*The Business Professor*, updated September 20, 2019, last accessed October 26, 2020, https://thebusinessprofessor.com/lesson/treynor-ratio-definition/.

### Treynor Ratio Definition

The Treynor ratio (also called the reward-to-volatility ratio and similar to the Sharpe Ratio), is a measurement for determining the excess returns of an investment per unit of risk.

### A Little More on What is the Treynor Ratio

This ratio is mainly calculated using a “beta coefficient.” These excess returns in Treynor ratio refer to profits earned above what was initially planned by the investor in a risk-free portfolio. So, if an investor was expecting 12% annual returns, and managed to get 16% returns, then we can say that the remaining 4% is the excess return, provided that the investment does not provide a chance for losses.

Short-term debt obligations which are backed by the US government (also known as Treasury bills) are some of the risk-free returns in Treynor Ratio. The only risk in Treynor ratio is volatility and it is measured by the investments beta. Beta, in this case, refers to the rate of volatility (also known as market risk), of a single investment with regards to the volatility affecting the whole market. Simply put, beta is a measure of the returns gotten from a particular treasury bill with regards to the total returns gotten from other treasury bills in the market. So, if Investor A gets an excess return of 4%, and the rest of the market experiences 5% excess returns, we can say that the measure of volatility in the market is the beta coefficient.

Jack Treynor, an American economist and one of the founders of the Capital Asset Pricing Model (CAPM) came up with the idea of this ratio.

Treynor ratio can be calculated mathematically as:

Treynor ratio = rp – rf

p

Where rp is the returns from investment

rf is the risk-free rate, and

βp is the beta coefficient

### What is the Treynor Ratio all About?

The Treynor ratio is a risk-adjusted (risk per reward) measurement of profits as a result of volatility. This ratio portrays the profit from an investment, say stocks, gotten from the amount of risk which this investment assumed.

If an investors portfolio has a negative beta (i.e. volatility went against the investment), then the results from this ratio will be useless. Higher results yield more profits and signifies that a particular portfolio is a good investment.

It is, however, important to note that the Treynor ratio is not a suitable tool for making investment decisions, as this measurement is based on historical data, and doesn’t reflect future market occurrences.

### Aim of the Treynor Ratio

The main aim of this tool is to measure how much an investor is compensated for taking on a high-risk portfolio. This ratio is dependent on the investments beta (the measure of returns with regards to market volatility) to determine risks. This ratio helps to make sure that investors are paid for the risk associated with each portfolio.

Noteworthy Details of the Treynor Ratio

- This ratio allows investors to adjust risk according to market movements
- A higher ratio means more returns, and ascertain the nature of a particular investment
- The only difference between the Sharpe and Treynor Ratios is by their mode of calculation.

Differences between the Sharpe and Treynor Ratios

Both the Sharpe and Treynor ratio measure the risk and returns of an investment portfolio. However, the Sharpe Ratio uses standard deviation to determine results, while the Treynor Ratio prefers to stick to beta coefficients.

### Shortcomings of the Treynor Ratio

As in every investment, past performance does not guarantee future returns, and this is the major shortcoming of the Treynor Ratio. Since this tool focuses on historical data, we cannot use it in predicting the future movement of the market. This tool is also dependent on comparison for measuring a portfolio’s beta. In other words, if this ratio is used to measure the performance of a stock in one market, we cannot use it to measure the performance of that same stock in another market. The only solution to this problem is measuring large-cap stocks (company shares with market value of over $5 billion dollars) as volatility rarely have effects on them.

The Treynor value is however, a great tool for comparing similar portfolios, ceteris paribus, but it doesn’t reveal which investment is better.

### References for “**Treynor Ratio****”**

https://en.wikipedia.org/wiki/Treynor_ratio

https://www.investopedia.com › … › Financial Ratios

https://www.readyratios.com/reference/analysis/treynor_ratio.html

### Academic research for “**Treynor Ratio****”**

The generalized Treynor ratio, Hübner, G. (2005). The generalized Treynor ratio. *Review of Finance*, *9*(3), 415-435.

INVESTOR-SPECIFIC PERFORMANCE MEASUREMENT: A Justification of Sharpe Ratio and Treynor Ratio., Scholz, H., & Wilkens, M. (2005). INVESTOR-SPECIFIC PERFORMANCE MEASUREMENT: A Justification of Sharpe Ratio and Treynor Ratio. *International Journal of Finance*, *17*(4).

The generalized Treynor ratio: a note, Hübner, G. (2003). The generalized Treynor ratio: a note. *University of Liege, Management Working Paper*.

[PDF] Von der Treynor-Ratio zur Market Risk-Adjusted Performance, Wilkens, M., & Scholz, H. (1999). Von der Treynor-Ratio zur Market Risk-Adjusted Performance. *Finanz Betrieb*, *1*(10), 308-315.

Beta, the Treynor ratio, and long-run investment horizons, Hodges, C. W., Taylor, W. R., & Yoder, J. A. (2003). Beta, the Treynor ratio, and long-run investment horizons. *Applied Financial Economics*, *13*(7), 503-508.

[PDF] Zur Relevanz von Sharpe Ratio und Treynor Ratio: Ein investorspezifisches Performancemaß, Scholz, H., & Wilkens, M. (2003). Zur Relevanz von Sharpe Ratio und Treynor Ratio: Ein investorspezifisches Performancemaß. *Zeitschrift für Bankrecht und Bankwirtschaft*, *15*(1), 1-8.

[PDF] The Generalized Treynor Ratio, Georges, H. Ü. B. N. E. R. (2009). The Generalized Treynor Ratio.

Penilaian Kinerja Produk Reksadana dengan Menggunakan Metode Perhitungan Jensen Alpha, Sharpe Ratio, Treynor Ratio, M2, dan Information Ratio Santosa, M., & Sjam, A. A. (2012). Penilaian Kinerja Produk Reksadana dengan Menggunakan Metode Perhitungan Jensen Alpha, Sharpe Ratio, Treynor Ratio, M2, dan Information Ratio. *Jurnal Manajemen Maranatha*, *12*(1).

[PDF] Performance evaluation of tax sav Key words: ELSS, Treynor ratio, Sharpe’s ratio. Available onl, Jain, A. (2017). Performance evaluation of tax sav Key words: ELSS, Treynor ratio, Sharpe’s ratio. Available onl.

A strong case to calculate the Treynor ratio using log-returns, Bednarek, Z., Firsov, O., & Patel, P. (2017). A strong case to calculate the Treynor ratio using log-returns. *Journal of Asset Management*, *18*(4), 317-325