The definition of Treynor ratio is given by $$ T = \frac{r_i-r_f}{\beta_i}, $$ where $r_i$ is the portfolio $i$'s return, $r_f$ is the risk-free rate and $\beta_i$ is the portfolio $i$'s beta. I am stunned after reading this definition. Isn't it exactly the market premium?
The CAPM model says that $$ E[r_i] - r_f = \beta_i (E[r_m] - r_f). $$ Compare the above two equations we then conclude that $T$ is universal for all $i$ as $T$ is nothing but the market premium $r_m - r_f$. Could you point out what I missed? thank you guys