How is the Treynor measure calculated?

The Treynor measure, also known as the reward-to-volatility ratio, is specifically calculated as the excess return of a portfolio over the risk-free rate divided by the portfolio's beta, which measures the portfolio's sensitivity to market movements. This calculation provides a way to assess how much excess return is generated per unit of systemic risk (market risk) that the portfolio takes on.

Using active returns divided by beta is an accurate representation of this relationship. The rationale behind the Treynor measure is to highlight the performance of a portfolio in relation to the risk that cannot be diversified away (systematic risk) instead of total risk, which would include unsystematic risk as well.

The other options do not correctly represent the Treynor measure. For instance, evaluating the excess return over the risk-free rate alone does not adjust for the level of risk taken by the portfolio; it only measures return without accounting for risk. Market return divided by portfolio volatility mischaracterizes the purpose of the Treynor measure, as it focuses on total risk rather than systematic risk. Lastly, overall returns adjusted for interest rate changes do not relate to the Treynor measure at all, as this calculation does not incorporate the portfolio's exposure to market risk.