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The Ulcer Index and Martin Ratio

edited June 2013 in Fund Discussions
Hi Guys,

Most importantly, Charles, David, and the remainder of the MFO gang deserve the highest commendation for accepting the challenge to organize the huge body of mutual fund data in a manner that facilitates comparisons and finally decision making. That is a daunting and Herculean task. Congratulations to them; they are making great progress.

Like an earlier Investor posting, I share a few detailed project reservations, mostly related to the preferred sorting criterion. Fundamentally, the criterion (the Martin Ratio) appears to be the Chosen One mainly because it differs from the more common criteria like the Sharpe Ratio, or more simply the return-risk (volatility, standard deviation) tradeoff. Just offering a dissimilar selection criteria should never be the determining factor. It must also provide some inherent and potentially exploitable advantages.

A few days ago, I posted a comment to an Investor submittal that referenced the Hindenburg Omen. I opined that the Omen is silly and an abuse of science-based methods.

I borrowed a speculation from a Gregory Baer book that the title of a best-seller is equally important to the book’s sales as its content, and if that’s the case, then a properly selected title is pure marketing genius.

Well, the naming of Martin’s work “The Ulcer Index”, might equally qualify as pure marketing genius. Peter Martin’s research in this arena is rather mundane. He published his work in a book that is out of print except on the Internet. If you are sufficiently motivated, here is a Link that provides a free download:

Chapter 6, “Return, Risk, and Performance”, introduces the Ulcer Index and the Martin Ratio. You might want to access this source. I conducted a brief Internet search and failed to identify any academic or industry studies that explored the forecasting record of either the Ulcer Index or the Martin Ratio. Regardless, these metrics are frequently quoted by investment professionals, but serious examination of their persistence or reliability as a prediction tool are missing-in-action.

My current assessment of the meager historical performance documentation is that the Ulcer Index and the Martin Ratio are entirely empirically proposed mutual fund measurements. They possess no fundamental grounding. These additional gauges are more or less perturbations from the more conventional Sharpe, Treynor, and Sortino ratios. The Martin invented measures use the same data sets arranged in a slightly modified format.

Let’s focus on the differences between the Martin formulations and the traditional Sharpe Ratio. The disparity is concentrated in the denominator of the equations. They both evaluate dispersion around a baseline.

To address this dispersion, Sharpe uses standard deviation which measures variation around an average value. Martin’s Ulcer Index measures variation below the maximum price value registered within the data collection period. In essence, this distinction is a translation of the selected anchor point within the data set. Will this impact forecasting potential? I don’t know, and I can’t locate a study that examines this critical issue. My guesstimate is that I doubt that it does.

The Sharpe Ratio offers advantages by design that are NOT embedded in the Martin formulation. The Martin approach seems to be very ad hoc (arbitrary) in its construction.

The Sharpe Ratio uses Standard Deviation which is a basic characteristic of a roughly Normally distributed statistical data set. Most investors are concerned with cumulative end wealth. To calculate end wealth, the average annual return must be reduced by a volatility factor, its standard deviation squared divided by two.

The average annual return and its standard deviation are useful to estimate the likelihood of a portfolio producing negative returns for any given year. For example, a portfolio has a 10 % chance of delivering a zero annual return when its annual expected return minus 1.28 standard deviations are calculated using a Bell curve distribution.

Because of fat-tails and Black Swan events, it is unwise to reach beyond about 1.5 standard deviations when applying these data. The Bell curve is merely a returns approximation and does not hold water when assessing rare occurrences.

Will another number, like the Ulcer Index or the Martin Ratio, enhance MFO member’s mutual fund selections? I really don’t have a definitive answer. It likely depends on each investor’s approach to constructing a portfolio. But I am not Panglossian in this arena. The behavioral researchers have concluded that too many choices can produce confusion, delay, and uncertainty in the final selection decision.

I certainty highly praise the MFO team for assembling this evolving mutual fund tool with its noble goal to enrich our fund selection process. In the end, the ultimate goal is to cobble together portfolio components that fit in a manner that keeps expected returns at an acceptable level while simultaneously minimizing portfolio volatility. It’s the combined portfolio’s interactions (correlation coefficients) that matter most.

I wish the MFO team success at completing their ambitious, self-imposed task; lots of hard work required. I know the MFO membership will find their end product useful, and I hope they find this early critique informative.

Great work team MFO.

Best Regards.


  • edited June 2013
    Hi again MJG. Thanks for kind words of encouragement on new rating system.

    I do indeed have Mr. Martin's book, entitled "The Investor's Guide to Fidelity Funds - Winning Strategies for Mutual Fund Investing," where the retracement index (aka Ulcer Index) is introduced. It's a good book with several topics covered, including other risk measures, like beta and its relationship to theoretical Capital Asset Pricing Model (CAPM), which Prof Sharpe helped develop.

    I thought it was interesting that when the book was first published in 1989, there was of course no mention of value or cap size parameters now recognized in the Fama/French three factor model. Think some day a momentum factor will be added? I believe Peter Martin and his co-author Byron McCann were both students of Prof Sharpe at Stanford, but have yet to confirm.

    While the new return ratings key on Martin because of its sensitivity to both excess return and draw down, the risk ratings utilize three measures - standard deviation, downside, and Ulcer, which are the denominators of Sharpe, Sortino, and Martin, respectively.

    Numerous risk and risk adjusted return measures have been developed, but Sharpe and Sortino certainly seem to be most popular, like you note. M* publishes these two along with beta, alpha, r-squared (correlation), Treynor, upside/down side capture. M* still has a place for something called "Bear Market Percentile Rank," which appeals to me, but its reference is so specific (the 5 year window) and is published so infrequently that I've stopped relying on it.

    Other measures include Modigliani, Calmar, Sterling, and maximum draw down (MAXDD), which are tougher to find, like Ulcer and Martin. Maybe it's just because some of them are harder to calculate? I believe that the draw down measures are becoming more common in today's trading software programs.

    After 2008, I think we all got more sensitive to draw down as a measure, but it's still not often published. For example, M* shows both gold rated funds DODGX and LLSCX performance at about -43% in 2008 or 6% below market. But they actually drew down nearly 60% by Feb 2009. MAXDD is included in the new MFO ratings tabulation, along with the Ulcer and Martin measures of draw down extent and duration. I suppose that given the choice, most folks would want to achieve comparable absolute return while experiencing less draw down. (But I'm heavy FAAFX, so I recuse myself from consideration.)

    All these measures are so-called ex post...historical, after the fact. Beta has been shown to have tendency to persistent, but certainly alpha does not. I believe CAPM predicts that those investing in riskier funds can expect higher returns over time. But has the debate been settled on whether there is an "optimal" risk level for a portfolio?

    I personally think Ulcer Index and attendant Martin Ratio are best measures available for identifying funds that have delivered superior returns while avoiding draw downs. In addition to the previous references posted, here are a couple supporting opinions: The Ulcer Index and The Ulcer Index: A better measure of risk. (I tried searching for contradictory opinions but came up empty.)

    I do find it gratifying that the new system highlights top notch 20 year funds, like VWINX, PRWCX, VWELX, OAKIX, SEQUX, YACKX, FMILX, MERDX, BCSIX as well as perhaps lesser known GLRBX, MAPOX, BHBFX, GASFX. In the forthcoming 10, 5, and 3 years ratings, you will find WRHIX, TGLMX, ARTKX, SGOVX, VILLX, PAAIX, TBGVX, PONAX, NSTLX, WBALX, WSCVX, MFLDX, PVFIX, COBYX, AKRIX, AQMIX, VVPSX among the stand-outs.

    Will their performance persist? So far so good, but your guess is probably better than mine regarding future. I do know that if Ulcer Index is creeping up on a fund I own, I'd want to know, especially if I expected it to maintain good down side behavior.

    Our hope was that the MFO community would find the new ratings both unique and helpful, like the legacy Three Alarm system. The system is not all encompassing, as it emphasizes certain measures and is based strictly on historical numerical returns. No other due diligence performed. No assessment of fund shop, manager's strategy, style drift, stewardship, etc. Those assessments can be found in David's many profiles and commentaries, on the active MFO board, and elsewhere (like M* with premium membership).

    Sorry for delayed response but have been a little busy lately and wanted to do the homework your posts often my betterment usually=).

    Hope all is well and thanks again.
  • Addendum

    Here is Mr. Martin's kind response to my recent inquiry:

    From: Peter Martin
    Sent: Friday, June 07, 2013 11:43 AM
    To: Charles
    Subject: Re: Martin Ratio

    I was not a student of Prof Sharpe. Byron McCann, with whom I wrote the 1989 book revealing the Ulcer Index, WAS a student of his. However, neither McCann nor Sharpe were involved in the technical development of the Ulcer Index.

    The origins of UI go back to about 1985, when I was developing software for mutual fund trading systems. I had concluded that standard deviation was a pretty awful measure of investment risk, for the reasons outlined at and elsewhere. This drove me to evaluate other known risk measures, and ultimately to develop my own. UI addresses the idea that real-world investors are concerned with the depth and duration of drawdowns in portfolio value.

    One of the findings I found most interesting was that the Martin Ratio reveals that known simple trading systems -- which are normally regarded as having little value -- actually have a much higher risk-adjusted performance than a buy-and-hold strategy. Such systems generally add little to average annual return, but are quite effective at avoiding long, deep drawdowns. This of course results in a higher risk-adjusted performance, if measured by the Martin Ratio.

    Kind regards

    Peter Martin

  • Reply to @Charles:

    Hi Charles,

    Thank you so very much for your extensive reply. It is thoughtful, seriously researched, and addressed many of the issues that both MFO participant Investor and I independently raised.

    There is no need to apologize for any delay in your response. A more careful reply prepared now is far more informative than one generated earlier simply to be speedy. Thank you for investing your valuable and limited time. I never intended to assign any tasks that you did not plan to do yourself.

    I did review the references you provided, and especially liked “The Ulcer Index: A better measure of risk” article. It certainly endorsed the Martin method. Also, I was impressed that Peter Martin responded to your query.

    It amazes me that these market researchers are often accessible to the general public. About two decades ago professor Sharpe generously answered a series of questions that I asked relative to a Monte Carlo simulation code that I was developing. His comments were encouraging and useful. I did finish the code and deployed it when making my retirement decision.

    The principle purpose of my original post was cautionary by design. I did not want you or the excellent MFO team to jump-the-gun and make a premature sorting criteria decision. At this juncture, all the various candidate ratios have both merits and shortcomings. I am not familiar with any research papers that demonstrate a universal advantage of one Ratio over the other. Much depends on the application and on the goals.

    In terms of a fund selection tool, perhaps an optimum approach would be to allow the tool user to select the sorting mechanism himself from a set of multiple options. Given the added complexity of permitting user options, I am definitely NOT recommending that you consider the optional route.

    None of the proposed Ratios are perfect forecasting tools. They are all grounded in accumulated rearview mirror data sets. The studies that I am familiar with all conclude that the most promising predictor of superior future returns is lower fund costs. Performance changes based on a host of unknowable factors; costs are relatively stable and predictable.

    Perhaps I misunderstand some details of your current ranking system, but I have some concern over both the coarseness of the benchmarking and the data collecting period. The Martin Ratio and Ulcer Index seem to have been historically developed for frequent trading, and consequently are best served using daily price entries. Also, scoring a mix of equity funds, international funds, and balanced funds together (as in the sample you included in your posting) might not be so useful when constructing a well diversified portfolio.

    Regardless of my present uninformed apprehensions, I have confidence that the MFO team will deliver a reliable and helpful fund evaluation tool. I recommend that you need not rush to a judgment. Even without a ranking, just the Ratio arrays provide fund selection guidance. Let the user decide for himself.

    I know you will challenge the robustness of your final format choice based on extensive out-of-sample data testing.

    Thank you for your commitment. It’s an outstanding match given your engineering experience, investing curiosity, and talents.

    Best Wishes.
  • Reply to @MJG: Thanks man. Confident we will adjust and improve the system to best of our ability in response to suggestions you and Investor have made so far and any new suggestions we receive from MFO community in weeks ahead.

    I too very much appreciated Mr. Martin's help. Strange, but I find truly accomplished people are usually pretty easy to approach. And the more they really do, the easier it is to talk with them. Kind of counter-intuitive...but maybe not.

    Have a great day. MJ and I are off to the beach.
  • Reply to @Charles: Thanks for the updates. I have no objection for having UI and MR to presented on the site and have a fund screener available. These are some odd measures and not generally available for public. While general verdict is sometimes different from sharpe/sortino ratio, the end result is pretty much in agreement.

    As you said, it is a useful feature for conservative investors. I think my issue was endorsing funds and assign owl ratings based on such quantitive screens. As important as the risk adjusted returns, just focusing on this (especially for a younger investor) is the wrong approach.
  • edited July 2013
    I must be missing something and must study these column criteria and the background thoroughly more deeply, as this certainly sounds and self-bruits to be a promising analytic methodology. But is there really no screen for manager start date and longevity? Surely that cannot be. Prwcx, for example, is rightly touted, including the longest term, but it is not the same manager; changeover at ~2006, right? Jabax (Jablx) otoh is not touted, appears to me equally fine on balance if not better and preferable, but again had its current manager start in 07 or something. Wbalx marginally preferable to Glrbx, with almost twice the bad-times dip? Also, any tool that calls out Fmilx (vv good fund, sure) but not Flpsx, which seems its peer or superior in many of these criteria, well, one has to ask why and how and what. So more study for this investor.
  • After reviewing the 'Ulcer ratio" and Martin Index several months ago, they seemed sensible, intriguing and not readily available (so far as I could tell, but I don't have time to research widely). Avoiding major downsides becomes even more important to those of us approaching geezerdom, since we may not have a decade to recover before the RMDs loom. If this information leads to better fund selections for us, great. Don't see how it could harm.
    Now I guess we need a couple of junior business/finance faculty who will run a comparison of returns using the various other ratios against Martin/Ulcer selected funds. I'd like to see if their selections show that funds with good M/U profiles before 2007 showed superior cumulative returns as of 2011, '12, &'13. If several other ratios select the same funds as those favored by M/U, then we know why M/U isn't widely included in fund ratings.
  • edited July 2013
    Reply to @davidrmoran: Hi David and thanks for sharing results from your study. I think you are considering the data with precisely the right attitude. All investors should be so prudent.

    The rankings are based strictly on past total monthly returns across periods evaluated for the categories noted. No regard for manager changes, consistency of strategy, stewardship, fund house, category drift, etc. Those attributes need to be assessed with other means, just like you are doing. Typically, I use Mr. Snowball's profiles, M* analysis reports, comments by MFO community, fund prospectus, and the manager's quarterly letters.

    The method does tag those funds that performed consistently top of category, including GLRBX, FMILX, and FLPSX, but funds like JABLX and WBALX also scored high (all 4s and 5s) and look just fine to me.

    Ratings have been updated through June and we're working to get them posted, but quick glance at the categories you noted for the 20 year funds:

    Large Growth - Hard to knock FMILX out of mix because it has returned an extraordinary 13.3% APR for the last 20 years, but it comes with higher volatility. (When UI and DSDEV get above 10%, warning lights blink for me...but that's just me.) The fund with highest risk adjusted return in the category is SEQUX, hands-down, perhaps the greatest mutual fund ever. VPMCX also ranks pretty high, consistently.

    Moderate Allocation - PRWCX, VWELX, MAPOX all get Great Owl status because they each rated top of class across all evaluation periods of 3 years or greater. Yes, it says something about T. Rowe Price to so consistently make PRWCX good. But ditto for Wellington and Mairs & Power. FPACX also looks good in this category.

    Conservative Allocation - VWINX and GLRBX top scores. BERIX and BRUFX look good too, but the latter gets flagged as a wolf in sheep's clothing from a risk perspective...not in same league and its -40% MAXDD shows it.

    Mid Cap Blend - FLPSX scores nothing but 5s for performance.

    All this seems reasonable to me, kind of makes sense just given the historical performance. Nonetheless, as system comes on-line and more readers like yourself provide feedback, I know we will work to refine and improve. Thanks again.
  • edited July 2013
    Reply to @STB65: I love it. I've often thought the same thing and when I get chance will go ahead and analyze the data say as of 1Q2007. D&C darlings come to mind - they had carefully navigated the tech bubble, but were slammed in 2008.

    Computing past returns is the easy part, all after-the-fact. The recent bond swoon is a reminder how quickly the world can go upside down. In 1Q2013 1 year ratings, AQRIX ranked 5 in of 2Q, it's 2.

    Or, much worse, the 1998 bond market, as described in Roger Lowenstein's great read "When Genius Failed: The Rise and Fall of Long-Term Capital Management."

    But I'll argue with you a bit on this point:
    If several other ratios select the same funds as those favored by M/U, then we know why M/U isn't widely included in fund ratings.
    My suspicion is that fund companies are inclined not to publish draw down performance, which is at the center of Martin ratio and Ulcer Index, because it can be the most frightening of metrics.

    In any case, I think your good points lead to these key questions: Do funds that have previously limited draw down while delivering healthy returns (ie., high Martin) have tendency to do so in future? And, is this any better a predictor than say Sharpe?

    I believe it is generally recognized that comparative volatility (or beta) tends to be remarkably stable over time, much more so than returns. But not was painfully learned by folks at LTCM.

    One thing I'm learning is that no matter what we show based past data, doubt will remain about about any predictor...and prudently so. That said, I'd still want to know how a fund has handled draw down in past compared to other funds, even if, like the ubiquitous qualifier says: "It is no guarantee of the future."

    Thanks STB65. More soon.
  • Reply to @Charles:
    Thanks much for your clear, thoughtful, comprehensive answer. I guess I myself do need a manager-length criterion; I mean, good on TRP, sure, for Prwcx and many other funds, but I think I would still rather give my moneys to (e.g.) Tillinghast, Aster, the Jameses and the Yacktmans. Currently trying to figure out why the last have better dip/ulcer performance than practically everyone else, even including, e.g., Prblx. I certainly concur in your view of a UI threshold; would love Prf even more than I do otherwise (also Sdy, Vnq, Pid, Pkw...). Helps explains why Gabsx is preferable to many other worthy s-c peers and indexes. Finally, you might want to familiarize yourself further with the AOx family of ETFs to compare against these partly bogus categories of 'moderate' and 'conservative' and 'growth' balanced allocations. Just to see what value is added, and when.
  • Oh yeah, this working editor asks, Can we get sitewide usage of 'drawdown' as one word, the way the financial world rightly does it, rather than two words? (Almost as bad as a construction abomination like 'Grown Ups'.)
  • Reply to @davidrmoran: Or maybe as bad as writing out ticker symbols as proper nouns... Prblx!?!? I'm with you on drawdown though.
  • >> maybe as bad as ...

    Wow, sure doesn't take much to trigger defensiveness around here!
  • edited July 2013
    Reply to @davidrmoran: No worries. We've starting switching over. So, from here on out at least, you will start seeing drawdown and downside as single words.
  • Reply to @Charles: rock
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