Here are two distribution fit charts for U.S. equities. The first illustration shows the laddering power transformations on the historical data. It reveals an unmistakable cluster, associated with a minimal barrier on systematic risk in the U.S., shown at the low end of the distribution (left side of the middle chart).
The second illustration advances this theme with a 12-variable, Chi-square (χ^2) quintiles chart for U.S. equities. The degrees of freedom (d.f.) associated with this χ^2 distribution are the number of variables, minus one.
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