Treynor Ratio Calculator
Reviewed by Hamza Gujjar, Algorithm Architect & Software Developer
Last updated: August 19, 2026Rewarding Return Per Unit of Market Risk
Two portfolios can post the same return while carrying very different amounts of market risk. The Treynor ratio strips that difference out by measuring excess return — return above the risk-free rate — per unit of beta, the portfolio's sensitivity to market moves. Unlike the Sharpe ratio, which divides by total volatility, Treynor isolates systematic (market) risk specifically, making it the more relevant tool for a diversified portfolio where unsystematic risk has already been diversified away.
The Formula
Rp is the portfolio's return, Rf is the risk-free rate over the same period, and Beta is the portfolio's beta relative to the market.
Where This Matters
- Comparing diversified portfolios — among portfolios that hold enough positions to have diversified away individual-stock risk, Treynor isolates who is being paid best for the market risk that remains.
- Manager evaluation — a manager running a high-beta portfolio needs a proportionally higher return just to match a lower-beta competitor's Treynor ratio; the metric adjusts for that automatically.
- Asset allocation decisions — ranking candidate portfolios by Treynor ratio rather than raw return avoids favoring a portfolio that simply took on more market risk.
| Input | Value |
|---|---|
| Portfolio return | 12% |
| Risk-free rate | 3% |
| Beta | 1.1 |
| Treynor Ratio | 8.18 |
(12% − 3%) ÷ 1.1 = 8.18. Interpreted as excess return per unit of market risk, higher values indicate better compensation for beta exposure taken.
How to Use This Calculator
- Enter the portfolio's return over the period as a percentage.
- Enter the risk-free rate over the same period (commonly a short-term Treasury yield).
- Enter the portfolio's beta.
- Select Calculate to get the Treynor ratio.
Related Calculations
See the Sortino Ratio Calculator for a downside-risk-focused alternative, or the Portfolio Beta Calculator to derive the beta input from individual holdings.
Principles of the Treynor Ratio and Systematic Risk Efficiency
Developed by American economist Jack L. Treynor in 1965, the Treynor Ratio (also called the reward-to-volatility ratio) is a foundational performance metric that evaluates the excess return generated by an investment portfolio per unit of systematic, non-diversifiable risk (Beta, β).
Where Rp is portfolio return, Rf is the risk-free rate, and βp is the portfolio's systematic beta relative to the market index.
Treynor Ratio versus Sharpe Ratio: Key Methodological Differences
| Characteristic | Treynor Ratio | Sharpe Ratio |
|---|---|---|
| Risk Denominator | Systematic Risk (Beta, β) | Total Volatility (Standard Deviation, σ) |
| Underlying Premise | Assumes unsystematic risk has been diversified away | Penalizes all volatility, diversifiable and non-diversifiable |
| Best Application | Evaluating sub-funds to add to an already diversified portfolio | Evaluating a standalone total-wealth portfolio |
| Unit of Output | Excess percentage return per unit of market beta | Excess percentage return per unit of standard deviation |
When to Use the Treynor Ratio
The Treynor Ratio is the preferred analytical tool for multi-manager institutional pension funds and endowment allocators. When an endowment trustee evaluates 10 competing sector-specialist equity managers to integrate into a well-diversified global multi-billion-dollar fund, idiosyncratic stock-picking volatility will be diversified away across the broader multi-manager portfolio. Therefore, managers should be ranked strictly by their excess return generated per unit of unavoidable systematic market risk (Beta).
Step-by-Step Worked Calculation Example
Example: Comparing Two Active Mutual Funds Using the Treynor Ratio
Problem: An investment committee evaluates two mutual funds to add to a well-diversified sovereign wealth fund. Fund A achieved an annualized return of 13.50% with a portfolio beta of 0.85. Fund B achieved an annualized return of 16.20% with a portfolio beta of 1.40. The prevailing risk-free rate is 3.50%. Calculate the Treynor Ratio for both funds and determine which manager utilized systematic risk more efficiently.
Step 1: Calculate Fund A Treynor Ratio:
Excess ReturnA = 13.50% - 3.50% = 10.00%
Treynor RatioA = 10.00% / 0.85 = 11.76% per unit of Beta
Step 2: Calculate Fund B Treynor Ratio:
Excess ReturnB = 16.20% - 3.50% = 12.70%
Treynor RatioB = 12.70% / 1.40 = 9.07% per unit of Beta
Conclusion: Fund A generated 11.76% excess return per unit of systematic risk, significantly outperforming Fund B (9.07%). Fund B's higher nominal return (16.2% vs. 13.5%) was achieved merely by taking on aggressive leveraged market beta (1.40) rather than superior systematic risk efficiency.
Common Pitfalls in Treynor Ratio Analysis
- Applying Treynor to Undiversified Portfolios: If an investor holds only a single stock or concentrated sector fund, the Treynor Ratio completely ignores massive idiosyncratic firm-specific risks that could wipe out investor capital.
- Negative Beta Distortions: For inverse or dedicated market-hedging funds with negative betas (β < 0), the mathematical sign of the Treynor ratio reverses, rendering simple ranking comparisons misleading.
The Security Market Line (SML) and Treynor Slope Geometry
In Capital Asset Pricing Model (CAPM) geometry, the Security Market Line (SML) plots expected return on the vertical Y-axis against systematic risk (Beta, β) on the horizontal X-axis. The SML connects the risk-free rate intercept (Rf, at β = 0) with the broad market portfolio (Rm, at β = 1.0).
Geometrically, the Treynor Ratio represents the exact mathematical slope of the line connecting the risk-free rate to the plotted portfolio coordinates:
Any investment portfolio that plots strictly above the Security Market Line exhibits a Treynor Ratio greater than the market risk premium [ (Rm - Rf) / 1.0 ], confirming that the investment delivers superior systematic risk-adjusted efficiency compared to the broader market index.
Multi-Period Geometric Treynor Compounding
For long-term track records, institutional analysts compute the Geometric Treynor Ratio by substituting the arithmetic mean return with the Compound Annual Growth Rate (CAGR): Treynorgeo = (CAGRp - CAGRrf) / βp, eliminating the positive bias introduced by volatile multi-year return swings.
Multi-Factor Treynor Generalizations
In contemporary multi-factor institutional equity management, the classical single-beta Treynor Ratio is generalized to multi-factor risk exposures:
This multi-dimensional formulation isolates whether a fundamental equity manager is generating excess returns beyond compensation for value, size, momentum, and quality systematic factor loadings, providing sovereign wealth funds with a comprehensive framework for multi-manager performance attribution.
Treynor-Black Model and Active Portfolio Weighting
The Treynor-Black portfolio construction model divides total capital between a passively indexed market portfolio and an active security selection portfolio. By weighting individual stocks proportional to their alpha-to-residual-variance ratio (αi / σ2(εi)), the model maximizes overall portfolio Sharpe and Treynor ratios.
Benchmark Market Index Selection in Treynor Attribution
Accurate Treynor analysis requires matching the benchmark index to the asset class (e.g., MSCI Emerging Markets for international funds) to ensure Beta accurately reflects relevant systematic market risk.