Deborah C. Wright, chief executive of Carver Bancorp in New York, the nation’s largest African-American-run bank or thrift company, speaks softly but carries a big stick — and a big ax.

Since taking over the top spot at the troubled, publicly owned, Harlem-based thrift in June of last year, Ms. Wright has beaten back a coup attempt by shareholders led by a former Harvard classmate; fired staff in the course of replacing half the employees, including every senior executive; and sold off two of Carver’s seven branches. Her aim was to transform a hallowed community institution into a profit-oriented, modern, full-service institution that is both an aggressive lender and cost-cutter.

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