Thursday, March 7, 2013

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

7 comments:

  1. Hi Tom,

    One question -- if banks have a reserve ratio, then why must they also maintain a capital requirement? The reserve ratio makes perfect sense to me. If person X comes and withdraws money from his account, Bank A must have a certain amount of money on hand.

    But what purpose does the capital requirement serve? I know it's a regulatory thing, but I would like to think about it in a layman's way so that it will make sense to me.

    Thanks,
    Anne

    ReplyDelete
    Replies
    1. Hi Anne,

      You write:

      "If person X comes and withdraws money from his account, Bank A must have a certain amount of money on hand."

      Actually reserve requirements (RR) do nothing to ensure that Bank A has enough cash on hand for Person X should he want to withdraw his deposit. The reason is because reserves are the sum of the bank's vault cash and it's electronic Fed deposits, thus a bank can meet its RRs entirely electronically. They are motivated to have vault cash only for the convenience of their depositors, not by regulation.

      I'm limited to 4096 characters here, so I'll try to be brief ;)

      RRs are a requirement on a banks demand deposits (e.g. checking deposits) and nothing more. They USED to limit bank lending in the gold standard days (look up the "money multiplier" etc.) but no longer since a bank can always obtain the RR by borrowing from other banks or from the Fed (see my examples #1, 1.1, and 2). I think of RRs as kind of a throwback to the gold standard days. In my opinion they really don't have much of a function any more. Plenty of countries get by w/o them (i.e. with RR = 0%). Those include Canada, the UK, and Australia.

      Capital requirements, in contrast, are actually effective at limiting a bank's risky lending activity because they fold in not only deposits and other liabilities, but a bank's loans and other assets. Capital requirements are what provide a bank a buffer: Not for cash withdrawals, but for bad loans (defaults).

      If a bank accumulates negative equity (liabilities exceeding its assets) it becomes insolvent and the Fed and FDIC must step in to change the management and make the depositors whole again (i.e. put it in receivership) or else they must bail it out. Nobody wants to do more of that! So a capital requirement of 10% means that 10% of a bank's risk weighted assets (loans) can default and the bank can still have non-negative equity. Does that help? See my Example #7 for more on how regulatory capital is calculated and how it relates to equity.

      Delete
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  2. Capital requirements

    All bank required to remain with a certain percentage.it is usually expressed as capital adequacy ratio that any banks must hold as the amount of risk weighted assets.

    ReplyDelete
  3. Capital requirements

    All bank required to remain with a certain percentage.it is usually expressed as capital adequacy ratio that any banks must hold as the amount of risk weighted assets.

    ReplyDelete
    Replies
    1. Thanks. I'm no expert, but I did spend a little bit of time investigating a few basic ideas.

      Delete
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