Pain Ratio vs. Standard Deviation
In a previous post we discussed the pain index as a better measure of risk. Now we’ll explore the concept further, to consider return as well as risk, using the pain ratio.
The pain index measures the depth, duration, and frequency of losses for an investment.
But what about the upside? If there is one drawback of the pain index, it is it only measures risk, not return. If one wanted to have the lowest possible pain index of 0.0% and never lose a cent, one would keep all of their money in a FDIC insured savings account.
However, most investors accept the fact that some risk must be undertaken in order to generate any decent amount of return.
The grandfather of risk/return measures is the Sharpe ratio. Developed by Nobel laureate William Sharpe, the Sharpe ratio attempts to measure the trade-off between return and risk (as measured by volatility).
- The numerator of the Sharpe ratio is an investment’s excess return over the risk-free rate. One would hope this number is positive.
- The denominator of the Sharpe ratio is a measure of risk. Sharpe used standard deviation as his measure of risk.
By taking a measure of return and dividing it by a measure of risk, Sharpe was able to quantify an investment’s “bang for the buck”, a very useful bit of information.
There are many variations to the basic return-divided-by risk concept, like Sharpe ratio, Treynor ratio, Sortino ratio, information ratio and many others. The pain ratio follows in these footsteps. Developed by Dr. Thomas Becker and Aaron Moore of Zephyr Associates, the pain ratio takes advantage of the innovations of the pain index.
The mathematic equation for the pain ratio is:
Pain Ratio = (AnnRtn(r1,..,r2) -(AnnRtn(c1,..,c2) / Pain Index(r1,..,r2)
r1,..,r2 = manager return series
c1,..,c2 = cash equivalent return series
The Pain Ratio for Swan DRS and S&P 500
In the above graphs we see the two components of the pain ratio.
The upper graph represents the numerator, the excess return over the risk free rate. The risk-free rate is in yellow while the Swan DRS is the blue line and the S&P 500 index is the dark red line. The graph illustrates the rolling three-year return differential versus the risk-free rate.
The bottom graph is the denominator of the equation. The pain ratio uses the pain index as its measure of risk. The graph illustrates the depth, duration, and frequency of losses. Once again the DRS is in blue and the S&P 500 Index in dark red.
Working through the numbers, we can see that the Swan DRS risk/return trade-off is much superior to the S&P 500 Index. Swan wins on both measures- the return has been higher and the risk lower. The pain ratio is 2.66 for the DRS vs. 0.35 for the S&P 500 Index during the period July 1997 to April 2016.
It is important to remember that when analyzing the pain ratio, the higher the value the better.
The pain ratio highlights the strengths of the Swan DRS. The vast majority of Swan DRS’s holdings are in broad market ETFs, giving the strategy upside potential. Typically 10–15% of the DRS’s holdings are in hedges to protect on the downside. The trade-off between return and risk are well illustrated in the pain ratio.
About the author: Marc Odo, CFA®, CAIA®, CIPM®, CFP®, Director of Investment Solutions, is responsible for helping clients and prospects gain a detailed understanding of Swan’s Defined Risk Strategy, including how it fits into an overall investment strategy. Formerly Marc was the Director of Research for 11 years at Zephyr Associates.
Swan Global Investments, LLC is a SEC registered Investment Advisor that specializes in managing money using the proprietary Defined Risk Strategy (“DRS”). SEC registration does not denote any special training or qualification conferred by the SEC. Swan offers and manages the DRS for investors including individuals, institutions and other investment advisor firms. Any historical numbers, awards and recognitions presented are based on the performance of a (GIPS®) composite, Swan’s DRS Select Composite, which includes nonqualified discretionary accounts invested in since inception, July 1997, and are net of fees and expenses. Swan claims compliance with the Global Investment Performance Standards (GIPS®). All data used herein; including the statistical information, verification and performance reports are available upon request. The S&P 500 Index is a market cap weighted index of 500 widely held stocks often used as a proxy for the overall U.S. equity market. Indexes are unmanaged and have no fees or expenses. An investment cannot be made directly in an index. Swan’s investments may consist of securities which vary significantly from those in the benchmark indexes listed above and performance calculation methods may not be entirely comparable. Accordingly, comparing results shown to those of such indexes may be of limited use. The adviser’s dependence on its DRS process and judgments about the attractiveness, value and potential appreciation of particular ETFs and options in which the adviser invests or writes may prove to be incorrect and may not produce the desired results. There is no guarantee any investment or the DRS will meet its objectives. All investments involve the risk of potential investment losses as well as the potential for investment gains. This analysis is not a guarantee or indication of future performance. Prior performance is not a guarantee of future results and there can be no assurance, and investors should not assume, that future performance will be comparable to past performance. All investment strategies have the potential for profit or loss. Further information is available upon request by contacting the company directly at 970.382.8901 or visit swanglobalinvestments.com. 119-SGI-052016