The Riddle of the Nile

What does an English hydrologist, a Harvard economics professor, and the Nile have to do with predicting the ups and downs of the stock market? A lot more than one would think…Chris Mayer explores…

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.

Price Jumps and Market Crashes: Father Nile

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.

Price Jumps and Market Crashes: Adapting the Formula To Finance

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.


Chris Mayer
for The Daily Reckoning
March 10, 2005

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.

Chris Mayer is a veteran of the banking industry, specifically in the area of corporate lending. A financial writer since 1998, Mr. Mayer’s essays have appeared in a wide variety of publications, from the Daily Article series to here in The Daily Reckoning. He is also the editor of the Fleet Street Letter.

We pause, pull out our sextant and take a sighting. For many months now we have been at sea. We wonder where we’ve come to. The sun, the moon, the stars are all we have to steer by. But we see nothing. Overhead, the clouds of news are so vast that they obscure our view.

So, the best we can do is dead reckoning.

We reckon today that we are near the end – finally – of the great rally. We have reckoned this before; we don’t deny it. But it has to come someday. Stocks have been in a bear market rally since October of 2002. They are destined to go down. Like death, we don’t know when exactly it will come. But it is the sort of thing you want to be prepared for all the time. You do not want to go to your grave after saying an unkind word to your mother. Neither do you want to wake up to a market crash with a portfolio of junk bonds and tech stocks. So, we avoid unkind words and unsound investments – and wait.

Americans are getting poorer. They don’t realize it. No newspaper tells them. No politician dares even to whisper the truth. No Fed economist proposes a remedy. Still, real wages are less today than they were a year ago…and no higher than they were at the bottom of the recession in November 2001. Worse, unmentioned in the "real" calculation is the cost of housing. Depending on where you live a house today could cost twice as much as it did in November of 2001. This, of course, is taken as good news to most people. But it is only good news if you are ready to leave the country or die. Otherwise, you are going to need some place to live. And it will cost you a lot more than it did a few years ago.

GDP figures are not bad. Inflation is under control. Consumers keep spending. Unemployment is low. And stocks are high. But beyond the fog of numbers, the stars put the U.S. economy at a completely different latitude. Each day, Americans spend 5% more than they make. That is the implication of a $600 billion current account deficit in a $12 trillion economy. And every day that passes, workers in India, China, Indonesia and many other countries become more skilled – readier to compete with Americans for the world’s resources. Oil goes up. Copper soars. Soon it will be meat.

Jobs are created in America…but they are poor-paying jobs, most of them merely helping to pave the road to ruin, as almost all of them are on the consumption side of the ledger. We build houses. We work in health care. We finance houses and business mergers. We lend. We sell. If ever you want to go into debt, dear reader, there are plenty of people to help you do it.

We are told that we are working towards an "ownership society." But our number one asset is our own home…and we own less and less of it. The truth is that we are becoming a nation of "sharecroppers" – but only a rich old man like Warren Buffett has the courage to say so. We do not earn enough to pay our way, so we borrow from our suppliers. Asia has become the "company store" to which we owe our souls.

But what’s this? We have been feeling sorry for Mr. Asakawa. The poor man keeps his eye on Japan’s huge pile of U.S. dollar holdings. He sleeps with an alarm by his bed that goes off whenever the dollar slips below a certain register. Lately, the man must be awakened often. For yesterday, the dollar fell to $1.34 per euro. The euro is not a great currency. But it is judged better than the dollar by most serious investors – including the aforementioned Mr. Buffett.

Well, apparently, the Japanese have had enough sleepless nights. Prime Minister Koizumi announced yesterday that Japan, too, would lighten up on the dollar.

We have no particular opinion on the euro. It’s virtue, as near as we can tell, is chiefly that it isn’t green and doesn’t have pictures of American presidents on it. But we have an opinion on the dollar; it is one we share with Mr. Buffett – the dollar is no place for your money now.

But what to do with dollars? You could give them away. You could buy real estate that you want to own – regardless of its price. You could buy a business that gives you an acceptable return on your investment. Or, you could buy gold.

There is never a good time to die. And never a good time for a crash or a slump. Still, they happen. We urge readers to be prepared. Say something nice to your mother. Offer a bum a drink. Buy gold.

More news, from our team at The Rude Awakening…


Eric Fry, reporting from Manhattan:

"Today we pay tribute to an important date…the fifth anniversary of the NASDAQ’s peak. Five years later, has the bear market finally run its course? Your Wall Street correspondent thinks not…"


Bill Bonner, back in London:

*** Oh, my…from Las Vegas comes shocking news. Residential property prices were stable in the month of January. We see no reason why they shouldn’t be stable all the time. But they are not. Instead, January’s prices were 39.4% higher than they were the year before. For some reason, in January, they did not rise.

*** We received this note from our friend, Chris Mayer:

"OFHEO, the acronym for Fannie Mae’s regulator-the Office of Federal Housing Enterprise Oversight – has for years been like a yippy Pekingese on heels of a Great Dane. And for years, the Dane has barely acknowledged the existence of the small pest nipping at its hind legs.

"Things are supposed to be different now, with Fannie in the spotlight. OFHEO suddenly has a new set of choppers. But, what are they doing with this opportunity to bring Fannie to heel? Not much.

"The Wall Street Journal reported yesterday that OFHEO announced some new rules for Fannie to follow. Among them, ‘limiting employees’ ability to alter database records,’ as well as a requirement that will ‘ban falsified signatures on accounting journal entries.’

"That’s right. After all these years of falsifying documents and signatures, apparently that stuff has got to stop. Or at least in the case of altering records, the new rules put some limits on that rough stuff. Are you kidding me?

"This is like robbing a bank and getting a slap on the wrist for muffing up the new carpet in the lobby."

[Ed. Note: Chris Mayer is one of the finest analysts we have ever worked with, is in the process of launching a new service called Crisis Point Trader.

Chris has harnessed and mastered an ancient trading system that has pummeled the market for over a century. Everyone else will have to wait until March 14th to get in…but as a special favor to the readers of The Daily Reckoning, we have the details now, hot off the press…

*** We know; everything is splendid. And becoming more so with each passing day. Still, bonds seem to have turned a dark corner. Yields are rising. Keep your eye on them. If this trend continues it really will be the big turnaround we have been expecting.

*** Did we hear a bell? Could France’s new 50-year euro bond mark the top? Who would have thought that you could sell a 50-year bond denominated in a currency that has only been around for six years? As recently as last month, you could still go into French banks and present francs – and they still wouldn’t laugh at you. Instead, it was the last chance to exchange the old currency for the new, said authorities. And now comes a chance to lock in an interest rate less than 4.5% for a half a century! Who, in his right mind, would want to do such a thing? Only someone who suspected that the world was entering a major slump…and that he’d have a chance to off-load his bonds to a greater fool sometime before the things turn to trash.

But we keep forgetting that this is a new era. All of the mistakes made by previous generations of paper money mongers have all been identified and corrected. So, has the spirit of man so improved over the centuries that we no longer need to worry about cheating, avarice, or incompetence? The euro, we can dream, will be as good in the year 2055 as it is today. Four and one half percent will seem like a reasonable yield. Our grandchildren will wish we had been wise enough to buy them…and beachfront lots in Antarctica!

*** "Oh, Daddy…I met his mother. And this weekend, I’m going to meet the rest of the family," said Maria last night.

"I thought he was Greek…and I thought you were still thinking this over."

"Well, I am. And he is. But his mother came yesterday. She seems very nice. She brought him a whole shopping cart of food. But he doesn’t eat meat. And his mother told him she thought he should have some meat. But he looks like a Greek god, if you know what I mean. Whatever he’s eating, other people should try it.

"And I don’t know if it’s the real thing or not. What does it mean when you think about someone all the time? And he thinks about you? And you’re both very happy?"

"I don’t know…you bought a winning lottery ticket…and each of you holds a half of it?"

"Oh Daddy, be serious…I don’t know what it is, but it’s very pleasant. We look at each other in class all the time. Well, we don’t really look at each other. We just know that we’re looking at each other…without actually looking, if you know what I mean…and while I wasn’t looking another boy stepped on my foot. And now it really hurts. We’re doing acrobatics. It’s very hard. But it’s probably very good for us….

"Maybe it’s not the real thing…but it’s growing on me. You have to meet him…"

"I can’t wait."