Making Sense of Chaos

Chaos Theory has more to do with mathematics and quantum calculations in particular than finance. But in spite of this, its relevance to the field of investments is very deep. Let us try and understand how Chaos Theory helps understand why markets are unsystematic, irrational and volatile but still manage to excite millions who try to predict its behavior. The basic interrelationship for Chaos Theory and finance lies in understanding its connection with Law of Large Numbers. Chaos Theory in Capital Markets states that the market behavior is guided by complete randomness or the absence of any order. This is because the theory sees the universe and everything in it as forces acting in a random and order-less manner and as such everything in the universe has to follow the same pattern.

Now if we relate this theory with the Law of Large Numbers then it states that any random occurrence with a large number of repetitions tends to move towards normal distribution. So over a large observation of occurrences the chaotic and random events tend to form a rational picture and eliminate and noise. But because for this rationale to be visible, the events required to be observed might be close to infinity, any predictions made to judge the outcome are never accurate. But this does not mean that they cannot be close to accurate or actual. This is the main reason why future predictions on stock prices and earnings of companies are never accurate but several times close to it. The accuracy largely depends on how many factors acting in the chaos chain have been considered in the prediction.

Now let’s come to the key point. Why are we talking about this? Try and understand that because predictions rest on the principles of chaos and law of large numbers, they should never be unrealistic, especially when a very small duration of time is considered. So when an analyst tells you that he predicts a stock providing 20% returns in 6 months, ask yourself a question whether the time span taken into consideration is enough to identify a close to accurate trend and the success rate banked on such limited a short duration is too optimistic or not? Now add to this the assumptions made in the model used and you will see that the analyst could be off the mark by much more than 20%. Here is something else you probably don’t know. The target price of a stock is provided to you based on some model that uses estimated future earnings and cash flows. Now in doing so, there are at least 5 assumptions used in any model. Statistically, by making 5 assumptions that are correct 95% of the times, the overall prediction can only be correct 77% of the time.

The long and short of the post is that Capital Markets should be used to take advantage of Market Cycles over a long period (Usually greater than 5 years). Whenever you enter the market for short term gains, statistically there is a 73% chance that you would not meet the prediction. How much the deviation from the prediction will be, depends on how many assumptions you have taken and how many of them are wrong.