Suits me.All I need to know is that an index strategy will probably do better than other strategy I could reasonably execute.
Misbehaviour of markets and the Black Swan
Re: Misbehaviour of markets and the Black Swan
Carol88888
Re: Misbehaviour of markets and the Black Swan
I think you might be missing the thrust behind this thread. There are a couple of questions being asked here which tie directly into the above strategy.
1. What should my AA consist of? i.e., risky equities to safe bonds?
2. What is the expected return of my portfolio? i.e. What should my savings rate be?
3. What is the chance that my plan will meet my goal? i.e., what is the chance that the market will blow up repeatably during my withdraw stage.
There are many Bogleheads who tend to gloss over these questions as unknowable and just plow ahead. However it is a important question.
Re: Misbehaviour of markets and the Black Swan
+1 “You don’t have to know a man’s exact weight to know that he’s fat.” – Ben Grahamfreyj6 wrote: ↑Mon Jul 01, 2019 3:54 pmIn my opinion, the key takeaway of these kinds of books is that we need to act as intelligently as possible in the face of uncertainty rather than making fragile assumptions and then supporting them with a gargantuan amount of math. As an analogy, no one knows the perfect diet for humans but we can be almost certain that whole foods are healthier than heavily processed ones, and that a strawberry is healthier than a Twinky. Likewise, we finance we can still make a lot of intelligence decisions, but at all costs we should avoid trying to make those decisions under the assumption that we understand more than we actually do.
Re: Misbehaviour of markets and the Black Swan
So returns are not Gaussian distributed and have fat tails. Instead of the distribution looking like305pelusa wrote: ↑Sun Jun 30, 2019 5:05 pmJust read these two books by Mandelbrot and Nassim and I'm absolutely fascinated by the material. I always kinda knew asset prices didn't follow a neat Bell Curve and that they displayed fat tails. These books go far beyond that though. That the distributions aren't Gaussian at all, and instead display wild variation (the standard deviation itself constantly changes) and follow the Power Law.
The implications are almost nihilistic in a way. Standard deviation doesn't just underestimate risk; it's totally innapropiate as a measure of risk. Correlation doesn't necessitate normality but it does require a finite standard deviation so that measure is also completely useless.
It always felt strange to use St. Dev and correlations to make portfolios when they are so widely varying depending on the period you measure them. Now I understand why. It seems to me that they are perhaps innapropiate for these distributions.
The conclusion has huge consequences on the application of MPT.
Anyone one else read these books and perhaps wants to talk about how they have changed their thinking with their finances? What action items could come out if you believe in they're material?
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I say big whoop. Everyone already knows that the distributions are unknown, that the parameters are unknown, the statistics vary over time, and that the market can gain or drop 50% or 100% at the drop of a hat. The distributions are just models. Nobody believes that the models are correct.
And if you don't like Gaussian, use another distribution, e.g. Student's tdistribution. MPT does not require Gaussian or stationarity. The models are just asking, what if? What if the distribution was this, with these parameters. What would be the range of outcomes?
 nisiprius
 Advisory Board
 Posts: 38510
 Joined: Thu Jul 26, 2007 9:33 am
 Location: The terrestrial, globular, planetary hunk of matter, flattened at the poles, is my abode.O. Henry
Re: Misbehaviour of markets and the Black Swan
Me, me, me! Me. Myself. Mine! Thank you so much for finally giving me the "attaboy" I've been dying for.protagonist wrote: ↑Wed Jul 03, 2019 4:58 pmI don't like [Taleb] either, but if he really said "In springtime, seed; in summer, cultivate; in fall, windsurf.", then my opinion of him just went up a notch.
On the other hand, if you wrote it, then my opinion of you did. (note: I had a good opinion of you to start with...much better than my opinion of Taleb.)
Annual income twenty pounds, annual expenditure nineteen nineteen and six, result happiness; Annual income twenty pounds, annual expenditure twenty pounds ought and six, result misery.
 nisiprius
 Advisory Board
 Posts: 38510
 Joined: Thu Jul 26, 2007 9:33 am
 Location: The terrestrial, globular, planetary hunk of matter, flattened at the poles, is my abode.O. Henry
Re: Misbehaviour of markets and the Black Swan
But "how fat are the tails" matter. And so does "how many decades/centuries/millennia of data do you need to take pin down the underlying distributions with enough confidence to stake important money on them?"grayfox wrote: ↑Thu Jul 04, 2019 8:05 am...So returns are not Gaussian distributed and have fat tails....
That's the huge revelation from M. and T. that makes MPT useless? Plus the statistics vary over time. So that makes investing meaningless?
I say big whoop. Everyone already knows that the distributions are unknown, that the parameters are unknown, the statistics vary over time, and that the market can gain or drop 50% or 100% at the drop of a hat. The distributions are just models. Nobody believes that the models are correct.
And if you don't like Gaussian, use another distribution, e.g. Student's tdistribution. MPT does not require Gaussian or stationarity. The models are just asking, what if? What if the distribution was this, with these parameters. What would be the range of outcomes?
I spent some quality time on a series of postings in which I explored the differences in outcome from following two different strategies, against the range of possible mighthavebeen outcomes based on a simulation. The simulation is based on historic data and makes no assumptions about distributions at all. A typical result was:
Posting, including links to methodology
Over this particular time period, a portfolio with a smallcap value tilt outperformed one without. But even taking everything at face value, even if you believed that this was almost guaranteed to happen over any similar time period, the difference attributable to a difference in strategy is small compared to the huge range of natural variation and mighthavebeens. You're talking about a $3,000 edge when the range of outcomes was over $20,000.
That, to me, is the big lesson. In order to sell product, people fuss over small statistical differences. The implicit assumption is always that they must matter because if you pretend that financial statistics are wellbehaved and compound them out for thirty years, they become huge. The reality is that, central limit theorem or no, the uncertainty in what you will actually experience in your own investing lifetime is so huge compared to the kinds of (dubious) differences people argue about, that it's all angelsontheheadofapin stuff.
And, yes, this is true for expense ratios, too. Buying lattes is not the difference between retiring poor versus retiring rich. Although I believe in Bogle's "cost matters hypothesis," if it's 1990 and we're talking about an 0.25% index fund and a 1.50% active fund, yes, cost matters. Once you get below 0.50% or so, not so much. I did matter/scatter chart on that, too. Once you get below 0.50%, expenses are still important as a governance issue, a matter of fairness, and "the principle of the thing," but the predictable difference in performance due to expenses is still tiny compared to the unpredictable difference from the "fickle finger of fate."
Annual income twenty pounds, annual expenditure nineteen nineteen and six, result happiness; Annual income twenty pounds, annual expenditure twenty pounds ought and six, result misery.
Re: Misbehaviour of markets and the Black Swan
That last paragraph  and it seems reasonable  very well might be part of the story for the past success of Wellington and Wellesley: fees just low enough to let their active (albeit seemingly systematic) strategies....I guess work is word.nisiprius wrote: ↑Thu Jul 04, 2019 9:33 amBut "how fat are the tails" matter. And so does "how many decades/centuries/millennia of data do you need to take pin down the underlying distributions with enough confidence to stake important money on them?"grayfox wrote: ↑Thu Jul 04, 2019 8:05 am...So returns are not Gaussian distributed and have fat tails....
That's the huge revelation from M. and T. that makes MPT useless? Plus the statistics vary over time. So that makes investing meaningless?
I say big whoop. Everyone already knows that the distributions are unknown, that the parameters are unknown, the statistics vary over time, and that the market can gain or drop 50% or 100% at the drop of a hat. The distributions are just models. Nobody believes that the models are correct.
And if you don't like Gaussian, use another distribution, e.g. Student's tdistribution. MPT does not require Gaussian or stationarity. The models are just asking, what if? What if the distribution was this, with these parameters. What would be the range of outcomes?
I spent some quality time on a series of postings in which I explored the differences in outcome from following two different strategies, against the range of possible mighthavebeen outcomes based on a simulation. The simulation is based on historic data and makes no assumptions about distributions at all. A typical result was:
Posting, including links to methodology
Over this particular time period, a portfolio with a smallcap value tilt outperformed one without. But even taking everything at face value, even if you believed that this was almost guaranteed to happen over any similar time period, the difference attributable to a difference in strategy is small compared to the huge range of natural variation and mighthavebeens. You're talking about a $3,000 edge when the range of outcomes was over $20,000.
That, to me, is the big lesson. In order to sell product, people fuss over small statistical differences. The implicit assumption is always that they must matter because if you pretend that financial statistics are wellbehaved and compound them out for thirty years, they become huge. The reality is that, central limit theorem or no, the uncertainty in what you will actually experience in your own investing lifetime is so huge compared to the kinds of (dubious) differences people argue about, that it's all angelsontheheadofapin stuff.
And, yes, this is true for expense ratios, too. Buying lattes is not the difference between retiring poor versus retiring rich. Although I believe in Bogle's "cost matters hypothesis," if it's 1990 and we're talking about an 0.25% index fund and a 1.50% active fund, yes, cost matters. Once you get below 0.50% or so, not so much. I did matter/scatter chart on that, too. Once you get below 0.50%, expenses are still important as a governance issue, a matter of fairness, and "the principle of the thing," but the predictable difference in performance due to expenses is still tiny compared to the unpredictable difference from the "fickle finger of fate."
Re: Misbehaviour of markets and the Black Swan
Hi pelusa,
I've read Mandelbrot's Misbehavior of Markets and Taleb's Fooled by Randomness. I have not read the Black Swan, but when it first came out in about 2007 I considered purchasing it and on several occasions I read parts of it in bookstores (remember those). But I couldn't decide if it added anything beyond what I already knew. Then I decided to search for relatively technical subjects in the book that I already knew a lot about. I think I picked three out of the index and looked to see what Taleb had to say about them. In each case it was utter nonsense. One was about Robert Engle and GARCH models. The only thing Taleb got right was that Engle is a "charming gentleman" in Taleb's phraseology. Rob is a very nice guy. Everything Taleb wrote about GARCH models was wrong. I know, I have estimated dozens if not hundreds of them.
If you are a day trader, or even better a high frequency trader with access to a super computer, then Mandelbrot is essential. If you are an investor over years or decades then, thanks to the Central Limit Theorem (CLT), Mandelbrot is irrelevant. (See me posts earlier in this thread about CLT.)
Read Taleb for the fun of figuring out when he is imparting the trite or well known vs. when he is handing out pure BS.
If you want to know more about how financial economists handle fat tails and volatility clustering check out the following about volatility from the man who won a Nobel Prize for his research on volatility in financial returns.
Rob Engle's Nobel address on volatility (very accessible)
Link  https://www.nobelprize.org/prizes/econo ... e/lecture/
GARCH 101  Rob Engle (a gentle introduction to ARCH and GARCH models in finance)
Link  http://www.cmat.edu.uy/~mordecki/hk/engle.pdf
Also check out the volatility lab Engle runs at NYU  VLab
Link  https://vlab.stern.nyu.edu/
Finally here is a survey of the development of financial risk management since the early 20th century by financial econometrician Francis Diebold.
Link  https://www.sas.upenn.edu/~fdiebold/pap ... dElgar.pdf
BobK
In finance risk is defined as uncertainty that is consequential (nontrivial). 
The two main methods of dealing with financial risk are the matching of assets to goals & diversifying.
Re: Misbehaviour of markets and the Black Swan
I work in the industry. I think you have it backwards. The more independent instances you have, the more you can approach it with stats. Mandelbrot/Taleb stuff is useless, nobody running a successfully HFT business considers it.
"whenever there is a randomized way of doing something, then there is a nonrandomized way that delivers better performance but requires more thought" ET Jaynes
Re: Misbehaviour of markets and the Black Swan
Since you work in the industry I take your word for it and stand corrected. In that case Mandelbrot has little useful to add either for ST or LT investors.
However, Mandelbrot's work is historically important. For one thing he was the first to discover volatility clustering in stock returns. Nevertheless, Mandelbrot always stressed fat tails and talked little about the volatility clustering that he was the first to observe. Here is Diebold (see my previous post) on the contributions of Mandelbrot.
BobKMandelbrot (1963) and Fama (1965) recognized all this, subjected Bachelier’s model to empirical scrutiny, rejected it soundly, and emphasized a new theoretical (stable Paretian) distributional paradigm. They emphasized that real asset returns tend to be symmetrically distributed, but that their distributions have more probability mass in the center and in the tails than does the Gaussian. The “fat tails,” in particular, imply that extreme events– crashes and the like, “black swans” in the memorable prose of Taleb (2007) – happen in real markets far more often than would happen the case under normality. In many respects those papers mark the end of “traditional” (linear, Gaussian) risk thinking and the beginning of “modern” (nonlinear, nonGaussian) thinking, even if traditional thinking continues to appear too often in both academics and industry. Mandelbrot continued, correctly, to emphasize fat tails for the rest of his career, even as much of the rest of the finance profession shifted focus instead to possible dependence in returns, in particular linear serial correlation or “mean reversion” in returns, a violation of the “iid” part of (4b). Reasonable people can – and do – still debate the existence and strength of mean reversion in returns, but no reasonable person can deny the existence of fat tails in distributions of highfrequency returns.
In finance risk is defined as uncertainty that is consequential (nontrivial). 
The two main methods of dealing with financial risk are the matching of assets to goals & diversifying.
Re: Misbehaviour of markets and the Black Swan
I think the OP should be quite pleased with the information in this thread.
He learned that annual equity returns are not wild distributions with infinite variance, but instead thanks to the CLT are approximately normally distributed, and that stock prices at an annual frequency are approximately lognormally distributed. This should allay his fears that nearly everything he has read about portfolio theory has not been invalidated by Mandlebrot and Taleb.
The thread also likely introduced him to volatility clusters and how both fat tails and volatility clusters can be addressed using GARCH models  So lots of information in this thread.
BobK
He learned that annual equity returns are not wild distributions with infinite variance, but instead thanks to the CLT are approximately normally distributed, and that stock prices at an annual frequency are approximately lognormally distributed. This should allay his fears that nearly everything he has read about portfolio theory has not been invalidated by Mandlebrot and Taleb.
The thread also likely introduced him to volatility clusters and how both fat tails and volatility clusters can be addressed using GARCH models  So lots of information in this thread.
BobK
In finance risk is defined as uncertainty that is consequential (nontrivial). 
The two main methods of dealing with financial risk are the matching of assets to goals & diversifying.
Re: Misbehaviour of markets and the Black Swan
We all know that really bad things can happen to good markets and that the timing of those bad things can happen at rather inconvenient times.
In more recent history, I can think of three long secular bear markets where the markets were essentially flat with 50% down or more bear markets. They were 19291946, 19681984, and 20002012. The first had the Great Depression, the second had to do with oil shocks and stagflation, the third one had a financial crisis which nearly created a second Great Depression but the crisis didn't hit until fall of 2008. The economy was a biggest factor in the first two secular bear markets but in the third case the economic crisis didn't hit until 2/3 the way through the 20002012 secular bear market. In the case of 19681984, the oil shocks and stagflation didn't kick in until 1973. So tying the three secular bear markets to the economy as their cause seems tenuous.
In all three cases, though, you did see a speculative fervor that preceded each of them. The first was the roaring twenties, the shoe shine boys giving stock tips to Bernard Baruch, and fortunes made on stock speculation. The 19681984 secular bear was preceded by the gogo years of the 1960's and the Nifty Fifty, blue chip stocks you could buy and hold forever or so the theory went. P/E ratios on some of those Nifty Fifty stocks got to be in excess of 50. 20002012 was preceded by the High Tech/Internet Bubble, the new paradigm, Dow 36,000, etc. In all three cases, you could see excessive valuations and excessive optimism.
So it would seem to me that your best chances of avoiding Black Swans would be to pay attention to both valuation and sentiment extremes in the market. Pretty much what I am saying is that in 1929, 1968, and 1999 that extremes in valuation and sentiment made the stock market a big accident waiting to happen. In 1929 and in 1973, economic shocks were sort of the straw that broke the camel's back. You could say the shocks were the catalyst for bear markets but not really the cause. Old Lady Leary's cow kicked the lantern over but so much fuel from excessive speculation that sooner or later something else would have set things ablaze even if there never was a cow. That was the case in 2000, so much optimism the market ran out of buyers and stocks had no where to go but down. The 911 attacks didn't help but the 20012002 recession was rather mild.
In the United States, such trauma as war, terrorist attacks, natural disasters seem to have sharp, negative but temporary effects on the market. Markets here turn around quickly. Works well until the war comes to your soil and you lose the war. Just ask Japan how the end of World War II affected their stock market. So the standard wisdom that the market rebounds from such temporary setbacks doesn't work when you lose World War II. No way to predict these type of traumatic events. Rare but they do happen. After all, Rome did get sacked and as I recall, a few times.
It would just seem that the best things to focus on would be market excesses in valuation and sentiment. Problem is how do you define excesses, not a precise definition out there. Then there is the problem of timing, the old being right too early problem or even worse being right way too early. A second thing would be to ride out volatility from traumatic events, you just cross your fingers and hope the disaster isn't too pervasive through the country. Nearly all the time, the market reaction is sharp, severe, and temporary. But the one time that it isn't could wipe you out. A crop failure in California would be okay but crop failures all across the country would be a different matter.
The next question, is how to you guard against these bad things happening to good markets? In most cases, time would heal all wounds with just a stock and bond portfolio. You could take the Larry Swedroe approach and diversify across asset classes, geography, and factors. You could add liquid alts and interval funds to round things out. But if we happen to lose WWIII, then all bets are off.
I have to admit much of this discussion, when it got into the stats got to be a bit over my head. But what a lot of it seems to be is explaining in mathematical terms what we already know. Really bad things can happen at the most inconvenient times. The best I can do is to pay attention when markets hit valuation and sentiment extremes, these are times when markets are accidents waiting to happen. If it isn't Mrs. O'Leary's cow, then it will be something else. As I said, the economy can be the equivalent of the cow kicking over the lantern but that isn't always the case.
In more recent history, I can think of three long secular bear markets where the markets were essentially flat with 50% down or more bear markets. They were 19291946, 19681984, and 20002012. The first had the Great Depression, the second had to do with oil shocks and stagflation, the third one had a financial crisis which nearly created a second Great Depression but the crisis didn't hit until fall of 2008. The economy was a biggest factor in the first two secular bear markets but in the third case the economic crisis didn't hit until 2/3 the way through the 20002012 secular bear market. In the case of 19681984, the oil shocks and stagflation didn't kick in until 1973. So tying the three secular bear markets to the economy as their cause seems tenuous.
In all three cases, though, you did see a speculative fervor that preceded each of them. The first was the roaring twenties, the shoe shine boys giving stock tips to Bernard Baruch, and fortunes made on stock speculation. The 19681984 secular bear was preceded by the gogo years of the 1960's and the Nifty Fifty, blue chip stocks you could buy and hold forever or so the theory went. P/E ratios on some of those Nifty Fifty stocks got to be in excess of 50. 20002012 was preceded by the High Tech/Internet Bubble, the new paradigm, Dow 36,000, etc. In all three cases, you could see excessive valuations and excessive optimism.
So it would seem to me that your best chances of avoiding Black Swans would be to pay attention to both valuation and sentiment extremes in the market. Pretty much what I am saying is that in 1929, 1968, and 1999 that extremes in valuation and sentiment made the stock market a big accident waiting to happen. In 1929 and in 1973, economic shocks were sort of the straw that broke the camel's back. You could say the shocks were the catalyst for bear markets but not really the cause. Old Lady Leary's cow kicked the lantern over but so much fuel from excessive speculation that sooner or later something else would have set things ablaze even if there never was a cow. That was the case in 2000, so much optimism the market ran out of buyers and stocks had no where to go but down. The 911 attacks didn't help but the 20012002 recession was rather mild.
In the United States, such trauma as war, terrorist attacks, natural disasters seem to have sharp, negative but temporary effects on the market. Markets here turn around quickly. Works well until the war comes to your soil and you lose the war. Just ask Japan how the end of World War II affected their stock market. So the standard wisdom that the market rebounds from such temporary setbacks doesn't work when you lose World War II. No way to predict these type of traumatic events. Rare but they do happen. After all, Rome did get sacked and as I recall, a few times.
It would just seem that the best things to focus on would be market excesses in valuation and sentiment. Problem is how do you define excesses, not a precise definition out there. Then there is the problem of timing, the old being right too early problem or even worse being right way too early. A second thing would be to ride out volatility from traumatic events, you just cross your fingers and hope the disaster isn't too pervasive through the country. Nearly all the time, the market reaction is sharp, severe, and temporary. But the one time that it isn't could wipe you out. A crop failure in California would be okay but crop failures all across the country would be a different matter.
The next question, is how to you guard against these bad things happening to good markets? In most cases, time would heal all wounds with just a stock and bond portfolio. You could take the Larry Swedroe approach and diversify across asset classes, geography, and factors. You could add liquid alts and interval funds to round things out. But if we happen to lose WWIII, then all bets are off.
I have to admit much of this discussion, when it got into the stats got to be a bit over my head. But what a lot of it seems to be is explaining in mathematical terms what we already know. Really bad things can happen at the most inconvenient times. The best I can do is to pay attention when markets hit valuation and sentiment extremes, these are times when markets are accidents waiting to happen. If it isn't Mrs. O'Leary's cow, then it will be something else. As I said, the economy can be the equivalent of the cow kicking over the lantern but that isn't always the case.
A fool and his money are good for business.
Re: Misbehaviour of markets and the Black Swan
To be honest, I didn't quite follow that point. You've certainly said it many times. Maybe I missed your proof/explanation?
I learned about CLT in the following context: Grab a probability distribution, take a random sample, and calculate the mean. Do it over and over again. Plot the various samples' means. They will form a normal distribution
You keep saying "you know those wildlyvarying annual return distributions that Mandelbrot talks about? Thanks to CLT, they're actually approximately normally distributed". I just don't follow.
I agree that if you take many samples of yearly returns and calculate their means, you'll get a normal distribution. I'm just not following what implication, if any, that has on me.
If you could explain/prove this one to me slowly, I'd appreciate it. Thank you very much
Re: Misbehaviour of markets and the Black Swan
If you sum up the fat tailed daily returns for a year that annual return has an approximately normal distribution. That daily returns are fat tailed has been known for over 50 years. It's not a big so what unless you are investing for much less than a year. So why did you read Mandelbrot and think that was a big deal?
CLT says that if you sum a stochastic variable that does not have a normal distribution (such as daily stock returns) then once the sum includes about 30 observations the summed variable will approach the normal distribution. You sum about 250 daily stock returns to get the annual stock return. So that annual return variable will be very close to normal.
BobK
CLT says that if you sum a stochastic variable that does not have a normal distribution (such as daily stock returns) then once the sum includes about 30 observations the summed variable will approach the normal distribution. You sum about 250 daily stock returns to get the annual stock return. So that annual return variable will be very close to normal.
I not only don't keep saying that, I have never said that. Mandelbrot is talking about the distributions of daily returns and I have always been careful to credit him with saying that.You keep saying "you know those wildlyvarying annual return distributions that Mandelbrot talks about?
BobK
In finance risk is defined as uncertainty that is consequential (nontrivial). 
The two main methods of dealing with financial risk are the matching of assets to goals & diversifying.
Re: Misbehaviour of markets and the Black Swan
First of all, annual returns aren't the sum of daily returns. They're the multiplication of them.bobcat2 wrote: ↑Fri Jul 05, 2019 10:56 pmIf you sum up the fat tailed daily returns for a year that annual return has an approximately normal distribution. That daily returns are fat tailed has been known for over 50 years. It's not a big so what unless you are investing for much less than a year. So why did you read Mandelbrot and think that was a big deal?
CLT says that if you sum a stochastic variable that does not have a normal distribution (such as daily stock returns) then once the sum includes about 30 observations the summed variable will approach the normal distribution. You sum about 250 daily stock returns to get the annual stock return. So that annual return variable will be very close to normal.
I not only don't keep saying that, I have never said that. Mandelbrot is talking about the distributions of daily returns and I have always been careful to credit him with saying that.You keep saying "you know those wildlyvarying annual return distributions that Mandelbrot talks about?
BobK
Secondly, if your logic above applied, then the following argument would be true:
The minute returns of the stock market are not normal. But if you add them for a full day, then by the CLT (more than 30 observations), they would become normal.
We know the above is not true because we both agree daily returns are not in fact normally distributed.
Could you point me to a website that explains the CLT the way you're applying it? I learned it in the past in the context of what I posted previously and I have never seen it applied the way you are here.
Re: Misbehaviour of markets and the Black Swan
What you know is a special case of the CLT, but it is a very special case of the CLT. It is the special case that makes the CLT such an important principle in statistics. In general, however, the CLT states that the sum of a large number of independent random variables will be approximately normal.
Earlier in this thread I quoted BH poster Grabiner on CLT. Let’s look again at that quote from a thread a few years ago. BTW poster Grabiner has a PhD in math from Harvard. So I believe he knows something about this.
Link to original thread  viewtopic.php?f=10&t=97022grabiner wrote: ↑Fri May 25, 2012 8:01 pmNote that this is a distribution of daily returns. With relatively low correlation between daily returns, the returns over longer periods are closer to a normal distribution.
This is a general principle in statistics. The Central Limit Theorem says that under certain conditions (independent identical distributions, for example), you can prove that the sum of a large number of events will have a nearlynormal distribution. But even when the conditions do not hold, you expect a normal distribution in practice when you add many small random variables to get a large one, such as 250 daily stock returns to get an annual return.

M.G. Bulmer’s fine book on intermediate statistics, Principles of Statistics, clearly lays out the definition of the CLT on page 115.
THE CENTRAL LIMIT THEOREM
The great importance of the normal distribution rests on the central limit theorem which states that the sum of a large number of independent random variables will be approximately normally distributed almost regardless of their individual distributions.
Here is the definition of the CLT from the MeriamWebster dictionary.
Definition of central limit theorem
: any of several fundamental theorems of probability and statistics that state the conditions under which the distribution of a sum of independent random variables is approximated by the normal distribution
(The dictionary then goes on to discuss the special case of the CLT that you are familiar with.)
especially : one which is much applied in sampling and which states that the distribution of a mean of a sample from a population with finite variance is approximated by the normal distribution as the number in the sample becomes large
Link  https://www.merriamwebster.com/diction ... %20theorem
Here is the definition of the CLT from Dictionary.com
any of several theorems stating that the sum of a number of random variables obeying certain conditions will assume a normal distribution as the number of variables becomes large.
Link  https://www.dictionary.com/browse/centrallimittheorem
So why are the annual returns instead of being normal only close to being normal. There are a few reasons here are two of the more important.
 Because the daily returns are not independent, but instead have low correlation (the acf is white noise) is one reason. If the returns were highly correlated the CLT would hold only very loosely.
 Because the annual returns are subject to the zero lower bound (they can't be less than 100%) is another reason annual returns are not quite normal, but have slightly fatter tails.
BobK
In finance risk is defined as uncertainty that is consequential (nontrivial). 
The two main methods of dealing with financial risk are the matching of assets to goals & diversifying.
 nisiprius
 Advisory Board
 Posts: 38510
 Joined: Thu Jul 26, 2007 9:33 am
 Location: The terrestrial, globular, planetary hunk of matter, flattened at the poles, is my abode.O. Henry
Re: Misbehaviour of markets and the Black Swan
Bob, I know the central limit theorem. In your post, I read:
"large number of independent random variables will be approximately normally distributed almost regardless of their individual distributions" and "as the number in the sample becomes large." Well, how long is a piece of string?
1) The question here is: how fast and how reliably do sumoffattailed distributions approach a Gaussian, in practice, in the real world, where you have no assurance at all that the individual samples are independent samplesor that they are from anything with a known and stable distribution at all.
One way to ask the question is "how big is N?" For example, consider the period 19262018, inclusive. It is 93 years. It is approximately 33,000 days.
And some might say it is approximately 9 "markets," bull and bear, each relatively uniform over a period of five or ten years, then turning a corner and entering a different distribution for another period of time. (To get the count of 9, I ignore the first "market" and include two that aren't shown...)
So, if we seek to apply the central limit theorem, put confidence limits on the underlying distribution, and assess the risk of future black swans, should we use N = 33,000, N = 93, or N = 9? How do we decide?
What is your personal answer to this specific question? How many independent random samples are contained in the historic record of the S&P 500 and predecessor, from 19262018? State an actual number, please.
2) Unless I misunderstand completely, the central limit theorem does not apply to the Cauchy distribution. And yet the Cauchy distribution is not wildly pathological. (We drew pictures of it in high school math class; we called it the "Witch of Agnesi" and drew witch faces under it around Hallowe'en). It's found in reallife physical situations, like light intensity on a surface from a long line source of light. So "central limit theorem" doesn't automatically govern everything. Mandelbrot says that realworld financial data is not as wild as the Cauchy distribution, but much wilder than the Gaussian distribution. Realworld financial data may be governed by the central limit theorem. It would be extreme to say that it is not governed by it at all. But, over investing lifetimes, how strongly is it governed? Strongly? Weakly?
3) If financial economists have accurate quantitative models of risk, how do you explain the constant and endless series of bizarre afterthefact claims that various strategies failed due to "oneintenmillionyear" or "tensigma" (i.e. many trillions of times longer than the lifetime of the universe) events. Doesn't this suggest that the financial economists responsible for risk estimates at places like Goldman Sach and LongTerm Capital Management are consistently overoptimistic about the taming of fat tails through averaging? Which is more likely: LongTerm Capital Management really experienced a tensigma event, or that their risk models were wrong? Why didn't the Central Limit Theorem work for them?
"large number of independent random variables will be approximately normally distributed almost regardless of their individual distributions" and "as the number in the sample becomes large." Well, how long is a piece of string?
1) The question here is: how fast and how reliably do sumoffattailed distributions approach a Gaussian, in practice, in the real world, where you have no assurance at all that the individual samples are independent samplesor that they are from anything with a known and stable distribution at all.
One way to ask the question is "how big is N?" For example, consider the period 19262018, inclusive. It is 93 years. It is approximately 33,000 days.
And some might say it is approximately 9 "markets," bull and bear, each relatively uniform over a period of five or ten years, then turning a corner and entering a different distribution for another period of time. (To get the count of 9, I ignore the first "market" and include two that aren't shown...)
So, if we seek to apply the central limit theorem, put confidence limits on the underlying distribution, and assess the risk of future black swans, should we use N = 33,000, N = 93, or N = 9? How do we decide?
What is your personal answer to this specific question? How many independent random samples are contained in the historic record of the S&P 500 and predecessor, from 19262018? State an actual number, please.
2) Unless I misunderstand completely, the central limit theorem does not apply to the Cauchy distribution. And yet the Cauchy distribution is not wildly pathological. (We drew pictures of it in high school math class; we called it the "Witch of Agnesi" and drew witch faces under it around Hallowe'en). It's found in reallife physical situations, like light intensity on a surface from a long line source of light. So "central limit theorem" doesn't automatically govern everything. Mandelbrot says that realworld financial data is not as wild as the Cauchy distribution, but much wilder than the Gaussian distribution. Realworld financial data may be governed by the central limit theorem. It would be extreme to say that it is not governed by it at all. But, over investing lifetimes, how strongly is it governed? Strongly? Weakly?
3) If financial economists have accurate quantitative models of risk, how do you explain the constant and endless series of bizarre afterthefact claims that various strategies failed due to "oneintenmillionyear" or "tensigma" (i.e. many trillions of times longer than the lifetime of the universe) events. Doesn't this suggest that the financial economists responsible for risk estimates at places like Goldman Sach and LongTerm Capital Management are consistently overoptimistic about the taming of fat tails through averaging? Which is more likely: LongTerm Capital Management really experienced a tensigma event, or that their risk models were wrong? Why didn't the Central Limit Theorem work for them?
Annual income twenty pounds, annual expenditure nineteen nineteen and six, result happiness; Annual income twenty pounds, annual expenditure twenty pounds ought and six, result misery.
Re: Misbehaviour of markets and the Black Swan
This boils down to an emperical question, Nisi. If the normal distribution doesn't apply to annual returns because the daily returns have infinite variance, then it follows that when we look at annual returns over many years they won't look like anything approximately normal. Here is a link to a histogram of 92 years of annual US stock returns. This histogram looks about what I would expect it to look like. It's not that far from being normal, but it's not quite normal. Perhaps a somewhat better fit would be a lognormal or a tdistribution. What it doesn't look like is a distribution with infinite variance.
Link  https://www.americaninvestment.com/comp ... s?Itemid=0
None of the above makes LT equity investing safe. There is plenty of risk in stocks that have a normal distribution and annual average nominal returns of 10% and an annual standard deviation of 20%. In fact, as you well know, stock investing becomes riskier over many years because one's forecast of the mean return is almost certainly wrong (at least to some small extent). That error gets compounded as the years go by and that adds to the riskiness of holding stocks.
If the above distribution were true then an annual return less than 30% should occur about once every 40 years. Such a bad return occurred in 2008. The one before that occurred in 1937. Two occurrences of once in 40 year returns happening in the last 82 years is certainly not unusual. Personally I assume annual returns are slightly more risky than if they came from the normal distribution. That is plenty risky but has nothing to do with infinite variance distributions.
BobK
Link  https://www.americaninvestment.com/comp ... s?Itemid=0
None of the above makes LT equity investing safe. There is plenty of risk in stocks that have a normal distribution and annual average nominal returns of 10% and an annual standard deviation of 20%. In fact, as you well know, stock investing becomes riskier over many years because one's forecast of the mean return is almost certainly wrong (at least to some small extent). That error gets compounded as the years go by and that adds to the riskiness of holding stocks.
If the above distribution were true then an annual return less than 30% should occur about once every 40 years. Such a bad return occurred in 2008. The one before that occurred in 1937. Two occurrences of once in 40 year returns happening in the last 82 years is certainly not unusual. Personally I assume annual returns are slightly more risky than if they came from the normal distribution. That is plenty risky but has nothing to do with infinite variance distributions.
BobK
In finance risk is defined as uncertainty that is consequential (nontrivial). 
The two main methods of dealing with financial risk are the matching of assets to goals & diversifying.
Re: Misbehaviour of markets and the Black Swan
Thank you for the explanation. So my claim is false presumably because the minute returns of the market are very dependent, so their sum won't be normally distributed.bobcat2 wrote: ↑Sat Jul 06, 2019 10:10 amWhat you know is a special case of the CLT, but it is a very special case of the CLT. It is the special case that makes the CLT such an important principle in statistics. In general, however, the CLT states that the sum of a large number of independent random variables will be approximately normal.
Earlier in this thread I quoted BH poster Grabiner on CLT. Let’s look again at that quote from a thread a few years ago. BTW poster Grabiner has a PhD in math from Harvard. So I believe he knows something about this.Link to original thread  viewtopic.php?f=10&t=97022grabiner wrote: ↑Fri May 25, 2012 8:01 pmNote that this is a distribution of daily returns. With relatively low correlation between daily returns, the returns over longer periods are closer to a normal distribution.
This is a general principle in statistics. The Central Limit Theorem says that under certain conditions (independent identical distributions, for example), you can prove that the sum of a large number of events will have a nearlynormal distribution. But even when the conditions do not hold, you expect a normal distribution in practice when you add many small random variables to get a large one, such as 250 daily stock returns to get an annual return.

M.G. Bulmer’s fine book on intermediate statistics, Principles of Statistics, clearly lays out the definition of the CLT on page 115.THE CENTRAL LIMIT THEOREM
The great importance of the normal distribution rests on the central limit theorem which states that the sum of a large number of independent random variables will be approximately normally distributed almost regardless of their individual distributions.
Here is the definition of the CLT from the MeriamWebster dictionary.
Definition of central limit theorem
: any of several fundamental theorems of probability and statistics that state the conditions under which the distribution of a sum of independent random variables is approximated by the normal distribution
(The dictionary then goes on to discuss the special case of the CLT that you are familiar with.)
especially : one which is much applied in sampling and which states that the distribution of a mean of a sample from a population with finite variance is approximated by the normal distribution as the number in the sample becomes large
Link  https://www.merriamwebster.com/diction ... %20theorem
Here is the definition of the CLT from Dictionary.com
any of several theorems stating that the sum of a number of random variables obeying certain conditions will assume a normal distribution as the number of variables becomes large.
Link  https://www.dictionary.com/browse/centrallimittheorem
So why are the annual returns instead of being normal only close to being normal. There are a few reasons here are two of the more important.
 Because the daily returns are not independent, but instead have low correlation (the acf is white noise) is one reason. If the returns were highly correlated the CLT would hold only very loosely.
 Because the annual returns are subject to the zero lower bound (they can't be less than 100%) is another reason annual returns are not quite normal, but have slightly fatter tails.
BobK
I still see two issues you have no addressed:
1) Annual returns are not the sum of daily returns. So I don't see the application here yet.
2) I have no reason to believe that daily returns are independent.
As an aside, thinking that this argument is any more applicable because some Harvard math Ph.D made it is literally the definition of the fallacy of the Appeal to Authority. I am sure he/she is a very smart person but degrees and titles aren't convincing to me personally. They have a place for very complex fields (I'll take a doctor or a quantum physicist's thoughts into account with little skepticism any day), but in something I believe I can understand (like here) it doesn't matter whether it's a high schooler or a math Ph.D saying it.
Aside over. Thank you for your time!
Re: Misbehaviour of markets and the Black Swan
Very often real bad outcomes happen when individuals or institutions are in highly leveraged positions and a state of the world that has low probability occurs. People and even sophisticated financial institutions become overly optimistic in good times and good returns with leverage and tend to forget that in bad financial times correlations among assets, even usually uncorrelated assets, move toward 1. This is more of a problem with human nature than with models IMO. Nevertheless, I think it's reasonable to assume that in really bad times things could be worse than your risk model and you should act accordingly. In other words, don't take risk up to the limits of your model. It's a model  not reality. The physicists at Chernobyl learned this lesson the really hard way.nisiprius wrote: ↑Sat Jul 06, 2019 10:31 am3) If financial economists have accurate quantitative models of risk, how do you explain the constant and endless series of bizarre afterthefact claims that various strategies failed due to "oneintenmillionyear" or "tensigma" (i.e. many trillions of times longer than the lifetime of the universe) events. Doesn't this suggest that the financial economists responsible for risk estimates at places like Goldman Sach and LongTerm Capital Management are consistently overoptimistic about the taming of fat tails through averaging? Which is more likely: LongTerm Capital Management really experienced a tensigma event, or that their risk models were wrong? Why didn't the Central Limit Theorem work for them?
BobK
In finance risk is defined as uncertainty that is consequential (nontrivial). 
The two main methods of dealing with financial risk are the matching of assets to goals & diversifying.
Re: Misbehaviour of markets and the Black Swan
For issue (1) you could work with the logs of the returns and sum.
The daily returns have low correlation. As I previously pointed out the ACF of the daily returns is white noise. So while they are not strictly independent they do have low correlation and in practice we should expect to see an approximately normal distribution. In the real world of annual returns that is what we do see. If OTOH the daily returns were highly autocorrelated then in that case the CLT would only very loosely hold.
In the case of the meaning of the CLT we need to know whether a poster at Bogleheads can be expected to know technical things such as the definition of the CLT or is simply Joe at the bar blowing off steam. I would imagine just about everyone with an advanced degree in statistics or math knows the definition of the CLT namely  the sum of a number of random variables obeying certain conditions will assume a normal distribution as the number of variables becomes large.
Grabiner happens to be one of those people. Individuals who know less about statistics typically don't know the definition of the CLT.
Financial economists have known that daily stock market returns have fat tails for over 50 years. They haven't ignored it. It's important for financial transactions of fairly high frequency. They have addressed it primarily thru GARCH modeling and the somewhat related stochastic volatility models. These modeling procedures address both volatility clustering and the fat tail aspects of high frequency returns. But being aware of the CLT they are not concerned that annual returns have infinite variance or follow the Cauchy distribution. If they did, the distribution of annual returns would look quite different from what it actually looks like.
BobK
In finance risk is defined as uncertainty that is consequential (nontrivial). 
The two main methods of dealing with financial risk are the matching of assets to goals & diversifying.
Re: Misbehaviour of markets and the Black Swan
i think nisiprius' first two points, or questions, remain valid/unanswered.
1) what scale are we talking about? how do we determine that scale? once we have the scale, how much data do we need? one of the most interesting aspects of mandelbrot's work is the selfsimilarity at varying scales, from daily returns to much longer periods. his approach is also very intuitive, which i think is a benefit.
2) once we figure out the first, how close is the fit? is it close enough to place us in a better position than we'd be in otherwise? im not sure i've seen anything that has proven that to be the case.
finally, and it may just be me that finds this interesting and relevant, but i just read the chapter in Menand's "The Metaphysical Club" on the Law of Errors and how CS Peirce used statistical analysis to present testimony in the Robinson v. Mandell case, which concerns a will and potential forgery of a signature. [another interesting tangent, the concerned party was Hetty Green, who went on to be one of the most successful investors in America, known as the Witch of Wall Street.]
one side presented evidence of many examples of individuals who could reproduce their signature exactly, not every time, but often enough.
Peirce analyzed the signature in question and found 30 downstrokes. he found 42 other samples of this signature. he compared each signature against all the others and observed that the frequency of coinciding downstrokes was 1 out of 5, on average. he, of course, assumed that each downstroke was independent of the others [i don't see how one could reasonably make this assumption. it seems to me that they would be somewhat dependent]. he then concluded that the expected probability of all 30 downstrokes coinciding (as the two signatures, real and alleged forgery, were a perfect match) was 1 in 5^30, or a number so large that there is nothing comparable to it in this universe. sound familiar?
of course, everyone thought his argument was ridiculous "mathematical voodoo." how in the world could someone make that claim in the context of one's signature, when the very intention is to reproduce it exactly! not to mention, there were in fact several examples in evidence of just that.
what's even better, is that if you chart the curve of actual coinciding downstrokes against expected, the curve "looks" like a pretty good fit. you can do it real quick in excel.
the reason i bring this story up is (well, other than being incredibly interesting to me) is that i cannot shake the feeling that one side here is overselling their case, just like Peirce did.
1) what scale are we talking about? how do we determine that scale? once we have the scale, how much data do we need? one of the most interesting aspects of mandelbrot's work is the selfsimilarity at varying scales, from daily returns to much longer periods. his approach is also very intuitive, which i think is a benefit.
2) once we figure out the first, how close is the fit? is it close enough to place us in a better position than we'd be in otherwise? im not sure i've seen anything that has proven that to be the case.
finally, and it may just be me that finds this interesting and relevant, but i just read the chapter in Menand's "The Metaphysical Club" on the Law of Errors and how CS Peirce used statistical analysis to present testimony in the Robinson v. Mandell case, which concerns a will and potential forgery of a signature. [another interesting tangent, the concerned party was Hetty Green, who went on to be one of the most successful investors in America, known as the Witch of Wall Street.]
one side presented evidence of many examples of individuals who could reproduce their signature exactly, not every time, but often enough.
Peirce analyzed the signature in question and found 30 downstrokes. he found 42 other samples of this signature. he compared each signature against all the others and observed that the frequency of coinciding downstrokes was 1 out of 5, on average. he, of course, assumed that each downstroke was independent of the others [i don't see how one could reasonably make this assumption. it seems to me that they would be somewhat dependent]. he then concluded that the expected probability of all 30 downstrokes coinciding (as the two signatures, real and alleged forgery, were a perfect match) was 1 in 5^30, or a number so large that there is nothing comparable to it in this universe. sound familiar?
of course, everyone thought his argument was ridiculous "mathematical voodoo." how in the world could someone make that claim in the context of one's signature, when the very intention is to reproduce it exactly! not to mention, there were in fact several examples in evidence of just that.
what's even better, is that if you chart the curve of actual coinciding downstrokes against expected, the curve "looks" like a pretty good fit. you can do it real quick in excel.
the reason i bring this story up is (well, other than being incredibly interesting to me) is that i cannot shake the feeling that one side here is overselling their case, just like Peirce did.
“TE OCCIDERE POSSUNT SED TE EDERE NON POSSUNT NEFAS EST"
Re: Misbehaviour of markets and the Black Swan
For crude purposes a simple normal monte carlo also accounts for 2008. A simple excel normal 40,0000 run parametric monte carlo (without taking into account any autocorrelation) based on =normal.inv(rand(),3.3%,20%) will give a minimum of about 70% with today's valuations and a 19% yearly sd. It underestimates the tails a bit, but gives you pretty good rough estimates.larryswedroe wrote: ↑Mon Jul 01, 2019 8:05 amGet out to a year and they are reasonably close to being log normally distributed. And no one should be equity investor if horizon is very short like days, weeks or even months. Good example, 2008 was worst crisis in post WW 11 era and it was well within the bottom 5% of the Monte Carlo Simulations we ran for clients.
PS. I thought there was a rule of thumb that over longterm equity prices were lognormal but equity returns were closer to normal? (I recall Fama concluded 30y returns were normally distributed in his recent paper?)
Last edited by jmk on Sun Jul 07, 2019 10:56 am, edited 2 times in total.
Re: Misbehaviour of markets and the Black Swan
I too think one side is overselling their case. I just happen to think it's the other side.
BobK
In finance risk is defined as uncertainty that is consequential (nontrivial). 
The two main methods of dealing with financial risk are the matching of assets to goals & diversifying.
Re: Misbehaviour of markets and the Black Swan
If I do that (and I assume the log of daily returns are not correlated to each other) then I conclude that the log of annual returns is normally distributed. So the annual returns themselves are lognormal, NOT normal.
Thoughts?
Thank you for your time Bob
Re: Misbehaviour of markets and the Black Swan
NVM I got it now. Had to look it up. Here's a reasonable explanation towards the end:
https://m.ebrary.net/7074/business_fina ... ns_finance
So if annual returns are not normally distributed, it would be purely due to volatility clustering. I understand why.
I'm reading Physics of Wall Street and it does an OK job of explaining this. Probably a little too much history for my taste but the information seems to be there.
I will munch on these thoughts for the upcoming weeks. Great food for thought
https://m.ebrary.net/7074/business_fina ... ns_finance
So if annual returns are not normally distributed, it would be purely due to volatility clustering. I understand why.
I'm reading Physics of Wall Street and it does an OK job of explaining this. Probably a little too much history for my taste but the information seems to be there.
I will munch on these thoughts for the upcoming weeks. Great food for thought
Re: Misbehaviour of markets and the Black Swan
I think it's best to think of annual stock market returns as approximately lognormal. My impression is that they are slightly more fattailed than the lognormal. How to handle that I am not sure. One could say this a model and the real world is somewhat riskier than the model implies. Perhaps you could compute the lower partial standard deviation (LPSD), and if it is larger than the overall sd, replace the sd with the LPSD as a measure of risk.
This thread has also stimulated my thoughts. To get more uptodate on financial risk management yesterday I ordered Analysis of Financial Time Series, by Ruey Tsay from Amazon. I am also considering Elements of Financial Risk Management by Peter Christoffersen. My books on these subjects are at least 15 years old and financial econometrics is moving fast in this area, making what I own somewhat dated.
BobK
PS  I think LPSD is what I used to know as semisd.
This thread has also stimulated my thoughts. To get more uptodate on financial risk management yesterday I ordered Analysis of Financial Time Series, by Ruey Tsay from Amazon. I am also considering Elements of Financial Risk Management by Peter Christoffersen. My books on these subjects are at least 15 years old and financial econometrics is moving fast in this area, making what I own somewhat dated.
BobK
PS  I think LPSD is what I used to know as semisd.
In finance risk is defined as uncertainty that is consequential (nontrivial). 
The two main methods of dealing with financial risk are the matching of assets to goals & diversifying.
Re: Misbehaviour of markets and the Black Swan
Huh? No, annual stock market returns would be approximately normal while annual market prices themselves would be lognormal.
That's what you meant to say right? Annual stock market returns can't be lognormal because we know they can be negative (which a lognormal variable cannot be).
Re: Misbehaviour of markets and the Black Swan
I believe that when working with logs we use the return relative which is (1+r) rather than the return r. So if the market return is 20% in a given year the corresponding return relative is 0.80, i.e. (1  0.20).
See SBBI chapter 11 for more on this.
BobK
See SBBI chapter 11 for more on this.
BobK
In finance risk is defined as uncertainty that is consequential (nontrivial). 
The two main methods of dealing with financial risk are the matching of assets to goals & diversifying.
Re: Misbehaviour of markets and the Black Swan
This thread is for folks that like to criticize and discuss investment theory. Questions 1, 2 and 3 are personal finance questions.alex_686 wrote: ↑Thu Jul 04, 2019 7:34 amI think you might be missing the thrust behind this thread. There are a couple of questions being asked here which tie directly into the above strategy.
1. What should my AA consist of? i.e., risky equities to safe bonds?
2. What is the expected return of my portfolio? i.e. What should my savings rate be?
3. What is the chance that my plan will meet my goal? i.e., what is the chance that the market will blow up repeatably during my withdraw stage.
There are many Bogleheads who tend to gloss over these questions as unknowable and just plow ahead. However it is a important question.
Re: Misbehaviour of markets and the Black Swan
I don't claim to know who this thread is for. But I can confirm my personal motivation in opening the thread was to have a better understanding and to answer some of the personal finance questions above in the context of my own circumstances. But I wanted to keep things a little more general so others could benefit too2pedals wrote: ↑Sun Jul 07, 2019 6:21 pmThis thread is for folks that like to criticize and discuss investment theory. Questions 1, 2 and 3 are personal finance questions.alex_686 wrote: ↑Thu Jul 04, 2019 7:34 amI think you might be missing the thrust behind this thread. There are a couple of questions being asked here which tie directly into the above strategy.
1. What should my AA consist of? i.e., risky equities to safe bonds?
2. What is the expected return of my portfolio? i.e. What should my savings rate be?
3. What is the chance that my plan will meet my goal? i.e., what is the chance that the market will blow up repeatably during my withdraw stage.
There are many Bogleheads who tend to gloss over these questions as unknowable and just plow ahead. However it is a important question.
Re: Misbehaviour of markets and the Black Swan
Nispiprius,nisiprius wrote: ↑Thu Jul 04, 2019 9:04 amMe, me, me! Me. Myself. Mine! Thank you so much for finally giving me the "attaboy" I've been dying for.protagonist wrote: ↑Wed Jul 03, 2019 4:58 pmI don't like [Taleb] either, but if he really said "In springtime, seed; in summer, cultivate; in fall, windsurf.", then my opinion of him just went up a notch.
On the other hand, if you wrote it, then my opinion of you did. (note: I had a good opinion of you to start with...much better than my opinion of Taleb.)
The Bogleheads forums are not that conducive to attaboys. There is no "+1" button or way to upvote a post (like Reddit has). With the emphasis on actionable items, people are also more reluctant to post an attaboy to a frivilous post... So I expect the lack of positive feedback you got belies the enjoyment many got from your post at viewtopic.php?p=1218617#p1218617.
The expression "Laughed out loud" or "LOL" has become metaphoric. Very few of the people who post an "LOL" literally did laugh out loud. I rarely do. But when I read your "review" I literally did laugh audibly.
Re: Misbehaviour of markets and the Black Swan
That's my thought as well.
The takehome actionable lesson from me from this books: There are a lot undefinable risks that cannot be avoided although they may be somewhat mitigated by measures such as following:
 Don't live "close to the edge." The larger your portfolio, the better your margin of safety. (A SFR of 3% is better than 4%. And 2% is better than 3%.
 Maintaining marketable work skills or an income producing business provides an additional margin of safety that goes beyond what a portfolio can provide. Imagine you were FIRE'd in the Weimar Republicwhen the currency was devalued down to near zero, your only hope was to go back to work.
Re: Misbehaviour of markets and the Black Swan
This thread is not about finance or investment theory; it is about empirical finance. It is not about the theory of equity returns. It's about testing to find the statistical distributions that empirically best describe real world equity returns.
empirical research  research based on observation and measurement in which knowledge is derived from actual experience rather than from theory or belief.
That said, it's likely true that those most interested in investment & finance theory are also the people very interested in empirical analysis of financial markets.
BobK
In finance risk is defined as uncertainty that is consequential (nontrivial). 
The two main methods of dealing with financial risk are the matching of assets to goals & diversifying.

 Posts: 225
 Joined: Thu Oct 24, 2013 12:32 am
Re: Misbehaviour of markets and the Black Swan
My understanding is that Black Swans could in some cases be foreseen, but that they bring unexpected changes that totally dominate outcomes. I think World War II was a black swan. Sure some people saw unrest in Europe, and knew that the Germans were unhappy, and the Japanese were ambitious, but very few realized that the coming conflict would entirely transform world politics and the world economy for the next 50+ years.ajjulee wrote: ↑Mon Jul 01, 2019 4:22 pmI'm not a huge fan of Taleb either. If one were to put a gun to my head, I could probably explain in a lengthy passage why I don't like his writing that will bore everyone including my mother (after making sure there are real bullets in the gun and that the gun holder knew how to fire a gun etc.,) but I have one comment on his big idea of 'Black Swan'  that which cannot be foreseen and hence no way to prepare for it. Do such events really exist in life? What are those? Aliens attacking earthlings? Men giving birth to children? Terrorists attack on major land marks (or Aliens attacking major landmarks such as White House, Capital Records Tower in LA etc., as an aside, aren't they better off attacking power grids or water supplies?), Subprime lending? US president who is in the pay of a foreign enemy government? All these have been discussed or written about long before such events happened or may happen in future. Black Swan, literally, isn't 'so out there' concept either. Everyone knows swans, black is just the opposite of white and there is that ugly duckling...Just thinking
If you were one of the unfortunates that suffered in the conflict, all of the planning you were doing, either growing your business, or working for a wage and saving for retirement, was entirely washed away and rendered irrelevant by the drastic changes from 19381945. Taleb even says that in retrospect the events and the changes may seem obvious or inevitable, but nonetheless before they actually happen they are usually not considered likely enough to upend your existing life plans.
Still I agree he's kind of lame.

 Posts: 35
 Joined: Sat Jul 13, 2019 4:54 pm
Re: Misbehaviour of markets and the Black Swan
Just wanted to circle back on the questions around Taleb offering any sort of practical advice or solution.
While I don't like Taleb on a personal level (I actually got in a small spat with him on a political topic), he does offer some practical advice in both Black Swan and Antifragile. He suggests trying to build a portfolio with a convex/asymmetric payoff; that is, limited downside, unlimited upside, and the ability to profit from volatility (rather than blow up). An example would be holding 80% treasuries and 20% futures and (long) options. This way your max drawdown is 20%, but you can still profit from upside leverage and you are long vol, so you want there to be fat tails. This is in opposition to building an "efficient" portfolio with min variance optimization and then leveraging (or delevering) the minimum variance portfolio to get a desired return; such a portfolio can blow up easily when exposed to fat tails.
As far as what you would invest in, if you just wanted a no effort solution, there is a SWAN ETF that is 90% treasuries and 10% LEAPS: https://www.amplifyetfs.com/swan. This is one of the only credible alternatives to typical index investing IMO.
Risk parity investing is also an interesting mid point between Taleb/Mandelbrot and MPT. Ray Dalio describes risk parity as "post MPT", and also alludes to risk parity as having lower tail risk. I think this is correct as long as one leaves for a solid margin below volatility of S&P 500 to account for nonnormality of returns. That is, a mildly levered portfolio with a lot of different betas will have less concentration risk, so if any one market blows up from a fat tail, you're not fully exposed to that single risk. The way Dalio approaches risk parity, he explicitly ignores historical correlations and returns so as to not overfit (unlike MPT). However, Taleb would likely still object to using volatility (measured in standard deviations) as the measure of "risk" in risk parity. Dalio would probably reply that the use of standard deviations is just a rough proxy, and that he is balancing based more on equal exposure to different economic scenarios.
Personally, I'm thinking of splitting the difference and going with 50% black swan portfolio and 50% risk parity. But neither is refuting the main Bogle head philosophy around stock picking or market timing. I don't believe in alpha in public highly liquid markets at this point in history.
While I don't like Taleb on a personal level (I actually got in a small spat with him on a political topic), he does offer some practical advice in both Black Swan and Antifragile. He suggests trying to build a portfolio with a convex/asymmetric payoff; that is, limited downside, unlimited upside, and the ability to profit from volatility (rather than blow up). An example would be holding 80% treasuries and 20% futures and (long) options. This way your max drawdown is 20%, but you can still profit from upside leverage and you are long vol, so you want there to be fat tails. This is in opposition to building an "efficient" portfolio with min variance optimization and then leveraging (or delevering) the minimum variance portfolio to get a desired return; such a portfolio can blow up easily when exposed to fat tails.
As far as what you would invest in, if you just wanted a no effort solution, there is a SWAN ETF that is 90% treasuries and 10% LEAPS: https://www.amplifyetfs.com/swan. This is one of the only credible alternatives to typical index investing IMO.
Risk parity investing is also an interesting mid point between Taleb/Mandelbrot and MPT. Ray Dalio describes risk parity as "post MPT", and also alludes to risk parity as having lower tail risk. I think this is correct as long as one leaves for a solid margin below volatility of S&P 500 to account for nonnormality of returns. That is, a mildly levered portfolio with a lot of different betas will have less concentration risk, so if any one market blows up from a fat tail, you're not fully exposed to that single risk. The way Dalio approaches risk parity, he explicitly ignores historical correlations and returns so as to not overfit (unlike MPT). However, Taleb would likely still object to using volatility (measured in standard deviations) as the measure of "risk" in risk parity. Dalio would probably reply that the use of standard deviations is just a rough proxy, and that he is balancing based more on equal exposure to different economic scenarios.
Personally, I'm thinking of splitting the difference and going with 50% black swan portfolio and 50% risk parity. But neither is refuting the main Bogle head philosophy around stock picking or market timing. I don't believe in alpha in public highly liquid markets at this point in history.

 Posts: 35
 Joined: Sat Jul 13, 2019 4:54 pm
Re: Misbehaviour of markets and the Black Swan
Another example of practically applying Taleb and Mandlebrot is early stage VC investing. There is an asymmetric, power law return to investments. It's also a great illustration of Jensen's inequality, e.g. E(F(X)) > F(E(X)) for any convex payoff function. The average company will yield a negative real return in early stage investing. But the average payoff of companies in a typical VC portfolio is 3.8X. This is because the minority of successful companies have huge gains that offset the losses of all the unsuccessful companies.
http://www.industryventures.com/2017/02 ... rnmatrix/
http://www.industryventures.com/2017/02 ... rnmatrix/
Re: Misbehaviour of markets and the Black Swan
Great thread! Thanks to everyone who contributed. Much of the higher math is a bit over my head but I enjoy learning from these in depth discussions.
I too struggle with how to integrate the knowledge that we cannot really expect future returns to correlate with predictions that are derived from using a normal distribution to model market history. At first it was a bit scary when I came to terms with the fact that on average investors may be underestimating risk because we look historical trends and think "well in long investing horizons the odds are slim of stocks losing value, go long equities! Just look at the history of the market!" So I thought the action to take would be to maybe change my AA to a more diverse and conservative portfolio. But then I started wondering if bonds are enough to protect against the type of risks that could lead to a 30+ year of decline equities. I even considered gold even though I had always been confident in the outlook that gold is speculating in an overpriced commodity that does not produce value. So I have not actually changed my AA in response to reading Taleb and the like regarding how modelling of the market probably gives a bit of false confidence.
However, if you bring in the concepts of behavioral economics into the picture it makes it even more murky. The fact is, now that I lost confidence in predictions based off normal distributions, believing I have high odds of earning 68% real returns in equities, I am not as aggressive in my savings or investing We can be reasonably sure that keeping expenses as low as possible increases the odds of building wealth but for me it was easier to do when I was more confident that every $ I saved would be making me $.07/yr for years until I decided to switch to the decumulation phase. I am still a decent saver but I have been more likely to leave funds in a MM or so while likely reading too much market pessimism content.
I too struggle with how to integrate the knowledge that we cannot really expect future returns to correlate with predictions that are derived from using a normal distribution to model market history. At first it was a bit scary when I came to terms with the fact that on average investors may be underestimating risk because we look historical trends and think "well in long investing horizons the odds are slim of stocks losing value, go long equities! Just look at the history of the market!" So I thought the action to take would be to maybe change my AA to a more diverse and conservative portfolio. But then I started wondering if bonds are enough to protect against the type of risks that could lead to a 30+ year of decline equities. I even considered gold even though I had always been confident in the outlook that gold is speculating in an overpriced commodity that does not produce value. So I have not actually changed my AA in response to reading Taleb and the like regarding how modelling of the market probably gives a bit of false confidence.
However, if you bring in the concepts of behavioral economics into the picture it makes it even more murky. The fact is, now that I lost confidence in predictions based off normal distributions, believing I have high odds of earning 68% real returns in equities, I am not as aggressive in my savings or investing We can be reasonably sure that keeping expenses as low as possible increases the odds of building wealth but for me it was easier to do when I was more confident that every $ I saved would be making me $.07/yr for years until I decided to switch to the decumulation phase. I am still a decent saver but I have been more likely to leave funds in a MM or so while likely reading too much market pessimism content.