A bank borrows at the Fed Funds Rate (say 0.1%) and buys one year Treasuries (currently 0.26%). On Treasury trades, banks can do leverage of 100x or more. So the bank's profit is 0.16 times 100 or 16%.
If the Federal Reserve raised the Fed Funds Rate to 1%, then the bank would be borrowing at 1% and lending at .26%, and they'd be .74% in the hole per bond, 74% accounting for 100x leverage. Big banks are comfortable doing this trade right now, because they know the Federal Reserve isn't going to raise interest rates. (It is more accurate to say that the Federal Reserve is owned by the big banks, rather than acting independently.)
Instead of buying Treasuries, they could invest in stocks, futures, corporate bonds, mortgages, houses, whatever. The bank borrows at zero and buys stuff that yields (on average) greater than zero. The bank can lend money to hedge funds who in turn invest in VC funds or startups. (ZIRP indirectly causes a startup valuation bubble.)
Most of the time, the banks make huge profits (borrowing low and lending high).
Every 20 years, there's a severe recession, and the big banks get a bailout.
When interest rates are lowered, that's an indirect bank bailout. Suppose the bank owns a 5 year duration bond, uses 10x leverage, and interest rates go down 1%. The bond prices go up 5*1 = 5%. With 10x leverage, that's 50% profit.
the problem with this theory is the bank doesn't borrow at zero. Goldman Sachs has 380 Bln of outstanding debt, and is paying roughly AA corporate rates on that debt. Overnight bank rate is 0.13 right now, which is the Fed Funds rate
If you have 30x leverage in 5 year duration bonds, and interest rates go up 1%, you lose 150%!
ZIRP (0% interest rates) is a wealth transfer to big banks, a backdoor bailout.