Both, but I always like to think nurture and environment always over come nature. Prepare yourself to take a dive into one of my long meaningless posts that is fueled by my lack of sleep and will contain a minimum of 5 grammatical errors.
Let's say you have two pairs of mice, two females and two males. Intelligence speaking, they are on equal footing. Now let's say we take a gene out of one pair of mice that impairs its ability to learn things fast. So one pair is perfectly normal, and the other pair is mentally impaired, but not challenged. They just have a harder time learning things. So these pairs breed and have babies. Take the normal off spring and put them in a dull environment with little to no stimulation. No toys, no colors, even their food is the same old pellet, just dull and extremely plain. They would also be deprived of interaction with humans. The normal mice will be about average intelligence. Now we go to the genetically altered mice, who lack the genes to learn well. Their environment is full of color, toys, tubes, and their food is diverse (not the same thing over and over again). You take them out for 30 minutes a day to do tests, cheese mazes, puzzles, and just give them the attention almost all animals crave. The mentally impaired mice will be nearly as curious, smart, optimistic, and social as the normal mice.
I personally think greed can be cured by the nurture method (but then again I'm a pseudo-science fan boy). I strongly believe almost all traits, from greed, to social skills, to intelligence, to self-motivation, are all nurtures traits. But I do believe in certain formulas of traits overcoming each other, and they are all greatly influenced by the environmental conditions. But that's just me.
edit:
This isn't the original story I based my post on, but I just so happened to have found it.