Granted, the study makes some assumptions that could be challenged. It doesn't have IQ stats on billionaires. Instead, it equates cognitive ability with attendance of top universities as defined by U.S. News and World Report.
But wealthy children can also get into top universities in part because their parents attended or gave the school large gifts.
Wai acknowledged that "some students attend an elite school with lower-than-typical test scores due to athletics, legacy status or political connections." He said that because some high-scoring kids don't attend elite universities "factors in both directions likely counterbalance one another."
Read MoreSelf-made billionaire: The how-to guide
The report also said billionaires who inherited their fortunes were more likely to attend elite institutions than self-made billionaires—suggesting that privilege is often passed down by parents rather than earned through brainpower.
While billionaires are much better educated in most countries around the world, especially the U.S., education is not as correlated with billionaires in China and Russia.
In those countries, "those with greater wealth were not more likely to have attended an elite school." (That's likely because getting rich in China and Russia depends more on political connections than degrees.)
Overall, Wai concluded that the wealth gap goes hand in hand with the education gap. The world's super rich, he said, are also "scary smart."
"I think we should deeply consider the implications when a select group of scary smart people also tend to hold a disproportionate share of global wealth and power," he said. "We depend on these people to make wise decisions for all of us. "
—By CNBC's Robert Frank.