I realized the other day that I didn't know the origin of this phrase and, as with most things in my life, it turned out to be (vaguely) Victorian.
According to Brewer's Dictionary of Phrase and Fable, a White Elephant is "some possession the expense or reponsibility of which is not worth while; a burdensome possession. The allusion is to the story of a king of Siam who used to make a present of a white elephant to courtiers he wished to ruin" (pg. 369).
I am amazed Anna Leonowens wasn't given one of these, considering her sassiness.
I guess white elephants are ALWAYS a bad investment, because the phrase actually became popularized in the Victorian era when P.T. Barnum bought one (Barnum already had had his share of elephant hijinx with Jumbo, the Civil Disobedience Elephant). Apparently Barnum
didn't do his research wanted to acquire a white elephant from the King of Siam who probably fainted when Barnum wanted to pay to be burdened with one.
I don't know if the King of Siam thought Barnum wanted the metaphorical white elephant as well as the literal one, but Barnum invested loads of time and money in trying to acquire Toung Taloung, the "Sacred White Elephant of Burma". When he finally got Toung Taloung home, he discovered that it wasn't white at all–it was grey, with some pink patches. SO MUCH FOR YOUR ADVERTISING, BARNUM. ENJOY THIS PET THAT WILL MAKE YOU NO MONEY AND COST YOU A GODDAMNED FORTUNE IN LEAVES AND BARK.
The moral of the story is: if the King of Siam gives you a present, he hates you.