Does your villain need a positive trait?
Of course not.
One word: JAWS.
If the antagonist of your story is doom and destruction without a conscience, by all means, lock and load. Pull the trigger and riddle that manuscript with evil.
Of course you will notice that the ONE WORD examples I offered are all ONE dimensional antagonists. Admittedly, there are some fine stories out there with thinking and functioning zombies, but grant me a little leeway on this. You know what I'm getting at.
What if you do provide your villain with a positive trait?
Two words: DARTH VADER.
Another: CERSEI LANNISTER
VADER was a henchman, lost in the dark side of the Force, a puppet for his master...but he could not stand by and watch his son die. Maybe not a heart of gold under all the mechanisms, but he showed us he had a heart.
Then we get prequels and find out what a sweet, cute and likable kid he was. We see how he was manipulated. And we know that he never wanted to be evil...but a very evil man recognized his power and did everything he could to ensure his control over Anakin.
Say what you will about the 'newer' SW movies with their quirks and flaws. But don't tell me you can watch Episode IV and see Vader the same way you did before you had the prequels. In that moment when the Emperor is electrocuting Luke, the indecision is clear. It has always been clear. But don't you now get the feeling that in that moment, his mind raced through the every moment since he met Palpatine, that he recognized in the man's actions in that moment, how he had been used and deceived for so very long?
LECTER was undeniably a brilliant psycho. But the...feelings...he had for Clarice humanized him just enough. She clung to her justice, risked everything for what she believed in, and this monster of a man who killed with ease and finesse chose to not kill her, to not hurt her, and to not go back to prison. Killing/maiming her surely must have gleamed like the more enticing solution, given his reputation, yet he chose self mutilation instead and removed his own hand. Evidence of madness, perhaps, but he elected not to take the "easier" course. Though it is still thoroughly creepy, when he spared Clarice, showed her--her, of course her--the depth of his mercy, when this surgeon sacrificed his own hand the dynamic created was infinitely more memorable.
CERSEI is a wicked, spiteful, ruthless, coldhearted bitch. But she would do anything for her children, for her family--except the dwarf little brother who's birth brought about her mother's death. Did the death of her mother create the monster that Cersei is? When she cries because she misses her daughter, are those tears real? Does Cersei Lannister truly have a heart that aches over such maternal sentimentality? Or are they crocodile tears that serve to maneuver her to some gain? We see how she deeply can hate. But we cannot help but feel uncomfortable and distrusting when she shows how deeply she can love.
So how do you choose a positive trait to give your villain?
Ask yourself, "What are my villain's negative traits?" Separate the answers into major and minor.
MAJOR: GREEDY (he's a wall street schemer)
MINOR: PARANOID/SUSPICIOUS (always watching his back, covering his tracks) Where does he feel safe? What makes him feel safe?
ARROGANT (he knows he's smart enough to pull this off) In what instance does he behave humbly?
DISORGANIZED (every part of his apartment is a mess, there's laundry everywhere, take out containers strewn...) Where is he organized? Maybe the room where 'the plan' is laid out on the wall with thumb tacks and pictures is the epitome of organized. Hmmm...what does this order among the chaos say about him?
MAJOR: INFLEXIBLE (he will rule the world and destroy anyone who gets in the way, and anyone of comrades who deviates from the plan)
MINOR: DEFENSIVE (do NOT question him) Who is allowed to question him without the usual repercussions?
CRUEL (he won't just kill someone who fails him, he'll torture them so they learn their lesson before dying) In what instance does he show mercy? Sympathy?
EXTROVERTED (in your face, not going to catch me) What would make him withdraw?
Your major trait should probably stand firm and unwavering, but in the minor traits, there will be something that stands out to you, something that has an opposite/positive side, and you'll probably have an instinctive idea of how to use this, a scene that will show this 'uncharacteristic' side of your antagonist and through this scene you will humanize him, shed light on his pain, weave complexity into his life and create depth to his character and, hopefully, make him more memorable.
Now get to it!