Recollateralisation and Collateral Chains in the Monetary Circuit Theory Banking Model

In a previous post we added collateral to our monetary circuit banking model and showed how collateral added to bank lending power, and how in effect lack of collateral added to lending costs and/or reduced lending power. (with a slightly simplified accounting treatment)

Fig 1 Collateral Model

Bank		Assets				Liabilities			Equity
Operation		Lending Power Value		Loan Ledger		Bank Working Capital	Required Reserves	Firm Deposits	Safe
Deposit Collateral						+Lend Money*Default Risk		-Lend Money*Default Risk
Add Collateral		+Lend Money*Default Risk				-Lend Money*Default Risk
Record Collateral		-Lend Money*Default Risk		+Lend Money*Default Risk
Adjust Required Reserves & Lending Power		– (Lend Money*Default Risk)*Reserve Ratio					+ (Lend Money*Default Risk)*Reserve Ratio

Recollaterolisation is despositing that asset again against a loan from another financial institution. Lets model this with bank B lending to Bank A. We are familiar with the operations for the lending bank so lets concentrate solely on the debtor bank.

Fig 1 Recollateralisation Model

Bank	Assets		Liabilities			Equity
Operation	Lending Power Value	Loan Ledger	Bank Working Capital	Required Reserves	Firm Deposits	Safe
Deposit Collateral			+Lend MoneyA*Default RiskA		-Lend MoneyA*Default RiskA
Add Collateral	+Lend MoneyA*Default RiskA		-Lend MoneyA*Default RiskA
Record Collateral	-Lend MoneyA*Default RiskA	+Lend MoneyA*Default RiskA
Adjust Required Reserves			– (Lend MoneyA*Default RiskA)*Reserve Ratio	+ (Lend MoneyA*Default RiskA)*Reserve Ratio
Reduce Lending Power	– (Lend MoneyA*Default RiskA)*Reserve Ratio		– (Lend MoneyA*Default Risk)*Reserve Ratio
Borrow Money Bank B		-Bank Loan B (1/ Lend MoneyA*Default RiskA)*(1/Default Risk B)	+ Bank Loan B (1/ Lend MoneyA*Default RiskA) )*(1/Default Risk B)
Transfer to Lending Power	+ Bank Loan B (1/ Lend MoneyA*Default RiskA)		– Bank Loan B (1/ Lend MoneyA*Default RiskA)
Deposit Collateral Bank B	-Lend MoneyA*Default RiskA		+Lend MoneyA*Default RiskA
Repay Loan		-Repay Loan	+Repay Loan
Adjust Lending Power	-Repay Loan	+Repay Loan
Adjust Required Reserves and Lending Power	–  (Bank Loan B (1/ Lend MoneyA*Default RiskA)* (1/Default Risk B)*Reserve Ratio)			+ (Bank Loan B (1/ Lend MoneyA*Default RiskA)* (1/Default Risk B)*Reserve Ratio)

So in terms of lending power the bank has received collateral and used it again as collateral for its own loan, and increased its own lending power by the reciprocal of the default risk. So if the default risk is 5% this can be levered by a factor of twenty. On the other hand this expansion is reduced both by the default risk on loan B and by the need to keep a proportion of the increased working capital to maintain any reserve ratio.

So to give an example lets say a bank receives $1million collateral on a loan and that bank has a reserve ratio of 5%. That bank would increase its lending power by $950,000. The difference being the need to reduce excess reserves.

Mow lets say that Bank A now deposits this as collateral with Bank B, with a default risk of 5%. The posted collateral cancels out the direct increase in lending power, however the loan gives an increase of $19 million to lending power, as $1 must be retained as deposits.

Why would a bank do this, it has dramatically increased lending power but at the cost of future repayments at the prevailing rate of interest, so how would it be able to make a profit? Again the reason being during times of moderation and expanding lending power banks can borrow short from each other and lend long. Because of the cost of funding such loans will not compete with relatively risk free lending not secured with loaned funds. Such additional loans will therefore be higher risk and secured at the margin, and therefore will require higher collateral. The higher the collateral the more it can be expanded. What this shows is that during periods of moderation there is an increasing tendency to try to secure riskier and riskier loans, even when the default risk for most loans is low, and that the ability to recollaterolise means that ensuring such periods lending power will increase as well as the systemic risks from the interlinking of risk through collateral of financial institutions. Yet another example of Minsky’s thesis that stability sows the seeds of instability.

We can also see that the theoretical boost across the whole banking system is a taylor series of the form we have encountered before, however this is only a theoretical upper limit and approaching it will take some period of time during financial stability.