Why is Antonio sad in The Merchant of Venice?

The first line in Shakespeare's The Merchant of Venice belongs to Antonio, the merchant of Venice.

ANTONIO: In sooth, I know not why I am so sad. [1.1.1]

Hamlet says the same thing.

HAMLET: I have of late—but wherefore I know not—lost all my mirth. [Hamlet, 2.2.301-302]

The difference between Hamlet and Antonio is that Hamlet knows exactly why he's lost all his mirth, and at that moment he's playing words with Rosencrantz and Guildenstern, who are trying to "glean" what they can from Hamlet to report back to Claudius.
Antonio has good cause to be sad later in the play, when he believes that all of his ships are lost at sea and his debt of "a pound of flesh" comes due to Shylock. At the beginning of the play, however, even Antonio can't figure out what's causing his sadness.
Antonio rejects out-of-hand the possible reasons for his sadness that Salanio and Salerio give him—that he's worried about his ships at sea or that he's in love.

SALANIO: Why, then you are in love.
ANTONIO: Fie, fie! [1.1.47-48]

Some scholars believe that the cause of Antonio's sadness is that he's already missing his best friend, Bassanio, who is hoping to marry Portia and plans to move away to be with her.
Gratiano suggests that Antonio wants to appear melancholy in order to enhance his reputation as a thoughtful, serious, respectable merchant.

GRATIANO: O, my Antonio, I do know of these,That therefore only are reputed wise,For saying nothing; who, I am very sure,If they should speak, would almost damn those earsWhich, hearing them, would call their brothers, fools.I'll tell thee more of this another time:But fish not with this melancholy bait,For this fool-gudgeon, this opinion. [1.1.99-106]

If this is the case, Antonio is simply putting on an act, just like Hamlet did, except that Antonio hasn't "put an antic disposition on." [1.5.192] Antonio is just acting sad so he appears more reserved and dignified to those around him.