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 3.2 is slightly simplified in that balance sheets associated with unnamed investors are not shown.
Setup: one central bank (CB), three commercial banks A, B and C and two people x and y. 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 (similar to
Example 3) person y has borrowed $10 from Bank C (with a $1 loan origination fee charged by C to meet its capital requirements), and that she (y) has withdrawn the remaining $9 in cash* (i.e. paper money). Assume further than Bank C has in turn borrowed these cash reserves from the CB.
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, C, x and y:
A, B, x
| Assets |
Liabilities |
| $0 |
$0 |
CB
| Assets |
Liabilities |
| $9 reserve loan to C |
$9 cash issued |
Bank C
| Assets |
Liabilities |
| $10 loan to y |
$9 borrowing of (cash) reserves from CB |
| Negative Equity |
Equity |
| ------------------ |
$1 retained earnings (required capital) |
Person y
| Assets |
Liabilities |
| $9 cash |
$10 borrowings from C |
| Negative Equity |
Equity |
| $1 |
----------------------- |
Balance sheet after Bank A sells $5 of stock to person y (keep in mind that vault cash is a form of bank reserves: assume it's sold back to the CB for electronic reserves as soon as cash is deposited at the bank rather than being held as a vault cash inventory):
CB
| Assets |
Liabilities |
| $9 reserve loan to C |
$4 cash issued |
| --------------------- |
$5 reserve deposit for A |
Bank A
| Assets |
Liabilities |
| $5 reserves at CB |
$0 |
| Negative Equity |
Equity |
| ------------------ |
$5 |
Person y
| Assets |
Liabilities |
| $4 cash |
$10 borrowings from C |
| $5 stock in A |
----------------------- |
| Negative Equity |
Equity |
| $1 |
----------------------- |
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 |
| $9 reserve loan to C |
$4 cash issued |
| $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 |
| $9 reserve loan to C |
$4 cash issued |
| $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 |
| $9 reserve loan to C |
$4 cash issued |
| $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 |
----------------- |
Bank C
| Assets |
Liabilities |
| $10 loan to y |
$9 borrowing of reserves from CB |
| Negative Equity |
Equity |
| ------------------ |
$1 retained earnings (required capital) |
Person x
| Assets |
Liabilities |
| $95 deposit at B |
$100 borrowing from A |
| Negative Equity |
Equity |
| $5 |
------------------------ |
Person y
| Assets |
Liabilities |
| $4 cash |
$10 borrowings from C |
| $5 stock in A |
----------------------- |
| Negative Equity |
Equity |
| $1 |
----------------------- |
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.
*The reason I chose to show cash withdrawn by person y was so that I
could slightly simplify the example by eliminating reserve requirements
for bank C by eliminating y's deposit at bank C. This puts y in the
slightly unrealistic position of purchasing stock in Bank A with cash. I
still needed to show bank C meeting its capital requirements though. To see a somewhat simplified example using unnamed stock investors (whose associated balance sheets are not shown) see
Example 3.2.
Hi Tom,
ReplyDeleteSorry for posting so many questions today. I have another one.
Cash is always a liability for the Fed, yes? So when the Fed lends to Bank C, I understand that it has created an asset for itself. However, when Bank C withdraws the $9, there is still and outstanding liability simply because cash is a liability for the Fed...?
Am I oversimplifying things?
Anne
Hi Anne,
DeleteI'm a little confused by your questions, but let's go through them:
"Cash is always a liability for the Fed, yes?"
Yes, cash is always a liability for the Fed (paper, not coins: see last two paragraphs under my "The Three Places..." post) after it has been sold to the banks. For simplicity, lets assume only paper money. When paper notes are stored at the Fed they are nothing: they don't appear on the Fed's balance sheets as an asset or a liability. The Fed paid Treasury for those notes, but only the cost of production: not the face value. They are exactly like electronic Fed deposits only in a paper format: when at the Fed they essentially cease to exist as money.
"So when the Fed lends to Bank C, I understand that it has created an asset for itself."
This part confuses me: the Fed has created a liability for itself after it distributes the paper money by selling it to the banks. Again, when at the Fed, the paper notes essentially don't exist.
"However, when Bank C withdraws the $9, there is still and outstanding liability simply because cash is a liability for the Fed...? "
In fact it's not until Bank C takes the $9 cash that the cash is a Fed liability. Assume that the bank then exchanges it's cash for electronic reserves. After the Fed receives the paper notes, it replaces them in the liabilities column of it's balance sheet with the electronic reserves and the paper notes essentially disappear in an accounting sense.
Like I say, this is actually a different story if we were talking about coins rather than paper money. See here:
http://brown-blog-5.blogspot.com/2013/04/the-three-places-reserves-can-go.html
Coins ARE created as an asset of Treasury! When it sells them at a profit to the Fed this is called seigniorage (in fact though, the Treasury loses money on pennies and nickles because it costs more to produce them than their face value!). When the Fed buys them they are then an asset of the Fed until the Fed sells them, at which point they disappear from the Fed's balance sheet.
So I think your questions are more appropriate for coins rather than paper notes, however, if it were coins I was assuming, then my balance sheets would look different.
When I wrote this post I didn't fully understand that distinction, so I left it vague.
This post is a little bit overly complicated. I tried to show everybody's full balance sheet which made it tough. Believe it or not, adding the cash concept was an attempt to simplify it slightly. Take a look at Example 3.2 for exactly the same concept regarding capital requirements, but with a little bit less unnecessary details.
Hope that helps!
-T
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. GetSomeDosh
ReplyDeleteOn the bank balance sheets which follow, loans and the capital requirements they induce will be colored green, money
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ReplyDeleteI think a simple example may be useful. Let us consider a market with a BB with the following balance sheet cpa torrance ca
ReplyDelete