Wednesday, February 15, 2017

Living in a non-linear world

“Humans best process information when relationships are linear.” – William Sharpe 

Linear thinking with investment management is simple and easy. Give me a straight-edge and I can show you the connection between two events.  A regression is just the fitted line to minimize deviations between two variables. Draw a trend line and you can find the direction of the market.  A multiple regression can provide more information on conditional behavior, but it may not capture the true link between markets because it is still trying to fit everything into a linear world. The concepts and the math are easy in a linear world. Unfortunately, reality is more complex. Markets move differently based on the environment, who is trading, and the associated risks. 

A real value in investment management is finding when markets move higher or lower with acceleration; a non-linear event. For example, the relationship between inflation and unemployment and its link with rates is very different when the economy is running at the natural rate of unemployment versus periods when the economy is far away from full employment. When there is a market accelerant or catalyst, price can become non-linear. 

The key for any investor is knowing when relationships may switch from linear to non-linear. There can be countless example of when market behavior becomes non-linear, but our fallback position is to use linear tools. The reason for falling back on a linear world is simple, the thinking is intuitive; if X moves Y percent, there will be a known response in variable Z. Success comes from moving beyond what is easy. Learning to anticipate or model a non-linear event s difficult.

While we mostly process linear relationships, investment success is also predicated on our ability to create or find non-linear trades. The best investors look for cheap convex trades. This can be done through the use of options or through buying instruments that have positive convexity. By creating non-linear trades in a linear world, investors can create a return edge. 

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