In the weeks before his bank collapsed last year, exacerbating the largest banking crisis in a generation, First Republic’s chief executive, James Herbert, was busy selling millions of dollars’ worth of his shares in the company. The sales, which netted the executive and his family nearly $7 million over the six months that preceded First Republic’s demise, were waved through by Mr. Herbert’s personal bankers at Morgan Stanley without their passing any judgment on whether he was trading on...