Treynor Ratio Calculator

Risk-Adjusted Return Analysis

Calculate the Treynor ratio to evaluate portfolio performance relative to systematic risk (beta). This metric helps investors assess risk-adjusted returns by considering market risk premium.

Example Calculations

Try these examples to understand how the Treynor ratio works

Conservative Portfolio

Conservative Portfolio

Low-risk portfolio with moderate returns

Portfolio Return: 8.5 %

Risk-Free Rate: 2 %

Portfolio Beta: 0.8 ratio

Balanced Portfolio

Balanced Portfolio

Moderate risk and return portfolio

Portfolio Return: 12 %

Risk-Free Rate: 2 %

Portfolio Beta: 1 ratio

Aggressive Portfolio

Aggressive Portfolio

High-risk, high-return portfolio

Portfolio Return: 18 %

Risk-Free Rate: 2 %

Portfolio Beta: 1.5 ratio

Market Portfolio

Market Portfolio

Portfolio that tracks the market index

Portfolio Return: 10 %

Risk-Free Rate: 2 %

Portfolio Beta: 1 ratio

Other Titles
Understanding Treynor Ratio: A Comprehensive Guide
Learn how to calculate and interpret the Treynor ratio for better investment decisions

What is the Treynor Ratio?

  • Definition and Purpose
  • Key Components
  • Historical Context
The Treynor ratio, developed by Jack Treynor in 1965, is a financial metric that measures the risk-adjusted return of an investment portfolio. It evaluates how much excess return a portfolio generates for each unit of systematic risk (beta) it assumes.
Core Concept
Unlike the Sharpe ratio which uses total risk (standard deviation), the Treynor ratio focuses specifically on systematic risk measured by beta. This makes it particularly useful for well-diversified portfolios where unsystematic risk has been eliminated.
Mathematical Foundation
The ratio is based on the Capital Asset Pricing Model (CAPM) and assumes that investors are only compensated for bearing systematic risk, not diversifiable risk.

Interpretation Examples

  • A Treynor ratio of 0.15 means the portfolio generates 15% excess return per unit of systematic risk
  • Higher ratios indicate better risk-adjusted performance relative to market risk

Step-by-Step Guide to Using the Treynor Ratio Calculator

  • Input Requirements
  • Calculation Process
  • Result Interpretation
Using our Treynor ratio calculator is straightforward. You need three key inputs: portfolio return, risk-free rate, and portfolio beta. The calculator will automatically compute the excess return and Treynor ratio.
Required Inputs
Portfolio Return: The total return of your investment portfolio, typically expressed as an annual percentage. Risk-Free Rate: The return on a risk-free investment like Treasury bills. Portfolio Beta: A measure of systematic risk relative to the market.
Calculation Steps
1. Calculate excess return: Portfolio Return - Risk-Free Rate. 2. Divide excess return by portfolio beta. 3. The result is the Treynor ratio, expressed as a decimal or percentage.

Calculation Examples

  • Portfolio Return: 12%, Risk-Free Rate: 2%, Beta: 1.2 → Treynor Ratio = (12-2)/1.2 = 8.33
  • Portfolio Return: 8%, Risk-Free Rate: 2%, Beta: 0.8 → Treynor Ratio = (8-2)/0.8 = 7.5

Real-World Applications of the Treynor Ratio

  • Portfolio Management
  • Investment Analysis
  • Performance Evaluation
The Treynor ratio is widely used in professional portfolio management and investment analysis. It helps fund managers, financial advisors, and individual investors make informed decisions about portfolio allocation and performance evaluation.
Portfolio Comparison
Investors can compare different portfolios or investment strategies using the Treynor ratio. A higher ratio indicates better risk-adjusted performance relative to market risk, making it easier to choose between competing investment options.
Performance Attribution
The ratio helps identify whether a portfolio's performance is due to superior stock selection or simply taking on more systematic risk. This is crucial for understanding the source of investment returns.

Practical Applications

  • Comparing mutual funds with different risk profiles
  • Evaluating hedge fund performance relative to market risk

Common Misconceptions and Correct Methods

  • Misinterpretation of Results
  • Inappropriate Comparisons
  • Data Quality Issues
Several misconceptions surround the use of the Treynor ratio. Understanding these pitfalls is essential for proper interpretation and application of this financial metric.
Beta Assumptions
A common mistake is assuming that beta remains constant over time. In reality, beta can change as market conditions and portfolio composition evolve. Regular recalculation is necessary for accurate analysis.
Risk-Free Rate Selection
The choice of risk-free rate can significantly impact results. It should match the investment horizon and currency of the portfolio. Using inappropriate risk-free rates can lead to misleading conclusions.

Common Mistakes

  • Using a 3-month Treasury rate for a 10-year investment horizon
  • Comparing ratios calculated with different risk-free rates

Mathematical Derivation and Examples

  • Formula Derivation
  • Advanced Calculations
  • Statistical Considerations
The Treynor ratio formula is derived from the Capital Asset Pricing Model (CAPM). It represents the slope of the Security Market Line (SML) for a specific portfolio, indicating the risk-adjusted return premium.
Mathematical Formula
Treynor Ratio = (Rp - Rf) / βp where Rp is portfolio return, Rf is risk-free rate, and βp is portfolio beta. This formula measures excess return per unit of systematic risk.
Statistical Properties
The ratio assumes normal distribution of returns and stable beta over time. It's most reliable for well-diversified portfolios where unsystematic risk is minimal.

Mathematical Examples

  • For a portfolio with 15% return, 3% risk-free rate, and beta of 1.1: Treynor Ratio = (15-3)/1.1 = 10.91
  • A negative ratio indicates the portfolio underperformed the risk-free rate on a risk-adjusted basis