# Treynor Ratio

The Treynor ratio is a performance metric that measures how a portfolio returns by considering the risks involved. Also referred to as the **reward-to-volatility ratio**, the purpose of the Treynor ratio is to compare the appeal of different portfolios on a risk-adjusted basis. The Treynor ratio was named after Jack Treynor, an American economist who helped develop the Capital Asset Pricing Model.

## Treynor Ratio Calculation – Treynor Ratio Formula

Treynor ratio is calculated using the formula below:

*Treynor ratio = (Portfolio return – Risk free rate)/Portfolio beta*

Going by this formula, the Treynor ratio calculates a portfolio’s performance per unit of risk. The portfolio return is straightforward. That is, it is the percentage return of a portfolio over some time. The risk-free rate is based on the return that would have been realized had the funds been invested in risk-free assets, such as treasury bills. Beta is a portfolio’s sensitivity to the movement of a relevant benchmark, such as the S&P 500. For instance, if the benchmark index moves 1% but the portfolio returns 2%, the beta is 2.

Generally, volatile assets have a higher beta because they tend to overextend directional moves and are riskier. The Treynor ratio thus shows the excess returns investors enjoyed for the added risk they absorbed.

## How to Use the Treynor Ratio?

The Treynor ratio is useful in evaluating the suitability of any investment opportunity. For instance, if a portfolio returns 10% and the risk-free rate is 4%, the excess return is 6% (10% minus 4%).

If the portfolio has a historical beta of 2, then the Treynor ratio is 3 (6% divided by 2). This implies that the portfolio generated three units of return for every additional unit of risk assumed in the market. Therefore, a higher Treynor ratio will imply that you will be better compensated for taking risks than a low Treynor ratio.

As an analysis tool, the Treynor ratio helps compare different opportunities by eliminating the volatility risk of each investment. One investment may deliver higher raw returns than the other, but its Treynor ratio may be lower if it has a high beta. Some portfolios may perform better in the short term rather than the long run, and the Treynor ratio can help make an objective choice by eliminating this volatility risk.

While performing backtesting, the Treynor ratio helps identify the best opportunities that will reward you for taking on more risk. But the Treynor ratio can also be used in forward testing to assess the impact of rebalancing a portfolio. For instance, if you add an asset class to your portfolio that lowers the Treynor ratio, it will mean that you have taken additional risks without any potential meaningful rewards.

Despite its benefits, the Treynor ratio also has its limitations. To start with, it is calculated using historical data, making it a backwards-looking performance metric. Markets are usually dynamic, so historical returns and beta may not influence future investment performance accurately.

The Treynor ratio does not quantify risk; it is just a ranking tool. When comparing two similar investments, the one with a higher Treynor ratio is considered a better opportunity. Still, it is impossible to know how much better it is than the alternative.

Additionally, the Treynor ratio is only ideal for assessing superior investments in a broader portfolio. When comparing different portfolios with similar systemic risks but variable total risks, the Treynor ratio may give an equal rating despite the inherent different risk propositions.

## Treynor Ratio vs Sharpe Ratio

The Treynor ratio is often compared to the Sharpe ratio. Both ratios compare risk-adjusted returns of investment portfolios, but the difference lies in their calculation. The Treynor ratio divides excess return by a portfolio’s beta, whereas the Sharpe ratio divides excess return by a portfolio’s standard deviation.

Thus, the Treynor ratio helps assess the excess return expected for each unit of risk. In contrast, the Sharpe ratio helps investors compare a portfolio’s return relative to its own risk.

## Final Words

The Treynor ratio is an excellent measure for comparing the performance of a portfolio per unit of risk. However, investors should be aware of its limitations (especially its backwards-looking nature) when utilizing it as a performance metric. The ratio should not be used as a standalone analysis tool- it should be combined with other tools for effective results.

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### FAQ

**What is the Treynor ratio?**Treynor ratio is a performance metric that measures how a portfolio returns per unit of risk.

**What is a good Treynor ratio?**Generally, when comparing two similar investments, the one with a higher Treynor ratio is considered more suitable. There is, however, no fixed figure of what a good Treynor ratio is.

*** Disclaimer – While due research has been undertaken to compile the above content, it remains an informational and educational piece only. None of the content provided constitutes any form of investment advice.*