Treynor Ratio

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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

where:

## 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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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.

- <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

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