Fractional Reserve Banking 2

The concept of "Fractional Reserve Banking" is tied to an unrealistic narrative regarding the nature of banking. While the traditional account of fractional reserve banking includes many truths, it is embedded in a framework that focuses on banks as storehouses of money rather than as financial intermediaries. In Fractional Reserve Banking 1, I gave such an account.

As financial intermediaries, banks borrow funds by issuing a variety of financial instruments. These bank liabilities serve as assets to households and other firms. All of these bank issued financial instrument can substitute for one of the functions of money--the less central store-of-wealth function. And, of course, some bank liabilities can substitute for the core function of money, as media of exchange. Under modern conditions, transactions accounts at banks are money, and make up the most important part of the total quantity of money.

Those bank liabilities that serve of as medium of exchange create special problems because of some of the essential qualities of the medium of exchange. People accept money in payment even if they don't intend to hold it. People can and do realize an increase in the demand for money by reducing habitual expenditures on other goods and services.

However, the fundamental nature of bank borrowing--even using monetary instruments--is based upon the demand by firms and households to hold those liabilities. Banks, as financial intermediaries, must find willing lenders. The "problems" that are seen by critics of fractional reserve banking are not problems with the banks, but are rather problems with the hand-to-hand currency. The banks adjust the amount of money they issue to reflect the "market share" of banks in the total demand for money. If the issue of hand-to-hand currency similarly adjusted in that fashion, the "problems" of fractional reserve banking would not develop.

The inflationary or deflationary impacts of fractional reserve banking are nothing more or less than showing how the market adjusts to a change in the demand for hand-to-hand currency, when the quantity is assumed to be fixed. It is little different from the fundamental proposition of monetary theory, explaining how the market adjusts the demand to hold money to a given quantity of money, or alternatively, how the real quantity of money adjusts to the real demand for money by changes in its purchasing power.

To explore these questions, consider an alternative conjectural history of banking. Again, money is initially made up of tangible, hand-to-hand currency. It could be gold coin, but paper fiat currency is more familiar.

Banks, however, develop as financial intermediaries. Money lenders, who are lending their own capital, begin to "leverage" by borrowing additional funds to lend as well. Suppose the banks make 90 day commercial loans to businesses. Aside from the capital invested by the owner, the loans are funded with 90 day certificates of deposit.

The banks are borrowing money from depositors--firms and households--with money to lend. And then the banks take those funds and lend them to firms that need to finance their operations. The banks charge more for these commercial loans than they pay on the deposits, which generates their revenue. After subtracting operating costs, the result is the banks' profit.

What benefit do depositors receive from lending to banks instead of directly to the firms? There may be some benefit in that the banks can issue CDs in various small or large denominations convenient to depositors while making loans in the amounts convenient to the firms needing to borrow money.

However, the key benefit is that depositors receive the benefits of diversification. If a small lender made a loan to a single business and that business failed, the borrower could take a substantial loss.

That the banks make loans to a variety of firms allows them to earn a given return with less risk of loss. While some of the businesses may fail and not fully pay, each bank is compensated by interest earned from all of the loans that are repaid.

From the depositors' point of view, this risk is buffered by the bank's own capital, or net worth. The bank must suffer sufficient losses, from bad loans or any other source, to run through all of the funds contributed by the owners, before the bank fails, and the depositors take a loss. However, because the banks can diversify and make loans to a variety of businesses, the chance that the losses will be so great as to cause a bank to fail is diminished.

So far, the banks have no part in the payments system. Depositors bring in currency to deposit. The banks lend businesses currency. Presumably, the businesses borrow currency to make payments with it.

As the bank undertakes its business through time, receiving deposits, making loans, receiving loan repayments, paying off deposits, it will need to maintain currency balances, much like any other business. Like any other business' money holdings, it will change based upon money received and paid. If new deposits plus loan repayments are greater than the redemption of deposits and new loans, a bank's currency holdings will rise. If new deposits and loan repayments are less than redeemed deposits and new loans, then a bank's currency holdings will fall.

Bank depositors often rollover their funds. When a CD matures, the depositor receives a new CD from the bank instead of currency. This reduces the banks currency needs. Similarly, a bank can rollover loans. If a business borrower is financing inventory with commercial loans, a bank can renew the loans without insisting that its customer show up at the bank and pay currency. The business can use the currency it receives from selling its products to purchase additional inventory.

A bank, as financial intermediary, needs to keep deposits and loans in balance. The interest rates paid on deposits and the interest rates charged on loans should be set to maintain the balance. If interest rates on deposits and loans are too low, new loans will be greater than new deposits. Loan repayments and deposits will generate too little currency to cover new loans and the repayment of deposits.

On the other hand, if interest rates on loans and deposits are too high, then new deposits will accumulate more quickly than new loans. A bank's currency holdings will build as loan repayments and new deposits outstrip new loans and the repayment of deposits.

However, even if the interest rates a bank pays and charges keeps deposits and loans balanced over time, its cash holdings will vary with daily variation in deposits, withdrawals, loan repayments and new loans.

The average amount of currency the bank holds could be expressed as a fraction of total assets or of deposits. But it unclear why such ratio would be especially significant.

Because the bank is assumed to borrow by issuing 90 day CDs and then make 90 day loans, it doesn't create liquidity. Suppose that one of the bank's customers asks for a six month loan, rather than the traditional 90 day loan. Suppose the bank agrees, but rather than finding a depositor who wants to purchase a 6 month CD, it funds the loan with a 90 day CD. When that CD comes due in 90 days, it must simply issue a new CD to pay off the existing CD.

This transaction creates liquidity. The six month loan is transformed into two sequential 90 day CDs. The depositors that are ultimately funding the six month loan only tie up their money for half of that time.

The bank, however, is taking liquidity risk. When the first CD comes due, the bank must somehow obtain the funds to pay it off. Perhaps a higher interest rate must be paid. Or, maybe the 6 months loan must be sold to a third party at a loss. But, of course, it is possible that the bank will have no trouble issuing a new C.D. to pay off the old one. Perhaps even the initial lender will roll-over his funds and purchase an additional C.D.

If the liquidity risk does result in some loss, then it comes out of the bank's capital. If losses from liquidity risk are severe enough, then the bank might run through all of its capital. It will be bankrupt. It will be unable to fully pay off all depositors.

All bank risks, including both credit and liquidity risk, have an impact on depositors. The bank's capital provides a partial shield or buffer. Bank capital increases the size of the losses a bank can suffer, that the owners of the bank can suffer, before the depositors must also take a loss.

It is this scenario where a bank can be said to be illiquid but not insolvent. If someone were willing to lend to the bank at a "reasonable" interest rate, then the bank can pay off maturing deposits, and eventually, its loans will mature and it will be able to repay the deposits. Or, if someone is willing to pay a "reasonable" price for the bank's loan, then the bank will be sell the loan and pay off the deposit. The inability of the bank to borrow at all, or sell its loans at all, or to borrow at only excessive interest or receive only prohibitively low prices for loans, is what results in the bank's default and failure. While the bank may fail, the losses to the depositors could be minimal.

Suppose that one of a bank's depositors rolls over less funds than usual. When asked what happened, the depositor explains that something might come up about two months from now, so that he cannot tie up as much money as usual in the 90 day CDs. The bank could offer to issue a 30 day CD. If the bank doesn't find someone interested in borrowing for 30 days, and instead funds a 90 day loan, the bank has created liquidity. After 30 days, the bank must either sell the loan to obtain the funds to repay the deposit, or borrow new funds. It could issue a standard 90 day CD or else another 30 day CD.

The result is no different from funding a 6 month loan with a 90 day CD. The bank has created liquidity and bears liquidity risk. Of course, the 30 day CD has a shorter term to maturity.

Generally, liquidity-creating banks can fund their operations with deposits of a variety of maturities and make loans of a variety of maturities. A bank's loans and other assets create credit risks. The mismatch between the maturities between a bank's loans and deposits creates liquidity risk. These risks can be source of bank losses. A bank's capital creates a buffer for taking losses before the bank fails and depositors take losses.

The banks' currency holdings (or reserves) is related to liquidity risk. If a bank needs funds to make a new loan or pay off deposits, and the amount of loans being repaid or else new deposits generate insufficient currency, then, at the very least, the bank must turn down loan business, or worse, will be unable to meet redemption demands. A bank's currency holdings provides a buffer against those adverse consequences--particularly the chance of default.

Fortunately, banks can make "loans" by holding marketable securities that can be sold to obtain funds. Also, banks can borrow short term, perhaps from other banks. From the point of view of the individual bank, the management of its currency holdings is largely a matter of trading off the transactions costs of selling securities or borrowing short term against the opportunity cost of holding zero-interest currency.

It would be possible to calculate the ratio of currency (reserves) to total assets, some subset of assets, total deposits, or some subset of deposits. It unclear why any of those ratios are of significance. What is important is the variance of the bank's currency balance, the interest rate that can be earned on liquid assets, and the transactions costs of trading securities or obtaining short term loans.

A 30 day CD has a very short term to maturity, however, that is hardly the limit. Banks could borrow for even shorter terms to maturity. They could borrow by issuing 14 day CDs. If the bank pledges some kind of securities as collateral, then these would be "repurchase agreements," and 14 days is a common maturity in that market. However, any term to maturity is possible.

Overnight is especially important because modern experience has shown that a payments system can be developed using overnight deposits. But 5 hour, one hour, 10 minute, 30 second, or even one nanosecond are possible--the term to maturity can approach zero. At some point, there could be no other reason than regulatory evasion to avoid describing the transaction as a traditional "demand deposit." That is, the bank borrows funds from depositors, promising to repay the funds at the request of the depositor.

Some critics of banking have insisted that if a bank promises to repay funds on demand, then that bank is obligated to store the money and keep 100 percent reserves. If such a rule is implemented, then banks must simply promise to repay money one nanosecond in the future, with automatic rollovers until notification. After the initial deposit, at any point in time, the funds are maturing, and the depositor can state that the rollover agreement ends now, pay up.

From the bank's point of view, its situation isn't much different. The problem isn't how many depositors could demand currency at any point in time, it is rather how many actually will demand payment in currency. And that calculation simultaneously includes estimates of how many loans will be repaid in cash at that point in time, how many new cash deposits will occur, and, while not relevant for the possibility of default, how many borrowers will request new loans.

Do these banks have any macroeconomic significance? Yes, it is almost certain that financial intermediaries would cause inflation. Return to the simplest scenario where the banks fund 90 day commercial loans with 90 day CDs. The banks create no liquidity. The CDs are not used as the medium of exchange. All payments are made with currency. Like any other businesses, banks hold currency for making payments.

If the financial system is very primitive, so that many households and firms are saving by accumulating money balances, then the development of these banks allows them an alternative method of saving. Rather than putting currency in the cookie jar, or burying it in the backyard, to save up to buy a car, buy a house, pay for college, for retirement, replace income that might be lost due to an extended illness, or start a business, households and firms that were accumulating money balances can lend the funds to banks.

This results in a decrease in the demand for money--for the gold coins or paper currency that serves as the medium of exchange. If the quantity of money, of hand-to-hand currency, does not change, then the market process that adjusts the real quantity of money to the real demand for money is for its purchasing power to fall. The money prices of all goods and services must rise.

For example, if the development of banking results in people shifting 50 percent of their money holdings to banks, having hoarded all of that currency for purposes of saving, then other things being equal, the price level would need to double. Each dollar would purchase approximately half as much. And the total value of all the currency would just match the amount households and firms want to hold to make transactions.

Of course, the banks do need to hold some currency, as explained above. If that is treated as a separate demand, then the increase in the price level would be less than in proportion to the decrease in the demand for currency by household and other businesses. What is interesting, of course, is that if the banks were not financial intermediaries, holding modest amounts of currency, but were "money warehouses," then moving "savings" from the cookie jar or backyard to the banks would leave the demand for currency unchanged, and there would be no inflationary impact.

So, banks, even creating no liquidity, and operating as financial intermediaries, could create inflation by reducing the demand for currency. Currency serves as a store of wealth as well as a medium of exchange. Bank CDs are an asset that savers can hold. This new financial instrument that competes for household savings results in a loss in "market share" for currency, a decrease in the demand for currency, and so, given the quantity of currency, a lower purchasing power of currency, and a higher price level.

Considering this scenario, it is clear that the problem isn't that banks have introduced a superior outlet for saving, but rather the problem is that the quantity of currency fails to adjust when the demand to hold it falls.

Suppose the quantity of currency was managed by a monetary authority whose mandate was to maintain the purchasing power of money. If the demand to hold currency as a store of wealth were to fall, because household and firms begin to hold 90 day CDs at banks, then the monetary authority would need to reduce the quantity of currency to reflect that lower demand. If the demand to hold money fell in half, then the monetary authority would need to drop the quantity of money by 50 percent. The nominal quantity of money would match the amount households and firms still want to hold for transactions. There would be no decrease in the purchasing power of money or increase in the price level.

If the quantity of currency is fixed, then it is possible for there to be a financial crisis centered on the banks, even if they create no liquidity, much less are involved in the payments system. Banks can, of course, make bad loans. If there are enough bad loans, the banks can suffer losses. If these losses are large enough, the banks may run through all of their capital, become insolvent and bankrupt. The depositors can take a loss. Fear of that prospect could lead depositors to stop rolling over their CDs and as they mature, return to storing currency in cookie jars or burying it in the back yard.

Suppose worries about the banks failing lead to an 20 percent increase in the demand to hold currency. If the quantity of currency is unchanged, the purchasing power of money must rise and the price level fall by 20 percent. This will cause the real quantity of currency adjust to the now higher demand. The banks should be hedged against this risk. While the real value of their liabilities, the CDs, increase 20 percent, the real value of their assets, the loans they have outstanding, also increase the same 20 percent.

But those borrowing from the banks are almost certainly not hedged against this decease in the price level. The cash flow that they would used to pay the loans is reduced. So, the first "cushion" is the capital, or net worth, of the borrowers. If it is too little, then they will be bankrupt and unable to pay their bank loans. Then, the banks receive only partial payment of the loans. This reduces profit and if large enough results in loss. If the losses are greater than the banks' capital, then banks fail. Depositors take a loss.

Of course, the real value of the partial funds the depositors receive from the bank is larger. Perhaps there is no real loss to the depositors. However, if there is any nominal loss, then holding currency would provide a larger real gain than bank deposits. And so, expectations of this scenario provide a rational motivation for depositors to collect on CDs as they come due and hoard currency.

Further, this same logic applies to the banks. If the banks expect that an increase in the demand for currency will develop, and the result will be nominal losses on loans, they can reduce their losses by accumulating currency. As old loans are repaid, they can accumulate currency rather than make new loans.

If the increase in the demand for currency was due to a correct anticipation of bad loans--credit risk-- then these losses due to an increase in the demand for currency and a decease in the price level compound the losses. The problem isn't that the banks are creating money. It isn't that they are creating liquidity. The problem is that the demand for currency increased, the quantity of currency remain unchanged, and the banks lent money to people who suffer losses due to the decrease in the price level.

With more sophisticated financial markets, it is possible that banks as financial intermediaries would have little impact on the demand for currency. For example, suppose households and firms wanting to save are purchasing 90 day Treasury Bills. Banks develop, as financial intermediaries, competing with the government by issuing 90 day CDs. Rather than imagining that nearly all the funds deposited into banks comes from currency hoards, in such a scenario, the more plausible, and more limited, source of funds would be those that would have been lent to the government. And while higher yields on these financial instruments might encourage those holding currency to manage their balances more closely and put more in a bank, this effect could be on the same order of magnitude as attracting new saving. That is, households might reduce consumption expenditures out of current income and deposit funds into CDs at banks.

By creating liquidity, financial intermediaries can have a much more significant macroeconomic impact. While creating liquidity is risky because of a mismatch between the maturity of assets and liabilities (loans and deposits,) the key macroeconomic impact is that banks creating liquidity can reduce the term to maturity on their borrowing. This makes bank liabilities into closer substitutes for currency. If banks fund their operations with deposits that can be used to make payments, a very large substitution away from currency is possible because banks are competing with the core role of currency as medium of exchange.

Consider a bank that funded a portfolio of 30 year treasury bonds with 10 year CDs. While such a bank would be creating liquidity, it is unlikely that 10 year CDs would provide a good substitute for currency and so would have much impact on the demand for currency. No, it is the very short terms to maturity, in particular, overnight borrowing, that have been shown to provide a near perfect substitute for money. Money deposited in such an account, with automatic rollovers, allows depositors to claim their funds whenever needed by providing notification that some or all of the funds should not be rolled over again.

While in the U.S., transactions accounts are not "overnight," but rather payable on demand, a payments system could be constructed using overnight accounts. When checks or electronic payments generate claims against such an account, the bank would be obligated to cease rolling over the amount of funds needed to cover the claim.

If financial intermediaries are able to develop a payments system, then a very significant decrease in the demand for currency is possible. If the MZM to currency ratio is taken as typical, then perhaps the demand for currency could be reduced by 90 percent. If the quantity of currency is fixed, then a 90% decrease in the demand to hold currency would require a roughly ten fold decrease in the purchasing power of currency. The price level would need to rise by a factor of 10.

The process by which this would occur is very similar to the traditional "money multiplier" story. Banks begin to offer financial instruments that provide a good substitute for currency. The demand for currency falls, as the demand for these bank-issued instruments rises. The banks meet this demand by issuing the instruments. The banks receive currency in exchange for those deposits, and then lend the money out, by making commercial loans or perhaps by purchasing liquid securities. If the banks are directly involved in the payments system, they can simply create deposits for borrowers, and as the borrowers spend the money and the checks clear, reserve balances (perhaps currency or balances at the clearinghouse) are shifted to the banks of those selling to the borrowers. And now those banks have excess currency (or clearing balances) and expand lending.

This process, however, is just an example of the fundamental proposition of monetary theory. Currency serves as the medium of exchange. People (including banks) accept it in payment without intending to hold it, and if they are holding more than they want, they spend it. The banks accept money in payment for deposits, and they spend it by purchasing securities or making loans. Monetary equilibrium returns when the real value of money (currency in this case) decreases to match the real demand.

Certainly, if banks begin to issue very liquid, short term deposits, and go so far as to develop a payments system, their demand for currency would rise. Retailers regularly make currency deposits at banks and withdraw currency from banks to make change. However, this demand should not be strictly proportional to the quantity of total deposits, or any class of deposits. There are just additional flows of currency to and from banks, and this additional variance in the level of currency holding, along with the interest rates on various short term assets and the transactions costs of those assets determine the optimal level of currency.

If banks organize a clearinghouse and deposit currency at the clearinghouse, then the banks' clearing balances creates a substantial demand for currency. However, the banks could easily avoid the opportunity cost of settling with currency by having the clearinghouse operate as a money market mutual fund.

If a banking system, based upon financial intermediation, gradually develops more liquid deposits and goes so far as to develop a payments system, the result could easily be a substantial reduction in the demand for currency. As this lower demand to hold currency develops, and the price level rises, then all the nominal values in the economy, including the dollar value of deposits, loans, and all the currency payments rise as well. And so the nominal demand for currency holdings by banks rise in proportion as well.

Suppose the quantity of currency were not fixed, but rather a monetary authority manages its quantity to offset any changes in the demand to hold it so that its purchasing power remains stable. As financial intermediaries develop shorter term, more liquid, deposits, or even a payments system, so that the demand for currency falls, then the monetary authority would be obligated to reduce the quantity of currency. The purchasing power of currency would be unchanged.

If money is defined as the medium of exchange, and bank deposits are used to make payments, then banks are creating money to match the demand for households and firms to hold (and perhaps use for payments) this new class of financial instruments. The banks certainly require currency for their operations, and the monetary authority's responsibility is to keep the quantity of the currency issued equal to the total demand to hold it, both by banks and households and other firms.

Considering this scenario, in what sense are the banks creating money equal to a multiple of reserves? Certainly, it is possible, even likely, that the monetary instruments bank create will be a multiple of the amount of reserves, currency holdings or clearing balances, that the banks hold.

But why is that ratio significant? Fundamentally, the banks supply monetary liabilities as demanded. They, like everyone else, demand some currency. They, like everyone else, with an excess supply (or demand) for money adjust spending. If the quantity of currency is taken as fixed, then equilibrium requires changes in the price level so that the real quantity of currency adjusts to the real demand by households, banks, and other firms. But if the monetary authority adjusts the nominal quantity of currency so that it remains equal to the total demand to hold currency by households, firms, and banks, then the total quantity of deposits issued by the banking system would not be inflationary. The quantity of deposits issued by the banks would be limited by the demand by households and firms to hold them.

An individual bank in a banking system must fund its assets. Any banks issuing deposits that are used as money can write a checks to purchase a securities or provide deposit accounts to borrowers. But the check used to purchase the security or the checks written by the borrowers end up deposited at other banks, generating adverse clearings. A bank must either sell some other asset or else find someone willing to lend it money, generally, someone willing to hold its deposits.

But all that process really does is limit each bank's supply of monetary liabilities to a market share that depends on depositor preferences. With a clearinghouse, any bank that issues too many deposits relative to customer preferences is going to see depositors shift funds to other banks and have adverse net clearings. And any bank that fails to create enough deposits to match the market shares reflecting depositor preferences will receive additional deposits.

Of course banks can impact depositor preferences. Even if they are tied together by a clearinghouse and accept each others checks (or electronic payments) for deposit at par, each bank can adjust the interest rate it pays to depositors to impact its market share.

What is important, however, is that the clearing process doesn't control the total quantity of deposits. As the logic of the "money multiplier" suggests, an individual bank that creates a deposit and creates a loan can expect to suffer adverse net clearings as the borrower spends the funds and they are deposited in other banks. However, the other banks receive those funds in deposit, and so the total quantity of deposits in the system adjust to the amount of loans. The banks receiving the new deposits have favorable clearing balances. Perhaps they could lend those funds to the bank that made the loan. And then, total loans and total deposits have increased.

However, just as each bank is limited to issuing monetary liabilities in proportion to market shares depending on the preferences of depositors, the total issue of all the banks is limited by the preferences of those holding money by the market share of deposits relative to currency. If all the banks issue monetary deposits beyond the level consistent with the share of total money holdings households and firms prefer to hold in the form of deposits, then banks will be required to obtain currency in order to pay off depositors.

And the opposite is true as well. If banks want to operate a payments system that includes fiat paper currency, they need to accept it for deposit. If banks issue too few deposits, then they will see increases in currency deposits. New deposits are created.

Just as an individual bank can impact its market share of monetary liabilities by changing the interest rate it pays on deposits, the interest rates that each bank sets impacts the market share of deposits in total money holdings. If banks pay higher interest rates on deposits, then one effect should be a larger demand for deposits relative to currency. And banks will expand the deposits they create to match the demand. And the opposite is true as well. Just as each bank can reduce its individual market share by lowering the interest rates it pays on monetary deposits, the banking system does the same relative to the market share of deposits in the total quantity of money.

Certainly, banks as financial intermediaries are imperfect, and are subject to failure due to credit risk--making bad loans. Further, if they create liquidity, they face an additional source of risk, that could also lead to failure. Since banks have very little opportunity to make overnight (or less) loans, if banks are creating monetary liabilities, they will face liquidity risk.

And while banks funding their operations partly with monetary liabilities can lend money into existence, they remain limited individually to their market share of the total amount of deposits by the preferences of depositors. Further, they remain limited collectively by the total market share of deposits relative currency as determined by the preferences of those holding money.

The "problem" of banks with "fractional reserves" creating a multiple expansion of the quantity of money with inflationary consequences is really a problem of the quantity of currency failing to decrease when the demand to hold currency falls. The banks adjust the quantity of deposits they create according to the preferences of those using money. If the quantity of currency is assumed to be fixed, then it is failing to adjust to reflect its market share as determined by those holding money. But if there is a monetary authority manipulating the quantity of currency, "the problem" is that the monetary authority is not adjusting the amount it issues to reflect the preferences of those holding money.

In conclusion, the money multiplier process that describes a banking system receiving deposits of currency, and then having that currency lent, and then deposited and the lent again, is really a story about how the quantity of currency has failed to decrease in response a decrease in demand because banks are providing a product that the households and firms using money find superior. Further, in the reverse situation, the economic difficulties that develop when depositors abandon banks and instead choose to hold currency occur because the issuer of currency is failing to increase the quantity of currency to meet the added demand.

It only by starting with the assumption that the quantity of currency fixed and unresponsive to changes in the demand to hold it, and that the sort of "banking" system that has no impact on the demand for currency, 100 percent reserves, is the base line, does the conventional analysis of fractional reserve banking become sensible. If instead, the baseline is banks as financial intermediaries, providing through liquidity or a payments system, financial instruments that are competitive with currency, then the ratio of currency or other reserves to some class or other of deposits fades to insignificance. The problem, instead, is the failure of the quantity of currency to adjust to changes in the demand to hold it. With a monetary authority manipulating the quantity of currency, the problem is with the monetary authority.