Downturns can happen in two directions: they can be severe, with steep drops in value, and they can be extended, with long times until recovery. Both types of drawdown matter, and the Ulcer Index (UI) is a fantastic metric that intuitively explains the extent of a downturn in one’s portfolio. Unsurprisingly, RP portfolios are less stressful than their traditional counterparts, as measured by UI.
Consider these two recessions: one is very steep but has a quick recovery, one is not quite as steep but takes forever to correct itself. Think of the “Corona Crash” of the late-winter 2020 as the former, and then 1981/1982 as an example of the latter. The Corona Crash saw a drop of about a third, but starting rebounding in about a month. The early 80s version, caused by a dramatic rise in interest rates, didn’t quite go down as much, but lasted 622 days. Which one would be worse to deal with? Which one would cause you to give up and just sell everything for cash?
Hopefully neither, but as an investor, you will inevitably have to face times when your portfolio is floundering (hopefully not foundering!). To measure the stress of these downturns with just one number, we have the concept of “Ulcer Index.” I love this term and support its more widespread use, since it takes a complex situation with different elements and boils it down to one easy-to-picture statistic. Even though we now know that bacteria are what causes stomach ulcers, not stress, we all can relate to the feeling that we get in our stomachs when our portfolios start sinking and remain sunk.
How to Calculate UI for a Portfolio
Good news: to figure out the Ulcer Index, you don’t have to calculate it yourself. Instead, use Portfolio Charts, as we do at this site. The Ulcer Index appears in the “Drawdowns” chart, the eighth section under the main part where you enter the allocations. You can see drawdowns by depth and by length, and the Ulcer Index appears in the bottom left.
If you’re interested in the math, the best explanation I have found is at Wikipedia:
The index is based on a given past period of N days. Working from oldest to newest a highest price (highest closing price) seen so-far is maintained, and any close below that is a retracement, expressed as a percentage
For example, if the high so far is $5.00 then a price of $4.50 is a retracement of −10%. The first R is always 0, there being no drawdown from a single price. The quadratic mean (or root mean square) of these values is taken, similar to a standard deviation calculation.
The squares mean it does not matter if the R values are expressed as positives or negatives, both come out as a positive Ulcer Index.
For more context, you can find a richer discussion of how to think about and calculate the number in this definitive paper on the Ulcer Index by its co-creator, Peter G. Martin:
How to Interpret the Number
Basically, the lower the better. The Ulcer Index is probably best understood in relative terms, since there aren’t obvious whole number thresholds where a figure below X is good and above X is bad. Instead, compare the Ulcer Indexes of portfolios over the same stretch of time to get a sense of which would be the smoothest rides and which would bring you pain.
Taking a look at the ten test portfolios, you can see the superiority of the Risk Parity portfolios in terms of this metric. The Golden Butterfly and All Seasons portfolios are the best at 2.6 and 3.6, and unsurprisingly so. Their loss frequencies, depth of drawdowns and lengths of drawdowns are also at or close to the top of the table. Meanwhile, the 100% Equities portfolio has an Ulcer Index of 16.1, or more than six times that of the Golden Butterfly.
Another thing to notice is that even with portfolios with the same standard deviation, the Ulcer Index shows which portfolio would likely lead to more sleepless nights. The 100% Equities portfolio and the RPC Growth portfolio both have the same standard deviation (16.6%), but the latter has an Ulcer Index 60% of the former AND projects 2% higher returns. To compare the RPC Income with the seemingly safe 60/40, the RPC Income has half the Ulcer Index and 1.6% higher projected returns.
Clarifications
The Ulcer Index seems to have caught on with the technical analysis crowd who use the number to express the difficulty of holding on to a particular position for the long-term, by which I guess they mean anything approaching two weeks (!). When you look for Ulcer Index explainers on YouTube, mostly what you get are analyses over a 14 day period. The calculations are the same though, since the Ulcer Index can work over whatever time period, and with daily, weekly, monthly, or annual returns, but I didn’t find the videos all that helpful.
Extending the Ulcer Index
You may also run across the Ulcer Performance Index, also sometimes known as the Martin Index. I had not heard of this before, but it is interesting: it’s kind of a replacement for the Sharpe Ratio in that it measures return per unit of risk, though this time with the Ulcer Index as opposed to standard deviation. The math for this is simple: you just take the portfolio returns, subtract the risk-free rate (currently .55%), then divide that number by the Ulcer Index. In this case, the higher number is better,and again, it's best to look at it in relative terms.
For the test portfolios, you can once again see the superiority of Risk Parity-style portfolios. The Golden Butterfly was first, the All Seasons and the RPC Income tied for second, and then the three traditional portfolios finished eighth, ninth, and tenth. Mean-Variance Optimization portfolios taking so many Ls…ouch.
Additional Resources on the Ulcer Index
I’d definitely start with the explainer by its co-creator linked above. Next, this blog post written by Tyler of Portfolio Charts is a great rundown of the Ulcer Index and explains why he included it in his site:
Tyler
As mentioned, lots of the video resources about the Ulcer Index were for technical traders. The best of that bunch is here, though actually it is focused more on the Martin Index/Ulcer Performance Index. The UI is explained at the beginning, though: