David

In the market section you say that the geometric average taked into account 1/2 the SD How does that work.  The formular is to multiply all the factors together and raise them to the 1/n power. less 1

Frank

Frank,

If you take a series of returns, say: +10%, -10%, +20%, -20%
The arithmetic average is 0%
As you say, the geometric average = [(1.1)(0.9)(1.2)(0.8)]^(1/4) - 1< 0
I like to say “the volatility erodes (geometric) return”

This geometric return will be approximated by: arithmetic average - (1/2) variance
(not 1/2 standard deviation), so in this case:

[(1.1)(0.9)(1.2)(0.8)]^(1/4) - 1 ~ 0% - S.D.^2/2

David