data. Anywhere data follows a trend you will see regression to the mean. Whether this trend is predictable, and how useful regression to the mean is in predicting the future is variable, obviously.
Your mistake is a scale issue again. Regression to the mean over a few generations is probable for any series beginning with an individual with an extreme attribute. over the long run (1000 generations) regression to the mean has happened over and over for many generations and manifests itself as a trend in the data. A observable trend in a data set suggests applicability, complete randomness suggests inapplicability.
We are not all exactly the same size because there is variability within the population. The concept of probability is very important in the above. Even with extreme cases, like the two tallest people in the world having children, it is still possible for them to have a taller offspring, it is just highly unlikely. For a 6'10" person to have offspring that are taller than 6'10" is not as unlikely, but still unlikely.
I assume that what you mean is that your best guess is that in 1000 years the interest rate will be near 10%, whatever you think 'near' means.
In my example of a feudal system in my earlier post, imagine a peasant who gives something like 80% of his profits (80% of PROFITS might be 1000% of the principal) to the lord solely because he does not control any capital of his own. Think how unimaginable it would be to him to think that today you can get a car loan for under 5%. 1000% to 5% is a huge variation, over the course of 500 years or less. In parts of the world today capital is probably that expensive. and throughout history and worldwide, interest rates have been everywhere in between 5% and 1000% and certainly beyond those extremes. If you have an economic condition of deflation, for example, markets are becoming less and less profitable, while currency is increasing in value. Here, credit is unavailable, and this has happened plenty of times through history (followed by a swift economic meltdown). My best guess for interest rates in 1000years is somewhere between 0% and infinity (borrowing is not possible).
Thanks for your comments..
DeleteI understand your trend line visual. My problem with it is that it lacks "regression" (the act of going back to a previous place or state) and it lacks "the mean". We are not all exactly the same size because there is no "regression" and no "mean". Speciation is an observable evolutionary phenomenon, and it is not compatible with population "regression to the mean".
Trying to understand your point of view, it seems that what you are saying is that all the babies born today will regress towards today's mean, and that all the babies born tomorrow will regress towards tomorrow's (higher / different) mean.
Given your concept of regression to the mean, future means cannot be predicted, as the mean could well be on a random walk.
So, the concept of "Regression to the mean" has gone from a powerful predictive force - no doubt used by Nassim Taleb and many others to make a lot of money - to something utterly useless, like your zero-to-infinity interest rate prediction.
Some future trends can be predicted within limits. some trends are more predictable than others, and most not at all. But, tomorrow's average height for a human will certainly not be 7'. Average height is not on a random walk, far from it. Randomness in the reproductive process produces variability, but it is limited by probability and does not undermine the concept of regression to the mean. Regression to the mean is in fact only observable in situations where you have some factor creating an amount of variability.
DeleteEvolutionary change and natural selection are compatible with regression to the mean. In a population, they determine the direction of the mean over the very very long term, alongside practical biological devices and limitations in the somewhat shorter term. Perhaps study of regression to the mean in another subject will help you get a firmer idea before you add the complexity of the biological systems.
There is a continuum of how prominent regression to the mean can be, and how predictable trends are. on one fairly predictable side you have the height of humans and on the other end you have interest rates over 1000 years.
Think on the subject more, seek out the devices like images and numbers that can make this abstract concept more concrete for you and perhaps you will be able to see it as a whole.
One of the important parts of understanding regression to the mean is that this statistical phenomenon can easily and convincingly be misconstrued as the effects of another cause, as pointed out in Daniel Khaneman's new book, thinking fast and slow (highly recommended).
Thanks for a respectful discussion and the chance to think on this very important part of our world! Good luck in all things to you!
Also, the chances you will out perform the market with any kind of speculative investment strategy are exceptionally low. So I think you are right to question everything anyone says about that...
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