Treynor Ratio Calculator
Use this tool to calculate the Treynor Ratio for a portfolio or asset. The Treynor Ratio measures the excess return earned per unit of systemic risk (Beta).
Enter the Portfolio Return, the Risk-Free Rate, and the Portfolio's Beta. Ensure all values are in decimal form (e.g., 0.10 for 10%).
Enter Investment Data
Understanding the Treynor Ratio & Formula
What is the Treynor Ratio?
The Treynor Ratio, developed by Jack Treynor, is a risk-adjusted measure of return. It is defined as the excess return generated by a portfolio over the risk-free rate, divided by the portfolio's beta. It tells you how much return a portfolio generated for each unit of *systemic risk* taken.
Systemic risk (or market risk) is the risk inherent to the entire market or market segment. Unlike unsystematic risk (specific to an individual asset), systemic risk cannot be diversified away.
Treynor Ratio Formula
The formula is:
Treynor Ratio = (Rp - Rf) / βp
Where:
- Rp = Portfolio Return
- Rf = Risk-Free Rate
- βp = Portfolio Beta
The numerator (Rp - Rf) is the "excess return" or "risk premium" of the portfolio.
Interpretation
A higher Treynor Ratio is generally preferred, as it indicates that the portfolio is generating more excess return per unit of systemic risk. When comparing two portfolios, the one with the higher Treynor Ratio performed better on a systemic-risk-adjusted basis.
The Treynor Ratio is best used to evaluate well-diversified portfolios, as Beta only accounts for systemic risk. For undiversified portfolios or single assets, the Sharpe Ratio (which uses total risk measured by standard deviation) might be more appropriate.
Treynor Ratio Examples
Here are 10 examples demonstrating how to calculate the Treynor Ratio:
Example 1: Standard Scenario
Inputs: Portfolio Return = 0.12 (12%), Risk-Free Rate = 0.03 (3%), Portfolio Beta = 1.1
Calculation: (0.12 - 0.03) / 1.1 = 0.09 / 1.1 ≈ 0.0818
Result: Treynor Ratio = 0.0818
Example 2: Lower Beta, Similar Performance vs. Market
Inputs: Portfolio Return = 0.09 (9%), Risk-Free Rate = 0.03 (3%), Portfolio Beta = 0.6
Calculation: (0.09 - 0.03) / 0.6 = 0.06 / 0.6 = 0.1000
Result: Treynor Ratio = 0.1000 (Higher than Ex. 1, despite lower return, due to much lower beta)
Example 3: High Return, High Beta
Inputs: Portfolio Return = 0.20 (20%), Risk-Free Rate = 0.04 (4%), Portfolio Beta = 1.5
Calculation: (0.20 - 0.04) / 1.5 = 0.16 / 1.5 ≈ 0.1067
Result: Treynor Ratio = 0.1067
Example 4: Portfolio Return Equals Risk-Free Rate
Inputs: Portfolio Return = 0.05 (5%), Risk-Free Rate = 0.05 (5%), Portfolio Beta = 0.8
Calculation: (0.05 - 0.05) / 0.8 = 0 / 0.8 = 0.0000
Result: Treynor Ratio = 0.0000
Example 5: Portfolio Return Less Than Risk-Free Rate
Inputs: Portfolio Return = 0.02 (2%), Risk-Free Rate = 0.04 (4%), Portfolio Beta = 0.9
Calculation: (0.02 - 0.04) / 0.9 = -0.02 / 0.9 ≈ -0.0222
Result: Treynor Ratio = -0.0222 (Negative ratio indicates underperformance relative to risk-free rate)
Example 6: Beta is Exactly 1 (Like the Market)
Inputs: Portfolio Return = 0.10 (10%), Risk-Free Rate = 0.03 (3%), Portfolio Beta = 1.0
Calculation: (0.10 - 0.03) / 1.0 = 0.07 / 1.0 = 0.0700
Result: Treynor Ratio = 0.0700 (This represents the market's risk premium per unit of market risk)
Example 7: High Risk-Free Rate Environment
Inputs: Portfolio Return = 0.15 (15%), Risk-Free Rate = 0.06 (6%), Portfolio Beta = 1.2
Calculation: (0.15 - 0.06) / 1.2 = 0.09 / 1.2 = 0.0750
Result: Treynor Ratio = 0.0750
Example 8: Very High Return, Moderate Beta
Inputs: Portfolio Return = 0.30 (30%), Risk-Free Rate = 0.04 (4%), Portfolio Beta = 1.1
Calculation: (0.30 - 0.04) / 1.1 = 0.26 / 1.1 ≈ 0.2364
Result: Treynor Ratio = 0.2364 (High ratio due to significant outperformance)
Example 9: Low Return, Very Low Beta
Inputs: Portfolio Return = 0.04 (4%), Risk-Free Rate = 0.02 (2%), Portfolio Beta = 0.5
Calculation: (0.04 - 0.02) / 0.5 = 0.02 / 0.5 = 0.0400
Result: Treynor Ratio = 0.0400
Example 10: Market Underperforms Risk-Free Rate (Rare/Theoretical)
Inputs: Portfolio Return = 0.02 (2%), Risk-Free Rate = 0.03 (3%), Portfolio Beta = 1.0
Calculation: (0.02 - 0.03) / 1.0 = -0.01 / 1.0 = -0.0100
Result: Treynor Ratio = -0.0100 (A negative market Treynor Ratio indicates a rare period of overall market decline below the risk-free asset)
Frequently Asked Questions about the Treynor Ratio
1. What does the Treynor Ratio measure?
It measures the amount of return a portfolio earned above the risk-free rate, per unit of its systemic risk (measured by Beta). It's a risk-adjusted performance metric focusing only on market risk.
2. How is Beta different from Standard Deviation?
Beta measures *systemic risk* (market risk) – how much a portfolio's returns tend to move with the overall market. Standard Deviation measures *total risk* – the overall volatility or dispersion of a portfolio's returns, including both systemic and unsystematic (specific) risk.
3. When should I use the Treynor Ratio versus the Sharpe Ratio?
The Treynor Ratio is more appropriate for evaluating well-diversified portfolios, as unsystematic risk is assumed to be diversified away, leaving Beta as the primary risk measure. The Sharpe Ratio is better for evaluating individual assets or undiversified portfolios where total risk (standard deviation) is a more relevant concern.
4. What is a "good" Treynor Ratio?
There's no single "good" number; it's a comparative measure. A higher Treynor Ratio is better when comparing it to other portfolios or the market itself over the same period. It indicates better performance for the level of systemic risk taken.
5. Why must Beta be greater than zero for this calculator?
The formula involves division by Beta. Division by zero is undefined. While negative Beta exists for assets that move inversely to the market, calculating a ratio per unit of positive market risk becomes less standard or meaningful in that context, and it's often excluded in basic ratio calculations.
6. What is the Risk-Free Rate?
It's the theoretical return of an investment with zero risk. In practice, the yield on a short-term government bond (like a Treasury Bill) of comparable duration to the investment period is commonly used as a proxy.
7. Can the Treynor Ratio be negative?
Yes. If the portfolio's return (Rp) is less than the risk-free rate (Rf), the numerator will be negative, resulting in a negative Treynor Ratio (assuming a positive Beta). This indicates the portfolio underperformed the risk-free asset on a systemic-risk-adjusted basis.
8. How do I find the Portfolio Return and Beta?
Portfolio return is calculated based on the change in the portfolio's value over a specific period, plus any income (dividends, interest). Portfolio Beta requires statistical analysis (regression) comparing the portfolio's historical returns to the returns of a relevant market index over the same period. Financial data providers or investment platforms often calculate Beta for you.
9. Is the Treynor Ratio a forward-looking metric?
No, the Treynor Ratio is based on historical data (past returns and Beta). It is used to evaluate *past* performance. It does not predict future returns or risk.
10. Does a high Treynor Ratio mean a portfolio manager is skilled?
A high ratio *can* suggest skill in generating returns relative to market risk, but it's not definitive proof. It's one metric among many (like Alpha, Sharpe Ratio, Information Ratio) used to evaluate performance, and its value can be influenced by the specific time period analyzed and the benchmark used for Beta calculation.
