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.

$T\; =\; \backslash frac\{r\_p\; -\; r\_f\}\{\backslash beta\}$

where

$T\; \backslash equiv$ Treynor ratio,

$r\_p\; \backslash equiv$ portfolio return,

$r\_f\; \backslash equiv$ riskfree rate

$\backslash beta\; \backslash equiv$ 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.

See also

• Modern portfolio theory
• Sortino ratio
• Upside potential ratio
• Sharpe ratio

Mathematical finance | Financial ratios

Treynor-Ratio