Treynor vs Sharpe

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hoan0106

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Can someone please explain in which situations you would use one over the other? I know Treynor is a measure of excess return per unit of systematic risk and sharpe is the same per total risk, but I’m not all that clear on the conditions for using them.
Thanks
 
If you have a well-diversified portfolio, then Treynor would be better (but would probably agree with Sharpe anyway).
If you don’t have a well-diversified portfolio, then Sharpe is better since it measures return vs. total risk, not just systematic - and in this scenario would end up not agreeing with Treynor
 
also if portfolio A scores higher on Treynor measure than portfolio B (i.e., it has higher return per unit of systematic risk as measured by beta) and portfolio A scores lower on Sharpe ratio than portfolio B (i.e., it has lower return per unit of total risk as measured by Std); it mostly likely means that portfolio A has larger unsystematic risk, which implies that it is less diversified
 
Suppose you want to add assets A, B to a well diversified portfolio. If treynor of A is higher than B, while Sharpe ratio of B is higher than A –> would you still pick A as the better choice?
If nothing is mentioned about level of diversification of current p/f, I assume Sharpe will over-rule Treynor, in case of conflicts?
- BN
 
it can actually be debated, so it is not a clear cut situation where one ratio dominates
you can argue that if your current portfolio is well diversified, even though A has high unsystematic risk (as implied by this example), this unsystematic risk may not be that big of an issue, since it will be diversified once it is included into well diversified portfolio, and in this case you would actually may go with Treynor measure, which tells you that A will have higher expected return per unit of systematic risk
 
I was just reading this stuff in Stalla, and my impression is that if your portfolio strategy involves using a substantial amount of non-systematic risk compared to systematic risk (say, a market neutral strategy), then Treynor is not so good, because beta will be low and it will tend to underestimate the true amount of risk you are taking. However, if you are well diversified and aren’t banking on non-systematic risk, Treynor is good to use.
The main advantage of Treynor (thank you Stalla), is that it is much easier to compute the beta of a portfolio (weighted average of betas of the components), than to compute the standard deviation of a portfolio, particularly if the portfolio has a short history. Therefore it is simpler to compute Treynor and not deal with Sharpe so much unless you have a long enough history to generate historical standard deviations.
But what about this M^2 measure. As far as I can tell, it’s just Sharpe reformulated. It’s nifty and all to see on a chart, but why would one use it (other than CFAI asks for it)?
 
if it’s a market neutral strategy, how would you be able to use Treynor (with 0 beta)? bchadwick
 
^– That’s my point. I used market neutral as an extreme case of where you are taking on primarily non-systematic risks and Treynor fails. But you could have a long-short fund that has a non-zero beta and still isn’t so good to use with Treynor.
 
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