I thought this site had a good explanation of how assets are weighted in the Treynor Black model. The most useful paragraphs are below From http://www.financewise.com/public/edit/riskm/ewrm/ewrm-port-x.htm "Except for rare instances when high return is accompanied by low risk, the Treynor-Black model tends to favour assets with low risk and low return. The weighting of high risk, high return assets is often lower than intuition would have it. The basic properties of the portfolios selected by the Treynor-Black model can be seen in the above example. First, the relative allocation among assets is independent of the amount of money to be allocated among them, because allocations are expressed in terms of shares, not monetary amounts. Second, adding or removing assets does not change the relative allocation among any of the existing or remaining assets. This property makes the Treynor-Black model suitable for use in decentralised applications. Assets can be partitioned into several groups, and the allocation decision within any individual group can be made without any knowledge of the assets in any other group. Another important property is the stability of the model, its lack of sensitivity to small changes in the parameters of the model. In particular, all allocations are “well-behaved” functions of all the risk and return parameters, so that a small change in any parameter (or set of parameters) cannot lead to a fundamental change in the portfolio.
Stuff to know on Treynor-Black … Choose high Active return/Low unsystematic risk as the criterion for assigning weightings in the portfolion. P.S. Active return / Alpha can be negative also