By completing the series of posts concerning deterministic indicators, which I consider a real and valid alternative to the indicators of mean and variance, today we analyze the Ulcer Index.
This indicator, presented in 1989 by Peter Martin in a book, if I'm not mistaken by Fidelity, has unfortunately never had the importance it deserves from the academic community because it has never been published a paper with the classic academic canons.
So the task of disclosing this indicator is up to the practitioners, or the market players who fight day after day to get the best possible returns for their customers.
Unlike Volatility, which is the practical term to call the standard deviation, less known by non-professionals, which is a symmetrical indicator, the ulcer index is an asymmetric indicator.
Take two historical series that have same returns but with opposite sign, the first gains 2% and loses 3% that we will call "Negative" and the second that gains 3% and loses 2% that we will call "positive".
As you can see, the two historical series have two completely different trends.
If we use volatility as an indicator of risk (although as I have explained several times, it is an indicator of uncertainty and not of risk), the two historical series have the same volatility, that should mean the same risk.
This situation is possible because in the calculation formula of standard deviation the returns are squared and lost the sign of positive or negative performance, and therefore the ability to distinguish if I'm taking a risk that is worth running or not.
While the ulcer index, valuing only the negative parts of the historical series has an entirely different value from the first historical series to the second, clearly indicating that the "positive" historical series is better than the "negative" series, since the ulcer index is much lower.
For those who want to understand better how the ulcer index works, I invite to read the official page of Peter Martin at http://www.tangotools.com/ui/ui.htm
Practically, the abdominal pain index relates the maximum loss, i.e. the drawdown (explained in the post Some considerations on the Drawdown and Deterministic maximum loss indicator ) with the recovery time.
The faster a fund recovers the new highs, the lower the ulcer index and consequently the comparison between more funds belonging to the same peer group (homogeneous group) the ulcer index is a very interesting indicator to be strongly considered.
But in reality, the ulcer index can provide very interesting indications to understand what is happening to a historical series.
If we analyse the volatility of a historical series with "rolling windows", that is, with windows of a specific time horizon that flow over time, taking a year of observation as a window, we realise that the same varies and also over time.
The same thing also happens obviously with the ulcer index with a window of a year: when the historical series begins to fall, the ulcer index begins to rise.
The exciting thing is that the Ulcer Index, due to its asymmetric characteristics, realises the change of the trend in advance of the volatility and this is very useful for those who must actively act on the financial markets to reduce the real risks to customers, i.e. risks of massive loss.
The due consideration ...
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At this link, you can download the add-on for excel to simply calculate both the max drawdown and the Ulcer Index: maxdd_e_u_20180630-100336_1.zip