Treynor Ratio Calculator

What is the Treynor Ratio?

The Treynor Ratio (also known as the reward-to-volatility ratio) is a financial metric that measures the excess return generated by an investment portfolio per unit of systematic risk. It is named after Jack Treynor, an American economist who was one of the developers of the Capital Asset Pricing Model (CAPM).

Unlike the Sharpe Ratio, which uses standard deviation to measure total risk, the Treynor Ratio uses Beta (β) to measure systematic risk. Systematic risk represents market-wide risk that cannot be diversified away.

The Treynor Ratio Formula

The formula to calculate the Treynor Ratio is:

Where:

• T: The Treynor Ratio.
• R_p: The portfolio return (expressed as a percentage).
• R_f: The risk-free rate of return (such as the yield on government bonds, expressed as a percentage).
• β_p: The portfolio beta (a measure of systematic risk relative to the broader market).

Treynor Ratio vs. Sharpe Ratio

While both metrics analyze risk-adjusted returns, they use different measures of risk:

• Treynor Ratio: Uses Beta as the risk measure. It is best suited for well-diversified portfolios because it assumes that unsystematic (portfolio-specific) risk has been eliminated through diversification.
• Sharpe Ratio: Uses Standard Deviation as the risk measure, representing total risk. It is better suited for undiversified portfolios because it accounts for both systematic and unsystematic risk.

Interpretation of the Treynor Ratio

A higher Treynor Ratio is preferable, as it indicates that the portfolio manager has generated a higher return for each unit of systematic risk taken. A negative ratio can occur if the portfolio return is lower than the risk-free rate. However, a negative ratio is difficult to interpret and generally indicates poor performance.