Is This the Best Way to Judge Risk/Return?

We round out our series on investment ratios with a primer on the Treynor Ratio.
By Morningstar |  06-08-12 | 

Developed by Jack Treynor, the Treynor ratio (also known as the "reward-to-volatility ratio") is available alongside a number of other risk-adjusted return measures under the "MPT Statistics" heading on the "Ratings and Risk" tab for each mutual fund.

Like the other risk/return metrics we've discussed so far, Treynor attempts to measure how well an investment has compensated its investors given its level of risk. The Treynor ratio relies on beta, which measures an investment's sensitivity to market movements, to gauge risk.

The premise underlying the Treynor ratio is that systematic risk--the kind of risk that is inherent to the entire market (represented by beta)--should be penalized because it cannot be diversified away.

As a reminder, beta attempts to gauge an investment's return variance relative to the broad market's movements. A low beta would indicate two things about an investment--first, that the investment has been less volatile than the market and second, that the fund takes on less risk with lower potential return. On the other hand, a high beta would imply that an investment has high-risk relative to the market but also has greater return potential.

How is it calculated?

The Treynor ratio relies on three figures: the fund's arithmetic average return over a specific time frame, the arithmetic average return for a risk-free investment over that same time frame, and the fund's beta during that period.

To calculate the fund's excess returns, the average return of the riskless asset is subtracted from the portfolio's average return. To arrive at the Treynor ratio, we divide that number by the fund's beta, which is calculated by comparing the fund's excess returns over Treasury bills during a given time period with those of the benchmark. (For more information on how to evaluate and use a fund's beta, click here.)

How can you use it?

Like the Sharpe ratio, the Treynor ratio is an assessment of the fund's historical risk/reward profile. The Treynor ratio is best used to compare two investments within the same category or to compare an investment's Treynor ratio with that of a market benchmark or category average. The higher the ratio, the greater the portfolio's returns relative to its beta (level of sensitivity to its market index).

For example, compare two funds in the large-cap category: Sundaram Growth and HDFC Equity. For Sundaram Growth, the Treynor ratios for the three-, five- and 10-year periods are negative 1.76, negative 4.26, and 16.79, respectively. HDFC Equity’s three-, five-, and 10-year Treynor ratios are 6.21, 2.31 and 24.78, respectively.

Based on the Treynor ratios alone, HDFC Equity offers a much more attractive reward-to-volatility profile. Moreover, given that the large-cap category Treynor ratios during the same periods were 0.06, -3.18 and 18.64, we can see that Sundaram Growth lagged the category average significantly over every time period while HDFC Equity handily outpaced the category average.

Also keep in mind that Treynor ratios can be negative at times. One possible (though somewhat atypical) scenario is if the portfolio return exceeds the risk-free rate, but the beta is negative (implying that the fund outperformed the risk-free rate by betting against the market). Funds can also wind up with negative Treynor ratios if the portfolio return is less than that of the risk-free rate while the fund's beta remains positive (implying that the fund took on systematic risk but didn't exceed the risk-free rate).

Take JM Multi Strategy, for example. The fund has a meaningful 3-year R-squared, or correlation, of 92 with the BSE 500 and sports a 3-year Treynor ratio of -9.32. Given its beta of 1.07, the fund's negative Treynor ratio indicates that the fund hasn't adequately compensated its investors for the risk it has subjected them to; its returns have been lower than the risk-free rate of return during the past 3 years.

The Treynor ratio is also a useful guide for tracking a portfolio's historical performance relative to market risk--for example, by comparing a fund's three-year Treynor ratio with its five- and 10-year figures. As you do so, keep in mind that Treynor ratios can exhibit dramatic changes over time--going from negative to positive, or vice versa--as a result of a market downturn, poor management, or other problems. Comparing a fund's historical Treynor ratios to those of its category average can help you put those numbers into context.

Remember these caveats

Because the Treynor ratio uses beta in its formula, it also shares beta's caveats. Besides the ever-present condition that beta (as is the Treynor ratio) is based on historical performance and thus has limited usefulness as a predictor of future performance, the usefulness of beta is also completely reliant upon the level of correlation with its market benchmark. Investors should use R-squared to help gauge how much weight to put on a fund's beta and, in turn, the Treynor ratio.

It's also worth mentioning that because the Treynor ratio is dependent upon the relevance of the fund's market benchmark, the Treynor ratio becomes a less relevant comparison metric if two portfolios are correlated with different benchmarks.

Finally, investors should note that the Treynor ratio captures only an investment's systematic, or market-related, risk; it assumes that the manager has built a diversified portfolio that effectively washes out the fund's idiosyncratic risks, such as the risks involved with holding giant positions in individual stocks. If a fund has a high level of idiosyncratic risk, it won't necessarily be reflected in the Treynor ratio.

Other articles in this series:

Investment Ratios

Modern Portfolio Theory

The article first appeared on, our sister US site, and has been formatted for India.

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