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The '''Treynor ratio''' (sometimes called the '''reward-to-volatility ratio''' or '''Treynor measure'''<ref>{{cite book|last=Brown|first=Keith C.|coauthors=Frank K. Reilly|title=Analysis of Investments and Management of Portfolios|publisher=Cengage Learning|edition=9th International|pages=941|chapter=25}}</ref>), named after [[Jack L. Treynor]],<ref>{{cite web|url=http://www.investopedia.com/terms/t/treynorratio.asp|title=Treynor Ratio|accessdate=20 February 2010}}</ref> is a measurement of the returns earned in excess of that which could have been earned on an [[investment]] that has no diversifiable risk (e.g., [[Treasury Bill]]s or a completely diversified portfolio), per each unit of market risk assumed.

The Treynor ratio relates [[excess return]] over the risk-free rate to the additional risk taken; however, systematic risk is used instead of total risk. The higher the Treynor ratio, the better the performance of the portfolio under analysis.

==Formula==
:<math>T = \frac{r_i - r_f}{\beta_i} </math>

where:

:<math>T \equiv</math> Treynor ratio,

:<math>r_i \equiv </math> portfolio ''i'''s return,

:<math>r_f \equiv </math> [[risk free rate]]

:<math>\beta_i \equiv </math> [[Beta coefficient|portfolio ''i'''s beta]]

==Limitations==
Like the [[Sharpe ratio]], the Treynor ratio (''T'') does not quantify the value added, if any, of [[active management|active portfolio management]]. It is a ranking criterion only. A ranking of portfolios based on the Treynor Ratio is only useful if the portfolios under consideration are sub-portfolios of a broader, fully diversified portfolio. If this is not the case, portfolios with identical [[systematic risk]], but different total risk, will be rated the same. But the portfolio with a higher total risk is less diversified and therefore has a higher unsystematic risk which is not priced in the market.

An alternative method of ranking portfolio management is [[Jensen's alpha]], which quantifies the added return as the excess return above the [[security market line]] in the [[capital asset pricing model]]. As these two methods both determine rankings based on systematic risk alone, they will rank portfolios identically.

==See also==
*[[Bias ratio (finance)]]
*[[Hansen-Jagannathan bound]]
*[[Jensen's alpha]]
*[[Modern portfolio theory]]
*[[Modigliani risk-adjusted performance]]
*[[Sharpe ratio]]
*[[Sortino ratio]]
*[[Upside potential ratio]]
*[[V2 ratio]]

==References==
{{Reflist}}

{{Financial ratios}}

[[Category:Financial ratios]]
[[Category:Statistical ratios]]

{{finance-stub}}

Projective line over a ring - Revision history

en>Rgdboer: /* Further reading */ restore cats, rmv re-sort template

en>Rgdboer: /* Notes and references */ Thas

en>Rgdboer: /* Instances */ lk GF(2)