Banking Example #3: Capital Requirements

Example loan and deposit transfer with both reserve and capital regulatory requirements.

Setup: one central bank (CB), two commercial banks A and B, and one person x. Reserve requirements are 10% of deposits, capital requirements are 10% combined Tier 1 and  Tier 2 and everyone's balance sheet is initially clear (empty). This example was inspired by this John Carney article at CNBC. Examples 3.1 and 3.2 are more complicated versions (with 3.1 being more complicated than 3.2) in that they show the required capital raised partially through a stock sale, whereas in this example capital is raised entirely through a loan origination fee.

On the bank balance sheets which follow, loans and the capital requirements they induce will be colored green, while deposits and the reserve requirements they induce will be colored red.

Initial balance sheets (for CB, A, B, and x):

CB, A, B, x

Assets	Liabilities
$0	$0

Balance sheets after x takes a $100 loan from bank A (note: I've chosen to show that bank A meets its capital requirements by charging a $10 origination fee to x for the loan [please read Carney above for other ways to find capital and reserves], which it keeps as retained earnings. This lowers x's deposit by $10, and thus lowers the reserve requirements from $10 to $9. I've chosen to show bank A borrowing this $9 from the CB):

Central Bank

Assets	Liabilities
$9 reserve loan to A	$9 reserve deposit for A

Bank A

Assets	Liabilities
$100 loan to x	$90 deposit for x ($100 loan - $10 origination fee)
$9 required reserves	$9 reserve borrowing from CB
Negative Equity	Equity
--------------------	$10 retained earnings

Person x

Assets	Liabilities
$90 deposit at A	$100 borrowing from A
Negative Equity	Equity
$10	------------------------

Balance sheets after x transfers deposit from Bank A to Bank B:

Central Bank

Assets	Liabilities
$9 reserve loan to A	$90 reserve deposit for B
$81 reserve overdraft for A	---------------------------

Bank A

Assets	Liabilities
$100 loan to x	$81 reserve overdraft at CB
--------------------	$9 reserve borrowing from CB
Negative Equity	Equity
--------------------	$10 retained earnings

Bank B

Assets	Liabilities
$90 reserves ($9 required)	$90 deposit for x

Person x

Assets	Liabilities
$90 deposit at B	$100 borrowing from A
Negative Equity	Equity
$10	------------------------

Balance sheets after Bank A borrows $81 of reserves from Bank B and repays CB overdraft by the end of the day (note: Bank A could have borrowed from any other bank, the money markets or the Central Bank's discount window or by attracting new transfer deposits, but I've chosen to show the case where it borrows from Bank B):

Central Bank

Assets	Liabilities
$9 reserve loan to A	$9 reserve deposit for B

Bank A

Assets	Liabilities
$100 loan to x	$81 reserve borrowing from B
--------------------	$9 reserve borrowing from CB
Negative Equity	Equity
--------------------	$10 retained earnings

Bank B

Assets	Liabilities
$9 required reserves	$90 deposit for x
$81 loan of reserves to A	-----------------

Person x

Assets	Liabilities
$90 deposit at B	$100 borrowing from A
Negative Equity	Equity
$10	------------------------

Note: as Carney states, these are simplified reserve and capital requirements. As in the Wikipedia article I link to above, what I'm really doing here for the capital requirements is calculating a capital adequacy ratio (CAR) as the ratio of capital to the sum of risk weighted assets. The loan on bank A's balance sheet is risky, thus it's weighted by the maximum weight 1 (lower risk assets get smaller weights, which increases the CAR, all else being equal). I'm also taking equity = capital. Thus the CAR in this case is $10 equity / $100 loan = 0.10 = 10% (10% or greater is satisfactory).

For an interesting discussion of what banks with 100% capital requirements might be like, look at this Nick Rowe article.