Growth
Overview
Asset growth is similar to
an assets arithmetic return. It is simply defined as taking the logarithm of the aritmetic return.
It servers as an alternate measure of asset performance. However, it has some properties that make it a good candidate
of long term performance. In particular, it can be shown to be able to beat alternative strategies over the long term with
a high probabilty.
Definition
Growth is a term that is used to refer the expected logarithm of asset returns. That is
{% growth = \mathbb{E} (ln R) %}
where R is the Price return
{% R_i = \frac{P_i}{P_{i-1}} %}
Using the basic properties of logarithm, this is equivalent to difference of log prices.
{% growth = \mathbb{E} [log(P_i) - log(P_{i-1})] %}
Growth Math
