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Computerized Investing > First Quarter 2013

Measuring Risk-Adjusted Performance With the Treynor Ratio

PRINT | | | | COMMENTS (4) | A A   Reset

by CI Staff

Last issue’s Fundamental Focus discussed the Sharpe ratio, a measure of return adjusted for risk. The Treynor ratio is another risk-adjusted performance figure that is very similar to the Sharpe ratio.

Both ratios measure how well an investment vehicle compensates the investor for a given level of risk. Both measure excess return above the risk-free rate per unit of risk. The main difference is that the Sharpe ratio uses standard deviation as the risk measure, whereas the Treynor ratio uses beta.

In this installment of Fundamental Focus, we discuss using and interpreting the Treynor ratio.

Components of the Ratio

As we know, the relationship between risk and return is essential in the investment process. Stocks that exhibit additional volatility, or risk, should compensate investors with additional long-term returns. Jack Treynor had this relationship in mind when he established the formula that became known as the Treynor ratio. The formula is written as follows:

Treynor ratio = (RI – Rf) ÷ beta

Where:

  • RI = average rate of return for an investment
  • Rf = risk-free rate

Average Return

There are two average return figures that can be used in this formula: historical or expected. Using an investment’s historical average return allows you to calculate the historical Treynor ratio over a time frame that you choose. Alternatively, you may use the expected average return to calculate the expected Treynor ratio. Of course, using expected average returns may not be accurate since predictions are used. However, historical averages are also potentially problematic, as there is no guarantee that past performance will carry forward.

Risk-Free Rate

The risk-free rate is the rate of return that investors require for investments with no risk. In essence, this return compensates investors for the time value of money. Inflation dictates that money in the future will not purchase as much as it does now, and the risk-free rate compensates investors for the time that their capital is tied up.

Typically, Treasury rates are used as measures of risk-free rates. It is generally good practice to match the duration of the Treasury holding to the length of time of the average return. Alternatively, there are arguments made that since equities are indefinite investment vehicles, the longest-term Treasury should be used.

Whatever you choose to use as the risk-free rate is not as important as staying consistent throughout your calculations. However, it is important that you choose a reasonable risk-free rate.

Beta

Simply put, in finance, beta measures the correlated price volatility of an investment compared to a benchmark. The concept of beta can be more easily described through examples. For instance, if a stock has a beta of 2.00, it is twice as volatile as the benchmark to which it is compared. If the benchmark appreciates by 10%, the stock should rise by 20%. Needless to say, the opposite is also true. Furthermore, a beta of 1.00 indicates that the stock should be expected to move in the same direction and at the same magnitude as the benchmark.

Interestingly, betas have no upper or lower limit. The figure can be very high for highly volatile stocks. It can even be negative. A negative beta means that the investment should move in the opposite direction of the underlying benchmark. For instance, an inverse ETF (exchange-traded fund), or a short position, would have a negative beta.

The biggest drawback of beta is that it’s only useful when calculated against a relevant benchmark. While the large-cap S&P 500 index is a commonly used index, it is composed of the 500 largest U.S. stocks. Therefore, it may not be appropriate when calculating the beta of a small-cap stock.

Calculating the Treynor Ratio

Table 1 collects the components of the Treynor ratio for two sample companies: Pfizer (PFE) and Wynn Resorts Ltd. (WYNN).

Return information for the two companies is readily available at websites online. The average return shown in Table 1 is a historical average based on the returns from 2008 through year-to-date 2012, a period of almost five years.

For the risk-free rate, the previous Fundamental Focus column used the average monthly return of Treasury bills over a period of time. Here, we use the yield of a five-year Treasury note, which is provided at the U.S. Treasury Dept. website (www.treasury.gov). The five-year yield is an annualized figure, which makes it comparable to the average annual return performance figures used for our example companies.

  Annual Return (%) Average
Return
(%)
Risk-Free
Rate
(%)
Beta
(X)
Treynor
Ratio
YTD 2011 2010 2009 2008 (X)
Pfizer (PFE) 18.0 28.2 0.2 7.2 –16.5 7.4 0.7 0.71 0.095239
Wynn Resorts Ltd. (WYNN) 10.9 12.7 92.9 47.3 –62.3 20.3 0.7 2.36 0.083178

Stock Investor Pro, AAII’s fundamental stock screening and research database, was used to find the beta for the two companies. Stock Investor Pro calculates the beta using the S&P 500 index as the underlying benchmark.

The last column in Table 1 shows the calculated Treynor ratios for Pfizer and Wynn Resorts. Because the Treynor ratio simply measures return per unit of risk as measured by beta, it is appropriate to use the Treynor ratio to compare companies from two different industries.

Interpreting the Ratio

As you can see, Wynn Resorts has a much higher average return over the past five years than Pfizer. Looking solely at return figures makes the choice very clear: One should invest in Wynn Resorts. However, the Treynor ratio paints a different story.

The Treynor ratio states that Pfizer provided a 9.5% return per unit of risk as measure by beta, while Wynn Resorts “only” provided an 8.3% return per unit of risk. Pfizer’s beta of 0.71 means that it is about 71% as volatile as the S&P 500, while Wynn Resorts’ beta of 2.36 indicates that the WYNN stock is more than twice as volatile as the S&P 500. This can easily be seen by the massive return volatility Wynn Resorts exhibits—down over 62% in 2008 but up over 90% in 2010. By comparison, Pfizer has been relatively stable, losing “only” 16.5% in 2008 when everything was down, yet up much less than Wynn Resorts in bull markets.

The Treynor ratio actually points to Pfizer generating a better risk-adjusted return. However, the Treynor ratios are close enough that investors choosing between these companies should base their decisions on their personal risk tolerance.

Conclusion

Like the Sharpe Ratio, the Treynor ratio is a relative measure of risk, so the number means nothing on its own. It is only useful when comparing two or more investments. In addition, beta has its own weaknesses as a measure of volatility. Since beta is a measure of correlated volatility to the market, an investment may have a very low beta, even as low as zero, but still be highly volatile in price. If this is the case, the investment simply does not correlate with the underlying benchmark.

Although the Treynor ratio is a great tool to use for comparison purposes, it should be used in conjunction with other research methodologies. Be sure to exercise proper due diligence with any potential investment.


Discussion

John Desantis from CA posted about 1 year ago:

The problem with both the Sharpe and the Treynor ratios is that they treat upside price movements the same as downside price movements. In my opinion, the denominator of the ratios should not increase due to upward price movements.

The Ulcer Index has the same numerator as Treynor & Sharp; but the denomonator includes only the amount of the price movement that is negative.

The concept is described in a book by Martin & McCann called "The Investor's Guide to Fidelity Funds".


Rene Barrios from FL posted about 1 year ago:

helpful for a new subscriber, thanks


Wayne Thorp from IL posted about 1 year ago:

@John,

I agree with you. Treating upside risk and downside risk is one flaw of traditional risk measures. In the Q2 issue of CI we will be discussing the Sortino Ratio, which focuses on downside risk and in a future Spreadsheet Corner I am going to apply the Ulcer Index to some of the more successful AAII stock screens.

@Rene,

Glad you enjoyed the article. Welcome to AAII & CI!

Wayne A. Thorp, CFA
Editor, Computerized Investing.


Ronald Longhofer from MI posted about 1 year ago:

A question about the use of the Treynor ratio for investment decisions. You write:
"Looking solely at return figures makes the choice very clear: One should invest in Wynn Resorts. However, the Treynor ratio paints a different story. . . . The Treynor ratio actually points to Pfizer generating a better risk-adjusted return."

I have calculated the ratio for 32 stocks I own or am following, and find that stocks that I, as a value investor, would consider buying (because they appear to be undervalued) tend to have lower Treynor ratios than the median for the market as a whole (which I calculated both for a universe of 1170 stocks screened for positive earnings and other measures such as positive book value, and separately for the components of the S&P 500). This is no doubt because, being undervalued, the stocks I follow do not have exceptional recent price performance. Conversely, stocks that have performed well in the recent past tend to be fully valued, and are therefore not necessarily good candidates for future returns, although they may have high Treynor ratios based on their historical performance.

I wonder whether the historical Treynor ratio isn't a better after-the-fact performance measure than it is a stock-picking tool? At least for value investors who want a margin of safety. You write that the Treynor ratio measures "how well an investment vehicle compensates the investor for a given level of risk." At least for the historical version of the ratio, wouldn't it be better to say "has compensated"?

Now, the "expected return" version would be a different story. I hope you are planning to do an article showing how this version might be implemented, as I, for one, would find it very useful in comparing potential investments.


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