Treynor measure

[Unusualskill]

Hi David and Nicole,

May I ask why when Treynor measure of a portfolio is greater than Treynor measure of market, then it means there will be positive alpha?

Thank you

 

[David Harper CFA FRM]

Hi @Unusualskill Yes, it will imply positive alpha. I recently added a youtube video that shows (at the link below) how the difference between the Treynor and the market's excess return is α/β. This is from Amenc.
It's simple and elegant: Jensen's α = R(p) - Rf - β*[R(m) - Rf] so that:

• α = R(p) - Rf - β*[R(m) - Rf],
• R(p) - Rf = α + β*[R(m) - Rf], dividing both side by β
  
• [R(p) - Rf/β = α/β + [R(m) - Rf], but the left term is the portfolio's Treynor so:
  
• T = α/β + [R(m) - Rf]. So the portfolio's Treynor exceeds the market's excess return (which is also necessarily the market's Treynor) by exactly α/β. Thanks!

 

[Unusualskill]

@David Harper CFA FRM Thank you! it is great.
If B(p) is negative, then alpha should be negative right? to have treynor(p) >treynor(market).