CAPM and Growth
Overview
Using portfolio growth as the performance measure to be optimvized versus risk alters the logic of
the
CAPM a little.
Similar to the standard CAPM logic, there exists a set of feasible portfolios and an optimal frontier.
Also similar to the standard model, the efficient portfolios can be created as a mix of the risk free
asset and a portolio on the frontier, in particular, the growth optimal portfolio.
The big difference with the stsandard CAPM model is that there exists an optimal growth portfolio,
that is, growth cannot be levered up indefinitely.
Growth Optimal Portfolio
In the presence of the risk free asset, the weights of the growth optimal portfolio satisfies the following set of equations
{% \sum_{i=1}^n \sigma_{i,j} = \nu_i - r %}
(see
Luenberger pg 432)
