# The Riddle of the Nile

This essay originally appeared at The Daily Reckoning.In 1906, Harold Hurst, who was a young civil servant at the time, came to the ancient city of Cairo, Egypt, which was then under British rule. While there, he solved one of the mysteries that had bedeviled the pharaohs for ages - and also provided a sign for how financial markets worked, a connection that was later uncovered in the 1960s by an ambitious Harvard economist and mathematician.

Hurst's problem was to solve the riddle of the Nile's great floods. He was not interested necessarily in why it flooded; he was interested in predicting how much the Nile flooded from year to year.

It was a very important question, in which the lives and wealth of millions hung in the balance. The budding population in the Nile Valley and their growing cotton industry depended on it. Their dams were inadequate to the task of protecting them in times of flood. And their reservoirs were incapable of sustaining them during periods of extended drought.

The fickle, wild and untamed nature of the Nile baffled them. While much time and energy was spent investigating the Nile's floods, they had yet to produce a practical answer. The people of the Nile remained at the mercy of the majestic river's seemingly unpredictable flows.

That is, until Hurst tackled the problem. His contribution here would earn him a lasting title of respect and it would bring him great fame. The Egyptians called him Abu Nile, or Father Nile.

Hurst, the son of a village builder, was a man of modest means and background. Born in 1880, his family hailed from Leicester, England, where his family had roots stretching back for some three centuries.

Determined and dedicated, he left school at age of fifteen and worked as a carpenter, and learned a bit of chemistry on the side. By the age of 20, he had - against all odds - earned a scholarship at prestigious Oxford, eventually winning honors in physics despite no mathematical training.

When the precocious Hurst left Britain and headed for Egypt, the Nile region had just entered a period of relative peace in which economic prosperity started to bloom and dam construction began in earnest as British engineers attempted to harness and manage the power of the Nile.

The Nile was, and remains, an immense river over 4,100 miles long. Hurst began by mapping and studying the river and its tributaries. With the help of other engineers, he sounded the river's depths and installed flood level gauges in various spots.

The fluctuations in the river ranged widely. In a particularly soggy year, it displaced as much as 151 billion cubic meters. Yet, just as the river proved overly generous in some years, it could be overly stingy in others. In a particularly parched year, the river could discharge as little as 42 billion cubic meters.

Hurst studied these patterns and noticed how they tended to cluster. Hurst abandoned many of the methods prior mathematicians used and started to work out his own formula to describe their behavior. He also looked at data from other rivers and discharges all over the world - Michigan's Lake Huron, Sweden's Dalalven Lake, and lakes in Russia, Canada and Norway.

More than that, he looked at other experiences as well, searching for the footprints of climate patterns in the tree rings of Flagstaff pines and Sequuia, in the thickness of lakebed sentiment, in sunspot readings, in temperature records - Hurst catalogued thousands of nature's patterns, a menagerie of natural phenomena.

To all these he worked out a formula, describing the patterns as functions of a unique power law, a fundamental number that seemed to be a fact of nature. Hurst's findings basically described the Nile's flood cycles and showed that they did follow a pattern.

From 1951 to 1956, Hurst, then in his seventies, published a series of papers describing his findings. These findings roiled the scientific community and invited both criticism and praise.

But, the things was, Hurst's formula worked. Other hydrologists working on other rivers soon confirmed his findings.

Benoit Mandelbrot made the connection with finance in 1960s, while he was a teacher of economics at Harvard. Mandelbrot was working on a study of cotton prices and worked out a power law to describe their behavior. He published his paper and a colleague of his noticed the similarity of his work with Hurst's.

Mandelbrot studied the work of Hurst and connected it with his own work. He thought that Hurst's floods were like big price jumps, and that the droughts were like market crashes. He found that cotton prices were similar to the Nile's pattern, that there existed what mathematicians call "dependence" - which simply means that what is going to happen next depends on what happened before. Cotton prices trend. This view was in opposition to the idea that price changes mimicked a random process, or a "random walk" as economists described it.

Mandelbrot measured the tendency of prices to trend and called his number "H" in honor of Hurst. If the H factor was 0.5, then the prices exhibited a random pattern. But, if the H factor was greater than 0.5, say .75, then the prices had trends and that they did not fluctuate randomly. Prices tended to persist in one direction much longer than would be predicted by a random process. If the H were less than .5, say .2, then this meant that prices tended to hew closely to some mean; it meant that they did not roam very far.

Other researchers plowed into price data and found varying H factors for different financial assets - more evidence that prices exhibited some trend. Interest rates and inflation had high H factors, indicating persistent moves in one direction. Later researchers studied the prices of Apple Computer, Xerox and IBM - each had H factors of .7 or better, again indicating trends.

This was a radical idea. All of orthodox finance had been operating under the assumption that prices behaved randomly, that they had followed a random walk. The thinkers and theorists of finance had created elaborate mathematical models and intricate theories that depended on the assumption of randomness. Their works were celebrated and the star theorists with feted with Nobel Prizes and prestigious tenured chairs at the nation's finest universities.

If Mandelbrot's findings were correct, then all of the models of modern orthodox finance - the Efficient Market Hypothesis, the Capital Asset Pricing Model, the Black Scholes Option Pricing Formula, and more - were wrong!

Not surprisingly, Mandelbrot's ideas have not yet gained widespread acceptance. There is too much invested in modern finance as it is constructed. Too many professors continue to try and patch up the existing theories, like Ptolemaic astronomers trying to resist Copernican theory. The evidence sits there right in front of them, but they choose not to see it.

P.S. Much of the story above is derived from Mandelbrot's excellent book, The (Mis)Behavior of Markets. I highly recommend the book to anyone interested in the flaws of orthodox financial theory.

Mandelbrot's ideas remain on the cutting edge of finance. The mathematics behind his ideas is very complex. However, there was another visionary who observed the persistence of trends in markets. He was born 80 years before Mandelbrot discovered the work of Hurst. He died before Hurst even made his trip to Cairo, while Hurst was still a teenager. The man I am talking about is Charles Dow and his theory, a set of observations about the stock market, form the basis of a powerful trading system that is used and understood by a very small group of investors.

This system is still used today, over 100 years since Charles Dow invented it&and many investors have since then honed and shaped this market-timing strategy to pinpoint the crisis points that tell you exactly when it's time to trade.

Regards,

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