Levels of economic concentration for the Treynor-Black model

The levels of economic concentration in investment portfolios are studied using the Herfindahl index (HI). From portfolios formed with the Treynor-Black (TB) model, only in its active part. Using the components included in the Dow Jones Industrial Average (DJIA) between 2000-2020. Although the TB model outperforms the DJIA, it presents investment periods with a low HI. Portfolios with HI>=0.885 (between 11 to 17 assets) do not outperform the DJIA. On the contrary, when TB portfolios with HI<0.05 (a single asset, 20.7% of total observations) outperform the DJIA and the rest of the combinations with HI>0.05. Having an average return of 17.1%, with an 83.2% probability of outperforming the DJIA, and. 85.3% probability of returns above zero.