A decade after Paulson shot to fame betting on the collapse of the U.S. housing market, the hedge-fund mogul is struggling to persuade investors to stick with him after a string of missteps on everything from gold to European bonds to drug stocks. Since the end of 2015 alone, assets at Paulson & Co. have fallen by $6 billion from losses and client withdrawals. The decline, underscored in the firm’s most recent regulatory filing, leaves Paulson and his employees with just $2 billion in client money. Most of the remaining $8 billion is Paulson’s own fortune. His personal wealth aside,...