Treynor-Black model as a simple experiment on active exposures

Sometimes a simple approach is useful of building portfolios. One of these simple approaches is the Treynor-Black model which builds a portfolio based on active and passive bets generate a portfolio that will be above the security market line. 

We start with the Treynor-Black ratio or appraisal ratio which is the alpha of a given stock divided by the standard deviation of the error term from regression withe market beta squared. This is the ratio of alpha to the square of unsystematic risk. 

The weights of the Treynor-Black model are based on the size of the weighted alphas which can be compared with the passive portfolio. The overall portfolio can then be adjusted to form an active portfolio and passive portfolio (1- active weight) that still has the market beta. 

The key issue is getting the right alpha measure. The Treynor-Black model just calculates alpha from past measurement, but forward-looking measures can be created to get a better subjective alpha which can be used to create an active portfolio.