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Wednesday, May 15, 2024

Bank Self-Funding Example

This is a potential section for my banking manuscript. It probably needs some diagrams, but I do not want to spend too much time on them if they end up not being used.

One way to get a better handle on the mechanics of the overall banking system is to work through an example that includes some of the important features we want to capture, but avoiding extraneous details. The example I am using has the following features.

  • There are five private banks (Bank A to Bank E) in the country. Conveniently, each has $10 billion in deposits, and we assume that each bank has 20% market share.
  • The country uses the simplified no reserve system I described in Understanding Government Finance. This means that all banks are expected to have a $0 balance at the central bank.
  • The only regulatory ratio we are considering is a liquidity ratio, which requires liquid assets that are 6% of deposits, but banks target a 10% ratio. This means that each bank starts with $1 billion in liquid assets to cover deposit loss risk.
  • Any other liquidity risk (e.g., lines of credit, etc.) coverage is ignored. (If you want to insist that these risks exist, assume that there is another liquidity buffer for those risks that we skip over.)
  • We assume that the banks have more than adequate capital ratios.

The Big Push By Bank A

The scenario starts by banks B to E being run by people who read economists’ descriptions of the banking system — they will only make loans if they raise funding that puts them over the 10% liquidity target. Since nothing is happening, they have sent their loan officers home for the day, and posted signs saying “Sorry, We Need Deposits Before We Make Loans! Have a Nice Day!” Meanwhile, Bank A is run by some radical hippie who decides to let lending rip. The loan officers manage to pump out $100 million in net new loans in one day (which is 1% of the size of the deposit base). Otherwise, we assume that all other bank transactions do not cause any net flows between banks.

We will assume that all the loan proceeds are immediately spent, and that the outflows go to recipients based on the 20% market share. This means that each bank ends up with $20 million in new deposits. This also means that Bank A faces a $80 million deficit in the payments system that has to be closed by the end of the day. Bank A sells $80 million of securities from its liquidity portfolio, and Banks B to E each buy $20 million for their portfolios (since they have to get rid of their surplus with the payments system).

At the end of the day, each bank has $10,020,000,000 in deposits ($10 billion plus their $20 million share of the $100 million in new deposits).

  1. Bank A has a liquidity ratio of 9.18%, which is below the target, but still well above the 6% minimum.

  2. The other banks have a liquidity ratio of 10.18%, which is now above the 10% target. The banks managements’ can put their loan officers back to work.

Is Bank A in Trouble?

Although alarmists might worry about the drop in the liquidity ratio of Bank A, we also need to take into account the rather curious management practices of Banks B to E. Bank A just racked up lots of fees that are embedded in things like mortgages, and will likely have gained market share — people tend to bank with the bank that lends them money. Meanwhile, the loan officers at the other banks were paid to do literally nothing all day. Although Bank A cannot keep lending out $100 million each day without doing something, the other banks also cannot keep doing nothing if they do not want their lunches eaten.

We will then look at various responses that might happen in the next day.


Bank A could put the pressure on the other banks by selling $100 million in loans on its balance sheet in a securitisation (or just issue $100 million in new notes). We will assume that all the buyers are non-banks. If we assume the 20% market share also applies to this transaction, buyers would drain $20 million from each bank (including Bank A). In order for all banks to have a flat balance with the payments system, each other bank has to sell $20 million in liquid assets, and Bank A buys $80 million.

  1. The buyers who bank at Bank A would lose $20 million in deposits and get $20 million in securities. This would return bank A to $1 billion in deposits, and it will have $1 billion in liquid assets. Thus, it has a 10% liquidity ratio again — and is free to do the same thing again.

  2. Each other bank ends up with a 10% liquidity ratio — but they missed out on the new loan frenzy at Bank A. Their market share would noticeably drop if they kept doing this.

What we see is that the deposits and bank liquid asset portfolios have done a round trip, and the non-traditional bank financial system has expanded.

  • If Bank A issued a securitisation, it has created $100 million in debt securities (non-bank financial instrument). The “non-bank sector” has expanded its balance sheet — it has $100 million in new loans, and there are $100 million in new securitisation notes.

  • If Bank A issued a bond, it has grown its balance sheet. Its loan book grows by $100 million, funded by issuing $100 million in debt.

The fact that the deposits make a round trip helps explain why Bank A should expect to be able to issue the securities. It seems unlikely that the entities that received cash inflows from the borrowers at Bank A will want to keep these inflows entirely as deposits. For example, people selling a house and leaving the housing market will probably invest the proceeds into retirement funds. (If they buy another house, the cash will then proceed along the chain of sellers.) In any event, Bank A is still a reputable borrower and should be able to access the bond market, at the cost of its bonds becoming slightly cheaper relative to other fixed income securities to encourage a rebalancing towards the new issue.

Other Banks Make Loans

If Bank A does not issue a bond/securitisation, it would still get some relief as the other banks start to attack their new “excess” liquidity.

If we assume that managements at Banks B to E are purely reactive to inflows, they had a $20 million inflow. Assume they allow their loan officers to go back to work and each issues $20 million in new loans. This implies $80 million in new loans being made. If we assume that market shares are still 20%, this implies that each bank (including Bank A) gets $16 million in new inflows.

  1. Bank A increases its liquidity portfolio by $16 million, since we assume for this scenario that it made no new transactions.

  2. Banks B to E made $20 million in loans, but end up with $16 million in new deposits. This implies that they lost $4 million each (the total liquidity losses matching the inflow to Bank A). So they still have (roughly) $16 million of excess liquidity so that they can repeat the process. (Since their deposits grew, they need a slightly larger liquidity buffer than $1 billion.) This process thus can repeat with smaller loan amounts. This would result in a steady flow of funds back to Bank A, and eventually erase most of its liquid asset shortfall.

If we want to work with simpler numbers, we could eliminate the multi-step rebalancing and just assume that all banks simultaneously issued $100 million in loans each. If we once again assume the perfect 20% market shares, then each bank has zero net flows when the loan proceeds are spent. In this case, there still is a reduction in the liquidity ratio: each bank has now $10.1 billion in deposits, but $1 billion in liquid assets. This means that the liquidity ratio is 9.9%. Eventually, the banks would need to issue new debt to raise the ratio — but the non-bank sector is also stuck with more deposits than before, and if it wants to keep portfolio allocations stable, will want to allocate deposits to that new debt (either bank notes or securitisations).

In other words, the banking system creates the deposits that can be swapped by depositors into debt that allows the private sector to expand its balance sheet — without waiting for new money to magically appear from somewhere.


Bank management generally hopes that the bank is profitable. Although profits can take the form of non-cash changes to the balance sheet, in most cases there will be a corresponding net cash inflow. This allows the bank to rebuild its liquidity portfolio.

Profits are most likely not going to be enough to allow a bank to grow its balance sheet rapidly, but will allow a certain growth pace while respecting liquidity ratios without the issuance of new debt instruments.

The Government

The usual state of affairs is that nominal GDP grows, and all but the silliest fiscal conservatives accept that the debt/GDP ratio must be stable — which implies that we expect government debt outstanding to be growing in steady state. This implies that the steady state situation for the government is to be running a fiscal deficit.

Government deficit spending means that the central government is sending out more cash to the non-government sector than it is taking back in taxes (or fees). Unless the government is mysteriously writing cheques to banks, the implication is that bank customers end up with new deposits courtesy of the government. (Despite the wacky theories of Monetarists, governments generally do not drop money from helicopters.)

The new deposit by the client is a liability to the bank, so the government also has to send a payment to the bank to give it a matching asset. In a system where banks do not hold excess reserves, this means that the bank will have to match these inflows with the purchases of liquid assets. (The consolidated central government would have to release government debt — or the economic equivalent — to the non-government sector to keep excess reserves from rising.)

Which means that if Bank A did nothing, it would still expect its liquidity shortfall versus the 10% target to be slowly eaten by the effect of government deficits.

Excess Reserves Allowed

If the conventions of the banking system allow excess reserves, they are just part of the liquidity portfolio. Bank A might be forced to sell some of its non-reserve liquid assets to keep the reserve ratio at its conventional target if the other banks decide to hoard more reserves than conventional.

Banks will always face unusual net inflows and outflows. Banking regulators would not be happy if a cartel of banks just decided to put another bank out of business if it has adequate liquidity and capital ratios (which Bank A still has) but has a temporary liquidity shortfall.

Capital Ratios — Slower Moving

Although I have ignored capital ratios in this example, they would be slower moving than the liquidity ratio, but the overall logic is similar. The extension of loan that results in an outflow directly hits the liquidity buffer — but has no effect on bank capital (other than a small increase in loan loss provisions, but that might be set off by “underwriting fees”).

If Bank A keeps expanding its loan book, it cannot patch up its equity ratio by issuing senior debt (that solves its liquidity ratio problem). It would have to issue subordinated instruments that count as capital, issue new common equity, or retain earnings.

The easy way for modern banking systems to bypass the equity ratio constraints is to get the assets of their balance sheet via securitisations.

Real World is Irregular

The numbers used in this example are nice and neat, and rely on convenient regular behaviour. In reality, behaviour will be irregular, and so a bank cannot predict exactly how much liquidity it will lose from lending operations. It is likely that increasing the pace of lending will result in similar outflows, but to the extent that banks engage in herding behaviour, it might also be getting hard-to-predict inflows courtesy of other banks making new loans. Meanwhile, there will be the ongoing cycle of inflows and outflows due to wages and spending, as well as commercial flows that can be highly seasonal.

However, a lot of lending decisions does not result in immediate outflows. Credit lines can be drawn upon in an irregular fashion. Banks will pre-approve mortgages — and they will have very unhappy customers with long memories if they decide to randomly dishonour those commitments.

To top it off, the bank treasury desk and lending officers are isolated within large banks. Banks cannot force people to accept loans, and so there is no guarantee that any loan negotiation will succeed. At the same time, there are a lot of loan officers in a big bank. Only a complete idiot would announce to loan officers that they should cut back on lending because the treasury team is worried about getting funding — the life expectancy of the bank might be measured in days. Bank lending is generally not done in huge chunks, and so a worried treasury desk would just increase the internal cost of funds and drop hints to senior lending officers to be a bit less aggressive growing their loan books. That is, there is not going to be a hard stop (outside of a banking crisis), rather a slow changing of lending policies.

Banks spend a good deal of analytical effort on forecasting their cash needs, and the hokey examples that populate primers — like this one — understate the complexity.

Cannot Make “Infinite” Loans

Although the financial system is self-funding, it cannot make arbitrarily large loans in a single day. In this example, if Bank A made loans that blew its liquidity ratio below the minimum of 6% (about $500 million under the assumptions), it would be in trouble, and would not have time to make the reactive points that are discussed.

Nevertheless, growing your loan book by 1% in a single day is going to result in a pretty decent annualised growth rate if you keep repeating the process.

(From a theoretical standpoint, the self-funded nature of financing means that models based on market clearing at period ends may be indeterminate — implying the potential for infinite growth. However, if the period in the model is monthly or quarterly, it should contain behavioural constraints that force loan growth to be finite. We do not see real world banking systems running at their theoretical expansion capacity, and a model should reflect this.)

Credit Losses!

For a bank that is not in the middle of a financial crisis or not on the edge of insolvency, liquidity management is a solvable problem that it pays people well to do competently. Despite what you might read in disreputable online sources, banks with solid equity ratios do not randomly keel over — they are usually able to find funding at some cost.

What kills banks is the spectre of insolvency — having its equity ratios drop below regulatory minimums. Nobody is going to want to provide funding to a bank that is about to go into restructuring — it needs an equity injection (or good luck in muddling through).

What stops banks from handing out “infinite loans” is the combination of the limited capacity of loan officers to evaluate loans, as well as the lack of an “infinite” number of credit-worthy entities that want to borrow.

The reason why we see high debt growth in housing bubble countries in the modern era is that banks use securitisations to get the mortgages off their balance sheet — eliminating credit risk (unless they are stupid enough to buy back dodgy securitisations). When governments eliminate the credit risk on mortgages (hello to any readers at the CMHC!) things can get pretty silly.

Concentration Risk

Concentration risk — excessively large loans, or excessive exposure to a certain type of loan or geographic region — also needs to be accounted for. Even if the loan officers think such loans are safe, it is dangerous to enter into exposures that can wipe out bank equity if there is some economic turbulence in a particular segment of the economy.

“Animal spirits” in a capitalist economy are not uniform — particularly in countries with distinctive economic regions. Demand for loans is therefore going to be segmented and rapid growth is likely going to be localised. This rapidly growing segments are going to hit concentration limits, and are the most likely reason that loan officers will disengage with certain classes of new borrowers.

Central Banks?

Central banks are expected to not cause domestic banking crises. They have no choice but to make sure that all banks that meet regulatory minimums can deal with short-term liquidity issues. In this case, if Bank A was running into problems because other banks withdrew from funding markets, Bank A would run to the central bank and re-discount assets there. That is, the central bank would act as a lender-of-last-resort while Bank A deals with what is supposed to be a temporary issue.

The central bank might hike rates if it sees that bank lending is getting too aggressive. However, that is not of immediate concern — the hike may occur weeks in the future. At the same time, there is no solid relationship between interest rates and lending, and the usual 25-50 basis point hike is unlikely to cause a dramatic change.

If central banks want to directly influence bank lending, they could attempt quantitative credit controls. In the current environment, such a step would easily be bypassed by securities markets. One would need to impose capital controls and re-regulate everything in the financial sector for such measures to have any effect.

But Bank A Needed Excess Liquidity in the First Place!

One entirely predictable word game that might be played is the observation that Bank A needed to have a liquidity portfolio in place that was in excess of the regulatory minimum in order to start off the lending cycle. One could then play further word games and try to pretend that this implies that loanable funds theories are correct.

The reason why this observation does not save loanable funds theories is that the lending operation created new deposits that allow Bank A to issue new debt to restore its liquidity ratio while keeping overall portfolio allocations between deposits and bank bonds (roughly) stable. Bank A did not need to wait for new inflows to magically appear from outside the system, it can start the debt growth cycle on its own.

The problem with these “what comes first?” arguments that are the feature of poorly-thought out economics is that everything is a cycle. And in this, it is a bad faith misrepresentation of the (reasonable) criticisms of classical banking stories. No serious scholars suggest that banks can appear out of thin air and start growing their balance sheet. (This is unlike neoclassical economics, where firms magically appear out of thin air in the macro models that ignore firms’ balance sheets.)

In order for an entity to be a bank, it needs to have a balance sheet with capital and liquidity ratios above regulatory minimums (as otherwise, it is on the path of becoming an ex-bank). If we want to go back to the “beginning” — which we should, if we want to purse such logic — a bank is created by a group of people injecting equity into a new legal entity. So yes, we need capital from “savers” for a bank to exist — but that may have happened more than a century earlier. As such, that capital injection would be an insignificant sum when compared to the bank’s current lending book.

So yes, banks needed to get monetary infusions in the past to be in a position to have the liquidity/capital buffers that allow new lending. However, that begs the question as to where those monetary infusions came from. The most likely sources would be government or bank money — which are financial assets that were in turn most likely created by balance sheet expansion (although physical gold may have been involved if the bank is sufficiently old).

What matters for economic theory is not the historical origin of all the actors in the economy, rather how they operate going forward. What we see is that (well run) banks generally start the business day with capital and liquidity ratios in excess of regulatory minimums, and they extend the loans that create deposits that allow the system to undertake balancing transactions so that banks will end the day in a satisfactory state so that the cycle can repeat.

What Did We Learn?

I think that these are the following key points to understand the basics of banking.

  1. The belief that banks’ fear of liquidity risk is the primary risk concern of banks with respect to traditional lending is not correct (outside of a financial crisis — which is why they are crises). Liquidity can be managed. The real concern is credit losses beyond what is covered by the loan pricing.

  2. Although I do not give examples, banks can experience net outflows regardless of the day’s lending decisions. Liquidity management must be done all the time.

  3. Banks are not going to run their balance sheets at the regulatory minimum for liquidity/equity ratios. They have to set a target level above that minimum, and accept that there will be variations over time.

  4. If liquidity ratios drop too far, the bank will generally want to issue debt or a securitisation (or unload some less liquid assets). Lending standards will generally adjusted slowly (although a bank may be able to exit some larger potential deals without causing too much disruption with its branch lending officer pool).

  5. Equity ratios are more sensitive to credit losses, although they will decay slowly if the balance sheet is expanding quickly for an extended period. Eventually, either growth must be slowed or more expensive equity instruments issued.

  6. Government deficits inject liquidity into the banking system.

  7. Otherwise, the decision of entities in the private sector create financial assets. In particular, the extension of bank loans injects a matching amount of deposits into the system, although those deposits will move around (and leak into other asset classes).

  8. Although the banking system cannot generate “infinitely large” loans in a short period (as might be suggested by a pure market clearing model), the “speed limit” on loan growth is going to be higher than what we see in the real world. The limit in practice is finding credit-worthy entities that want to borrow.

  9. Concentration risk may curtail lending to rapidly-growing segments of the economy.

  10. Unless the central bank is enforcing quantitative credit controls (which requires major structural changes to have a chance to work), it pretty much has no choice but to ratify the reserves needs of banks. Although they can try to adjust interest rates, that might only influence the dim future, and says little about the current funding situation.

  11. Any discussion about banks being self-funding is based on the premise that the entities meet the definition of being a bank — implying it already has capital and liquidity. Although bank deposits appear out of thin air, banks do not.

Concluding Remarks

Banking is yet another area where a mass burning of existing writing by economists would largely benefit humanity’s understanding of the topic. Running a bank properly is complicated, but there is no reason for the mystification of the process of lending. Banks extend loans if they think they will be profitable, and we see cyclical changes of bank credit growth in response to animal spirits. (And interest rates, for believers in conventional economics.) Lending creates the new deposits that creates the funding for the instruments that need to be issued to restore liquidity and capital ratios.

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(c) Brian Romanchuk 2024

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