Tuesday, March 12, 2013

Banking Example #6: QE: CB Holds Gov Debt to Maturity

This example looks at what happens when the central bank (CB) purchases Treasury bonds from the public and holds them to maturity. For just the purchase see Example 4.

Setup: one central bank (CB), one government Treasury Department (Treasury), one commercial bank (A), and one person (x). No reserve or capital requirements. All balance sheets are initially clear (empty). This post was inspired by a question posed in a comment here. This post doesn't really answer that question directly, but reflects a thought experiment I did at the time, wherein I wondered what would happen if the CB kept purchasing and holding Treasury bonds to maturity.


Initial balance sheets :

CB, Treasury, A, x
Assets Liabilities
$0 $0


Balance sheets after x takes a 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 buys a Treasury bond from Treasury (I'm skipping the step where A experiences an overdraft at the CB when x's deposit is transferred to Treasury to clear the bond purchase, and I'm going straight to bank A borrowing funds to cover the overdraft, in this case from the CB):

Treasury
Assets Liabilities
$100 reserves $100 Treasury bond held by x

CB
Assets Liabilities
$100 loan of reserves to A $100 deposit for Treasury

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

Person x
Assets Liabilities
$100 Treasury bond $100 borrowing from A


Balance sheets after the CB purchases the Treasury bond from x:

Treasury
Assets Liabilities
$100 reserves $100 Treasury bond held by CB

CB
Assets Liabilities
$100 loan of reserves to A $100 deposit for Treasury
$100 Treasury bond $100 deposit for A

Bank A
Assets Liabilities
$100 loan to x $100 reserve borrowings from CB
$100 reserves $100 deposit for x

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


Balance sheets after Bank A repays its reserve borrowings from the CB:

Treasury
Assets Liabilities
$100 reserves $100 Treasury bond held by CB

CB
Assets Liabilities
$100 Treasury bond $100 deposit for Treasury

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 Treasury pays x for services rendered to the government:

Treasury
Assets Liabilities
$0 $100 Treasury bond held by CB
Negative Equity Equity
$100 --------------------------------

CB
Assets Liabilities
$100 Treasury bond $100 reserve deposit for A

Bank A
Assets Liabilities
$100 loan to x $200 deposit for x
$100 reserves ------------------

Person x
Assets Liabilities
$200 deposit at A $100 borrowing from A
Negative Equity Equity
------------------ $100


Balance sheets after x repays loan to A:

Treasury
Assets Liabilities
$0 $100 Treasury bond held by CB
Negative Equity Equity
$100 --------------------------------

CB
Assets Liabilities
$100 Treasury bond $100 reserve deposit for A

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

Person x
Assets Liabilities
$100 deposit at A $0
Negative Equity Equity
------------------$100


Balance sheets after Treasury sells another bond to x to cover its upcoming principal payment to the CB:

Treasury
Assets Liabilities
$100 reserves $100 Treasury bond held by CB
------------------ $100 Treasury bond held by x
Negative Equity Equity
$100 --------------------------------

CB
Assets Liabilities
$100 Treasury bond $100 reserve deposit for Treasury

Bank A
Assets Liabilities
$0 $0

Person x
Assets Liabilities
$100 Treasury bond $0
Negative Equity Equity
------------------$100


Balance sheets after the first Treasury bond matures and Treasury repays the principal to the CB:

Treasury
Assets Liabilities
$0 $100 Treasury bond held by x
Negative Equity Equity
$100 ------------------------------

CB
Assets Liabilities
$0 $0

Bank A
Assets Liabilities
$0 $0

Person x
Assets Liabilities
$100 Treasury bond $0
Negative Equity Equity
------------------$100


Balance sheet after CB buys Treasury bond from person x:

Treasury
Assets Liabilities
$0 $100 Treasury bond held by CB
Negative Equity Equity
$100 ------------------------------

CB
Assets Liabilities
$100 Treasury bond $100 reserve deposit for A

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

Person x
Assets Liabilities
$100 deposit at A $0
Negative Equity Equity
------------------$100

Now at this point, if the government wants to continue deficit spending, it must now sell another Treasury bond (e.g. to x), and continue this process. As this cycle of events continues, x's equity will continue to climb by $100 each time and Treasury's equity will continue to decrease by $100 each time (with the CB's and Bank A's equity staying at $0). Person x will not need to take a loan the next time around since he has $100 of deposits with which to purchase the next bond. Of course the government can also tax Person x to reduce the amount of deficit spending it must engage in to keep this process going. If the CB were to purchase every Treasury bond in this manner, the effect would look similar to "monetizing the debt." Ultimately CB and A are performing as intermediaries. In reality the CB only purchases a small fraction of the outstanding Treasury bonds under Quantitative Easing (QE) operations, for example. Plus, it's ultimately up to x whether or not to sell the bonds, since the CB does not directly purchase bonds from Treasury.

This example is over simplified and has many shortcomings. Interest, taxes, fees, and changing bond prices are not covered. These would be significant over the course of a bond's issuance to maturity. Also, Bank A would not likely borrow from the CB to repay its reserve overdraft, but instead would most likely borrow from another bank. Also, x would not likely take a loan out to purchase a Treasury bond, since it would probably experience a negative spread on the two interest rates if it did so. However, someone else may take out such a loan to hire x for his services, which would provide x with the funds to purchase a Treasury bond: thus you can think of x and A as stand-ins for the aggregate non-bank and bank private sectors.

6 comments:

  1. Hi, Tom.

    Nice work. (I've been helped by your blog considerably lately.)

    I see pretty well from your example above the basics of what were to happen if the CB held treasuries to maturity.

    Could you show a basic example of the CB "rolling over" its maturing treasuries?

    What is not clear to me is the following: would rolling over maturing treasuries on the CB's balance sheet be (or would it not be) one exception to the rule that the CB is not allowed to purchase treasuries directly from the Treasury (and thereby "monetize the debt")?

    ~~~~~

    When the treasuries mature, and if the CB wishes to "roll over" the maturing treasuries, does it just follow (basically) the example you have outlined above - letting the treasuries mature, and, in that way, start over with 0 assets (essentially extinguishing the payment of reserves from the treasury, because the CB, by definition, does not hold reserves as assets) - and then, simply go about purchasing the same value of treasuries again from the private market?

    (If the above is correct, then maybe it isn't particularly meaningful to think in terms of "rolling over" maturing treasuries when thinking of the CB. If the CB balance sheet would essentially "start over" at 0 in the case of treasuries, then any further treasury purchases from that point could be thought of as starting over too, but according to the needs of monetary policy at the time... whether or not to purchase more treasuries from the private sector, and to what value - not necessarily to the same value of the maturing treasuries.)

    Or, at the point of maturity of the CBs treasury holdings, would the CB be allowed to work directly with the Treasury? Would the CB be allowed to renew its current treasury assets and, in turn, newly credit the Treasury's general account (along with renewing the same set of treasury liabilities in the Treasury's account), thereby "rolling over" the maturing treasuries in that way?

    ~~~~~

    I've searched the internet for an answer about that possible exception of direct purchasing of treasuries by the CB (in the case of "rolling over" already owned maturing treasuries), but I haven't found a definitive answer.

    I was hoping you might have better luck.

    Linda G

    ReplyDelete
    Replies
    1. Hi Linda G,

      Sorry, I'm not spending much time on this blog anymore, but I'm glad you found this helpful.

      I don't think there's any exception. I don't think of the CB as the entity doing the "rolling over" ... I think of the Treasury as doing that in that they sell more bonds to pay the principal on maturing ones. That's really all I know about it! The CB doesn't specifically come into play there. Different countries have different rules, so what I'm writing here applies to the Fed which can't normally buy directly from Treasury. The Bank of Canada lives by different rules and I believe they can buy directly from their treasury.

      Delete
  2. All balance sheets are initially clear (empty). This post was inspired by a question posed in a comment here. Get Some Dosh

    ReplyDelete
  3. This post doesn't really answer that question directly, but reflects a thought experiment I did at the time, wherein I wondered what would happen if the CB kept purchasing and holding Treasury bonds to maturity. Debt Asset Limited

    ReplyDelete
  4. This post doesn't really answer that question directly, but reflects a thought experiment I did at the time, wherein I wondered what would happen if the CB kept purchasing and holding Treasury bonds to maturity.Debt Consolidation Strategies

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  5. 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...? cpa torrance ca

    ReplyDelete