A well-known activist hedge fund that had the backing of billionaire William Ackman has lost more than 90% of its assets.

Marcato Capital Management LP’s assets fell to around $250 million at midyear from $3.2 billion in 2015, people familiar with the numbers said. Marcato’s decline in assets is due to poor performance and client redemptions, the people familiar said. In recent months, Marcato founder Richard “Mick” McGuire sold investment positions to meet redemption requests, though he has no plans to shut his firm, according...