Misled by models II

Many financial models use a Guassian model for characterizing risk.  This model is a normal distribution of movements.

It is used in Modern Portfolio Theory, Efficient Market Hypothesis, and other “random walk” models of investments.

Why use Guassian bell curve?  Because it is well-understood, simple, and works well for the average case.

But the model breaks down outside of typical days.  The phase "black swan" popularized this known problem of mis-matched volatility.

How much mismatch?

• In the past century of the Dow-Jones Index, the model would predict a few dozen days of +/- 3.4% changes.  In reality, about 1,000 days had moves that large.
• For bigger moves of +/- 4.5%, instead of the 10 or so predicted days there were several hundred.
• For even bigger moves of +/- 7% where less than one was expected, in reality there nearly 50.

Clearly it is not a good strategy to blindly follow the simple model.