"Bear market" / "Bull market" : what relationship those animals have with economy?

Solution 1:

From Wikipedia:

The precise origin of the phrases "bull market" and "bear market" are obscure. The Oxford English Dictionary cites an 1891 use of the term "bull market". In French "bulle spéculative" refers to a speculative market bubble. The Online Etymology Dictionary relates the word "bull" to "inflate, swell", and dates its stock market connotation to 1714.[14] The fighting styles of both animals may have a major impact on the names. When a bull fights it swipes its horns up; when a bear fights it swipes down on its opponents with its paws.[15] When the market is going up, it is similar to a bull swiping up with its horns. When the market is going down it is similar to a bear swinging its paws down.

See the Wikipedia article for even more theories.

Solution 2:

Perhaps because a bull is considered an aggressive animal, one that charges against its enemies, it has been connected to initiative and activity that marks an upward trend. On the other hand, bears spend a long time hybernating in winter, therefore being inactive, a trait that could have connected them to a downward trend in markets.

Solution 3:

Some suggestions as to possible etymologies are made here citing various characteristics of bulls and bears; I don't believe a word of it myself, and I'd think a far better answer is to be found here; for what it's worth, I'd bet on the estimable Mr Quinion.

To summarise (for bear):-

A noble gentleman of this city, who has the honour of serving his country as major in the Train-bands, being at that general mart of stock jobbers called Jonathon’s, endeavouring to raise himself (as all men of honour ought) to the degree of colonel at least; it happened that he bought the Bear of another officer.

The Tatler, 7 July 1709. This tongue-in-cheek tale is saying that the major, wanting to buy a promotion, speculated by selling some stock short. When the transaction went wrong, the story goes on, the major described his fellow officer as a bear-skin man, among other epithets, and called him out, satisfaction being achieved through a fist-fight, neither man being keen on firearms.

Solution 4:

I just ran across a reference to "Bulls" and "Bears" in an anonymous open letter from Jonathan's—the "general mart of stock jobbers" cited in Brian Hooper's answer—to "the Treasury," published in London in (approximately) 1763:

You tell us a[t] your End of Town that we are to have the Liberty of cutting Logwood in the Bay of Honduras, and the free Navigation of the Ships laden therewith; ... that the French give up their Pretensions to the Captures made before the Declaration of War, and that we are to be paid the Expence we have been at for supporting the Prisoners here during the War, which were Objects we could never before obtain, and which we cannot compute by the opposite difference at less than two Millions and a half,—But pray will this Money circulate in the Alley? — Had it not been better that another Campaign should have taken place? Twenty Millions more had been raised for the ensuing Year ;—we might then have had the fingering of a little, for Jobs, Commissions, Contracts, Advance-money, Bulls, Bears, good News and bad News, Peace and War, Scrip. above and under Par, for one more Year. Our Harvest is at an End ; and if those who are Losers have a Right to complain, we certainly have the justest Cause to find Fault with the Preliminaries, rail at the M——r, and abuse the Plenipotentiary.

I can't tell what "Bulls" and "Bears" represent in this paragraph, but they seem very likely to have been set up in opposition to each other, much as "good News and Bad News," "Peace and War," "and Scrip. above and under Par" in the phrases that follow their appearance do. As far as I can tell, this is the earliest confirmed instance where "Bulls" and "Bears" in a financial context are mentioned together and with the strong suggestion of being opposites. That the opposition dates back to the 1760s is a surprise to me.