The national discussion over race has resulted in an accelerated push for diversity on boards and in companies across the U.S. It has also prompted some investors to look at investment management, one of the least diverse fields on Wall Street. A 2019 study commissioned by the Knight Foundation found women- and minority-owned firms held less than 1% of assets managed by mutual funds, hedge funds, private-equity funds and real-estate funds in 2017, despite performance typically on par with firms not mostly owned by women or minorities.

Yale’s endowment, one of the biggest in the country, is watched closely by other schools given Mr. Swensen’s stature. He has championed the idea that big investors should diversify beyond stocks and bonds and incorporate qualitative assessments of managers into investment decisions. His approach has generated big gains for Yale and reshaped how endowments and foundations invest.

“Our goal is a level of diversity in investment-management firms that reflects the diversity in the world in which we live. Genuine diversity remains elusive, giving investors like Yale and your firm an opportunity to drive change,” Mr. Swensen wrote in a letter to money managers this month. Yale plans to ask its managers for relevant data on diversity annually, the letter said.

Mr. Swensen said firms would be measured annually on hiring, training, mentoring and retaining women and minorities on their investment staffs. Though Yale isn’t mandating specific targets, Mr. Swensen said the university could pull its money from firms that show little progress over time. Small firms that rarely make new hires will likely have more time to show progress, he said.

In a recent Zoom interview, Mr. Swensen, age 66, said he and others at Yale’s endowment had long discussed diversity with managers they were invested in. He said he had held off on systematic efforts to encourage more diversity at those firms in part because of a belief it resulted from an insufficient pipeline of diverse candidates entering asset management.

But the Black Lives Matter movement has had a galvanizing effect on him and the team, Mr. Swensen said, prompting discussions over Zoom about how to address the lack of diversity in the investing world. He immersed himself in newspapers’ coverage of the protests and said he was reminded of the activism of the 1960s, when he was a high-school student reading about the civil-rights and Vietnam War protests from his hometown of River Falls, Wisc. He said he was astonished and heartened by the movement’s impact.

“I’m not going to make a contribution by marching anywhere,” said Mr. Swensen, who was diagnosed with late-stage renal-cell cancer in 2012, seated on a couch in his Killingworth, Conn., home. “So I figured, what can we do?”

Mr. Swensen said his thoughts on the benefits of diversity in investment management reflect the benefits he has seen at Yale itself.

Yale’s polyglot student body has enriched the university community and made Yale a more meritocratic place than decades ago, before women were admitted and when a quota on Jews existed, he said. He similarly hopes investment firms staffed by people with the broadest set of backgrounds will outperform those that are overwhelmingly white and male.

Mr. Swensen suggested in the letter, sent to the 70 U.S. managers Yale is invested with, that they consider recruiting directly from college campuses rather than traditional recruiting grounds such as investment banks.

He also wrote that he wasn’t focused on whether a firm was majority-owned by a woman or racial or ethnic minority. In the interview, Mr. Swensen said that approach could let managers off the hook too easily and take the focus off of how those firms are building their broader workforce. He also said firms can artificially engineer their ownership structures to fit the bill of being considered a firm owned by women or minorities.

It is a contrarian view compared with that held by many institutional investors. Firm ownership has become a common proxy for diversity.

The ownership metric was crucial in an inquiry earlier this year by Reps. Emanuel Cleaver II (D., Mo.) and Joseph P. Kennedy III (D., Mass.), when the legislators surveyed the largest U.S. college and university endowments to ask about their use of diverse-owned investment firms. Endowments haven’t routinely tracked the diversity of their money managers, but the inquiry and possibility of legislation have helped sparked discussion at multiple endowments beyond even those included in the inquiry, said several endowment chiefs.

Despite the push, some female and minority founders say formidable hurdles exist in raising money and that expanding how diversity is considered could make it even more difficult for their firms to grow. In addition, some asset managers say it could be intrusive to make their employees identify their race and gender.

The Yale Investments Office will report on the progress it makes on the diversity of its own staff annually, Mr. Swensen said. While the number of female protégés of Mr. Swensen’s that have gone on to run the endowments of schools or foundations outnumbers that of their male counterparts nine to five, Mr. Swensen said Blacks and Latinos should be better represented on Yale’s investment team.