This section is from the book "Banking Principles And Practice", by Ray B. Westerfield. Also available from Amazon: Banking principles and practice.

The necessity of this common ratio as among the banks of a system may be illustrated numerically. Assume the following data: Bank A has $100,000 cash reserve, and likewise all the other banks, B, C, D, and E, have together, $100,000 cash reserve; bank A keeps 10 per cent reserve, the other banks, B, C, D, and E, keep 20 per cent; one-fifth of the deposits of each bank is not checked out, three-fourths of the checks are redeposited in the drawee bank, and the rest are deposited in the other banks and presented through the clearing house. Then the situation will be as follows:

All Other Banks, B, C, D, and E | ||||

Bank A | Each Smaller Than A | Each Equal to A | Each Larger Than A | |

Cash Reserve......... | $ 100,000 | $100,000 | $ 400,000 | $ 800,000 |

Per cent Reserve...... | 10% | 20% | 20% | 20% |

Deposits ...................... | 1,000,000 | 500,000 | 2,000,000 | 4,000,000 |

Checks Drawn........ | 800,000 | 400,000 | 1,600,000 | 3,200,000 |

Checks Redeposited in Drawee Bank....... | 600,000 | 300,000 | 1,200,000 | 2,400,000 |

Checks on it Presented Through Clearing House ........................ | 200,000 | 100,000 | 400,000 | 800,000 |

It is seen that bank A suffers an adverse clearing house balance of $200,000 less $100,000, or $100,000, which wipes out its reserve. Had it kept the same per cent reserve as the other banks its clearing house balance would have been zero. On the other hand, a more slender reserve would have resulted in suspension and failure. In fact, the above adverse balance of $100,000 is a minimum, for in all probability some of the checks on B would have been deposited in C, D, or E, and presented by them and not by A at the clearing house. If the cash reserve of B, C, D, and E combined had been assumed to be less than $100,000, the adverse balance of A would have been greater.

If, instead of supposing that bank A's cash reserve is equal to the total reserve of banks B, C, D, and E, combined, we suppose that the reserve of each bank is $100,000, then the total reserve for B, C, D, and E will be $400,000, deposits $2,000,000, and clearing house items $400,000. One-fourth of $400,000, or $100,-000, of these clearing house items will be presented against, let us say, B. The banks presenting checks on B are A, C, D, and E, and, as it has been assumed that they are all the same size, one-fourth of $100,000, or $25,000, will be presented by A. By the same reasoning A will present $25,000 against each of the other banks, C, D, and E, in the group, thus presenting a total of only $100,000 to be deducted from the $200,000 which B, C, D, and E present against it. Under these assumptions it is evident that A would suffer an adverse clearing house balance of $100,000.

If instead of supposing A equal to B, C, D, and E, combined, or equal to B, C, D, and E, severally, A is assumed to be smaller than B, C, D, and E, severally, adverse balances will likewise exist. For if it is assumed that each of the banks B, C, D, and E, has, say, twice the cash reserve that A has, then the checks on B presented by A, C, D, and E, will be divided somewhat in the proportions of 1, 2, 2, and 2; and one-seventh of $800,000, or $114,285, will be less than the checks presented against A. Therefore, whether bank A is considered as smaller, equal to, or greater than the other banks, it may expect adverse clearing house balances if its ratio of reserve to deposits is more slender than that which the other banks of the system maintain.

This limitation does not apply to deposit rights arising from the deposit of cash; it applies only to those additional deposits built upon cash holdings by the method of loan and discount. For if $100,000 in cash is deposited, checks drawn later to that amount can be fully met. Any one bank can build up any amount of deposit liabilities by the cash method, and proceed to loan them all out except such a proportion as business expediency proves proper as a reserve. The adverse clearing house balances which follow the loans will be met by the cash that has been received over the window. Accordingly bankers solicit accounts and offer various inducements to get cash deposits and build up their demand liabilities in that way, whereas they guard very carefully against overextension of demand liabilities by the loans process.

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