Treynor ratio

The higher the Treynor ratio, the better the performance of the portfolio under analysis.

Therefore, all assets should have a Treynor ratio less than or equal to that of the market.

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.

All of the portfolios on the SML have the same Treynor ratio as does the market portfolio, i.e.

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

In fact, the slope of the SML is the Treynor ratio of the market portfolio since .

Sharpe ratios, along with Treynor ratios and Jensen's alphas, are often used to rank the performance of portfolio or mutual fund managers.

While the Treynor ratio works only with systemic risk of a portfolio, the Sharpe ratio observes both systemic and idiosyncratic risks.

Nevertheless, Alpha is still widely used to evaluate mutual fund and portfolio manager performance, often in conjunction with the Sharpe ratio and the Treynor ratio.

These downsides apply to all risk-adjusted return measures that are ratios (e.g., Sortino ratio, Treynor ratio, Upside-potential ratio, etc.).

A stock picking rule of thumb for assets with positive beta is to buy if the Treynor ratio is above the SML and sell if it is below (see figure above).

In consequence, if there is an asset whose Treynor ratio is bigger than the market's then this asset gives more return for unity of systematic risk (i.e. beta), which contradicts the efficient market hypothesis.