On a crisp morning last October, a few dozen students with wildly diverse backgrounds and expertise filed into the red-brick building of Harvard University's Kennedy School. Three things united them: they were young, they wanted to do good and they were all staggeringly wealthy.

The group was attending a joint course run by Harvard and the University of Zurich, in collaboration with the World Economic Forum, called "Impact Investing for the Next Generation." In this context, that generation means the heirs to some of capitalism's greatest fortunes. Participants had to pass an interview before paying up to $12,000 for a week of classes in the U.S. and Switzerland, not including airfares and board. A more intensive related course costs $58,000.

The program has barely been advertised since its founding in 2015 and word is spread through old-money networks and among European royalty. Alumni include Chung Kyungsun, grandson of Hyundai Group's founder, and Antonis Schwarz, who came into his fortune aged 16 when the drugmaker his grandfather founded was sold for €4.4 billion ($5 billion).