Distribution Of Wealth

[Almighty Colin]

So Adelphia was down here for a few days last week. I was bored and became interested in wealth distribution. Why do so few people hold so much money? According to Pareto's law, 80% of the people will hold 20% of the wealth. That old 80/20 rule. While it is not a perfect fit it is pretty damned good. In every country a small group of people hold a disproportionately large amount of money.

Dean M. Maki and Michael G. Palumbo performed a study of stock ownership in America and concluded that 80% of stock ownership was held by 20% of the individuals.

So I wondered if maybe 20% of the people make 80% of the income. It turns out that is not true. 60% of people make 87% of the income. It is not that unevenly distibuted. I wrote a computer program that disributes income at random to 1000s of individuals and it turned out that 68% of people made 80% of the income. Not too unlike the real curve. There is little difference between how much money people make and what it would be if income was given out at random $1 at a time.

So then I became interested in what happens if you allow people to accumulate wealth at random and earn interest on it. In the computer model, I permitted people to increase or decrease their existing wealth every year as a percentage of their income. Amazingly and quite quickly, Pareto's Law popped up. The more interest people could possibly accumulate the greater the difference between the wealthy and poor became. With the right amount of interest and/or time, Pareto's Law appeared.

People always say "the poor get poorer and the rich get richer". This is completely true. If you graph income for any population, you will get a bell shaped curve. As time goes by and there is both more income and more people, the curve widens so that the rich are richer and indeed (relatively) the poor get poorer. In 1967 4% of the income in the US was earned by the poorest 20% of the people and 44% was earned by the top 20%. In 1998, the poorest only made 3.6% and it has slipped quite steadily in that time. The top 20% meanwhile were earning 49%.

Well, that's what I did on my summer vacation.



Last edited by Colin at Nov 14 2002, 11:50 AM

[Peaches]

Once again, Colin does more thinking in his spare time than I've done in my whole life

But damn if I don't learn a heck of a lot just from reading what YOU'VE learned

[wig]

Colin,

This is very interesting to me and exactly what one should expect. One of my old partners in the commodities business developed Market Profile. MP is nothing more than the bell curve applied to price and time of markets. The unique thing that he did was to calculate his mean, mode and deviations not on price and time, but by incorporating the volume that took place at each point.

It was amazing that we would often come up with the same areas of support / resistance, as well as potential magnetic extremes while using two completely different methods.

In addition to years of observation, it was another mathematical model that helped me understand that, despite how much we believe we are unpatterned individuals, there is a natural phenomenon that governs our behavior.

As is clearly described in many ways over thousands of years, from the Bible to Nietzsche, we are doomed to repeat ourselves.

[Almighty Colin]

Wig-

The relationship between mathematical models and the reality they describe has always fascinated me. The patterns that result from randomness are often indististinguishable from the ones that result from choice and ability.

For example, baseball batting averages are distributed normally. If you graph them, you will see the classic bell-shaped curve we have all seen at one time or another. In other words, if baseball batting averages were completely random with no player better than another - it would look very similar to what we see in real-life where some players are better than another. What about a Tony Gwynn who batted .338 in his career? Doesn't he prove that some baseball players are better at hitting the ball? Well, you can't prove it by looking at the statistics. With enough players in the league and enough seasons - guys like Tony Gwynn will always appear even if everyone were of the same skill.

Why does a graph of something involving skill look random? I think it's because a skill involves an ability that influences the results in your favor but does not absolutely control it. The greatest hitters in the game go 0 for 4 all the time. The greatest quarterbacks have days where they complete less than 50% of their passes and throw more INT's than TD's. But over a whole season, the better players are more or less obvious. This bit of randomness whether it is 50% random factors, 25%, or even 75% leads to a bell-shaped curve. Batting average reflects a players ability to hit the ball, his competition, some random factors like twist on the ball, relative humidity, barometric pressure, winding of the core or whatever. A graph of all players batting averages has enough randomness to give us the bell curve. (Colin's guess anyway).

Heights are the same way. All our heights are influenced by our parent's heights but many random factors including genetic recombination, diet, and other things add a random element that shows up in the graph.

If this is truly the reason, then the bell curve shape should shrink in width as played become more skilled and there is less randomness to the game. Stephen Jay Gould pointed out that exactly this has happened. Players used to bat .400 and some used to bat under .200 but not anymore.

Many white papers have been written saying that all market returns are completely random. I think those academics are completely mistaking something that looks completely random from something that is completely random. I truly believe Mr. Buffett has understood the markets better than nearly everyone else and probably better than everyone else. He has imperfect skills though and can be taught a lesson or two by the markets just as Michael Jordan had days when he was 4 for 15 shooting and there didn't appear to be any good reason for it.



Last edited by Colin at Nov 14 2002, 11:53 AM

[Almighty Colin]

Peaches,

Once again you make me blush.

[wig]

Originally posted by Colin@Nov 14 2002, 08:53 AM
Many white papers have been written saying that all market returns are completely random. I think those academics are completely mistaking something that looks completely random from something that is completely random. I truly believe Mr. Buffett has understood the markets better than nearly everyone else and probably better than everyone else.

Colin,

I agree completely. Often, one has to take a few steps back before seeing the pattern in otherwise random looking events.

I would also add Sir John Templeton in with Warren Buffett.

[Almighty Colin]

Wig-

Ever read "Market Wizards"?

[wig]

Originally posted by Colin@Nov 14 2002, 10:38 AM
Wig-

Ever read "Market Wizards"?

Colin,

Yes. It has been a while... but I have the book by Jack Schwager.

I use some of his work, primarily reversal patterns like the 2 close reversal that was later made popular by E. Hadic.

[Almighty Colin]

Schwager on Futures? If so, I have it but haven't looked at it much. It looks good on the shelf though and helps way down the bottom of the book shelves so they don't tip over.

[Almighty Colin]

I have New Market Wizards also. I liked the Eckhardt interview best.

[wig]

When I first started getting interested in tech analysis, I read everything. Then, about 7 years ago, I realized that the methodology was only about 10% of what it took to be a successful trader / investor and that my methodology was good enough.

Execution is the real key, which is our ability to eliminate fear / greed, to be patient, humble and exhibit control. These were and are my weaknesses, so I started concentrating on that. The Disciplined Trader is a good book in this regard.

Once I started concentrating on this, the money has been much easier to attain through speculation.

[Nickatilynx]

hmmm wonder what proportion of porn is bought with Platinum cards

You are too smart, Colin. Scarey smart

We GOTTO met.You love the numbers of a given market, I love the psychology.The results are the same

[Almighty Colin]

Originally posted by Nickatilynx@Nov 14 2002, 11:47 AM
We GOTTO met.You love the numbers of a given market, I love the psychology.The results are the same

Will we begin by discussing the numbers of psychology or the psychology of numbers?



Last edited by Colin at Nov 14 2002, 12:09 PM

[Nickatilynx]

hahahahahaha

Per - fucking -ect

[ulfie]

Market Wizards by Schwager is a great book. I've read it 2 or 3 times and learned a lot from it. Reminiscenses of a stock operator by Lefevre is another good one.

[RawAlex]

What about a Tony Gwynn who batted .338 in his career? Doesn't he prove that some baseball players are better at hitting the ball? Well, you can't prove it by looking at the statistics. With enough players in the league and enough seasons - guys like Tony Gwynn will always appear even if everyone were of the same skill.

Colin, when working statistics, there are a few important things to remember:

Within a a bell curve result group, there are always exceptional results that lie to the extreme ends (both ends) of the result curve. These results often greatly affect the group mean. These results are so exceptional as to fall outside of the "curve". In order to avoid skewing results, normally up to 10% of results (5% top and 5% bottom) are ignored or discarded to avoid misleading results.

In a discussion of "rich and poor", once you remove certain EXCEPTIONAL wealth cases, and remove EXCEPTIONAL povery, the remaining bell curve of earnings withing a given society hasn't greatly changed in the last 50 years. The mean income has moved, of course, but the shape and distribution of results remains fairly constant.

The difference in the last 50 years has to do with the extremes of wealth and poverty, and how the 5% top and bottom are now more extreme. As executive pay, stock options, and such have come into play in the last 15 years, the gap between workers and high management has increased at an alarming rate. In the 5% normally thrown out for being outside the curve, you see a greater concentration of wealth than ever before.

When you leave ALL results in the pool, there appears to be a huge skew to "rich getting richer", which is true - but the small percentage of super billionaires is draggin up the average at the top. Poor can't get any poorer, but rich can always get richer!

While the numbers can't lie, they sure can tell some interesting tales!

Alex

[Almighty Colin]

Alex- data should only be discarded in curve fitting if it is so improbable as to not reasonably be expected. Many if not most statisticians/scientists would say NO data should EVER be thrown away. I agree with that school. But either way, 10% would be ludicrous by anyone's standards.

One standard deviation = 68%
Two standard deviations = 95%

1.6 standard deviations would contain roughly 90% of the data. You're saying to throw away everything outside of 1.6 standard deviations of data? The only reason data is discarded anyway is in curve-fitting and when you have more than 100 million points you don't have to worry that you can't fit the data properly. Then you have a gaussian curve with no ends and you'd be throwing away 10 million + points of data. Throw away millions of points and THEN you would have misleading data.





Last edited by Colin at Nov 15 2002, 04:34 AM

They said in Q4 of 2001 42 people dropped off the billionaires' list. I believe 28 of them were women. I was impressed to learn we had more than 28 female billionaires. The idea of a having a billion dollars is pretty much beyond the realm of my comprehension.

C.

one thing Colin has taught me RawAlex is NEVER argue with the calculator.
never argue math with a math teacher
never debate reality with a man with a Physics degree from Yale.

[Mutt]

well this is fascinating reading in this thread. way over my head. I am going to wait for Billy to show up and explain it all to me!

Its above me too at times Mutt.

basically, Pareto explained some time ago that there is a basic formula that explains wealth distribution in society. 20% of the people generally control 80% of the wealth. the number may not be exact i.e. 15/85 etc, but that in general it is fairly accurate.

Various mathematicians have tested this model much in the same way that Colin did by simply writing a program for example that takes a sum of money, say $10,000,000 and gives it away at random to say 10,000 individuals, 1$ at a time. The results usually follow the 80/20 rule as Pareto predicts.

Wealth distribution, in contrary to RawAlex's romantic notions about "how things should be" can be explained just as easily by natural laws of numeric distribution as it can by "greed" and "selfishness" and any other colorful description such liberal minded people can think of.

RawAlex goes further to suggest that the "rich get richer, poor get poorer" at (i like this choice of words) "at an alarming rate" because poor people cannot get poorer. He ignores the basic premise of wealth distribution being discussed which is that there is a total amount of wealth and a total number of people and that wealth is distributed over that total number of people in some way. He refers to removing "exceptional cases" of wealth and poverty from the formula from the equation, which is totally irrelevent to the conversation. i am sure that Bill Gates is exceptionally wealthy... i dont know what "exceptionally poor" means or what formula explains the relationship between the two that would make it ok to remove those "groups" or even identify each as such... and of course, he caps it off with a typically colorful liberal remark "the poor cant get poorer, but the rich can certainly get richer". This of course, is ignoring the fact that the rich cannot get richer in a vacuum but generally through the creation of jobs, businesses, factories etc etc etc, which still affects everyone else on the curve in a more or less proportionate way. For example, Bill Gates is super rich. Bill Gates did not print his own money. He got rich by creating Microsoft, by creating 50,000 plus high paying jobs and approximately 2000 millionaires working directly for Microsoft and thousands of spin off companies started by ex-employees. Rich people "create wealth" they dont confiscate it... just as economies "grow", so does wealth.

Colin is saying that the saying "the rich get richer, poor get poorer" is true and is explained by simply by population growth and interest earned on wealth over that same time.

RawAlex is saying this is true because as Liberals believe, the economy is a "Zero Sum" system where for one person to gain, another must lose. Or, for me to make money, someone must lost a proportionate amount of money and it is only through my own selfishness, heartlessness and greed that i can make myself rich. Of course this completely ignores the most basic fundamentals of Macro economics and economic growth... but hey... its easier to get a rise out of people by using colorful adjectives and descriptions and emotional appeals about "fairness" than it is to simply understand the math.



Last edited by -= JR =- at Nov 16 2002, 04:01 AM