Respect the Magical Power of Mean Reversion

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CULater
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Respect the Magical Power of Mean Reversion

Post by CULater » Wed Aug 01, 2018 7:00 pm

It appears that mean reversion is very important concept, and that it actually accounts for a number of well-known phenomena. For example, it has been shown that the well-known Placebo Effect in medicine is largely attributable to mean reversion and not psychosomatic healing as is commonly thought.

But what is this powerful force, anyway?
Reversion to the mean, also called regression 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. In other words, an extreme event is likely to be followed by a less extreme event.

Although this phenomenon appears to violate the definition of independent events, it simply reflects the fact that the probability density function P(x) of any random variable x, by definition, is nonnegative over every interval and integrates to one over the interval (-infty,infty). Thus, as you move away from the mean, the proportion of the distribution that lies closer to the mean than you do increases continuously.
http://mathworld.wolfram.com/ReversiontotheMean.html

But is mean reversion a useful concept in finance? Jason Zweig says yes

“From financial history and from my own experience, I long ago concluded that regression to the mean is the most powerful law in financial physics: Periods of above-average performance are inevitably followed by below-average returns, and bad times inevitably set the stage for surprisingly good performance.”

But how can we harness this Power in our investments?
I can’t predict the future, but after the nice run up we’ve had for the past five years or so, it will probably make sense to look for markets that offer better value than the US markets do currently.
~ Ben Carlson

Unfortunately, Mr. Carlson said this in July, 2013 and since that time, the U.S. market advanced about 90% while emerging markets did 40%, while Europe the Pacific did about 50%. The good-looking markets didn't deliver -- Mr. Mean Reversion didn't show up.

What is the problem here? I'm guessing the problem is that Mean Reversion isn't anything more than a statistical abstraction, a chimera. We've been duped again. Phooey.
Faced with the choice between changing one’s mind and proving that there is no need to do so, almost everyone gets busy on the proof. ~ John Kenneth Galbraith

Ron Scott
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Re: Respect the Magical Power of Mean Reversion

Post by Ron Scott » Wed Aug 01, 2018 7:43 pm

Not looking forward to seeing the PE revert, but it will...
Retirement is a game best played by those prepared for more volatility in the future than has been seen in the past. The solution is not to predict investment losses but to prepare for them.

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Re: Respect the Magical Power of Mean Reversion

Post by Dale_G » Thu Aug 02, 2018 12:35 am

I am still waiting for my railroad, canal and buggy whip companies to return to their former glory.

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JoMoney
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Re: Respect the Magical Power of Mean Reversion

Post by JoMoney » Thu Aug 02, 2018 3:55 am

"...after the nice run up we’ve had for the past five years or so..."
It has been "nice", but the 13% over the most recent 5 year period doesn't look to be a large deviation from the "mean" to me:
Image
"To achieve satisfactory investment results is easier than most people realize; to achieve superior results is harder than it looks." - Benjamin Graham

B. Wellington
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Re: Respect the Magical Power of Mean Reversion

Post by B. Wellington » Thu Aug 02, 2018 4:54 am

The problem with reversion to the mean is that we don't know if or when that will happen. Or how swiftly that movement could take place. It could be a slow and steady process that may take years to develop and we just don't know for sure. Following the advice and acting on it in 2013 would have resulted in disappointment and then more second guessing. Leading to even worse investor performance. :confused

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Re: Respect the Magical Power of Mean Reversion

Post by asif408 » Thu Aug 02, 2018 8:07 am

CULater wrote:
Wed Aug 01, 2018 7:00 pm
What is the problem here? I'm guessing the problem is that Mean Reversion isn't anything more than a statistical abstraction, a chimera. We've been duped again. Phooey.
And I'm guessing the problem is the impatient aren't, by definition, patient enough to wait for it to happen. So patience is rewarded for those who have it, as least historically speaking. Phooey.

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JPH
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Re: Respect the Magical Power of Mean Reversion

Post by JPH » Thu Aug 02, 2018 8:24 am

There have been other threads on mean reversion versus regression to the mean. I don't pretend to understand much about mean reversion as that term is used in finance. Bogle also has described it as a "Powerful Force" as does the author of your quote. I doubt it.

Regression to the mean is well known in probability and statistics. The key term in your quote is "random variate." Regression to the mean depends on random measurement error. Say you do a coin flipping experiment to estimate the true probability of a Heads outcome. You have 100 people flip a fair coin 10 times. The mean of your sample data will fairly closely approximate the true population value of 0.50. But one person got 9 heads in 10 trials. If you repeat the experiment, then that person probably will obtain a result much closer to the true mean value of 0.50. That's regression to the mean. It is trivially obvious in this example because the outcome depends 100% on chance. So the departure of the sample outcome from the true mean is random measurement error. The sample outcome is in error due to chance. In finance the outcome is not totally determined by chance, but our measurement of it contains a chance component. Any stock in the S&P 500 can be over or under priced on a given day. The market average overcomes this, so it probably should not concern investors.

Turning to the placebo effect, I believe the research does demonstrate a psychological influence. There also is a nocebo effect, where a patient's negative expectations about treatment are associated with a worse outcome. When I was analyzing data for medical researchers, and the experimental treatment was shown to be of no value, they sometimes would ask me to see if just the sickest patients might have benefited. That would be walking right into the regression to the mean trap. If you repeated the experiment, then some of those sickest patients would no longer be such because of some error in the measurement of their baseline score.

As I said, I don't know much about mean reversion. But what people might be referring to is simply the fact that any process that oscillates will eventually change direction. In medicine, let's take pain as an example. Pain tends to fluctuate in intensity over time. Patients have good days, and they have bad days. They are most likely to seek medical care when they are suffering most. If they receive effective treatment, many will improve. But many also will improve following ineffective intervention because their pain is cyclical. Both patient and practitioner can be convinced that the intervention worked.

The financial markets also oscillate. If we happen to be at a very high point when the change in direction occurs, there is a temptation to believe the market was too high, over priced, in need of a "correction" or some such thing. Again, there is more than just chance going on here. We see a lot of posts by people fearing that the market has gone too far, and they are nervously thinking about selling. If enough people act on their impulse, there could be a real selloff. I don't know if people would call this mean reversion or not. It's the closest thing that I can think of to a "Powerful Force."
While the moments do summersaults into eternity | Cling to their coattails and beg them to stay - Townes Van Zandt

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Re: Respect the Magical Power of Mean Reversion

Post by grok87 » Thu Aug 02, 2018 2:11 pm

tell that to the japanese investors from 1990

https://en.wikipedia.org/wiki/Lost_Decade_(Japan)
wrote: The Lost Decade or the Lost 10 Years (失われた十年 Ushinawareta Jūnen) is a period of economic stagnation in Japan following the Japanese asset price bubble's collapse in late 1991 and early 1992. The term originally referred to the years from 1991 to 2000,[1] but recently the decade from 2001 to 2010 is often included,[2] so that the whole period is referred to as the Lost Score or the Lost 20 Years (失われた二十年, Ushinawareta Nijūnen). Broadly impacting the entire Japanese economy, over the period of 1995 to 2007, GDP fell from $5.33 trillion to $4.36 trillion in nominal terms,[3] real wages fell around 5%,[4] while the country experienced a stagnant price level.[5] While there is some debate on the extent and measurement of Japan's setbacks,[6][7] the economic effect of the Lost Decade is well established and Japanese policymakers continue to grapple with its consequences.
[\quote]
RIP Mr. Bogle.

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CULater
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Re: Respect the Magical Power of Mean Reversion

Post by CULater » Thu Aug 02, 2018 2:43 pm

JPH wrote:
Thu Aug 02, 2018 8:24 am
There have been other threads on mean reversion versus regression to the mean. I don't pretend to understand much about mean reversion as that term is used in finance. Bogle also has described it as a "Powerful Force" as does the author of your quote. I doubt it.

Regression to the mean is well known in probability and statistics. The key term in your quote is "random variate." Regression to the mean depends on random measurement error. Say you do a coin flipping experiment to estimate the true probability of a Heads outcome. You have 100 people flip a fair coin 10 times. The mean of your sample data will fairly closely approximate the true population value of 0.50. But one person got 9 heads in 10 trials. If you repeat the experiment, then that person probably will obtain a result much closer to the true mean value of 0.50. That's regression to the mean. It is trivially obvious in this example because the outcome depends 100% on chance. So the departure of the sample outcome from the true mean is random measurement error. The sample outcome is in error due to chance. In finance the outcome is not totally determined by chance, but our measurement of it contains a chance component. Any stock in the S&P 500 can be over or under priced on a given day. The market average overcomes this, so it probably should not concern investors.

Turning to the placebo effect, I believe the research does demonstrate a psychological influence. There also is a nocebo effect, where a patient's negative expectations about treatment are associated with a worse outcome. When I was analyzing data for medical researchers, and the experimental treatment was shown to be of no value, they sometimes would ask me to see if just the sickest patients might have benefited. That would be walking right into the regression to the mean trap. If you repeated the experiment, then some of those sickest patients would no longer be such because of some error in the measurement of their baseline score.

As I said, I don't know much about mean reversion. But what people might be referring to is simply the fact that any process that oscillates will eventually change direction. In medicine, let's take pain as an example. Pain tends to fluctuate in intensity over time. Patients have good days, and they have bad days. They are most likely to seek medical care when they are suffering most. If they receive effective treatment, many will improve. But many also will improve following ineffective intervention because their pain is cyclical. Both patient and practitioner can be convinced that the intervention worked.

The financial markets also oscillate. If we happen to be at a very high point when the change in direction occurs, there is a temptation to believe the market was too high, over priced, in need of a "correction" or some such thing. Again, there is more than just chance going on here. We see a lot of posts by people fearing that the market has gone too far, and they are nervously thinking about selling. If enough people act on their impulse, there could be a real selloff. I don't know if people would call this mean reversion or not. It's the closest thing that I can think of to a "Powerful Force."
Informative. I think the key is the notion of randomness and stock prices simply being a random distribution around some kind of "true mean" or "true value". Is there such a thing in the distribution of equity prices? It is only in hindsight that it might look like there's a trend line, but that doesn't prove anything does it?
Faced with the choice between changing one’s mind and proving that there is no need to do so, almost everyone gets busy on the proof. ~ John Kenneth Galbraith

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Re: Respect the Magical Power of Mean Reversion

Post by willthrill81 » Thu Aug 02, 2018 2:48 pm

Ron Scott wrote:
Wed Aug 01, 2018 7:43 pm
Not looking forward to seeing the PE revert, but it will...
There's no rule saying that it will. The CAPE ratio for U.S. stocks has been above its historic average since 1992.
“It's a dangerous business, Frodo, going out your door. You step onto the road, and if you don't keep your feet, there's no knowing where you might be swept off to.” J.R.R. Tolkien,The Lord of the Rings

TomCat96
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Re: Respect the Magical Power of Mean Reversion

Post by TomCat96 » Thu Aug 02, 2018 3:07 pm

Mean Reversion is one of those concepts that when used in finance borders on sophistry.

It's a more legitimate equivalent of saying "what goes up must come down." It gives no timeline to when it may occur, and thus has an unlimited window to gain acceptance as a legitimate tool of analysis.

As others have stated, there is no guarantee such a thing will occur. Statistically yes, it make sense that it should occur. But it's a prediction that almost can never be disproven. At best, the counterargument is "just you wait." Finally when it does occur, it can occur in a myriad of possible outcomes. In other words, the manner in which reversion to the mean can occur are so multifarious, it really doesn't do much work as a predictive tool.

I shy away from threads of analysis that yield poor fruit. The idea that markets will revert to the mean is right up there with that.

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Re: Respect the Magical Power of Mean Reversion

Post by david1082b » Thu Aug 02, 2018 3:48 pm

grok87 wrote:
Thu Aug 02, 2018 2:11 pm
Broadly impacting the entire Japanese economy, over the period of 1995 to 2007, GDP fell from $5.33 trillion to $4.36 trillion in nominal terms,[3]
Nominal dollar terms are not really relevant for Japan, what you need to look at is real GDP in Japanese yen terms or PPP dollars at least. Looking at exchange rates and nominal dollars is very misleading. The Japanese economy is not priced in US dollars and does not change in real size just because the exchange rate changes. The same fallacy was used after Brexit to say that the UK economy had somehow become "smaller than France's" just because the exchange rate for the pound dropped a lot, as if the UK economy is priced in Euros and as if its change in size is decided by the exchange rate.

To give an example, in 2012 the yen started a significant decline in value versus the dollar, so Japan's GDP in dollars went down a lot, it peaked at over $6 trillion in 2012 and is now $4.8 trillion, smaller than the 1995 number! https://www.google.com/publicdata/explo ... &ind=false

Do did Japan's economy get smaller from 1995 to now or is the analysis flawed? Let's look at Japan's Gross National Income in PPP dollars https://www.google.com/publicdata/explo ... &ind=false

We can see growth from 1995 to 2007 and to now too. PPP dollars are not nominal but will better reflect purchasing power in inflation-adjusted terms.

Japan hasn't had meaningful population growth for a long time, while other nations get a boost to GDP growth simply because of population growth. GDP per capita is more useful, as well as using PPP to give a better idea of purchasing power

GDP per capita, PPP (constant 2005 international $ https://www.google.com/publicdata/explo ... &ind=false

There we see the real growth. GDP per working age person in Japan has done even better, and is also seen as even more useful since Japan has had such a decline in its working age population, which is a drag on pure GDP numbers.

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Re: Respect the Magical Power of Mean Reversion

Post by david1082b » Thu Aug 02, 2018 3:50 pm

JoMoney wrote:
Thu Aug 02, 2018 3:55 am
"...after the nice run up we’ve had for the past five years or so..."
It has been "nice", but the 13% over the most recent 5 year period doesn't look to be a large deviation from the "mean" to me:
Image
The "past five years" quote is from 2013 and reflects the post-2008 stock boom, it's from an article called "Respect the Power of Mean Reversion", note no "magical", I don't know why OP put that in there http://awealthofcommonsense.com/2013/07 ... reversion/

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Re: Respect the Magical Power of Mean Reversion

Post by david1082b » Thu Aug 02, 2018 4:07 pm

CULater wrote:
Wed Aug 01, 2018 7:00 pm
I can’t predict the future, but after the nice run up we’ve had for the past five years or so, it will probably make sense to look for markets that offer better value than the US markets do currently.
~ Ben Carlson

Unfortunately, Mr. Carlson said this in July, 2013 and since that time, the U.S. market advanced about 90% while emerging markets did 40%, while Europe the Pacific did about 50%. The good-looking markets didn't deliver -- Mr. Mean Reversion didn't show up.
The blog post from Ben Carlson carries on with these words:
I don’t recommend wholesale changes to your asset allocation, but if you don’t have any international or emerging market stock exposure, these are two markets that are widely hated by investors at the moment.

If you are in it for the long haul, looking to rebalance into undervalued markets is one way to increase your long-term results. These things don’t always reverse right away, but buying undervalued assets and selling overvalued assets is the goal of buy low, sell high. http://awealthofcommonsense.com/2013/07 ... reversion/


"these things don't always reverse right away", so the idea is that you need to be patient. The next ten years could see USA do poorly and emerging do well, just like 2000 to 2010.

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CULater
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Re: Respect the Magical Power of Mean Reversion

Post by CULater » Thu Aug 02, 2018 4:35 pm

The problem with Ben Carlson's advice about shifting between U.S. and non U.S. stocks based on valuations is that it doesn't work. For example, using 5/25 rebalancing bands between U.S. and non U.S. stocks produces a lower cumulative return from 1986-present (dates of available data) than not rebalancing at all. If mean reversion was at work, it was working pretty short hours for the last 30+ years. Similar results for using bands to rebalance between U.S. market and Emerging market. Yes, things that go up will go down and vice versa but unless you happen to time the exact inflection points this information would seem to be of little practical use.
Faced with the choice between changing one’s mind and proving that there is no need to do so, almost everyone gets busy on the proof. ~ John Kenneth Galbraith

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Re: Respect the Magical Power of Mean Reversion

Post by JPH » Thu Aug 02, 2018 4:40 pm

What comes down must go up? I think so. But when to make the move? I had a research assistant once that did a lot of fancy technical analysis to note when the price of a stock crossed a threshold band a "critical" distance from its running mean. She had fun, then went to law school.
While the moments do summersaults into eternity | Cling to their coattails and beg them to stay - Townes Van Zandt

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Re: Respect the Magical Power of Mean Reversion

Post by garlandwhizzer » Thu Aug 02, 2018 6:33 pm

The timing and degree of mean reversion cannot be accurately predicted beforehand. After it has occurred some can look at the charts and say that this market action was inevitable at this point. So it was in the tech boom and collapse of 2000. Most market mavens during the tech boom argued that "This time is different," that tech had created an entirely new rapidly expanding landscape where the old investment rules didn't apply any more. Like technical analysis, after the collapse, the experts change their theories. Theories that explain recent market action recently tend to get widely accepted, whatever that action was. So the same folks who were blind to the coming collapse became proponents of mean reversion after the collapse. Predicting when some major market change will occur and how severe it will be before the fact is much less predictable than the flip of a coin. Experts often create theories to explain why whatever works right is reasonable and likely to persist. After it stops persisting and crashes, new theories are quickly embraced which explain that it is obvious that the change was inevitable. Hindsight is always 20/20. Foresight is essentially blind.

I confess that, being a guy who believes in compelling valuation fundamentals, I have lost money in EM relative to a US only portfolio for years and especially to US high flyers with jokes for fundamentals like Amazon, Tesla, and Netflix. In spite of this, I am not yet throwing in the towel. I still expect EM to eventually reward me but, like everyone else, I could be wrong. That's why I own US, DM, and EM. I'll always own something that's underperforming but likewise something that's outperforming. When you're not certain where the outperformance is going to come from that seems reasonable to me.

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Re: Respect the Magical Power of Mean Reversion

Post by MotoTrojan » Thu Aug 02, 2018 6:55 pm

willthrill81 wrote:
Thu Aug 02, 2018 2:48 pm
Ron Scott wrote:
Wed Aug 01, 2018 7:43 pm
Not looking forward to seeing the PE revert, but it will...
There's no rule saying that it will. The CAPE ratio for U.S. stocks has been above its historic average since 1992.
Furthermore it could revert without any price decline.

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Re: Respect the Magical Power of Mean Reversion

Post by Chaconne » Thu Aug 02, 2018 7:14 pm

I don't know much about anything, but this has me wondering:

In investing, should we really be talking about reversion TOWARD the mean rather than reversion TO the mean?

Perhaps an extreme will tend to revert toward the mean, but not get there entirely. I wonder if markets always get TO the mean or just trend TOWARD it.

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Re: Respect the Magical Power of Mean Reversion

Post by david1082b » Thu Aug 02, 2018 11:17 pm

grok87 wrote:
Thu Aug 02, 2018 2:11 pm
tell that to the japanese investors from 1990
Getting back to the subject of investment reutrns, Japanese who had a global portfolio did OK since 1989. The blog post that seemed to inspire the thread title was based on the idea of getting global exposure and not being overly-concentrated in one nation. Clearly we can point out individual nations that did terribly compared with the world average, which points towards global investing as a way to mitigate that risk before it happens http://awealthofcommonsense.com/2013/07 ... reversion/

grok87
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Re: Respect the Magical Power of Mean Reversion

Post by grok87 » Fri Aug 03, 2018 4:39 am

david1082b wrote:
Thu Aug 02, 2018 11:17 pm
grok87 wrote:
Thu Aug 02, 2018 2:11 pm
tell that to the japanese investors from 1990
Getting back to the subject of investment reutrns, Japanese who had a global portfolio did OK since 1989. The blog post that seemed to inspire the thread title was based on the idea of getting global exposure and not being overly-concentrated in one nation. Clearly we can point out individual nations that did terribly compared with the world average, which points towards global investing as a way to mitigate that risk before it happens http://awealthofcommonsense.com/2013/07 ... reversion/
makes sense.
the part of the global portfolio i still struggle with is international bonds. I tend to follow Swensen and just use treasuries and tips.
RIP Mr. Bogle.

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