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"Think of dimension, not as an inherent property, but as a tool of measurement. So how do you actually measure something? If you want to measure a straight line, you get a ruler. If you want to measure a curved line, you could use a smaller ruler, inching it along the curve and counting how many times you moved it. You could get a more accurate, if tedious, measure by using a still-smaller ruler; its measurement will be a bit longer than the first, crude one. Eventually, as the ruler keeps shrinking, the measurement settles down to one number that you call the curve's length. But what if the curve is jagged and irregular? What if it is the coast of Scotland? You can start off with a surveyor's glass--a big ruler--and measure from promontory to promontory. Then a long tape might measure point to point. Then a yardstick, then calipers, then a microscope. But this is useless: Unlike the smooth curve, the rocky coastline never provides just one "best" estimate of length. It depends on the scale of the map you want to draw--or your political motives. One researcher, Lewis Fry Richardson, who investigated this paradox nearly a century ago, looked in official references for the surveyed length of political borders between countries. Spanish authorities reckoned their border with Portugal to be 987 kilometers long, whereas the plucky Portuguese counted 1,214 kilometers. The Netherlands measured its border with smaller, poorer Belgium at 380 kilometers, whereas the Belgians counted 449 kilometers." --Benoit Mandelbrot, The (Mis)behavior of Markets

It is easy to see by reading the quote from the great mathematician Benoit Mandelbrot above, that our dimensional view can easily alter our fortunes. Mandelbrot pointed out that much in nature and markets is scalable. Meaning, if you look at a chart of a certain stock without a time scale it will look very similar to a chart of the same stock that is of a different time scale. The first chart may be a minute by minute chart, while latter may cover years, but both bear a common resemblance.

Many ask, why are high frequency traders (HFT) so successful? Is it their technology and speed that gives them the edge? Why is Warren Buffett so successful in markets? It is his lack of technology and lack of speed that gives him his edge?

I propose that both share a common factor that is contributing to their relative success in markets. If we think of dimensional time in markets along the lines of the radio spectrum, high frequency traders would be way out on one end - say the microwave area - while Warren Buffett would be way down at the other end, say Ultra Low Frequency. Meanwhile, the vast majority of market participants are crowded into the middle in a wild melee of competition, where it is extremely difficult to find any major opportunity simply because millions of others are constantly looking in the same place for the same opportunity.

Meanwhile, Warren and the HFT guys in their respective, relatively quiet and uncompetitive corners--Warren with his surveyor's scope and the HFT guys with their microscopes--are having a much easier time finding profit and opportunity. It appears to me that the success of these two extremes holds much in common. One goes in for a lifetime, the other goes for the nanosecond. While virtually all the rest are using a time horizon of a few months to a few years--or rulers and yardsticks (see Mandelbrot quote above).

This fractal phenomenon, as pointed out by Mandelbrot, can be seen all through nature and human behavior. The employment markets are an excellent example. If more attention was placed on education and development in specialized fields--fields outside the mad rush of competition, more jobs and higher paying jobs would be the result. This theory is evidenced by silicon valley, it is truly a field that has developed and thrived due to expanding in a new dimension--and they cannot get enough skilled employees.

A Mandelbrot Set:

File:Mandel zoom 00 mandelbrot set.jpg

The power of specialization has been recognized for hundreds of years by such notable individuals as Adam Smith, who wrote The Wealth Of Nations in 1776. He explained to the world the potential economic power of the division of labor and specialization. The result was exponential growth. In 1492 Columbus had a bold vision to push the envelope of the current map and see what lay beyond. His new dimension was the modern discovery of the new world.

Most people are not comfortable, mostly due to their dimensional view of life, in purchasing a stock with the intent of holding it for the rest of their lives. Warren Buffett has been willing to go into that dimension and has been greatly rewarded because of it.

Many others do not see the point of spending millions of dollars on the fastest computers and the finest software only to make $3.00 on a $50,000 trade, but this is what High Frequency Traders do and they do it efficiently and often hundreds or thousands of times a day--each trade is executed in a fraction of a second. Clearly they have entered another dimension of the market that is profitable.

As the market is largely unbounded by physical restraints and instead operates in the realm of money and time, the potential to discover or create new dimensions is unlimited.

Potential Practical Applications:

The power of the fractal view and how to act on it is and should be largely subjective to the individual--that is the essence and the potential power of it. However, to continue the theme of the article into the practical, investors can take advantage of Warren Buffett's dimensional view by investing in Berkshire Hathaway (NYSE:BRK.A), voting shares and (NYSE:BRK.B), non-voting shares.

Berkshire Hathaway's class A shares have never seen a stock split. One share currently trades at over $166,000, giving it the most expensive share price on the NYSE. The intent is to attract long-term investors, as opposed to short-term investors. The B shares were offered in the 1990s to discourage funds wanting to mimic Berkshire's performance and offer smaller investors an opportunity to participate at a fractional share price.

Berkshire wholly owns numerous large companies such as; GEICO, Dairy Queen, NetJets, Helzberg Diamonds, BNSF and Fruit of the Loom, they have controlling and significant interest in many others. The investment company has averaged an annual growth of 19.7% in terms of book value over the last 48 years.

The basic ideas of investing are to look at stocks as business, use the market's fluctuations to your advantage, and seek a margin of safety. That's what Ben Graham taught us. A hundred years from now they will still be the cornerstones of investing. - Warren Buffett

Given the fact that Warren Buffett is 82 years old, much discussion and diligence has been given to succession in regards to the leadership of Berkshire Hathaway. The attempt is to carefully analyze and understand the dimensional view that has helped make Warren Buffett so successful and to preserve that view long beyond his passing for the continued benefit of the company.

Berkshire Hathaway's market cap is now about $273 billion. The trailing P/E ratio is about 16.65. For those investors who share Buffett's dimensional view, Berkshire Hathaway has been hard to beat as a long-term investment.

Chart forBerkshire Hathaway Inc.

High Frequency Trading:

Most individual investors that are interested in the high frequency trading dimensional view will obviously find more challenges associated with effectively engaging in the HFT space, given the technological requirements, than they would with the Buffett view.

The practice of high frequency trading has been under intense scrutiny over last few years, as many market participants believe that given the extreme volume of trades (HFT accounts for around 40% of stock trade volume) share prices and buy/sell orders are potentially being manipulated. HFT traders argue that they bring needed liquidity to the market. Please see the links below for some informative articles on high frequency trading.

A Possible New Dimension For Investors:

Those seeking investment opportunities in new dimensions that have truly unlimited potential, may want to look into the commercial space travel business. Virgin Galactic is at the forefront of commercial space travel and has hinted at an IPO.

Disclaimer: Nothing in this article is to be taken as professional financial advice, nor is it a solicitation to buy or sell any type of securities. All financial decisions are your own, seek professional advice before taking action.

Source: From Warren Buffett To High Frequency Trading: A Fractal View Of Market Dimension