The (Mis)behavior of markets, Beniot Mandelbrot, 2004 - Taleb sort of spoiled the book for me since he has exposed these concepts in his derivative works. Mandelbrot has been a phenomenally original thinker. He founded fractal geometry - fractals are shapes when broken into smaller parts resemble the whole (self-similar), like the florets of a cauliflower or leaves, branches in a tree. We have had obsession for the symmetrical and perfect (pythagoras?) - from triangles to spheres when life was rough on the edges - Mandelbrot set out to understand roughness - be it in tree rings, boundaries of countries, rhythms of war and peace or in price trends of financial assets.
His ideas were widely adopted in chaos theory later on. This work is his application of fractal geometry to understanding price movements in financial assets (cotton in specific). Some of these ideas go all the way back to the 60s but being a lone-wolf who shunned academia and practitioners equally and operated from the periphery, his ideas remained broadly undiscovered (other than the curiosity those fractals generated)
My notes -
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GFC causes - Over-confidence of our understanding of the markets and over-optimism, coupled with the belief that what had been seen before would, more or less, persist into the future (house prices would keep rising, default rates will stay within forecast range etc.)
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Better models make allowances for the atypical - but many models are based on ‘close enough’ approximations of the past
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Financial economics as a discipline is where chemistry was in the 16th century (misty folk wisdom, unexamined assumptions and grandiose speculation)
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Fundamental idea of Mandelbrot - price changes today are dependent on changes in the long past. Prices have a fractal kind of long-memory (sometimes strong, sometimes weak). Today’s big changes make tomorrow’s big changes more likely. Wild Tuesday may lead to a wilder Wednesday. (Momentum works because of long-memory)
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Reaction to bad news might be today for quick-triggered investors while others with different financial goals and longer time-horizons might react after a month or year (reason for long-memory)
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When the historic 90s bull market tired, multiple problems emerges all at once - from recession in japan, devaluation in china, impeachment in Washington and Russia hitting a cash crunch (like we have Ukraine war, high bond yields, high inflation, Israel conflict, China trade war etc. now)
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Market models underestimate financial ruin greatly - Crash of ‘98 was a 1 in 500 billion event, 1987 crash a 1 in 10^50 event and yet they happened. Extremes are the norm, not the exception.
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While it’s impossible to predict stock prices, it is possible to model and measure risk conservatively using mathematical models (non-Gaussian). It would be something of a Richter scale of risk to which we can subject the strategy to a what-if (what if size 7 financial quake hits)
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Power laws - area of land grows as square of its side and gravity weakens as an inverse power of distance. Incomes, forest fires, earthquakes and price changes follow power laws - when plotted, they form fat tails - unlikely events with high impact don’t taper off quickly
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Economics is faddish - what is right or wrong is formed by consensus (Investing is not very different)
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Market time is relative and quite distinct from ‘clock time’. During high volatility market time speeds up and slows down in low volatility (see the similarity to gravity?)
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Asset prices don’t rise or fall by pure chance (As assumed by the drunkard’s walk) but by anticipation, individual and mass psychology.
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A macroscopic rather than microscopic, stochastic rather than deterministic approach might help. When magnets are heated above Curie point, magnetism disappears and comes back on cooling down. We don’t how and why the individual particles interact and what causes what but we don’t need to. That’s why reasons for a crash are dispensed by journalists after the fact. A better approach would be to look at risk
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An archer who is missing the mark makes a measurable error. One wild error that misses by a mile make his errors diverge from the mean. They have infinite expectation and hence infinite variance (One error could be more than the sum of a 100 errors)
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Coin tosses are mildly random while the archer is wildly random. Former is Gaussian and latter is Cauchy (Taleb calls it Mandelbrotian)
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Fourier’s heat equation, Einstein’s Brownian motion, Bachalier’s model for bond prices - all use similar concept - of radiation of probability, similar to how heat diffuses through metal (felt information percolates in the markets same way as heat diffuses through metal - while reading 12 equations book)
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Wind in a wind tunnel blows nice and smoothly at low speeds (laminar flow - currents gliding in steady lines, planes and smooth curves). As wind speed increases, it breaks into gusts here and there, forming eddies and returning to smooth flow alternating between rough and smooth (turbulence as experienced in an aircraft). Traded prices are very comparable
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Big events are concentrated in time causing discontinuities and abrupt lurches among quiet activity (similar to wind turbulence)
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Fractals are generated using simple rules, using a initiator (a geometric object like a straight line, triangle) and a generator which acts as a template and a rule of recursion (Note to self: Try generation using MandelbrotSet the objects in the Fractal Gallery)
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Roughness of a fractal is measured by the fractal dimension (British coastline has a FD of 1.25. Aus 1.13 while SA has 1.02 which is almost a straight-line). FD of 2 would be a 2-D plane and 3 a 3-D space. Bronchia in our lungs have a FD of 3 thus forming very large surface area using simple rules of replication (power of 3 is like volume - 3-dimensional)
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Fractality appears repeatedly in nature’s toolkit - when waves hit the coastline, the energy dissipates on the rocky surface forming the coastline or in lungs the iterative division works in similar fashion during its development (patterns on animal skin too, like that of zebras or tigers). Complex structures deconstruct into simple rules
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Zipf’s law - Value of nth entry in a descending sorted list is inversely proportional to n. Work freq vs work rank. One of the earliest known occurrences of power law. Later in economics Pareto principle of wealth distribution was discovered (Model thinker explains these beautifully)
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When plotted on a log-log plot, phenomena that follow power laws form a straight-line whose slope is the power of the power law
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Absolute odds of being a billionaire are low, but by Pareto’s formula, odds of making a billion when having half a billion are same as making million when having half a million (Money begets money - limits to growth should apply though). Alpha in pareto’s formula signifies how inequitable a society is
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The formula that was discovered in how Nile flooded one year to the next (Hurst), from data in the flood plains could be applied to how clay accumulated in crimean lake bed to rainfall in NY or growth of tree rings - and to how stock prices fluctuate (Long memory at play - wet years cluster together. Back-to-back floods or droughts were very common - thats why dams can’t be built based on 100 yr data)
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Inflation too isn’t random like a coin-toss. High inflation in April, makes it highly likely in May - it becomes persistent too beyond a point like in the 70s. Production, inflation, unemployment all have dependence on the past. (That’s why volatility clusters together)
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When reservoirs hold water from wet years and wet years continue, each year can be worse than the last - prior years leave their memory. (Most of long-memory can be modeled using stock/flow from systems thinking?). Such long-dependence is common in radio-active decay too. When short, medium and long components are present, long dependency can persist much after the short half-life components are gone.
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Long-dependency provided collective brakes to the stock market long after the 1929 crash was over (And such is the momentum these days from last 15 years that compression in P/E multiples is unfathomable even when rates are up significantly. Such is long-dependence)
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Each financial asset had a different H (H and alpha from earlier) which signifies long-dependence. 0.5 signifies independence while 0.7 a strong dependence and long-memory (Can be calculated from price histories). H < 0.5 shows anti-persistence
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Alpha measures the Noah effect (Extremes can be very extreme) and Joseph effect (Extremes can cluster together). Simplest is for coin-tossing H = 1/alpha. Alpha is 2 and H is 1/2. **H and alpha interact together to form booms and busts (Note to self: simulate this)
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Mandelbrot’s theory applies in normal scale of the market but not in quantum or cosmic scales (say not in minutes/hourly or decadal charts)
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Jumps, skips and leaps of discontinuity / dislocations is what distinguishes financial markets from physics, esp. more so in the information age
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Distribution of natural resources, say gold or uranium also follow power laws (Beautiful simulation of how random looking geographic distribution can be generated using simple rules)
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90% of insurance claims come from just 5% of land area. Likewise biggest moves come from small set of days in financial prices. Dollar-yen descended between ‘86-’03 over a long bumpy ride. But half the decline occurred in 10 out of 4695 trading days. Timing (the market) matters
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Intrinsic value of financial assets as a concept is slippery and its value vastly overrated
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Investors vary greatly in importance and impact on the market (A company may have 10k shareholders but < 100 might determine the marginal changes in price)
Mandelbrot doesn’t like technical analysis (calls it financial astrology) and doesn’t think absolute intrinsic value exists either there by dumping on fundamental analysts too. No wonder he isn’t popular. He is very critical on beta as risk, VaR and other such concepts that have been used to model risk and have caused lot of blow-ups. Instead he advocates building models that stress the portfolio with risks that are an order of magnitude higher than any previously foreseen risk (hence unpopular on Wall St.). I specifically loved the idea of long-memory and clustering volatility and reasons why such things happen repeatedly in nature. These are very useful ideas to incorporate into our thinking. 10/10
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