Example loan and deposit transfer with both reserve and capital regulatory requirements. Required capital is partly raised by a stock issuance and partly by retained earnings (from a loan origination fee).
Example #3 is a simpler variation on this without the stock sale (i.e. capital requirements are met entirely through retained earnings).
Example 3.1 is a more complicated example documenting the balance sheets associated with a stock investor as well.
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. This example was inspired by this
John Carney article at CNBC.
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. Assume starting out that that any preexisting entries on the CB's balance sheet (e.g. having to do with stock investors owning $5 in the first place*) are summarized in the cells "preexisting assets" and "preexisting liabilities." You can assume, of course, that the CB's balance sheet is initially in balance, i.e.: preexisting assets = preexisting liabilities
Note that all balance sheets are shown only on the first and last steps.
Only balance sheets which change are shown on the intermediate steps.
Initial balance sheets for CB, A, B and x:
A, B, x
| Assets |
Liabilities |
| $0 |
$0 |
CB
| Assets |
Liabilities |
| preexisting assets |
preexisting liabilities |
Balance sheet after Bank A sells $5 of stock to unnamed investors:
CB
| Assets |
Liabilities |
| preexisting assets |
preexisting liabilities - $5 |
| ----------------- |
$5 reserve deposit for A |
Bank A
| Assets |
Liabilities |
| $5 reserves at CB |
$0 |
| Negative Equity |
Equity |
| ------------------ |
$5 |
Balance sheets after x takes a $100 loan from bank A (note: I've chosen to show that bank A meets half its capital requirements by charging a $5 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 $5, and thus lowers the reserve requirements from $10 to $9.50. I've chosen to show bank A borrowing $4.50 of this reserve requirement from the CB):
CB
| Assets |
Liabilities |
| preexisting assets |
preexisting liabilities - $5 |
| $4.50 reserve loan to A |
$9.50 reserve deposit for A |
Bank A
| Assets |
Liabilities |
| $100 loan to x |
$95 deposit for x |
| $9.50 required reserves |
$4.50 reserve borrowing from CB |
| Negative Equity |
Equity |
| ------------------------ |
$10 required capital |
Person x
| Assets |
Liabilities |
| $95 deposit at A |
$100 borrowing from A |
| Negative Equity |
Equity |
| $5 |
------------------------ |
Balance sheets after x transfers deposit from Bank A to Bank B:
Central Bank
| Assets |
Liabilities |
| preexisting assets |
preexisting liabilities - $5 |
| $4.50 reserve loan to A |
$95 reserve deposit for B |
| $85.50 reserve overdraft for A |
-------------------------- |
Bank A
| Assets |
Liabilities |
| $100 loan to x |
$85.50 reserve overdraft at CB |
| -------------------- |
$4.50 reserve borrowing from CB |
| Negative Equity |
Equity |
| -------------------- |
$10 required capital |
Bank B
| Assets |
Liabilities |
| $95 reserves ($9.50 required) |
$95 deposit for x |
Person x
| Assets |
Liabilities |
| $95 deposit at B |
$100 borrowing from A |
| Negative Equity |
Equity |
| $5 |
------------------------ |
Balance sheets after Bank A borrows $85.50 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 CB's discount window or by attracting new transfer
deposits, but I've chosen to show the case where it borrows from Bank B):
CB
| Assets |
Liabilities |
| preexisting assets |
preexisting liabilities - $5 |
| $4.50 reserve loan to A |
$9.50 reserve deposit for B |
Bank A
| Assets |
Liabilities |
| $100 loan to x |
$85.50 reserve borrowing from B |
| -------------------- |
$4.50 reserve borrowing from CB |
| Negative Equity |
Equity |
| -------------------- |
$10 required capital |
Bank B
| Assets |
Liabilities |
| $9.50 required reserves |
$95 deposit for x |
| $85.50 loan of reserves to A |
----------------- |
Person x
| Assets |
Liabilities |
| $95 deposit at B |
$100 borrowing from A |
| Negative Equity |
Equity |
| $5 |
------------------------ |
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% which just meets the CAR requirement (10% or greater is satisfactory).
Joe in Accounting helped me with this example, but I still need to run it by him to make sure it's correct.
*To see a related example documenting the balance sheet changes associated with a stock investor as well (rather than having unnamed investors) see
Example 3.1.
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