First Republic Bank's efforts to secure a capital infusion continued without success on Tuesday, as the troubled regional lender started to plan for the possibility it may need to downsize or get a government backstop, Reuters reported. Major banks and private equity firms have so far balked at offering First Republic the capital infusion it craves for fear of releasing losses on the bank's loan book and investment portfolio amid a rise in interest rates. Reuters reported yesterday that First Republic is examining how it can downsize and sell parts of its business, including some of its loan book, in a bid to raise cash and cut costs. This could help the bank tackle its negative book value — the gap between its liabilities and its assets — which analysts and investors estimate to be between $9.4 billion and $13.5 billion.