Treynor ratio

The Treynor ratio, also referred to as the Treynor index, measures the excess return for each unit of risk in a portfolio or investment. This is also called the risk-adjusted return.

Excess return is the return made over and above the risk-free rate of return. The risk-free rate is often considered to be the rate offered on US Treasury Bills, or, you could also think of it as the amount you get in a savings account. In both cases, there is very little chance that your money will be lost. If an investment yields 9% in a year, and the risk-free rate for one year is 1%, the excess return is 8%.

The Treynor ratio also factors in risk using beta, which is part of fundamental analysis​​. Beta measures how a stock moves relative to a major market index. The market index represents market risk, also known as systematic risk. This is the risk inherent in investing in a certain product, such as stocks.

Here is the formula for calculating the Treynor index:

Calculating the Treynor ratio for an individual stock requires gathering information for the yearly return and beta for the stock, along with the risk-free rate. For example, let’s assume that a stock has averaged 15% gains over the past several years. The risk-free rate is 1%, while the beta of the stock is 1.3.

Treynor ratio = (15 – 1) / 1.3 = 10.77

Now assume that the beta is 2.7.

Treynor ratio = (15 – 1) / 2.7 = 5.19

While the two stocks returned the same amount, the Treynor ratio indicates that the one with the 1.3 beta is a better option because it has less risk. Beta is a measure of risk because it determines how much the stock moves relative to an index.

When multiple assets are involved, the calculation requires the portfolio return and the risk-free rate, plus the average beta of the portfolio. To calculate the average, take the weighting of the stock in the account, multiply by the return, then add up all the returns. Do the same for the beta, multiplying it by the weight in the portfolio, and then adding up those numbers.

Let’s calculate the measurements for a simple two-stock portfolio. 60% of the portfolio is invested in Stock A. It returned 10%. The beta is 1.7. 40% is invested in Stock B. It returned 17%. The beta is 2.1.

Return for the portfolio = (0.6 x 10) + (0.4 x 17) = 12.8%

Beta for the portfolio = (0.6 x 1.7) + (0.4 x 2.1) = 1.86

The risk-free rate is 1%.

Treynor ratio = (12.8% – 1%) / 1.86 = 6.34

Learn more about how to perform company analysis​ in order to assess whether an investment will provide worthy returns in the long-term.

A higher Treynor ratio is typically seen as better than a lower one, because the investor is receiving a higher return relative to the risk (beta) being taken. However, the Treynor ratio is used to compare investments and does not explicitly say whether an investment is good or bad. Some traders are willing to trade riskier assets in the hopes of catching a big price movement and profit, whereas others are not.

There is no set level at which an investment becomes good or bad. Furthermore, the Treynor ratio is based on historical data. A lower Treynor ratio one year could become very good the next if volatility dies down or returns increase, or a high ratio could become worse. The Treynor ratio is not necessarily predictive as it only looks backwards, therefore, most traders do not use the tool in isolation.

The Treynor index is not typically used with negative numbers because it becomes harder to interpret. It is more often used with positive returns and betas. There are two ways in which a Treynor ratio can be negative: there is a negative return or there is a negative beta.

In either case, we cannot simply say if one ratio is better than another. Logic would say that since we want to get the ratio positive and moving higher, a smaller negative number is better. This may not always point to the best investment though, because, if the returns of two stocks are equally negative (-15%), the one with a higher beta will have the less negative Treynor ratio. The investor will need to decide if they want to trade on a more volatile stock with a less negative Treynor, or a less volatile stock with a more negative Treynor. Learn more about trading on volatility​​.

As an example, let’s look at how to calculate the Treynor ratio for a share basket​, such as the ones offered on our Next Generation trading platform. A share basket tracks the movement of many stocks, often belonging to the same sector or industry group. The Big Tech share basket​ tracks the shares of large technology companies, such as Google, Apple and Microsoft.

This share basket has a beta of 1.06.

At the time of writing, the one-year US treasury bills rate is 0.13%, which is the risk-free rate.

The chart shows that, over the past year, the share basket returned 39.62%. The S&P 500 Index is also shown for comparison. The S&P 500 has a beta of one, since it is a benchmark index often used for calculating beta.

The Treynor ratio and Sharpe ratio​​ are similar. The only difference lies in the denominator of the formulas. The Treynor ratio uses beta to assess risk, whereas the Sharpe ratio uses standard deviation of returns.

Standard deviation​​ is how far returns are dispersed around the mean or average. A stock that has an average yearly return of 10% but swings wildly will have a higher standard deviation than a stock that edges higher and more slowly on most weeks.

Beta and standard deviation both have drawbacks. Beta compares an asset to an index to establish volatility, although this is not always the most useful comparison. Some assets do not have a relative index for comparison. Standard deviation only works well when data is normal and evenly distributed, although stock returns can be erratic. However, this does not necessarily mean that they are bad investments. Once again, both these ratios are tools and are not meant to be used on their own when making trading decisions.

Traders may wish to consider using the Treynor index as an additional tool when making investment decisions. For short-term trades, Treynor is not particularly useful since it is based on longer-term values which may not apply to trades lasting just a couple of weeks or less.

If you are considering two investments, you could calculate the Treynor ratio on each to help to assess which one provides better returns for the risk (usually a higher figure). When the Treynor value is negative, the ratio is not as useful.

The main pitfalls of the Treynor ratio include the fact that it is only backward looking and historical returns and betas may not accurately reflect the future. Stocks have pre-calculated betas but, for other markets, they will likely need to be manually calculated. To calculate the beta, an index must be selected to compare the asset to. For example, you could analyse a commodity index​​ to get the beta of a commodity. This can complicate computing the Treynor ratio when there are multiple assets within a portfolio. These drawbacks should all be taken into consideration, along with its advantages, when deciding to trade using the Treynor ratio.