Overview
Fernholz optimization is a portfolio optimization technqiue developed by Fernholz in Stochastic Portfolio Theory. It tries to find an optimal portfolio in a world where individual asset returns are hard to forecast. (some would argue that is the world we live in).
Fernholz makes the assumption that the best (at least most conservative) hypothesis about future asset returns is that the growth rates are all equal. Given that assumption, and the setup given in stochastic portfolio theory, he derives the optimal portfolio.
Definitions
The Fernholz assumption can be written as
{% \alpha_i(t) = \alpha(t) %}
That is, the growth rate of each asset {% \alpha_i(t) %} is equal to the common growth rate, {% \alpha(t) %}.
Then the portfolio growth rate can be written as
{% \alpha_{\pi}(t) = \alpha(t) + \frac{1}{2} \sum \pi_i(t) \tau_{ii}(t) %}