As originally used in the financial jargon ex-dividend date, ex is used correctly and has the sense "after (in time)". That is, if you buy something ex-dividend, the dividend has already been paid (you're buying after the payment), and so you won't get it. [1] It's sense II in Lewis and Short ( http://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%... ) (Note sense II.A.2, which gives us the more vernacular English prefix ex-, as in ex-wife.)
"Outside" is not even one of the many senses of ex in Latin; ex always has a sense related to the core concept of "from". "Outside" is extra.
[1] For some reason, the ex-dividend date is one day before the actual payment, but the idea is still that you're buying after the date of the dividend.
>> [The ex-date] is the day after holders of the security are entitled to the dividend.
> It's not the day when holders are entitled to the dividend because if you trade on a particular day, you don't own the securities until settlement occurs
Imagine that the ex-date for a security is 2017-05-19. You sell one such security on 2017-05-18. Settlement clears on 2017-05-22. Because of the delay in settlement, you held the security on the ex-date (and on the day before the ex-date), but you're not entitled to the dividend because you sold the security before the ex-date.
That's my reading of the two comments. I take no position on this. The point I'm making is different, that in the phrase "ex-dividend date", the "ex" and the "dividend" are not related to each other. They both relate to "date"; "ex-dividend" is not a logical unit within the phrase. However, the phrase "ex-dividend date" (good Latin usage) was clipped to "ex-dividend", and then people started assuming "ex" meant "without", because an "ex-dividend security" (no longer good Latin usage) was one that traded without rights to the dividend.
Stated another way --
A "dividend date" is a kind of date, a date related to the concept "dividend". "Ex-dividend date" is (originally) a prepositional phrase meaning "after the dividend date". It's not a kind of date related to the concept "ex-dividend"; "ex-dividend" is not a concept.
But then, English-speaking traders who didn't know Latin reanalyzed the phrase "ex-dividend date" as a noun phrase referring to a kind of date, which required a further reanalysis of what exactly "ex" meant. That new meaning, "without", is original to English.
In tree form, we have an original phrase (ex-(dividend date)) being reanalyzed as ((ex-dividend) date).
That's right. The ex date is relevant to the day you trade (which in practice means entering into a contract to buy and sell securities at a certain price, not actually delivering those securities/money), whereas the record date is the equivalent for the day of ownership. The ex date will be X-1 business days before the record date with X and the definition of business day depending on the market settlement convention. In some markets X=1 hence the confusion between the two, I think.