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Chaos & the Butterfly Effect Theory

To those already initiated with Chaos and its theory, the article maybe not state something new (okay my interpretation maybe), but for those of you who don’t know what I am referring to, read on.


Chaos Theory: Contrary to the definition of the word chaos, which defines chaos as “a state of utter confusion or disorder; a total lack of organization or order”, Chaos theory attempts to identify outcomes in dynamic systems, whose behavior appears to be random but in fact are not random and are dependent on underlying variables.


The formal definition of Chaos Theory is thus “Chaos theory describes the behavior of certain dynamical systems – that is, systems whose state evolves with time – that may exhibit dynamics that are highly sensitive to initial conditions (popularly referred to as the butterfly effect). As a result of this sensitivity, which manifests itself as an exponential growth of perturbations in the initial conditions, the behavior of chaotic systems appears to be random. This happens even though these systems are deterministic, meaning that their future dynamics are fully defined by their initial conditions, with no random elements involved. This behavior is known as deterministic chaos, or simply chaos.


What the definition suggests is that a complex system (Such as Weather, population Growth, Stock Market etc) whose behavior, over an extended period of time, appears to be random with no underlying pattern and thus no predictability does in fact follow a particular order which is influenced by the underlying variables that work together as catalysts to generate the outcome (results). The theory thus focuses on identifying the underlying pattern (order) in apparently random data and attempts to predict outcomes in a given time frame.


The genesis of the Chaos theory is the butterfly effect (referred in the definition above).


Butterfly Effect: This theory describes the catalytic effect of small actions leading to a bigger consequence. It’s called the ‘Butterfly effect’ because the theory refers to the idea that a flap of a butterfly’s wings might create tiny changes in the atmosphere that may ultimately alter the path of a tornado or delay, accelerate or even prevent the occurrence of a tornado in a certain location. The small action in the above is the butterfly flapping its wings and the bigger consequence is its effect on the tornado.


Formally butterfly effect can be defined as “Small variations of the initial condition of a dynamical system that produce large variations in the long term behavior of the system.     


To illustrate the definition above, let’s take a simple example.


We know that 100*10 = 1000. Now let’s introduce a small variation of 1 in the original equation, thus 101*10 = 1010. The introduction of 1 lead to a variation of 1%. Lets extrapolate further 100^3 vs. 101^3. The % gap in data is 3% thus the difference starts to widen. Finally lets take 100^10 vs. 101^10. The difference is a staggering 10.46%


Thus an initial variation of 1% in the data has resulted in a variation of over 10.46% in a given outcome. This is the essence of Butterfly Effect.


In the next article I will try to explain the chaos theory, its implications and its effects on the Stock Market. Though I am not the first one to identify the correlation, I did identify it independently, so the topic is a lot closer to my heart than you think.


August 5, 2008 Posted by | Mathematical Theories, Uncategorized | , , , | Leave a comment


You must be wondering what in Gods name is ‘Fear’o’nomics. Sure you know economics (Supply, Demand, Inflation theories, Budget theories, Malthusian Theory, law of DMU… the list is endless) and more recently heard  of Freakonomics by Steven Levitt & Stephen Duber (which does a great job of integrating Economic theory to real life observation), but “Fear ‘o’ nomics” ?? Well! No right, that’s because there no such word (not until I coined it) and this article is just about that.


Fearonomics is that economic behavior by participants which does not fall under the current rationale of Economic theories but seems to be an overriding factor in a lot of Macro economic decisions.


Does the definition provide any clue at all? Id be damned if it does. So let me illustrate what I mean.


Just think back for a few minutes of the global (pressing) issues that you have heard of, known of that you can recall. Can you think of any time at all when the global economy has not been facing any serious issue which seems insurmountable and where the naysayer have professed that it is the end of the world as we know it. Probably No!


When I look back, I can think of the Cold War in the early 1990’s which ended by the fall of the soviet union, then came the advent of Global Warming where the world consciousness of human parasitic behavior and its effect on nature came into focus, then in late 2001, the world was introduced to terrorism which post 2001 became a house hold word, then Israel-Palestine conflict surfaced which indicated impact on the world economy, then came the “War on Terror “ where Coalition forces leveled Iraq and Afghanistan to eliminate Terror (only the future will let us know if this even left a dent on terrorism).


In the same time frame, we had the Y2K fear in 1999, the Dot com bubble burst in 2001-2002 which prophesied that the meltdown of a zillion .com companies will lead to severe global economic recession, then the fear of anti sentiments against outsourcing and its impact on the global economy and esp. on emerging economies like India, China etc, then in 2006, the fall of the dollar when compared to other currencies, then late last year and this year the sub prime crisis and now our favourite the rise in the crude oil prices.


While I do agree that all the above were and are true global economic & geo-political issues, what I find surprising is how in all the fear and the psychosis that was created during these issues, a section of people and even economies created wealth for themselves. Let’s look at few examples:


Cold War, War on Terrorism, US relationship in intermediating between Iran & Palestine: What common on all of the above – Its US and its military build up. Let me simply quote wikipedia to prove my point “In the Cold War Era, arms exports were used by both the Soviet Union and the United States to influence their standings in other countries, particularly Third World Countries. Since the fall of the Soviet Union, global arms exports initially fell slightly, but have since grown again to cold war levels. The United States is the overall top supplier of weapons. The United States is also the top supplier of weapons to the developing world, accounting for around 36% of worldwide weapons sales, followed by Russia, Britain, Germany and China”  Now does it look like an ordinary co-incidence ?


Another evidence “The Control Arms Campaign, founded by Amnesty International, Oxfam, and the International Action Network on Small Arms, estimates that there are over 600 million items of small arms in circulation, and that over 1135 companies based in more than 98 different countries manufacture small arms as well as their various components and ammunition”


Global Warming:  This term needs no introduction. So we all know that Global Warming exists, but do we really? How many know that extent to which the temperature has increased? Does any media report provide any factual evidence than to speculate the aberrations in temperature, or to mention the hole in the ozone layer? No!

Let me provide you with some evidence again quoting wikipedia “The average global air temperature near the Earth’s surface increased 0.74 ± 0.18 °C (1.33 ± 0.32 °F) during the hundred years ending in 2005.[1] The Intergovernmental Panel on Climate Change (IPCC) concludes “most of the observed increase in globally averaged temperatures since the mid-twentieth century is very likely due to the observed increase in anthropogenic (man-made) greenhouse gas concentrations” via an enhanced greenhouse effect. Natural phenomena such as solar variation combined with volcanoes probably had a small warming effect from pre-industrial times to 1950 and a small cooling effect from 1950 onward.”


The point is nobody knows for sure. We cannot identify all the variables that influence temperature, weather patterns or even our impact on the temperature. We can only speculate and try to estimate.  While I appreciate the awareness, the steps that are being publicized to reduce carbon emissions, what I am skeptical about is the fear that is being created around global warming, the media frenzy, the number of research reports that are being written.

Who are the immediate beneficiaries of the fear? It’s the 1000 odd companies doing research on climate changes. How are these companies funded? Well through governments, other companies, private donations from foundations and through us the people (taxes and donations). If this fear or psychosis was not created, do you think these companies would be in existence? I don’t think this is a mere co-incidence.


Increase in Crude oil price: The most favourite and obvious one of all. The price of the crude oil has been on a steady upside momentum (hovering around 140$ per barrel). The question is whats driving this movement. Clearly its not the Demand and supply, atleast not the current short term trend. There has been no significant change in either the Demand or the supply of Oil in the recent past. Maybe geo-political changes in ownership but again that has not changed significant and does not seem will change in the short term. Irrespective of the factors, one thing is clear, it’s the speculators who seem to be making money using the price movement (hedging against the price movement).


These examples clearly indicate that the fear is the key factor that helps a particular segment of people or individual economies overriding economic theories, principles and rationale and thus the term Fear’o’nomics.

July 22, 2008 Posted by | Economics | , , | 2 Comments