Here is some more detail on the use of bear from Merriam-Webster’s Word for the Wise, but it doesn’t explain the reason for using the bull.
"According to an old proverb, it isn’t wise to sell the bear’s skin before one has caught the bear. This saying inspired the 18th-century phrase "selling (or buying) the bearskin." Bearskin, shortened to bear, was soon used to refer to certain stock. Here’s how it worked. A speculator would sell a borrowed stock (the bear) with a future delivery date. Why? Because he expected stock prices would go down so that the stock could be bought back at the lower price and the difference from the selling price kept as profit.
This sort of speculation rocked England in the huge South Sea scandal of 1720. Although this sense of bear was already established, the bursting of the South Sea Bubble ensured its spread far and wide.
By the way, the stock market sense of bull seems to have been chosen simply as a fitting alter ego to the bear. "
Here is a similar explanation paraphrased from the Wall Street Journal. It supports Demojohn’s idea about bear and bull baiting being the reason for the word bull.
"Long ago, "bear skin jobbers" were known for selling bear skins that they did not own; i.e., the bears had not yet been caught. This was the original source of the term "bear." This term eventually was used to describe short sellers, speculators who sold shares that they did not own, bought after a price drop, and then delivered the shares.
Because bull and bear baiting were once popular sports, "bulls" was understood as the opposite of "bears." I.e., the bulls were those people who bought in the expectation that a stock price would rise, not fall. "
For those of you who wish to be able to identify a bull from a bear at first glance, here are some tips from 1785 by one Thomas Mortimer in Every Man His Own Broker, or, A Guide to Exchange Alley [London’s Wall Street in the 18th century]. First off, "according to Mortimer’s definitions, it would appear that bull and bear had much more specific meanings in 1785 than they do today. A bull wasn’t just someone who thought—and hoped—that the market would go up. He was the equivalent of a modern investor who uses margin—and lots of it!...A bear wasn’t just a pessimist—he was a short-seller."
[The Bear] is easily distinguished from the Bull, who is sulky and heavy, and sits in some corner with a melancholy posture: whereas the Bear, with meager, haggard looks, and a voracious fierceness in his countenance, is continually on the watch, seizes on all who enter the Alley, and by his terrific weapons of groundless fears—and false rumors—frightens all around him out of property he wants to buy; and is as much a monster in nature, as his brother brute in the woods.
Ilka
Sources:
Merriam-Webster’s Word for the Wise
The Investment FAQ (Wall Street Journal paraphrased)
Thomas Mortimers description