I have gathered a lot of experience using min-var optimization of the form $$ w' \Sigma w \rightarrow Min, $$ where $w$ are the weights of the assets and $\Sigma$ is the covariance matrix. Of course we have to take care to use a meaningful $\Sigma$ and we need a lot of constraints in real life.
Now, assume we have calculated a set of scores (e.g. momentum over the last 2 months) or P/B ratio which can be ranked (the higher the better, transform if necessary). What are practical approaches to add this to the objective in the above problem?
Something like
$$ a (w' \Sigma w) - b(scores) \rightarrow Min $$ with some constants $a,b>0$. But wouldn't it be really difficult to choose $a$ and $b$?
How would you approach this? Are there reference on the web?
