Treynor ratio
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In finance, the Treynor reward-to-volatility model (sometimes called the reward-to-volatility ratio or Treynor measure[1]), named after American economist Jack L. Treynor,[2] is a measurement of the returns earned in excess of that which could have been earned on an investment that has no risk that can be diversified (e.g., Treasury bills or a completely diversified portfolio), per 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.
where is the Treynor ratio, is the return of portfolio , is the risk free rate, and is the beta of portfolio .
Example
Taking the equation detailed above, let us assume that the expected portfolio return is 20%, the risk free rate is 5%, and the beta of the portfolio is 1.5. Substituting these values, we get the following:
