Much of the discussion around the health of banks now focuses on the imposition of new regulations, which will be phased in gradually. But the Bank for International Settlements says financial institutions have plenty of other hurdles to overcome in the meantime, all while adapting to a new business model.

While bank balance sheets worldwide have improved, aided by $1.24 trillion in new capital raised by mid-April, and tier 1 capital ratios are at their highest levels in 15 years, the sustainability of bank profits is questionable, said the BIS report. Indeed, the BIS went as far as to call banks "fragile."

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