Chaos as most people use the word really stands for complete randomness or the absence of any order. However that is not how most scientists define chaos. To them chaotic systems too follow established laws of gravity, motion, thermodynamics and electro-magnetism. In other words they are completely deterministic and if the state of the system is precisely known at any point in time it is possible to precisely predict the state of the system at a future point in time.
If the state of the system can be precisely predicted then how can it be chaotic? Well it turns out that such systems are chaotic because although they can be predicted the computing power required to predict them doesn’t exist in the world today and never will. These systems are extremely complex and involve interactions of multiple components where each of these interactions is completely deterministic. As it turns out there isn’t a system in the world that is not complex. Let us discuss an example to explain the problems with complex systems before we start to apply chaos theory to investing.
The solar system is an apt example of a complex system. Since most of the universe is empty (a vacuum) the only interaction between the different bodies is gravity. When trying to predict the precise orbit of the earth around the sun we need to understand the gravitation pull of each planet, asteroid and star on the earth and amongst each other because as each body affects earth they also affect one another. Then again what is earth? It isn’t a single body but is made up of trillions and trillions of small particles that are also exerting a force on each other and on all other the particles in the universe. We all know that the gravitation force between two particles is proportional to the product of masses of the two particles and inversely proportional to the square of the distance between them. Therefore to precisely calculate the orbit of the earth around the sun we need to do the following
- Identify all planetary bodies in the universe
- Precisely calculate the mass of each body
- Precisely calculate the position of each body
This needs to be done for each pair of objects in the universe and the integrated to get the desired result. This innocuous looking high school physics equation itself is a complex system since any error in the measurement of distance or mass can distort the results due to the non-linearity in the relationship. The computing power required to find the exact orbit of the earth is nearly infinite. Before any computing machine can derive the location of the earth (on its orbit) in the future, the future would have already unfolded and would really be the past. Thus a complex system is chaotic because prediction is of no use and therefore seems completely random although all interactions are completely deterministic.
But all is not lost as for most practical purposes the problem can be simplified. The stars too far away in space can be assumed to exert no force on the earth and the mass of relevant cosmic bodies can be approximated as can the distance. What we get is an imprecise result of the earth’s orbit around the sun but useful enough to launch spaceships into space and to predict solar and lunar eclipses.
What could chaos theory have in common with investing? A whole lot if you get the general drift of complexity and the limitations of precise predictions. After all a company is also a complex system. Its financial results are an outcome of many decisions and choices made by the personnel working for the company. Just as the orbit of the earth cannot be predicted with a great deal of accuracy, the value of the company is also a very rough estimate.
To elaborate the point let me take an example of a fictitious company making widgets and selling it through various retail formats. The value of such a company is the net present value of all future cash flows. The cash flows of the company are determined by the number of units sold and the profit margin on each unit. The number of units sold is determined by factors that are many times beyond the control of the company. These factors include competitor action, production capacity, distribution logistics efficiency (mostly by a third party vendor which is again a complex system), changing customer preferences, macro economic outlook and a host of others that I can’t think of right now. The profit margin of each unit again depends on the price of raw material, technology of production, inventory management efficiency, quality of management, customer brand awareness, price of substitutes, wages etc. Calculation of net present value requires discounting future cash flows at an appropriate rate. This rate itself is dependent on the interest rate, risk involved, saving rate of the country and the rest of the world, oil prices, government action etc.
Then again there are other factors that are involved such as environmental concerns, labor relations, labor availability, imports and government policy. We could go on and on but I think I have made the point on the complexity of the entire exercise.
The computation of the value is a non-linear equation and any error in incorrectly measuring any one of these known variables (forget for a moment the unknown variables) will impact the value of the company and therefore the price of the stock by varying orders of magnitude. Again the error can be not just in magnitude but also in direction. What if we incorrectly assume falling interest rates when actually they go up? No one knows the direction of such variables again because these are complex systems themselves.
I may have convinced you that investing in stocks is a hopeless activity but that is not my intention at all. I personally believe that equity is the best investment asset class and I have most of my net worth invested in equity. My interest in writing this article is to make investors appreciate the inherent complexity and make them aware of the limitation of a valuation exercise. Recently I have seen many research reports by analysts of stellar credentials making recommendations to buy stocks with a 15% upside in 3 months. This in my opinion is absolutely crazy. Given the assumptions that go into the valuation model the analyst could be off the mark by much more than 15%. I am sure none of you will believe your driver if he told you that the breaking distance of the car is 5 meters and 7 inches when driving at a speed of 80 miles/hour on a rainy day but the same people believe these self appointed equity analyst claiming 15% return in 3 months.
The best protection from such investment follies is to ask the right set of questions before you decide to invest and remain cognizant of limitations of the prediction and then maintain a huge margin of safety. The important thing in investing is not how right you are but how wrong you can be. If investing was a mathematical exercise all mathematicians would be rich. Using mathematics to value a company tends to portray a sense of precision and accuracy but nothing could be farther from the truth. It is common for people to believe that the errors in assumptions to cancel out but cursory knowledge of statistics will tell you that errors don’t cancel but multiply. A result derived by making 5 assumptions that are correct 95% of the times can only be correct 77% of the time. Show me a valuation exercise where less than 5 assumptions are made and you will start to appreciate the magnitude of the error that can seep into stock price calculations. Before you get carried away with such precise analyst reports and call up your broker give it a moment and think of all the assumptions made and the difference to the outcome if any one of them was incorrect. Not being stupid and thinking independently can be a huge competitive advantage in the field of investing. Let me leave you with this very powerful quote by Benjamin Franklin.
If you follow the advice of others do not expect to get better results in life than theirs – Benjamin Franklin.
