The Ulcer Index Is A Helpful Way To Quantify Portfolio Pain


As we all recover from a happy Halloween full of way too much candy and possibly a bit too much to drink, I imagine that many of you may not feel so great.  Indulgence has its downsides, and once the excitement of the sugar high wears off sometimes all you’re left with is an upset stomach.  Whether that discomfort is really bad but you recover quickly or is relatively minor but persists for a long time doesn’t really matter, as both situations are equally undesirable.

There’s a similar problem with investing, and scores of articles have been written on risk tolerance, sleeping well at night, and all sorts of downside mitigation strategies to help reduce that pain in your stomach that you just can’t shake when markets aren’t going your way and your life savings are struggling to stay afloat.  I’ve written before about how smart asset allocation can help solve the problem, and I’ve just added a really cool metric to take that analysis one step further.  It’s appropriately called the Ulcer Index, and understanding how it works can help you find just the right portfolio for your personal pain tolerance.

The Ulcer Index was first described in The Investor’s Guide to Fidelity Funds: Winning Strategies for Mutual Fund Investors, by Peter Martin and Byron McCann.  The basic idea is to find a single number that can serve as a reference point for historical portfolio pain that 1) is far more informative than the standard deviation number most often quoted as a proxy for risk; and 2) accounts for both the depth and length of a drawdown.  After all, a shallow drawdown that persists for a long time is not necessarily any less painful than a sharp one that recovers relatively quickly.

Let’s tackle point #1 first.  I’ve long been a proponent of ditching standard deviation as a portfolio metric for how it obscures lots of important information, but never have I seen such an effective justification as the one Martin offers in his excellent Ulcer Index explanation.  The entire thing deserves a read, but let me highlight this chart in particular that tracks the compound growth of three different portfolios that all end up in the same place.


Which portfolio do you believe has the lowest standard deviation? 

Which would you be the most comfortable with?



If you’re like me, the yellow portfolio intuitively seems to have the lowest volatility and the magenta option seems downright terrifying.  Well guess what — they all have the identical average return and standard deviation!  The blue series is taken from a real fund.  The magenta series takes the exact same returns numbers and simply reorders them from worst to best while the yellow series juggles them to stay as flat as possible.  While the order of returns has a massive effect on the personal experience of the investor, it has no impact at all on the standard deviation calculations.  Or as Martin puts it, while the standard deviation may be the same in all three situations “no rational investor would consider them as having the same risk.”  I completely agree.

So if standard deviation is a poor proxy for the risk of an investment, what’s a better option?  My personal approach has been to answer that question from two different practical angles and quote both the deepest and longest historical drawdowns.  Martin’s insight is to combine the two into a single metric — the “Ulcer Index” — to measure the relative pain of a portfolio no matter how deep or wide the drawdown may be.  I think it’s a great reference point, and am happy to add it to the Drawdowns calculator.

You can read his full explanation for how it’s calculated, but for the layman version just check out the Drawdown charts for a few different portfolios.


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Long story short, the Ulcer Index is a pretty decent measure of the total white area above each of those red lines representing every time your investments fell below a previous high.  So a theoretical investment that never lost money would have an Ulcer Index of zero, and the more painful the history the higher the number.  And going back to point #2, it doesn’t really matter if the drawdown is deep and short or shallow and long as both can potentially generate the same Ulcer Index.

I personally wouldn’t focus so much on the absolute value of the number, but instead use it as a reference point for comparing the relative pain of two portfolios.  For example, according to the Ulcer Index the stock market in Australia has historically been about 80% more painful than the stock market in the United States.  Any Aussies should keep that in mind the next time you read investment advice written from a US perspective!





There are lots of interesting data points like that and it’s impossible to cover them all in one article.  So don’t take my word for it — explore the data for yourself.  In addition to the new calculator feature, every Portfolio has also been updated with Ulcer Index data so it’s always right there at your fingertips.

While a volatile portfolio can definitely leave you with a sour stomach, my personal advice differs a bit from the common mantra that significant risk is a requirement for investing and you just have to get used to it.  In my opinion, the answer is not to pop an antacid to help you tolerate the symptoms but to attack the root cause and address the underlying volatility via intelligent asset allocation.  I think the Ulcer Index is a very interesting metric when exploring those possibilities, and I hope you find it as helpful as I do.

So don’t just sit there complaining about the pain in your gut — start studying how to fix it!