Practical examples of evaluating performance using the Treynor ratio

Real-world examples of evaluating performance using the Treynor ratio

When investors ask for examples of evaluating performance using the Treynor ratio, they usually want to know one thing: how do I compare two funds that don’t take the same amount of market risk? The Treynor ratio answers that by measuring excess return per unit of beta.

The classic definition is:

Treynor Ratio = (Portfolio Return − Risk‑Free Rate) ÷ Portfolio Beta

Think of it as: How much extra return did I earn for each unit of exposure to market risk?

Let’s walk through several concrete examples, using realistic numbers and current market context.

Example 1: Two US equity funds with different betas

This is the cleanest example of evaluating performance using the Treynor ratio.

Assume the following 1‑year results:

• Risk‑free rate (3‑month T‑bill yield): 4.5% (in line with elevated short‑term U.S. rates in 2024; see current data from the U.S. Treasury at treasurydirect.gov)
• S&P 500 total return: 10%

Fund A – Aggressive Growth

• Return: 14%
• Beta vs S&P 500: 1.4

Fund B – Core Equity

• Return: 11%
• Beta vs S&P 500: 0.9

First, calculate excess returns:

• Fund A excess return = 14% − 4.5% = 9.5%
• Fund B excess return = 11% − 4.5% = 6.5%

Now the Treynor ratios:

• Fund A Treynor = 9.5% ÷ 1.4 ≈ 6.8%
• Fund B Treynor = 6.5% ÷ 0.9 ≈ 7.2%

On raw returns, Fund A looks better (14% vs 11%). But on a risk‑adjusted basis, Fund B actually delivered more excess return per unit of beta. This is one of the best examples of evaluating performance using the Treynor ratio: it flips the story you’d get from just looking at returns.

When you’re reviewing manager reports or fact sheets, this is exactly how institutional investors judge whether a “high return” manager is simply riding higher beta.

Example 2: Comparing Treynor and Sharpe for a balanced portfolio

Another set of examples of evaluating performance using the Treynor ratio comes from multi‑asset or balanced funds, where total volatility and market exposure can tell different stories.

Assume a 60/40 balanced fund over 3 years:

• Annualized return: 8%
• Risk‑free rate: 4%
• Annualized standard deviation: 9%
• Beta vs a 60/40 benchmark: 0.8

First, the Sharpe ratio:

• Excess return = 8% − 4% = 4%
• Sharpe ratio = 4% ÷ 9% ≈ 0.44

Now the Treynor ratio:

• Treynor = 4% ÷ 0.8 = 5.0%

Imagine a second balanced fund with:

• Return: 8.5%
• Standard deviation: 11%
• Beta vs benchmark: 1.1

Its metrics:

• Excess return = 8.5% − 4% = 4.5%
• Sharpe = 4.5% ÷ 11% ≈ 0.41
• Treynor = 4.5% ÷ 1.1 ≈ 4.1%

Sharpe says Fund 1 is slightly better (0.44 vs 0.41). Treynor also prefers Fund 1 (5.0% vs 4.1%), but the reasoning is different: Fund 1 produced more excess return for each unit of systematic risk. If you’re a CIO allocating among multiple balanced managers, these examples of evaluating performance using the Treynor ratio show how Treynor helps you reward managers who are efficient with beta, not just those who tolerate more volatility.

Example 3: Low‑volatility equity vs high‑beta tech strategy

In 2023–2024, low‑volatility strategies lagged during sharp growth and AI rallies, while high‑beta tech strategies often outperformed. Treynor helps you see whether that outperformance is skill or just higher market sensitivity.

Assume 2‑year annualized data:

• Risk‑free rate: 4.25%
• Global equity index return: 9%

Low‑Vol Fund

• Return: 8.5%
• Beta: 0.65

High‑Beta Tech Fund

• Return: 12.5%
• Beta: 1.5

Excess returns:

• Low‑Vol: 8.5% − 4.25% = 4.25%
• High‑Beta: 12.5% − 4.25% = 8.25%

Treynor ratios:

• Low‑Vol Treynor = 4.25% ÷ 0.65 ≈ 6.5%
• High‑Beta Treynor = 8.25% ÷ 1.5 = 5.5%

A surface‑level comparison says, “Tech wins.” But this example of evaluating performance using the Treynor ratio shows that, per unit of market exposure, the low‑volatility fund actually used its beta more efficiently. This kind of analysis is common in institutional risk reports and academic work on factor investing (for a deeper theoretical background, see resources from the CFA Institute at cfainstitute.org).

Example 4: When Treynor breaks down – concentrated or single‑stock positions

Not all examples of evaluating performance using the Treynor ratio are flattering. Some show you where the metric simply doesn’t work.

Imagine a concentrated stock portfolio:

• 10 stocks, heavy in a single sector
• 1‑year return: 18%
• Risk‑free rate: 4.5%
• Beta vs S&P 500: 0.4 (because the sector behaved differently than the broad market)

Excess return:

• 18% − 4.5% = 13.5%

Treynor ratio:

• 13.5% ÷ 0.4 = 33.75%

That looks spectacular. But this portfolio might have huge idiosyncratic risk (stock‑specific risk) that beta doesn’t capture. Standard deviation could be 25% or more, meaning the ride was extremely bumpy.

In other words, this is a textbook example of evaluating performance using the Treynor ratio where the result is technically correct but economically misleading. Treynor assumes the portfolio is well diversified so that beta is the primary risk that matters. For concentrated or single‑stock portfolios, Sharpe or downside risk measures are usually more informative.

Example 5: Treynor ratio in a 2024 pension fund review

Large pension funds and endowments routinely use Treynor in manager scorecards. Here’s a stylized real‑world scenario based on how U.S. public plans report performance (you can see similar structures in public documents from funds like CalPERS or state retirement systems, often linked through .gov domains).

Assume a pension fund is reviewing two external U.S. equity managers over 5 years:

• Risk‑free rate (5‑year average T‑bill yield): 3%
• S&P 500 annualized return: 9%

Manager X – Enhanced Index

• Return: 9.8%
• Beta: 1.0

Manager Y – Opportunistic Equity

• Return: 11.2%
• Beta: 1.3

Excess returns:

• Manager X: 9.8% − 3% = 6.8%
• Manager Y: 11.2% − 3% = 8.2%

Treynor ratios:

• Manager X: 6.8% ÷ 1.0 = 6.8%
• Manager Y: 8.2% ÷ 1.3 ≈ 6.3%

The board sees that Manager Y has the higher raw return, but Manager X has the better Treynor ratio. In the performance review, staff might argue that Manager Y’s outperformance is largely due to taking higher beta, not generating superior risk‑adjusted returns.

This kind of case is one of the best examples of evaluating performance using the Treynor ratio in practice: it directly influences allocation decisions and fee negotiations.

Example 6: Evaluating a factor ETF vs a broad market ETF

Factor ETFs (value, quality, momentum, etc.) have grown rapidly, and investors want to know whether they’re being rewarded for taking on different kinds of risk.

Consider a quality factor ETF vs a broad market ETF over 3 years:

• Risk‑free rate: 3.5%
• Market ETF (beta = 1): return 9.5%

Quality ETF

• Return: 10.2%
• Beta vs market: 0.95

Excess returns:

• Market ETF: 9.5% − 3.5% = 6.0%
• Quality ETF: 10.2% − 3.5% = 6.7%

Treynor ratios:

• Market ETF: 6.0% ÷ 1.0 = 6.0%
• Quality ETF: 6.7% ÷ 0.95 ≈ 7.05%

Here, the quality ETF not only beats the market on raw return but also on a Treynor basis. For advisors building model portfolios, this is a practical example of evaluating performance using the Treynor ratio when deciding whether a factor tilt is actually earning its keep relative to a simple cap‑weighted benchmark.

Example 7: Private wealth portfolio vs a custom benchmark

High‑net‑worth investors often use multi‑asset portfolios with custom benchmarks. Treynor can still be applied as long as you can estimate beta to that benchmark.

Suppose a private client has a 70/30 global portfolio with a custom benchmark of 70% global equities / 30% global bonds.

Over 5 years:

• Client portfolio return: 7.4%
• Benchmark return: 6.8%
• Risk‑free rate: 3%
• Portfolio beta vs benchmark: 0.95

Excess return:

• Portfolio: 7.4% − 3% = 4.4%

Treynor ratio:

• 4.4% ÷ 0.95 ≈ 4.63%

If the advisor also tracks the benchmark’s own Treynor ratio (using its beta to a broader market index), they can show whether the portfolio is using market exposure more efficiently than the reference mix. For client reviews, this is one of those real examples of evaluating performance using the Treynor ratio that turns a dense risk report into a simple story: “We earned more per unit of market risk than your benchmark.”

How to interpret Treynor ratio results in 2024–2025 markets

Recent years have featured:

• Higher short‑term interest rates (raising the risk‑free rate input).
• Elevated equity volatility around inflation and rate decisions.
• Big performance dispersion between sectors (e.g., tech vs defensives) and regions.

That context matters for Treynor:

• A higher risk‑free rate means managers must deliver more return to maintain the same Treynor ratio they had in the near‑zero rate era.
• Strategies that simply add beta (e.g., leveraged ETFs, high‑beta stock baskets) can look good on raw returns but weak on Treynor once you adjust for their market exposure.
• Diversified, risk‑controlled strategies may look relatively better on Treynor than they did in the 2010s, because they earn reasonable excess return without ramping up beta.

When you review performance today, the best examples of evaluating performance using the Treynor ratio are those that explicitly state the risk‑free rate used, the time period, and the benchmark for beta estimation. Without those, the number is easy to misinterpret.

When Treynor is useful vs when it misleads

Treynor is particularly informative when:

• You compare well‑diversified portfolios or funds.
• Beta is measured against a clear, appropriate benchmark.
• You want to separate market exposure from manager skill.

It can mislead when:

• The portfolio is concentrated or heavily exposed to idiosyncratic risk.
• Beta is unstable or poorly estimated (short history, regime shifts).
• You compare across very different strategies (e.g., equity vs market‑neutral hedge funds) where beta doesn’t capture all the risk.

Used alongside Sharpe ratio, information ratio, and drawdown metrics, Treynor becomes a sharp tool rather than a blunt instrument. Most institutional performance groups treat it that way.

For readers who want a more formal treatment of risk and return concepts that underpin the Treynor ratio, university finance departments often publish open materials; one example is MIT OpenCourseWare’s finance resources at ocw.mit.edu, which cover CAPM and beta estimation in detail.

FAQ: Treynor ratio and performance evaluation

Q1. Can you give a simple example of using the Treynor ratio to compare two funds?
Yes. Suppose Fund A returns 10% with beta 1.2 and Fund B returns 9% with beta 0.8, while the risk‑free rate is 4%. Excess returns are 6% and 5%. Treynor ratios are 6% ÷ 1.2 = 5.0% for Fund A and 5% ÷ 0.8 = 6.25% for Fund B. Even though Fund A has the higher raw return, Fund B is better on a risk‑adjusted basis. That’s a simple example of evaluating performance using the Treynor ratio where the ranking flips once you account for beta.

Q2. What are good real examples of evaluating performance using the Treynor ratio in practice?
Real examples include pension funds comparing external managers, wealth managers assessing model portfolios vs benchmarks, and ETF analysts judging factor funds vs broad market indexes. In all those cases, the decision makers care about extra return per unit of market risk, not just headline performance.

Q3. How often should I calculate the Treynor ratio?
Professionals typically look at Treynor over rolling 3‑year and 5‑year periods, sometimes 10‑year where data allows. Short periods (under 1 year) can produce noisy beta estimates and unstable ratios. For individual investors tracking mutual funds or ETFs, updating annually with at least 3 years of data is a reasonable practice.

Q4. Is a higher Treynor ratio always better?
Higher is better within the same context: similar asset class, benchmark, and time period. Comparing the Treynor ratio of a U.S. equity fund to that of a global macro hedge fund is not meaningful. Use it to rank peers, not to compare apples and oranges.

Q5. Where can I find reliable inputs for the risk‑free rate and benchmark returns?
For U.S. investors, Treasury bill yields are published by the U.S. Department of the Treasury at treasurydirect.gov. Major index providers and financial data platforms provide historical benchmark returns and betas. Academic and educational sites such as harvard.edu and mit.edu often explain the underlying theory if you want to understand how those inputs are derived.

The bottom line: the strongest examples of evaluating performance using the Treynor ratio don’t treat it as a magic score. They use it as one lens—focused on systematic risk—to test whether a manager’s story about performance actually holds up once you adjust for the amount of market exposure they’re taking.