From http://en.wikipedia.org/wiki/Social_mobility:

Research on American mobility published in 2006 and based on collecting data on the economic mobility of families across generations looked at the probability of reaching a particular income-distribution with regard to where their parents were ranked. The study found that 42 percent of those whose parents were in the bottom quintile ended up in the bottom quintile themselves, 23 percent of them ended in the second quintile, 19 percent in the middle quintile, 11 percent in the fourth quintile and 6 percent in the top quintile.

(Now, it's possible that “ability in managing wealth” is heritable to some extent, but it seems unlikely that that alone would cause such an effect, without your parents being wealthy ‘directly’ causing you to be wealthy. And note that that study was across one country -- if they took quintiles worldwide I'd expect the results to be even more dramatic.)