Treynor RatioDefined with Examples, Formula & Calculations
What is the Treynor Ratio?
The Treynor Ratio, often known as the reward-to-volatility ratio, is a metric for measuring the amount of return that a portfolio generates in excess of the risk that is taken for a particular portfolio.
In other words, this financial ratio allows analysts to adjust investments to account for market volatility and the associated risks to compare different investment opportunities.
To do this, the Treynor ratio attempts to cancel out the effects of market volatility and place different investments on the same basis so that the investments are judged solely on their performance.
The Treynor ratio was developed by Jack Treynor, an American economist who was one of the inventors of the Capital Asset Pricing Model (CAPM).
Calculating the Treynor Ratio
Treynor Ratio = (Portfolio Return – Risk-free rate)/Portfolio Beta
The Treynor formula is:
T = (rp–rf ) / βp
rp=The portfolio’s return
rf=The risk-free rate
βp=The portfolio’s beta
What Does the Treynor Ratio Reveal?
Ultimately, it indicates the risk-adjusted performance of an investment.
This means it shows how much an investment, such as a mutual fund or portfolio of stocks, earns for the risk the investor is taking.
How the Treynor Ratio Works
The Treynor ratio is used to try to measure how good of a job an investment does at compensating investors for the risk they are taking.
It judges risk by considering how sensitive a portfolio is to changes in the market.
The idea of this ratio is that an investor should be compensated for taking a risk in their portfolio.
They should be compensated because even if the investor does diversify, it will not entirely remove risk.
Treynor Ratio vs. Sharpe Ratio
There are certain similarities between the Treynor ratio and the Sharpe ratio.
Each of these ratios measures the return and the risk of a portfolio.
However, these ratios differ in that the Treynor ratio uses systematic risk or a portfolio beta to calculate volatility rather than the standard deviation that is used by the Sharpe ratio.
What Are the Limitations of the Treynor Ratio?
The Treynor Ratio does have some weaknesses. Its primary weakness is the backward-looking design of the ratio.
This design is a problem because investments will probably perform in a different way in the future as compared to the way they behaved in the past.
The Treynor ratio’s accuracy depends heavily on using the right benchmarks to measure market risk.
An example of this would be using the Treynor ratio to calculate the risk-adjusted performance of a small-cap fund.
In this case, it would not be a good idea to compute the beta with respect to the S&P 500, where large-cap stocks are likely to result in an inaccurate comparison.
An accurate beta is critical for making this comparison, but large-cap stocks typically have lower volatility in comparison to small-cap stocks.
It would be more appropriate to instead measure the beta against an index that better represents the volatility of small caps, such as the S&P 600 index.
It is also important to remember that the Treynor ratio is only one metric upon which to measure an investment opportunity.
Assuming that all other factors are equal, a greater Treynor ratio indicates a better investment.
However, this is not definite. Other metrics should also be considered before making a decision to invest.
Key Highlights
- The Treynor ratio is a measure of a portfolio’s risk and returns which allows investors to measure a portfolio’s return in excess of the risk-free rate.
- When comparing portfolios, the portfolio with the higher Treynor ratio is generally a better investment.
- The Treynor ratio is a similar metric to the Sharpe ratio; however, the latter uses the standard deviation of a portfolio for adjusting portfolio returns.
- The Treynor ratio was created by Jack Treynor, expanding on William Sharpe’s contributions to modern portfolio theory.
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University of Wyoming "Sharpe and Treynor Ratios on Treasury Bonds" White paper. January 3, 2022
California State University "Performance measures: Traditional versus new models" Page 4. January 3, 2022
Stanford.edu " Quantitative Finance Overview" Page 1. January 3, 2022