Driven IFS and Data Analysis

β scaling

The β factor of a stock is the volatilty of the stock relative to that of the market.
β > 1 means the stock is more volatile than the market.
β = 1 means the stock and the market are equally volatile.
β < 1 means the stock is less volatile than the market.
The 1-4 diagonals of the tech stocks reflects larger daily percentage changes, so we would expect higher volatility.
As a quantitative test of this, Thornton scaled the bin boundaries with each stock's β. For example, Qwest has β = 2.15, so the first and third bin boundaries are set at 2.15⋅2.5% = 5.38% above and below 0.
Here are the rescaled driven IFS (left), each grouped with its original (right) for comparison.
Citigroup: β = 1.33
American International: β = 0.85
General Electric: β = 1.08
Dell: β = 1.83
Sonus: β = 4.95
Qwest: β = 1.83
Tyson: β = 0.47
Colgate-Palmolive: β = 0.76
Lucent: β = 2.23
Note that in general rescaling the bin boundaries by the stock's β makes the driven IFS look much alike. Note particularly the change in the Sonus IFS.
The obvious exception is Tyson, whose β is so small that the rescaling puts many more points into bins 1 and 4.

Return to Comparing Stocks and Indices by Driven IFS.