Ranking portfolios

[wrongsaidfred]

Hi David,

This may be another dumb question, but if the Shapre ratio is used for comparing portfolios that are not well diversified and Jensens alpha is used for comparing portfolios with similar betas, does this mean that the Treynor ratio is just used to compare well diversified portfolios with much different betas?

Thanks,
Mike

 

[David Harper CFA FRM]

Hi Mike,

The theory is, as you suggest in the first statement, in my summary view: if the portfolio is well-diversified, you only need the Jensen's or Treynor because your diversification eliminates all idiosyncratic (specific) risk so it counts for zero, and your only risk is the beta exposure to the single common factor (the market risk premium). That's two big assumptions, in my book: that diversification sends everything else to zero, and (as usual with the CAPM, it's glaring weakness) that ERP/MRP is the only common factor risk. It doesn't surprise me that I perceive Sharpe to be popular but I'm not sure where Treynor is actually used in practice?

With respect to Treynor vs. Jensen's, the party line from assigned Amenc is:

Treynor: Usage:

• Ranking portfolios with different levels of risk
• Well-diversified portfolios
• Portfolios that constitute part of an individual’s personal wealth

Jensen Usage:

• Portfolios with the same beta

... I guess that's the answer ...

But I never got the difference. Mathwise, they are both simple applications of the same exact CAPM. For an efficient portfolio (i.e., expected alpha = 0), far as i can tell:

• ex ante E[Jensen's alpha] = 0; it should be noted the Jensen's alpha is, by design, an ex post measure
• ex ante E[Treynor] = MRP; given this, it seems to me Treynor is really intended as ex post also, but i don't perceive that claim

To me, Jensen's is true difference and Treynor is a ratio: as the portfolio outperforms, it is reflected in higher Jensen's alpha (in % terms) and a higher Treynor ratio. I can't see the difference frankly as more than formatting! Ergo, I can't really see the application difference.

Thanks, David

 

[wrongsaidfred]

Thanks again and sorry for all of the recent questions. I know you are really busy and I truly apreciate it.

Thanks,
Mike

 

[David Harper CFA FRM]

Hi Mike,

It's okay, it takes a lot of time truly, but in your case the reason i can't so far object is that an uncanny percentage of your questions/comments are either (i) useful corrections to errors or imprecisions or (ii) really insightful questions that sometime tax my understanding of concepts i've had years to study... my Advisor disagrees strongly with my "tolerance" in the forum, but this is how i stay sharp and get sharper so .... (but I may not be able to keep up as the exam approaches and volume tends to increase)

thanks, David

 

[wrongsaidfred]

I completely understand.

Thanks again,
Mike