KKR's KKR -1.15%decrease; red down pointing triangle largest private-credit fund held by individual investors took a $560 million loss in the first quarter when a growing number of loans tipped into default.

The write-down—equivalent to about 10% of the fund's net asset value—is one of the biggest indicators so far of underlying problems in a large private-credit fund. Defaults in the fund jumped to 8.1% in the first quarter from 5.5% in December, KKR said.