In banking, quite often, I see "thousands" abbreviated as "M", or
"millions" as "MM", the idea being the "M" is Roman numerals (ex. $10M
= $10,000 or $1MM = $1,000,000).  I'm looking for some sort of
professional banking / investment site which details this, or ideally,
a historical reason for this use.

In the banks I have worked for, I have never seen $1,000,000 expressed as $1,000m

Thinking about it, in the other products of the company that I used to
code for, it was universally the case that lowercase 'M' eg: 'm' meant
millions, and that was used by hundreds of banks Worldwide.

I doubt that is current practice, and if anyone is using it then they
are asking for trouble.

Thousands are "K" (Kilo).  "M" means millions and "MM" means billions
(a billion in UK English and in Europe used to mean a million million,
but the US usage of a thousand million, which the Europeans called a
"milliard" is now standard).  The capital letters are used because
some old-fashioned Telex machines don't have a lowercase character
set.

Your bank is different from any other I have seen.
M is often 1000 as the romans used letters instead of the number
system we use. If you bank use any of the following letters as well I
would say that it is based on roman numerals.

I = 1
V = 5
X = 10
L = 50
C = 100
D = 500
M = 1000

MM would relate to algebra as a variable next to another variable
means multiplied, (eg xy = x times y)

Anyway the reasons the romans used these letters is

A) they were mostly straight lines (except D and C) therefore easier
to carve into stone.

B) they had already invented this system of writing and didn't want to
take the time to invent new characters. Since none of these letters
were vowels they could not be confused with words.

C)It would used to many symbols to keep representing the next tenth
power as another letter so they did MM instead of say S.

I hope that answers your question.

31415926-ga

There are two conventions:
In Europe (frde-ga), a lower-case m is used for millions.
In the States, M has been used for thousand and MM for Million.

I have noticed in the last couple of years a trend to use K for
thousand in the States (maybe not in banks), probably to avoid
confusion.  I found that K has been used since the 1970s.

This site may be of interest:

http://www.techwr-l.com/techwhirl/archives/9412/techwhirl-9412-00729.html