Let’s revisit Mandelbrot’s book again – “The (Mis)behaviour of Markets”. In this post, I will share with you his argument against the random walk hypothesis of the financial market. He argued that prices are dependent, and not independent as Random Walk suggests.
First Illustration – The basketball player
“If a basketball player sinks two shots in a row, evidence suggests, odds are greater that his third shot will also score. By prowess or psychology, a player can have “hot” streaks; successive shots are, to some degree, dependent on one another. But how long will his scoring streak last? Is it broken after just one miss? Two? Five? Over how many shots, precisely, does the “hot-hands” effect linger? Put in mathermatical terms, over how many time periods is the dependece significant?”
Second Illustration – The reservoir
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“Say a series of wet years fills the reservoir. Then some years of mostly moderate weather follow – but the reservoir is full; the prior wet years are still having an effect. Then some dry years arrive. Now the reservoir is emptying. But it has more water than it otherwise would; still the prior wet years are still having an effect.”
Third Illustration – The Tree
“Adjacent tree rings, the marks of growth only a year or two apart, are highly correlated. Beyond a few years, the correlations fall; the pattern from one decade or century to the next is more haphazard. But the correlations fall more slowly than expected. In fact, it is 150 years before they are so insignificant that to distinguish them statistically from chance.”
In Financial Markets
“Now think finance. In 1982 IBM, then the world’s biggest computer company, decided some upstarts at Apple were threatening its future with a new product called the personal computer. Uncharacteristically, IBM acted quickly. It bypassed its own big chip factories and software departments. It picked a struggling semiconductor company named Intel to make its microprocessors and a bright but insignificant kid named Bill Gates to provide its software. The rest is well-known: Intel and Microsoft grew wildly, beyond any imaginable bounds. IBM stumbled, and sharnk. But the fates of these three companies are still intertwined. Their stock prices affect one another, as profits or troubles at one rebounds on the business or market-ratings of the others. That event of three decades ago, IBM’s midwifery to two new industry giants, continues to reverberate today in IBM’s stock price. The dependence there is about thirty years long. One can easily imagine even longer dependence: The court-ordered breakup of John D. Rockefeller’s Standard Oil Trust in 1911 continues to affect its surviving children today, ExxonMobil, ConoccoPhillips, Chevron Texaco, and BP Amoco.”
“No act is without consequences for others. It is a tenet of chaos theory that, in dynamical systems, the outcome of any process is sensitive to its starting point – or, in the famous cliche, the flap of a butterfly’s wings in the Amazon can cause a tornado in Texas. I do not assert markets are chaotic, though my fractal geometry is one of the primary mathematical tools of “chaology.” But clearly, the global economy is an unfathomably complicated machine. To all the complexity of the physical world of weather, crops, ores, and factories, you add the psychological complexity of men acting on their fleeting expectations of what may or may not happen – sheer phantasms. Companies and stock prices, trade flows and currency rates, crop yields and commodity futures – all are inter-related to one degree of another, in ways we have barely begun to understand. In such a world, it is common sense that events in the distant past continue to echo in the present.”
Prices have momentum
Here is what I draw from these: The shorter the time frame, the larger the dependence. We shall not talk about his examples of IBM or Standard Oil, or any dependence lasting 30 years. I am interested in days, weeks or months, as their dependence would be stronger. If what his observations and concept are accurate, trend following strategies will be profitable in the financial markets since they anchor on the same principle – if price has been going up, it is likely to continue in the same direction. In other words, yesterday’s price will have an effect on today’s price as well as tomorrow and thereafter. Price has momentum. As the basketball illustration suggests, how long will the significant dependence lasts so that we can rip the maximum profits from the stock? It is a holy grail that we can never find out. Read more about price dependence and the Joseph’s effect.