Rare is the gifted teenager who is not bored in high school. Yet few have signaled their boredom as extravagantly as Martin Shkreli, the pharmaceutical company founder who was sent to jail on Wednesday to await sentencing for a fraud conviction.

Mr. Shkreli was a chronic class-skipper who, friends have said, preferred to spend his time on chess and playing guitar in a band. His highly selective Manhattan school asked him to stop attending.

Entrepreneurs, it turns out, do not just move fast and break things, as Facebook’s longtime credo put it. They are also more likely than others to cross the line.

According to research by the economists Ross Levine and Yona Rubinstein, people who become entrepreneurs are not only apt to have had high self-esteem while growing up (and to have been white, male and financially secure). They are also more likely than others to have been intelligent people who engaged in illicit activities in their teenage years and early 20s.