A 2017 study for the National Institutes of Health found that Black people were incarcerated at rates between five and seven times those for whites convicted for similar drug-related offenses.

Black people were nearly four times as likely as whites to be arrested for marijuana possession in the U.S. in 2018, despite statistics showing that whites have higher lifetime rates of pot usage, according to the American Civil Liberties Union.

“It’s really unbelievable how that can happen,” said the musical artist, born Shawn Carter. “We were the ones most negatively affected by the war on drugs, and America has turned around and created a business from it that’s worth billions.”

Mr. Carter is starting his fund with $10 million in seed money.

Cannabis is now a $20 billion legal business in the country and estimates by the New York investment bank Cowen & Co. predict it will surpass the $70 billion market for U.S. wine by 2030. In November, voters in Arizona, Montana, New Jersey, and South Dakota approved recreational marijuana use, while Mississippi approved medicinal use, bringing the total number of states that have legalized cannabis in some form to 35.

In Massachusetts, where cannabis has been legal since 2016, fewer than 6% of the almost 7,000 agents registered to sell or grow cannabis in the state are Black. In Denver, where cannabis sales have been legal since 2014, Black ownership of cannabis businesses is under 6%, while in Washington State the share is roughly 3%, according to state statistics. Around 10% of businesses in the U.S. were Black-owned in 2017, the most recent year for which numbers are available from the Census.

The fund will be run by Mr. Carter and Desiree Perez, chief executive of Mr. Carter’s Roc Nation entertainment conglomerate.

“I wanted to do something in a real, concrete way, where I do my part,” said Mr. Carter.

Mr. Carter said he and Subversive’s chairman, Michael Auerbach, were influenced by investor Robert Smith’s “2% Solution,” a proposal for corporations to channel 2% of their net income to Black-owned businesses.

Kareem “Biggs” Burke, one of the co-founders of Mr. Carter’s record label, Roc-A-Fella Records, was incarcerated for almost five years on marijuana charges which made an impact on the entertainer.

“It’s not a spreadsheet, it’s real people,” said Mr. Carter.

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