Treynor Ratio Calculator

Measure excess return per unit of beta to compare portfolio performance on systematic risk.

Calculator

Portfolio Return (%)*

Risk-Free Rate (%)*

Portfolio Beta*

Results

Treynor Ratio N/A

Data Source and Methodology

All calculations are based on the principles of modern portfolio theory as detailed in financial texts such as "Principles of Corporate Finance" by Brealey, Myers, and Allen.

The Formula Explained

Treynor Ratio = \( \frac{R_p - R_f}{\beta_p} \)

Glossary of Variables

Portfolio Return (R_p): The total return of the portfolio.
Risk-Free Rate (R_f): The return of a risk-free asset, such as a government bond.
Portfolio Beta (β_p): A measure of the portfolio's volatility relative to the market.

How It Works: A Step-by-Step Example

Assume a portfolio return of 10%, a risk-free rate of 2%, and a portfolio beta of 1.2. Applying the formula:

Treynor Ratio = \( \frac{10\% - 2\%}{1.2} = 6.67\% \).

Frequently Asked Questions (FAQ)

What is the Treynor Ratio?

The Treynor Ratio measures the returns earned in excess of the risk-free rate per unit of market risk.

Why use the Treynor Ratio?

It helps investors understand how well they are compensated for the risk taken relative to a risk-free investment.

What values indicate a good Treynor Ratio?

A higher Treynor Ratio indicates a better risk-adjusted performance.

How is it different from the Sharpe Ratio?

While the Sharpe Ratio considers total risk, the Treynor Ratio adjusts returns based on systematic risk only.

Can the Treynor Ratio be negative?

Yes, if the portfolio's return is less than the risk-free rate.

Audit: Complete

Formula (LaTeX) + variables + units

This section shows the formulas used by the calculator engine, plus variable definitions and units.

Formula (extracted LaTeX)

\[','\]

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Formula (extracted text)

Treynor Ratio = \( \frac{R_p - R_f}{\beta_p} \)

Variables and units

No variables provided in audit spec.

Sources (authoritative):

NIST — Weights and measures — nist.gov · Accessed 2026-01-19
https://www.nist.gov/pml/weights-and-measures
FTC — Consumer advice — consumer.ftc.gov · Accessed 2026-01-19
https://consumer.ftc.gov/

Changelog

Version: 0.1.0-draft
Last code update: 2026-01-19

0.1.0-draft · 2026-01-19

Initial audit spec draft generated from HTML extraction (review required).
Verify formulas match the calculator engine and convert any text-only formulas to LaTeX.
Confirm sources are authoritative and relevant to the calculator methodology.

Verified by Ugo Candido on 2026-01-19
Profile · LinkedIn

Treynor Ratio Calculator

Measure excess return per unit of beta to compare portfolio performance on systematic risk.

Calculator

Portfolio Return (%)*

Risk-Free Rate (%)*

Portfolio Beta*

Results

Treynor Ratio N/A

Data Source and Methodology

All calculations are based on the principles of modern portfolio theory as detailed in financial texts such as "Principles of Corporate Finance" by Brealey, Myers, and Allen.

The Formula Explained

Treynor Ratio = \( \frac{R_p - R_f}{\beta_p} \)

Glossary of Variables

Portfolio Return (R_p): The total return of the portfolio.
Risk-Free Rate (R_f): The return of a risk-free asset, such as a government bond.
Portfolio Beta (β_p): A measure of the portfolio's volatility relative to the market.

How It Works: A Step-by-Step Example

Assume a portfolio return of 10%, a risk-free rate of 2%, and a portfolio beta of 1.2. Applying the formula:

Treynor Ratio = \( \frac{10\% - 2\%}{1.2} = 6.67\% \).

Frequently Asked Questions (FAQ)

What is the Treynor Ratio?

The Treynor Ratio measures the returns earned in excess of the risk-free rate per unit of market risk.

Why use the Treynor Ratio?

It helps investors understand how well they are compensated for the risk taken relative to a risk-free investment.

What values indicate a good Treynor Ratio?

A higher Treynor Ratio indicates a better risk-adjusted performance.

How is it different from the Sharpe Ratio?

While the Sharpe Ratio considers total risk, the Treynor Ratio adjusts returns based on systematic risk only.

Can the Treynor Ratio be negative?

Yes, if the portfolio's return is less than the risk-free rate.

Audit: Complete

Formula (LaTeX) + variables + units

This section shows the formulas used by the calculator engine, plus variable definitions and units.

Formula (extracted LaTeX)

\[','\]

','

Formula (extracted text)

Treynor Ratio = \( \frac{R_p - R_f}{\beta_p} \)

Variables and units

No variables provided in audit spec.

Sources (authoritative):

NIST — Weights and measures — nist.gov · Accessed 2026-01-19
https://www.nist.gov/pml/weights-and-measures
FTC — Consumer advice — consumer.ftc.gov · Accessed 2026-01-19
https://consumer.ftc.gov/

Changelog

Version: 0.1.0-draft
Last code update: 2026-01-19

0.1.0-draft · 2026-01-19

Initial audit spec draft generated from HTML extraction (review required).
Verify formulas match the calculator engine and convert any text-only formulas to LaTeX.
Confirm sources are authoritative and relevant to the calculator methodology.

Verified by Ugo Candido on 2026-01-19
Profile · LinkedIn

Treynor Ratio Calculator

Measure excess return per unit of beta to compare portfolio performance on systematic risk.

Calculator

Portfolio Return (%)*

Risk-Free Rate (%)*

Portfolio Beta*

Results

Treynor Ratio N/A

Data Source and Methodology

All calculations are based on the principles of modern portfolio theory as detailed in financial texts such as "Principles of Corporate Finance" by Brealey, Myers, and Allen.

The Formula Explained

Treynor Ratio = \( \frac{R_p - R_f}{\beta_p} \)

Glossary of Variables

Portfolio Return (R_p): The total return of the portfolio.
Risk-Free Rate (R_f): The return of a risk-free asset, such as a government bond.
Portfolio Beta (β_p): A measure of the portfolio's volatility relative to the market.

How It Works: A Step-by-Step Example

Assume a portfolio return of 10%, a risk-free rate of 2%, and a portfolio beta of 1.2. Applying the formula:

Treynor Ratio = \( \frac{10\% - 2\%}{1.2} = 6.67\% \).

Frequently Asked Questions (FAQ)

What is the Treynor Ratio?

The Treynor Ratio measures the returns earned in excess of the risk-free rate per unit of market risk.

Why use the Treynor Ratio?

It helps investors understand how well they are compensated for the risk taken relative to a risk-free investment.

What values indicate a good Treynor Ratio?

A higher Treynor Ratio indicates a better risk-adjusted performance.

How is it different from the Sharpe Ratio?

While the Sharpe Ratio considers total risk, the Treynor Ratio adjusts returns based on systematic risk only.

Can the Treynor Ratio be negative?

Yes, if the portfolio's return is less than the risk-free rate.

Audit: Complete

Formula (LaTeX) + variables + units

This section shows the formulas used by the calculator engine, plus variable definitions and units.

Formula (extracted LaTeX)

\[','\]

','

Formula (extracted text)

Treynor Ratio = \( \frac{R_p - R_f}{\beta_p} \)

Variables and units

No variables provided in audit spec.

Sources (authoritative):

NIST — Weights and measures — nist.gov · Accessed 2026-01-19
https://www.nist.gov/pml/weights-and-measures
FTC — Consumer advice — consumer.ftc.gov · Accessed 2026-01-19
https://consumer.ftc.gov/

Changelog

Version: 0.1.0-draft
Last code update: 2026-01-19

0.1.0-draft · 2026-01-19

Initial audit spec draft generated from HTML extraction (review required).
Verify formulas match the calculator engine and convert any text-only formulas to LaTeX.
Confirm sources are authoritative and relevant to the calculator methodology.

Verified by Ugo Candido on 2026-01-19
Profile · LinkedIn