Treynor Ratio Calculator

With this Treynor ratio calculator, you can easily analyze your portfolio's performance against systematic risk. The Treynor ratio is commonly used to analyze a portfolio's investment performance. Most importantly, it tells us how much return you are getting per unit of systematic risk you are taking. You can check out our risk calculator and investment calculator to understand more about this topic.

We have prepared this article to help you understand what Treynor ratio is and how to calculate it using the Treynor ratio formula. By demonstrating some Treynor ratio examples, we aim to instill you with the concept. Now, let's start by discussing the fundamentals.

The Treynor ratio, or Treynor measure, is a widely used performance metric that measures how much a portfolio returns are above the risk-free rate by taking on an extra unit of systematic risk. In essence, the Treynor ratio helps you to analyze if the risk you are taking on is rightly compensated.

Unlike the Sharpe ratio, which uses the total risk as the denominator, the Treynor ratio uses the systematic risk. When we compare the Treynor ratio vs. Sharpe ratio, the former is usually considered to be the fairer variant. This is because, according to the efficient market theory, investors will only be compensated by taking on more systematic risk. You can check out our Sharpe ratio calculator to understand more on this topic.

Next, let's look at some examples to understand how to calculate the Treynor ratio.

Taking Company Alpha as the Treynor ratio example, which reports the following information, let's talk about how we should use the Treynor ratio formula:

• Beginning portfolio value: $2,000,000
• Ending portfolio value: $2,200,000
• Portfolio beta: 1.25
• Risk-free rate: 1.5%

1. Determine your portfolio return.

   We need to first calculate the portfolio return using the formula below:

   portfolio return = (ending portfolio value − beginning portfolio value) / beginning portfolio value

   For our example, portfolio return is:

   ($2,200,000 − $2,000,000) / $2,000,000 = 10%

2. Determine the risk-free rate.

   As for the risk-free rate, we can safely assume it to be equivalent to the yield of a 10-year US government bond. This is because the 10-year US government bond has almost no credit risk. If you want to look for this information, visit the Federal Reserve website.

   In our example, we will assume the risk-free rate as 1.5%.

3. Determine the portfolio beta.

   To calculate the portfolio beta, we need to calculate the weighted average from the beta of the portfolio's holdings. For this portfolio, the portfolio beta is 1.25.

4. Calculate the Treynor measure using the Treynor ratio formula.

   Finally, we can use the Treynor ratio formula to calculate the Treynor ratio:

   Treynor ratio = (portfolio return − risk-free rate) / portfolio beta

   Thus, the Treynor ratio for the Company Alpha portfolio is:

   (10% − 1.5%) / 1.25 = 6.8%

Since we now have an understanding of what the Treynor ratio is and its calculation, we can now talk about how to interpret what is a good Treynor ratio.

The Treynor ratio is mainly used to measure the amount of return you are getting by taking on an extra unit of systematic risk. It is vital to understand the importance of measuring your return against the systematic risk, which is represented by the portfolio's beta, instead of the standard deviation, which is the total risk.

Total risk is equivalent to the sum of the systematic risk and the unsystematic risk. As unsystematic risk is the risk that can be diversified away, according to the efficient market theory, investors should not expect to be compensated by taking on more unsystematic risk. That's why the Treynor ratio is often considered to be theoretically more accurate.

However, there are a few limitations that you should keep in mind when using the metric. Firstly, it is a backward-looking metric. Its reliability is hence heavily dependent on the accuracy of the historical data. Moreover, the difference between Treynor ratios has little meaning. Although we can rank the Treynor ratios, as the higher Treynor ratios are generally better, we cannot say that a Treynor ratio of 5 is 2 times better than a Treynor ratio of 2.5.

Speaking in general, the higher the Treynor ratio the better, as it means you are earning more return for each unit of systematic risk you take. However, it is crucial to keep in mind that the difference between Treynor ratios has little meaning. A Treynor ratio of 3 does not necessarily mean it is 3 times better than a Treynor ratio of 1.

Mathematically speaking, the Treynor ratio can be negative. In reality, though, it is highly unlikely, as that means the return of your portfolio is lower than the risk-free rate.

The Sharpe ratio measures the return of your portfolio against the total risk, whereas the Treynor ratio uses systematic risk. From the comparison Treynor ratio vs. Sharpe ratio, the former is generally considered more accurate as investors are normally only compensated by taking on more systematic risk.

The risk-free rate is the annual rate of return of an investment that has practically zero risks involved. The 10-year and 20-year US Treasury yields have typically been used as the proxies for the risk-free rate.