Why are external PhDs considered to take "decades"?

Being a PhD student is a full-time job.

True, "officially" you may be assigned to 20 hours of "study" and 20 hours of "work" by the university, but this is just a way to determine your salary, and does NOT reflect the amount of time you actually spend on research studies.

In the U.S., the nominal time for PhD is about five to six years average. This assumes the student is a full time student. While some people finish their PhD in three years or less, this is truly exceptional. The average is six. (This was the case at least in the school I attended, in the Computer Science department. Length may vary in other departments.) It also depends on what you aim for in your PhD: is graduating after publishing just one paper good enough for you?

Now let's do the math. If it takes about six years to finish a degree, assuming full time, then how much time would it take for a part-time student? Take into consideration also 20%-30% extension of time due to context-switching, but also reduce 15%-25% of the time due to being more efficient (it's easier to waste time when working full-time, in my opinion).

You arrive at 10+ years.

Then again, I know people that worked part-time and studied part-time, and were able to complete their PhD studies in four to six years. I also know people that took five to six years to finish their MSc degree (which nominally takes two years), due to having another full-time job.. It depends mostly on your abilities and aims from PHD (but also quite a bit on your luck).

This advice is based on Computer Science mostly, and it may or may not apply directly to you. As far as I understand your area is only marginally related to Computer Science through the fact that you're interested in Algorithmic Trading.

Everything depends on two factors: your goals and the speed with which you are able to learn and create the things that you need to do in order to achieve your goals. If your goal is to be a professor at TU Vienna, then you will obviously at some point need to submit a PhD thesis and later a Habilitation thesis. The PhD thesis can have 3 to 6 papers in good conferences and one - two papers in some journals, and your habilitation thesis will consist of a minimum of 5 articles in good journals (A-level journals). You will also have to submit some grant proposals and after you manage to get those grants to finish them successfully (typically the requirement is to have EU grants or ERC grants). So you will have to produce at least 15 conference articles, 8-10 journal articles, 2 thesis, and 2 grants in order to get to an Assistant Professor or Professor in Vienna. If you manage to get every paper accepted first time when you submit it (something unheard of), you will still need 6 - 15 years to get to Assistant Professorship or Professorships (counting from the first year of your PhD). Keep in mind that at TU, Assistant or Junior Professorships appear only once at two years or so (and just one position). Most of the people I know from Vienna (TU Vienna, WU, IST Austria, etc) were able to finish PhD thesis in 4-5 years (full time) or 7-8 years (part-time), so there is no reason to consider that it might take a decade.

The system also makes you quit really fast (after 1-2 years) if you do not want (or you are not able for some reason) to put in the effort that is required in order to create at least a decent thesis. The professor will stop talking to you if you don't make any progress for a number of months, for example, or if your papers are not accepted at top conferences. What you need to understand is that your supervisor is your guide, but you will eventually make the journey alone. The supervisor will just help you polish your articles or thesis.

These being said, before applying for a PhD, I would check the CVs, thesis and articles written by TU Professors (Thomas Eiter, Georg Gottlob, Radu Grosu, Silvia Micksh, Stefan Woltran, etc). It helps a lot, as their expectations are that you will produce some work that is at least partially connected to their last articles (so that your work will also fit into their various research projects). Also try to talk with some of their students (you can easily detect them by looking through their CVs - they might have a PhD students entry - or through DBLP or Scholar by looking at their latest publications and identifying collaborators that only published few papers in the last 2-3 years). Try to understand what a PhD means, what are the expectations, and what is the amount of work you need to put in order to get to good results.

I would also recommend you to check these interesting slides from one of the professors I just mentioned: http://www.ifs.tuwien.ac.at/~silvia/research-tips/.

The idea is to try to estimate the expectations, the amount of work needed and the time you think you will need in order to fulfill this work. The actual number of papers depends a lot on the domain in which you are working, but also on the quality of the outlets where you will publish (you might end up with a smaller number of papers if all of them are only in the top outlets for your field). Good luck!

Disclaimer: I do not directly work with any of the persons already mentioned, but I do work at a university from Vienna.