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Subject:  CAGR/GSD Limits of Blends Date:  11/16/2007  12:46 AM
Author:  JuanBobsDad Number:  203944 of 263916

Recently there has been some revisiting the subject of blends with particular concern about what is possible and/or realistic (see Zeelot’s recent posts #203794 and #203916, for example). I only want to say something about what is possible of a blend in numeric terms (realism isn't my strong suit). I claim the following to be true.

1. The blend CAGR cannot be as large as the largest component CAGR nor can it be less than the smallest CAGR component of the blend.
2. The blend GSD cannot be any smaller than the smallest GSD component value.
a. The reduced GSD goal of a blend can be achieved if, and only if, at least two of the components are negatively correlated (i.e., the components vary “out of phase” so that when one tends to go up, another tends to go down).
b. If all the components are independent the GSD is a value in the neighborhood of the weighted sum of all the component GSD values.

As we all know, a blend is composed N simultaneous positions, each of which is customarily described by CAGR and GSD statistics (Note that periodic price ratios are also (1+%gain) values):

M = ln(1+CAGR) = m * average{ ln(price