What Is the Treynor Ratio?
The Treynor Ratio, developed by Jack Treynor, an American economist and co-creator of the Capital Asset Pricing Model (CAPM), is a metric used to evaluate a portfolio’s performance after adjusting for systematic risk.
It tells investors how much return was earned beyond the risk-free rate for each unit of market risk (beta) the portfolio carried. In simpler terms, it measures how efficiently a portfolio rewards investors for taking on unavoidable market risk.
Formula
Treynor Ratio=rp−rfβp\text{Treynor Ratio} = \frac{r_p – r_f}{\beta_p}Treynor Ratio=βprp−rf
Where:
- rpr_prp = Portfolio return
- rfr_frf = Risk-free rate (usually the yield on Treasury Bills)
- βp\beta_pβp = Portfolio beta (systematic risk relative to the market)
The risk-free rate represents the return an investor could earn without taking any market risk. Treasury bills are commonly used as this benchmark because they are considered virtually risk-free.
Understanding How the Treynor Ratio Works
The Treynor Ratio helps investors compare portfolios or funds that may have similar returns but different levels of exposure to market risk.
- A higher Treynor Ratio suggests that the portfolio has provided better returns per unit of risk, indicating more efficient risk management.
- A lower Treynor Ratio indicates that the investor is not being adequately compensated for the level of market risk taken.
However, the Treynor Ratio is only meaningful if the portfolio’s beta is positive. A negative beta makes the ratio unreliable or meaningless since it implies that the portfolio moves inversely to the market.
Example: Comparing Two Portfolios
Let’s say you are comparing two portfolios — Equity Fund A and Bond Fund B:
| Portfolio | Portfolio Return (rpr_prp) | Risk-Free Rate (rfr_frf) | Beta (βpβ_pβp) | Treynor Ratio |
|---|---|---|---|---|
| Equity Fund A | 10% | 3% | 1.4 | (10 – 3) / 1.4 = 5.0 |
| Bond Fund B | 7% | 3% | 0.8 | (7 – 3) / 0.8 = 5.0 |
In this example, both funds have the same Treynor Ratio of 5.0, meaning they deliver equal compensation per unit of market risk despite differences in total returns and volatility.
If a third portfolio had a Treynor Ratio of 6.0, it would be considered superior on a risk-adjusted basis.
Treynor Ratio vs. Sharpe Ratio
| Feature | Treynor Ratio | Sharpe Ratio |
|---|---|---|
| Risk Measure | Systematic Risk (Beta) | Total Risk (Standard Deviation) |
| Ideal Use | Diversified portfolios | Any portfolio |
| Key Assumption | Unsystematic risk eliminated | Includes all risk |
| Formula | (Rp – Rf) / β | (Rp – Rf) / σ |
Both ratios are designed to measure risk-adjusted performance, but they differ in how they define “risk.”
- The Sharpe Ratio considers total volatility — ideal for portfolios that are not fully diversified.
- The Treynor Ratio focuses on systematic risk, making it more appropriate for well-diversified portfolios that are primarily affected by market movements.
How to Interpret the Treynor Ratio
- Higher is better: A higher Treynor Ratio means more return for each unit of market risk.
- Relative measure: It should be used to compare multiple portfolios or funds within the same category.
- Not an absolute ranking: A ratio of 0.6 isn’t necessarily “twice as good” as 0.3 — it simply indicates better relative efficiency.
General Guidelines
| Treynor Ratio | Interpretation |
|---|---|
| Negative | Portfolio underperformed risk-free rate or has negative beta |
| 0 to 0.5 | Low risk-adjusted return |
| 0.5 to 1.0 | Moderate risk-adjusted return |
| 1.0+ | Strong performance relative to market risk |
Limitations of the Treynor Ratio
While valuable, the Treynor Ratio has important limitations:
- Historical dependence: It relies on past returns and beta, which may not predict future performance.
- Requires correct benchmark: Beta must be calculated using an appropriate market index; otherwise, results can be misleading.
- Ignores unsystematic risk: The ratio assumes diversification has eliminated idiosyncratic risk — not always true in smaller portfolios.
- Ordinal, not cardinal: The ratio ranks portfolios but doesn’t quantify how much better one is than another.
- Not meaningful for negative beta portfolios: Negative betas distort the risk-return relationship.
When to Use the Treynor Ratio
The Treynor Ratio is best used by:
- Portfolio managers comparing mutual funds, ETFs, or diversified portfolios.
- Analysts and investors evaluating risk-adjusted performance within the same asset class.
- Financial planners assessing client portfolios in relation to market benchmarks like the S&P 500.
It’s a valuable tool when systematic risk is the primary concern, but should be complemented with other metrics like the Sharpe Ratio, Alpha, or Information Ratio for a fuller performance assessment.
The Bottom Line
The Treynor Ratio remains one of the foundational measures in modern portfolio analysis. By relating excess returns to systematic market risk, it helps investors determine whether a portfolio’s performance justifies the risk taken.
However, it should not be used in isolation — understanding the context, diversification level, and market conditions is key. When used correctly, it empowers investors to make smarter, more risk-efficient investment decisions.
