# What is the Treynor ratio and how do you calculate it?

The Treynor ratio compares your returns against underlying market volatility and systematic risk. Here we’ll take you through the Treynor ratio and show you how to calculate it.

## What is the Treynor ratio?

The Treynor ratio is a financial metric used to evaluate a portfolio’s return relative to the return of a benchmark – like a leading index. It’s sometimes known as the reward-to-volatility ratio and it’s not too dissimilar to other reward-to-volatility metrics such as the Sharpe ratio, in that it compares the return of a portfolio against the risk-free rate.

See how the Treynor ratio differs to the Share ratio

## How to calculate the Treynor ratio

To calculate the Treynor ratio, you’ll need to follow this calculation:

Treynor ratio = (portfolio return - risk-free investment return) ÷ beta of the portfolio

So, let’s suppose that the portfolio return is 30%, the risk-free rate is 2% and the beta of the portfolio is 1.4. This gives us the following calculation: (0.3 – 0.02) ÷ 1.4 = 0.2, which is the Treynor ratio.

As another example, let’s assume that the portfolio return is 50%, the risk-free rate is 0.0125% and the beta of the portfolio is 1.2. This gives us the following calculation (0.5 – 0.0125) ÷ 1.2 = 0.41.

0.41 is a higher Treynor ratio than 0.2, and a higher Treynor ratio is preferred because it implies greater returns for each unit of risk that the portfolio assumed compared to the risk of the benchmark.

### Treynor ratio calculation explained

There are several different terms used in the Treynor ratio, and some of them can seem confusing. We’ve explained each of them below.

• The portfolio return is quite simply how much a portfolio has returned in a specific period. An investor would usually hope that their portfolio performs similarly to or exceeds the performance of their country’s leading index
• The risk-free investment return is the theoretical return of an asset with zero risk. But, no asset is completely without risk so people will often use three-month US treasury bonds as a proxy for the risk-free rate of return
• Beta measures the rate of change in a portfolio’s return relative to changes in return for a benchmark for the overall market – like the S&P 500 (US 500) or the FTSE 100

## What is a good Treynor ratio?

A higher Treynor ratio is preferable because it denotes higher returns for each unit of risk. Furthermore, it means that the asset or portfolio of assets has generated better returns than might’ve been expected considering its level of assumed risk.

But, it’s worth pointing out that if the beta value of the portfolio is negative, the Treynor ratio will not give an accurate or meaningful value. In this case, you might want to consider using the Sharpe ratio to determine the potential return of a portfolio in relation to the underlying risk.

## Treynor ratio vs Sharpe ratio: what are the differences?

The Sharpe ratio is another return and risk ratio, and it seeks to understand how well an asset performed compared to a risk-free investment. This is different to the Treynor ratio, which analyses how well a portfolio performed relative to a benchmark for the underlying market.

Three-month US treasury bonds are often used as a proxy for a risk-free investment, because while no investment is completely risk-free, the risk in US treasury bonds is usually thought to be incredibly low.

The formula for the Sharpe ratio is:

Sharpe ratio = (portfolio return – risk-free investment return) ÷ standard deviation of the portfolio

The Sharpe ratio divides the equation by a standard deviation of the portfolio, which is the biggest difference between the Sharpe ratio and the Treynor ratio. Standard deviations can help to determine the historical volatility of an asset. Beta on the other hand, is a measure of an asset’s volatility as it relates to the overall market.

There’s another ratio to be aware of – the Sortino ratio. This is similar to the Sharpe ratio, but it only applies to a portfolio’s downside risk. Some analysts find that the Sortino ratio is better at measuring risk-adjusted returns than the Sharpe ratio because it discounts upside volatility, which is what will generally lead to profits for investors.

As a result, upside volatility is positive for an investor, and is excluded from the risk-adjusted return equation when using the Sotrino ratio.

You can use the Treynor ratio to measure the degree of excess profit you have achieved for every unit of risk that you have assumed above the level of risk in the underlying market. This can be useful to know, because it can denote whether you have outperformed against the market.

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Publication date : 2020-09-24T13:46:04+0100

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