Someone told me once that a contributing factor to the "jewish lawyer stereotype" was caused by law firms who discriminated against jews — who then started up their own law firms, and outcompeted all the other law firms because it's easier to find talent if you don't discriminate.
The Harlem Globetrotters picked the best of the african-american basketball players, who were not welcome on other teams. The result was predictable in hindsight, they beat the other teams by humiliating margins.
I've heard that story as well. Same thing happened with investment banks. Legend has it that Goldman Sachs was started because Marcus Goldman and Samuel Sachs couldn't get jobs at WASPy firms.
The other side of the coin is that the white-shoe firms didn't touch certain types of businesses (like M&A or IPOs) because those businesses were considered "ungentlemanly." So they were left to the Jewish firms, who developed an expertise in the fields during the decades that they were considered unimportant.
If you really want to trace the origin of the Jewish finance/law stereotypes back to their root, it goes all the way back to Middle Ages (and possibly earlier). Money handling and the trades were considered unclean/uncouth professions, and the landed aristocracy were so rich that they didn't need to concern themselves with such business. Some countries even mandated that Christians couldn't engage in such businesses. Jews took up finance, merchandizing, artisanry, etc., and placed a great deal of importance on professional success -- it being the only way that Jews could advance in society. To whatever extent that my people are stereotyped as "naturally" good at finance, etc., it's usually because nobody else was touching those things for hundreds of years.
I think the "unclean/uncouth" bit for handling money came from e.g. Exodus 22:24 (25), which prohibits charging interest to "my people". So if you're Jewish and believe that you're the chosen people, you can charge interest to Christians. If you're Christians and think the Jewish rejected the messiah, then you can charge interest to Jews — except there aren't very many, so you won't be able to make a living.
Another part of the medieval stereotype I think came from Jewish cultural emphasis on literacy so good Jewish boys could read the Torah. As a side effect, it's hard to do e.g. banking if you can't read.
Also see: hospitals with names like Beth Israel or Mount Sinai.
Jewish American doctors, facing discrimination from the WASP elite of the era, leveraged their talents, innate ability, and entrepreneurial drive to create institutions with names that now stand for the best in the business.
The Harlem Globetrotters picked the best of the african-american basketball players, who were not welcome on other teams. The result was predictable in hindsight, they beat the other teams by humiliating margins.