Monday, December 17, 2007

The Importance of the Step Function

Stocks on Radar - GIC Housing Finance

The most important thing in life is freedom - particularly intellectual freedom. And in my quest for intellectual freedom, I think I have discovered some unusual things. Perhaps the most important of these is the step function.

I think human beings have an innate attraction for the linear function. So, we try to reduce everything to linearilites. Force =mass * acceleration, Price =EPS*P/E multiple etc. Over centuries, we have also become more comfortable with the cubic order equations. Where, however, we fail is the step function.

What I have observed, and this might be wrong, is that while systems often change state linearly, at some crucial times, systems jump from one state to another. This is most readily observed in stock markets. Markets might not adjust to something (say subprime) for months, and then in 2 days, there would be crash-and-burn and the system moves to another state. Weather systems also seem to follow a similar pattern - that is why climate scientists are worried that we might jump to a state of no-return in our fight against global warming.

Why is this important? Because, in stock markets, the point of maximum profits is the point of the step change. Simply extrapolating last 3 years revenue growth, margins and ROEs into the future is wrong and dangerous. And we might be more close to a step change in the global economic, political and social outlook than we have been in the last few years.

My personal life has definitely moved in step functions. Nothing will happen for years, and then suddenly, something will happen which will take into another state for the next few years.

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