Treynor Ratio Calculator — Risk-Adjusted Return
Calculate the Treynor Ratio to measure risk-adjusted portfolio returns using beta.
Compare portfolio performance per unit of market risk.
What Is the Treynor Ratio?
The Treynor Ratio measures how much excess return a portfolio earns for each unit of market risk (measured by beta).
Think of it like miles per gallon for your car. A car that gets 40 MPG is more efficient than one that gets 20 MPG — you get more distance per gallon of fuel. Similarly, a higher Treynor Ratio means you are getting more return per unit of risk.
It was developed by Jack Treynor, one of the founders of modern portfolio theory, in the 1960s.
The Formula
Treynor Ratio = (Rp - Rf) / Beta
Where:
- Rp = Portfolio return (what your portfolio actually earned)
- Rf = Risk-free rate (what you would earn with zero risk, like Treasury bills)
- Rp - Rf = Excess return (the “extra” return above the safe rate)
- Beta = Portfolio beta (sensitivity to market movements)
Treynor Ratio vs. Sharpe Ratio
These two ratios are cousins — they both measure risk-adjusted return, but they define “risk” differently:
| Feature | Treynor Ratio | Sharpe Ratio |
|---|---|---|
| Risk measure | Beta (market risk only) | Standard deviation (total risk) |
| Best for | Diversified portfolios | Any portfolio |
| Ignores | Unsystematic risk (company-specific) | Nothing — captures all risk |
| Formula | (Rp - Rf) / Beta | (Rp - Rf) / StdDev |
When to use which?
- If your portfolio is well-diversified (like an index fund plus some active picks), use the Treynor Ratio — because diversification has already eliminated most company-specific risk.
- If your portfolio is concentrated (just a few stocks), use the Sharpe Ratio — because company-specific risk matters.
Worked Example
Suppose:
- Portfolio return: 14%
- Risk-free rate: 4%
- Portfolio beta: 1.1
Treynor Ratio = (14% - 4%) / 1.1 = 10% / 1.1 = 9.09
Now compare this to another portfolio:
- Portfolio return: 18%
- Risk-free rate: 4%
- Portfolio beta: 1.8
Treynor Ratio = (18% - 4%) / 1.8 = 14% / 1.8 = 7.78
Even though Portfolio B earned a higher return (18% vs. 14%), Portfolio A has a better Treynor Ratio (9.09 vs. 7.78). Portfolio A delivered more return per unit of risk taken. It was the more efficient portfolio.
How to Interpret the Treynor Ratio
| Treynor Ratio | Interpretation |
|---|---|
| Higher is better | More excess return per unit of market risk |
| Positive | Portfolio outperformed the risk-free rate |
| Zero | Portfolio matched the risk-free rate (no excess return for the risk taken) |
| Negative | Portfolio underperformed the risk-free rate (lost money on a risk-adjusted basis) |
There is no universal “good” number — the Treynor Ratio is most useful for comparing portfolios or fund managers to each other.
Understanding Beta Deeper
| Beta | What It Means | Example |
|---|---|---|
| 0.5 | Half as volatile as the market | Defensive stocks, utilities |
| 1.0 | Moves exactly with the market | S&P 500 index fund |
| 1.5 | 50% more volatile than the market | Growth stocks, tech sector |
| 2.0 | Twice as volatile as the market | Leveraged funds, volatile sectors |
A portfolio with a beta of 1.5 is expected to go up 15% when the market goes up 10%, but also drop 15% when the market drops 10%. The Treynor Ratio asks: for that extra volatility, are you being properly compensated?
Where to Find the Inputs
| Input | Source |
|---|---|
| Portfolio Return | Your brokerage account performance summary |
| Risk-free Rate | US 10-year Treasury yield or 3-month T-bill rate |
| Portfolio Beta | Weighted average of individual stock betas (your broker may calculate this) |
Limitations
- Beta is based on historical data and may not predict future sensitivity
- Assumes the portfolio is well-diversified (otherwise, use the Sharpe Ratio instead)
- A negative beta makes the ratio difficult to interpret
- Does not account for the magnitude of the portfolio — two portfolios can have the same Treynor Ratio but very different dollar amounts at risk