# Difference between the two definitions of Ulcer Index

The Ulcer Index (UI) is defined as follows on page 89 of the book "Practical Portfolio Performance Measurement and Attribution, 2E" by Carl Bacon:

$$UI= \sqrt{\sum_{i=1}^{i=n} \frac{D_{i}^{'2}}{n}}$$

where $$D^{'}_i$$ is the drawdown since the previous peak in period i.

Investopedia on the other hand defines it procedurally as:

The indicator is calculated in three steps:

1. Percentage Drawdown = [(Close - 14-period High Close)/14-period High Close] x 100
2. Squared Average = (14-period Sum of Percentage Drawdown Squared)/14
3. Ulcer Index = Square Root of Squared Average

Evidently, the Bacon version results in a number without any parameters, while Investopedia's calculates it as a series given a number of periods taken into consideration as a parameter. So,

1. Why is the number of periods not needed for Bacon's version?
2. Why does the most recent value (and every other value, as I can notice) of Investopedia series differ from the number calculated by Bacon's formula?
3. Which of these definitions is a) correct (as per the original paper) and b) most commonly used?
4. When we are calculating Martin ratio, should we use Ulcer Index a) as per Bacon formula or b) the most recent value in the Investopedia's series?
• I can't say anything about this case in particular but I suggest not putting too much trust in what Investopedia or similar non-professional investing web sites say on anything in finance. Yes, it is nice that the articles on such sites try to explain things in as much simple terms as possible and they are usually well-formatted, but, from what I have seen, the backgrounds of their writers are far from being ideal to provide such information and their articles sometimes include significant amounts of misleading or erroneous information. Jun 24 at 10:18
• I second @Alper with regards to investopedia. It seems Peter Martin, who developed the index, has a webpage dedicated to the index. I'd follow this page and interpret all else as modifications to the original formula. This also applies to the Martin ratio, which got it's name from Peter Martin it seems. Jun 24 at 11:48
• In Bacon's version above, is $n$ not the number of periods? If not, what is it? Jun 24 at 12:17