Money multiplier

In monetary economics, a money multiplier is one of various closely related ratios of commercial bank money to central bank money under a fractional-reserve banking system. Most often, it measures an estimate of the maximum amount of commercial bank money that can be created, given a certain amount of central bank money. That is, in a fractional-reserve banking system, the total amount of loans that commercial banks are allowed to extend (the commercial bank money that they can legally create) is equal to an amount which is a multiple of the amount of reserves. This multiple is the reciprocal of the reserve ratio, and it is an economic multiplier.

Although the money multiplier concept is a traditional portrayal of fractional reserve banking, it has been criticized as being misleading. The Bank of England and the Standard & Poor's rating agency (amongst others) have issued detailed refutations of the concept together with factual descriptions of banking operations. Several countries (such as Canada, the UK, Australia and Sweden) set no legal reserve requirements. Even in those countries that do (such as the USA), the reserve requirement is as a ratio to deposits held, not a ratio to loans that can be extended. Under the Basel III global regulatory standard, it is the level of bank capital that determines the maximum amount that banks can lend.Basel III does stipulate a liquidity requirement to cover 30 days net cash outflow expected under a modeled stressed scenario (note this is not a ratio to loans that can be extended) however liquidity coverage does not need to be held as reserves but rather as any high-quality liquid assets

In equations, writing M for commercial bank money (loans), R for reserves (central bank money), and RR for the reserve ratio, the reserve ratio requirement is that ${\displaystyle R/M\geq RR;}$ the fraction of reserves must be at least the reserve ratio. Taking the reciprocal, ${\displaystyle M/R\leq 1/RR,}$ which yields ${\displaystyle M\leq R\times (1/RR),}$ meaning that commercial bank money is at most reserves times ${\displaystyle (1/RR),}$ the latter being the multiplier.

...
Wikipedia