  We investigate and extend the result that an alpha-weight angle from
unconstrained quadratic portfolio optimisations has an upper bound dependent on
the condition number of the covariance matrix. This is known to imply that
better conditioned covariance matrices produce weights from unconstrained
mean-variance optimisations that are better aligned with each assets expected
return. Here we relate the inequality between the alpha-weight angle and the
condition number to extend the result to include portfolio optimisations with
gearing constraints to provide an extended family of robust optimisations. We
use this to argue that in general the equally weighted portfolio is not
preferable to the mean-variance portfolio even with poor forecast ability and a
badly conditioned covariance matrix. We confirm the distribution free
theoretical arguments with a simple Gaussian simulation.
