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Treynor measure

Thread starter #1
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

David Harper CFA FRM
Staff member
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#2
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!
 
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