Treynor ratio

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The Treynor ratio is a measurement of the returns earned in excess of that which could have been earned on a riskless investment (i.e. Treasury Bill) (per each unit of market risk assumed).

The Treynor ratio (sometimes called reward-to-volatility ratio) relates excess return over the risk-free rate to the additional risk taken; however systematic risk instead of total risk is used. The higher the Treynor ratio, the better the performance under analysis.

T = \frac{r_p - r_f}{\beta}

where

T \equiv Treynor ratio,
r_p \equiv portfolio return,
r_f \equiv risk free rate
\beta \equiv portfolio beta

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 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.

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