Message Font: Serif | Sans-Serif

No. of Recommendations: 1
In message 65627 (I was far behind in my reading, but I've since caught up), klouche said we've been relying for some time on the average of CAGR over all starting months to evaluate screens for non-monthly holding periods. However, in message 40510, DeepBlue proposed what I think is a better approach, and in message 40534, Elan suggested calling it CASM, Compound Average of Starting Months. If I may, I'd like to explain it again, starting with a clean sheet of paper, so to speak.

For a given starting month,

VN = V0*(1 + R/100)^N

where

V0 = initial investment, or value at end of year 0

VN = final value, or value at end of year N

R = %CAGR, Compound Annual Growth Rate in %

For the same initial investment in each starting month of a quarterly screen, say, the average of the final values for starting months 1, 2, and 3, ignoring the time displacements, is

(VN1 + VN2 + VN3)/3 = V0*(F1 + F2 + F3)/3

where

F1 = VN1/V0 = (1 + R1/100)^N

F2 = VN2/V0 = (1 + R2/100)^N

F3 = VN3/V0 = (1 + R3/100)^N

The compound annual growth rate in %, corresponding to the average of the final values is

%CASM = {[(F1 + F2 + F3)/3]^(1/N) - 1}*100

By extension, for semi-annual screens

%CASM = {[(F1 + ... + F6)/6]^(1/N) - 1}*100

and for annual screens

%CASM = {[(F1 + ... + F12)/12]^(1/N) - 1}*100

Mostly lurking thanks,

Ratio