We’ve all heard that no risk equals no reward, right? Some volatile investments pay big returns – but others aren’t worth the risk. The Treynor ratio is one of several metrics that help investors rank portfolios according to their risk-adjusted performance so you can choose investments that match your risk appetite and maximize your returns. The Treynor ratio is an important tool for investors, fund managers, and executives and it could mean the difference between a thriving portfolio and a failing one when applied well.

Here’s our guide to calculating, analyzing, and applying the Treynor ratio.

## What Is The Treynor Ratio?

The Treynor ratio measures the performance of an investment portfolio or fund relative to systematic risk. It is a reward-to-volatility ratio and a measure of risk-adjusted return.

You can use the Treynor ratio to determine the excess returns yielded per unit of systematic risk taken on by investors.

The Treynor ratio is used by traders and investors of all kinds to compare investment opportunities.

A higher Treynor ratio is preferable because it means an investment is expected to offer better compensation for the risk assumed.

The Treynor ratio was named after American economist Jack Treynor.

## How to Calculate Treynor Ratio

Treynor ratio formula is (portfolio return – risk-free rate)/portfolio beta.

Let’s take a closer look at the variables that make up the Treynor Ratio.

### What Are Excess Returns?

The numerator of the Treynor ratio is excess return.

In this context, excess return is the return from an investment that exceeds the return that could have been earned from a risk-free investment. This is kind of like the opposite of opportunity cost. It gives you an idea of the investors’ reward for taking on risk.

You can calculate the excess return generated by an investment by subtracting the risk-free rate from the portfolio’s total return for the chosen period.

### What Is The Risk-Free Rate?

No investment is 100% risk-free but US treasury bills (aka T-bills) are often used as a proxy for a risk-free investment because they are secured by the US government. The current yield of the 3-month T-bill can be used as the risk-free rate for a Treynor ratio calculation. At the time of writing, therefore, the risk-free rate is 5.24%.

## What Is a Portfolio’s Beta?

Beta represents the systematic risk level of an investment. It is an indication of the volatility of an asset relative to the market as a whole.

To calculate beta, a benchmark market index (e.g. the S&P 500) is selected. The benchmark index is allocated a beta of 1. A portfolio with a beta of:

• >1 is more volatile than the market
• <1 is less volatile than the market
• exactly 1 moves in sync with the market

Some assets have a negative beta. This means that the asset increases in price as the market falls. If you calculate the Treynor ratio using a negative portfolio beta, the result will be unusable.

Check out Ryan O’Connel’s quick guide to calculating beta in Excel for a full walkthrough.

### What Is Systematic Risk?

It’s worth noting that beta measures systematic risk, or market risk, which is tied to the broader market. This is in contrast to unsystematic risk which is specific to a company and can be mitigated by having a well-diversified portfolio.

## Treynor Ratio Calculation Example

Suppose you wanted to use the Treynor ratio to compare two portfolios, Portfolio A and Portfolio B. Portfolio A’s portfolio return is 8%. The beta of the portfolio is 1.14. The risk-free rate is 5.24%. We can plug these numbers into the Treynor ratio formula as follows.

Portfolio A’s Treynor ratio = (portfolio return – risk-free rate)/portfolio beta = (0.08 – 0.0524)/1.14

= approximately 0.024

Portfolio B’s portfolio return is 12%. The beta of the portfolio is 0.8. Therefore, according to the Treynor ratio formula:

Portfolio B’s Treynor ratio = (0.12 – 0.0524)/0.8 = 0.0845

The Treynor ratio of Portfolio A is lower than Portfolio B’s, even though it delivers lower raw returns, because its beta is higher. Therefore, Portfolio B seems like a better investment because it offers the best return per unit of systematic risk taken.

## What Are the Limitations of the Treynor Ratio?

The Treynor ratio is calculated using historical data and past performance, but there’s no guarantee that the portfolio will behave similarly in the future.

In addition, the Treynor ratio measures systematic risk and therefore does not account for unsystematic risk e.g. legal or operational problems.

To mitigate these limitations and assess the future performance of an investment, the Treynor ratio should be considered alongside factors like the quality of the company’s leadership team, industry trends, and economic conditions.

Finally, the Treynor ratio is only useful as a ranking or comparison tool and cannot provide useful insight when analyzing an investment in isolation.

## Treynor Ratio vs. Sharpe Ratio

Both the Treynor ratio and Sharpe ratio are popular methods of measuring risk-adjusted return.

The numerator for both ratios is excess return i.e. the portfolio’s returns over the risk-free rate. The only between them is the denominator.

While the denominator for the Treynor ratio is the beta of the portfolio, the denominator for the Sharpe ratio is the standard deviation of the investment.

These are both measures of volatility. While standard deviation looks at the disparity of a fund’s returns over time, beta compares the volatility of the fund to a benchmark.

A higher ratio is generally preferred. A ratio of >1 is acceptable, while a ratio >3 is considered excellent.

## Other Metrics For Measuring Risk

The Treynor ratio should be analyzed in conjunction with other financial metrics. Here are three more tools for assessing the risk-return trade-off of an investment.

### Jensen’s Measure

Jensen’s Measure, known as alpha, measures the excess returns on an investment relative to expected returns, given its level of risk.

The expected portfolio return is based on the capital asset pricing model (CAPM).

The capital asset pricing model measures expected returns using:

• expected returns on the market
• expected returns on a risk-free asset
• beta

A positive alpha means the portfolio has outperformed the market.

### Sortino Ratio

The Sortino ratio is a variation of the Sharpe ratio. It measures the risk-adjusted return of an investment with a focus on downside risk. It indicates how likely it is that an investment will lose value or fall below a threshold.

It is calculated by dividing an investment’s excess return by its downside deviation.

A higher ratio indicates higher additional expected returns per unit of downside risk.

### Information Ratio

The information ratio compares excess returns to the volatility of an investment.

Excess returns, in this context, are portfolio returns that exceed a chosen index e.g. the S&P 500.

The denominator of the ratio is tracking error – which represents how closely the portfolio tracks the index.

A higher information ratio indicates an investment that is more successfully and consistently outperforming the index.

## Avoid Risks That Don’t Pay Off

At the heart of it, great investing has a simple goal: find the greatest risk-adjusted return. Taking on additional risk as an investor can bring you additional returns, but not in every case and not necessarily in proportion. Comparing investments by assessing their returns ignores the element of risk. Calculating the Treynor ratio allows you to rank similar portfolios according to their risk-adjusted performance so you can make better-informed decisions – and, hopefully, generate more wealth.