Treynor Ratio Definition, Formula, What It Shows

Both are named for their creators, Nobel Prize winner William Sharpe and American economist Jack Treynor, respectively. While they may help investors understand investments and risk, they offer different approaches to evaluating investment performance. The Sharpe ratio helps investors understand an investment’s return compared to its risk while the Treynor ratio explores the excess return generated for each unit of risk in a portfolio. The Jensen ratio measures how much of the portfolio’s rate of return is attributable to the manager’s ability to deliver above-average returns, adjusted for market risk.

Portfolio Management

Named after its creator, Michael C. Jensen, the Jensen ratio calculates the excess return that a portfolio generates over its expected return. Because this measure only uses systematic risk, it assumes that the investor already has an adequately diversified portfolio and, therefore, unsystematic risk (also known as diversifiable risk) is not considered. As a result, this performance measure is most applicable to investors who hold diversified portfolios. The Treynor ratio and Sharpe ratio have many characteristics in common since they both measure risk-adjusted return for portfolio. The only difference between the two is how they measure risk related to the investment.

The Treynor ratio is calculated by taking the portfolio return, subtracting the risk-free rate, and dividing that number by the beta of the portfolio. Provided all else is equal, a higher ratio is usually better when comparing similar investments, but it cannot define by how much exactly. In any case, it is important to note that for negative beta values, Treynor ratio values will not be useful. And because these values are ordinal, the significance of their differences could not be determined as portfolios are compared. For instance, while a 0.8 Treynor ratio is better than a 0.4, it’s not automatically twice as good. The Treynor Ratio has limitations, including an overemphasis on systematic risk, inappropriateness for non-diversified portfolios, and sensitivity to input assumptions.

Risk-Free Rate

The Treynor ratio relates excess return over the risk-free rate to the additional risk taken; however, systematic risk is used instead of total risk. The higher the Treynor ratio, the better the performance of the portfolio under analysis. The Treynor ratio, also known as the reward-to-volatility ratio, is a performance metric for determining how much excess return was generated for each unit of risk taken on by a portfolio.

Treynor Ratio – What is it? How to calculate?

First developed in 1966 and revised in 1994, the Sharpe ratio aims to reveal how well an asset performs compared to a risk-free investment. Generally, the greater the value of the Sharpe ratio, the more attractive the risk-adjusted return. The Sharpe Ratio (SR) measures a fund’s risk-adjusted return based on its total risk, represented by the portfolio’s standard deviation. In contrast, utilizing its beta, the Treynor Ratio evaluates portfolio performance relative to market risk. Similar to the previous performance measures discussed, the Jensen measure is calculated using the CAPM.

1. Learn more about these measurements and how to use them to evaluate portfolios.
2. If one needs to calculate a portfolio’s rate of return (Rp), it can be calculated as follows.
3. As a proxy for the risk-free rate, we use the return on U.S Treasury Bills – 2%.
4. In this sense, excess returns refer to returns that exceed those earned by risk-free investments.
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Take self-paced courses to master the fundamentals of finance and connect with like-minded individuals. Our goal is to deliver the most understandable and comprehensive explanations of financial topics using simple writing complemented by helpful graphics and animation videos. Finance Strategists is a leading financial education organization that connects people with financial professionals, priding itself on providing accurate and reliable financial information to millions of readers each year. Over the years, several enhancements to the Treynor Ratio have been developed to address its limitations and improve its applicability to different investment scenarios.

This approach allows investors to identify the optimal combination of active and passive investments to maximize risk-adjusted return. These enhancements include the Modified Treynor Ratio, the Treynor-Black Model, and the incorporation of alternative risk measures. Changes in these inputs can have a significant impact on the calculated ratio, which may lead to different conclusions about a portfolio’s risk-adjusted performance. For example, if the Treynor ratio is used to measure the risk-adjusted return of a domestic large-cap mutual fund, it would be inappropriate to measure the fund’s beta relative to the Russell 2000 Small Stock index. Investments are likely to perform and behave differently in the future than they did in the past.

Since the Treynor ratio is based on historical data, however, it’s important to note this does not necessarily indicate future performance, and one ratio should not be the only factor relied upon for investing decisions. Risk in the Treynor ratio refers to systematic risk as measured by a portfolio’s beta. Beta measures the tendency of a portfolio’s return to change in response to changes in return for the overall market. Where the Sharpe ratio fails is that it is accentuated by investments that don’t have a normal distribution of returns like hedge funds. Many of them use dynamic trading strategies and options that can skew their returns.

The difference between the two metrics is that the Treynor ratio utilizes a portfolio beta, or systematic risk, to measure volatility instead of adjusting portfolio returns using the portfolio’s standard deviation as done with the Sharpe ratio. Conversely, the Treynor and Sharpe ratios examine average returns for the total period under consideration for all variables in the formula (the portfolio, market, and risk-free asset). Similar to the Treynor measure, however, Jensen’s alpha calculates risk premiums in terms of beta (systematic, undiversifiable risk) and, therefore, assumes the portfolio is already adequately diversified. As a result, this ratio is best applied to an investment such as a mutual fund.

Get instant access to lessons taught by experienced private equity swiss franc to hungarian forint exchange rate pros and bulge bracket investment bankers including financial statement modeling, DCF, M&A, LBO, Comps and Excel Modeling. If a portfolio manager has a positive alpha, they have earned beyond what was required to compensate for the investment’s risks. If one needs to calculate a portfolio’s rate of return (Rp), it can be calculated as follows.

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Ultimately, the Treynor ratio attempts to measure how successful an investment is in providing compensation to investors for taking on investment risk. The Treynor ratio is reliant upon a portfolio’s beta—that is, the sensitivity of the portfolio’s returns to movements in the market—to judge risk. If a portfolio has a negative beta, however, the ratio result is not meaningful. A higher ratio result is more desirable and means that a given portfolio is likely a more suitable investment.

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The Treynor Ratio is calculated by dividing the portfolio’s excess return over the risk-free rate by the portfolio’s beta, which measures its sensitivity to market movements. The Sortino Ratio is another risk-adjusted performance measurement that emphasizes downside risk, or the risk of negative returns. This metric is particularly useful for investors who are more concerned about the potential for losses than the overall volatility of their investments. The Treynor Ratio focuses solely on systematic risk and assumes that unsystematic risk has been eliminated through diversification. This can lead to misleading review of exness forex broker results when comparing non-diversified portfolios or portfolios with high levels of unsystematic risk.

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