Friday, February 22, 2013

Banking Example #1: Loan and Deposit Transfer

Example of a loan and deposit transfer. For a more colorful version see Example #1.2.

Setup: one central bank (CB), two commercial banks A and B, and one person x. No reserve requirements or capital requirements and everyone's balance sheet initially clear (empty).


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 A:

Bank A
Assets Liabilities
$100 loan to x $100 deposit for x

Person x
Assets Liabilities
$100 deposit at A $100 borrowing from A


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

Central Bank
Assets Liabilities
$100 reserve overdraft for A $100 reserve deposit for B

Bank A
Assets Liabilities
$100 loan to x $100 overdraft at CB

Bank B
Assets Liabilities
$100 reserves $100 deposit for x

Person x
Assets Liabilities
$100 deposit at B $100 borrowing from A


Balance sheet after Bank A borrows $100 of reserves from Bank B and repays the CB the overdraft amount by the end of the day (note: Bank A could have borrowed from any other bank, the money markets, the Central Bank's discount window or by attracting transfer deposits, but I've chosen to show the case where it borrows from Bank B):

Central Bank
Assets Liabilities
$0 $0

Bank A
Assets Liabilities
$100 loan to x $100 reserve borrowings from B

Bank B
Assets Liabilities
$100 loan of reserves to A $100 deposit for x

Person x
Assets Liabilities
$100 deposit at B $100 borrowing from A


Note that at the end, the central bank's balance sheet is again clear, yet there are $100 of reserves on loan to A from B. To see a similar case where the deposit transfer is accomplished with a purchase instead, see Example 1.1. A purchase scenario is more typical since most loans are taken out with the intention of buying something. For example, each time you swipe your credit card to make a purchase, the loan, deposit creation and deposit transfer (between two deposit holders) are all done in one process. However, in many of the examples on this blog I end the process with a deposit transfer (single deposit holder) rather than a purchase simply because the transfer is slightly simpler (it requires one less person and corresponding balance sheet), but the two processes are similar enough that I hope the reader could fill in the details to change the concluding transfer to a purchase if need be.

I recommend this writeup on the monetary system by Cullen Roche for more information. Also, I must credit this article. Also, this site animates balance sheets, and has an especially good macro page with consolidated balance sheets.  Look at this to see this same example with reserve requirements, and here to see it with both reserve and capital requirements.

As a final step, consider what happens if we are to consider banks A and B aggregated together on one consolidated balance sheet. Considering various sectors of the financial economy as aggregates is often very useful when analyzing macro economics.

Here are the resulting aggregated balance sheets (the CB's balance sheet is still clear):

Aggregated Banks A & B (AB)
Assets Liabilities
$100 loan to x $100 deposit for x

Person x
Assets Liabilities
$100 deposit at AB $100 borrowing from AB

As can be seen, the loan and borrowing of reserves present on the individual bank balance sheets cancel each other out when the two banks are aggregated together. We're thus essentially back to where we were right after person x first borrowed $100 from Bank A, only the name has changed from "A" to "AB" on the "bank." This demonstrates the conceptual power of aggregation: it allows analysis at a higher level without getting too bogged down in the details of individual actors. The fact that Bank A was borrowing $100 of reserves from Bank B is less important than noticing that no reserves are required by the aggregate banking sector for person x to take a loan out and move his deposit around. In a similar fashion, person x could be aggregated with person y in some of the following posts (e.g. Example 1.1) to represent the aggregate non-bank private sector.

4 comments:

  1. I've been too lazy to do this but I have always (a long time) thought that this would be enlightening exercise.

    Curiously I haven't before find anything like this done before in a such systematic way. Should be mandatory in econ101.

    I guess I'm saying: thanks!

    ReplyDelete
  2. one central bank (CB), two commercial banks A and B, and one person x. No reserve requirements or capital requirements and everyone's balance sheet initially clear (empty). GetSomeDosh

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  4. I hope the reader could fill in the details to change the concluding transfer to a purchase if need be.
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