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Treynor Ratio Calculator

A risk-adjusted performance measure based on systematic risk (Beta) rather than total risk.

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Treynor Ratio

Formula first

Overview

The Treynor Ratio measures the excess return earned per unit of systematic risk, as represented by beta. It is a performance metric that evaluates how well an investor is compensated for taking on risk that cannot be diversified away.

Symbols

Variables

T = Treynor Ratio, R_p = Portfolio Return, R_f = Risk-free Rate, \beta_p = Portfolio Beta

Treynor Ratio
Portfolio Return
Risk-free Rate
Portfolio Beta

Apply it well

When To Use

When to use: This ratio is best applied when evaluating well-diversified portfolios where unsystematic risk has been eliminated. It is specifically used to compare different portfolios or fund managers against a market benchmark to see who provided the best return relative to market volatility.

Why it matters: It allows investors to distinguish between returns generated through high-risk market exposure and returns generated through skilled management. By focusing only on beta, it provides a clearer picture of a portfolio's performance within the context of the broader market movement.

Avoid these traps

Common Mistakes

  • Confusing Beta with Standard Deviation (which is used in the Sharpe Ratio).
  • Using inconsistent time periods for the portfolio return and the risk-free rate.
  • Applying the ratio to undiversified portfolios where unsystematic risk is still significant.

One free problem

Practice Problem

An investment fund reports an annual return of 12% during a period where the risk-free rate is 3%. If the portfolio's beta is measured at 1.2, calculate the Treynor Ratio.

Portfolio Return0.12 0.08
Risk-free Rate0.03 0.01
Portfolio Beta1.2 0.8

Solve for:

Hint: Subtract the risk-free rate from the portfolio return to find the excess return before dividing by beta.

The full worked solution stays in the interactive walkthrough.

References

Sources

  1. Zvi Bodie, Alex Kane, Alan J. Marcus, Investments, McGraw-Hill Education
  2. Jack L. Treynor, How to Rate Management of Investment Funds, Harvard Business Review, 1965
  3. Wikipedia: Treynor ratio
  4. Bodie, Zvi; Kane, Alex; Marcus, Alan J. (2021). Investments (12th ed.). McGraw-Hill Education.
  5. Zvi Bodie, Alex Kane, Alan J. Marcus, Investments, 12th ed., McGraw-Hill Education, 2021
  6. University Finance — Portfolio Performance Measurement