Treynor ratio

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Description:
The Treynor ratio (sometimes called the reward-to-volatility ratio or Treynor measure), named after Jack L. Treynor, 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 Bills 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 </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> portfolio i's beta


Limitations

Like the Sharpe ratio, the Treynor ratio (T) does not quantify the value added, if any, of 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...
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