Thursday, March 4, 2010

Reserves and Capital Confused?

In the economics of banking, "reserves" are a type of asset. There are two types of reserves: vault cash and reserve balances at the central bank. Vault cash is hand-to-hand currency held by a bank and epitomizes the concept of reserves. In the U.S., vault cash made up the bulk of reserves until recently. Banks need to hold reserve balances at the central bank to clear checks, but banks can deposit or withdrawal currency to or from those accounts.

From the point of view of a bank, reserves are "cash" or "money." In fact, banks often follow accounting conventions and describe their reserves as "cash." Since banks have direct access to the payments system, they can make payments by writing checks against themselves or else making electronic payments. However, if checks are "cashed," they must be paid out of vault cash. Wire payments going to other banks or checks deposited into other banks are covered out of the bank's balance in its reserve account.

In the economics of banking, "capital" is net worth. It is the difference between the total of all a bank's assets and all of its liabilities. It is not a type of asset. Capital is not "cash" or "money" from the point of view of a bank. It is owners' equity.

Suppose a wealthy entrepreneur starts a bank. He has $10 million to invest in the bank. He sells some of the stocks and bonds he currently owns. He sells his place in Vail. All of these sales of assets result in deposits in his checking account at his bank. He makes a major withdrawal of currency-- $10 million.

He rents a storefront for $100,000 per year. Hires a manager for $75,000 per year. And hands the manager a suitcase with $10 million of currency.

Before paying the first month's rent or any salary, the bank has capital of $10 million and reserves of $10 million. The capital is found by taking the bank's assets, $10 million of reserves and subtracting off its liabilities, which are zero. The reserves is the vault cash sitting in the suitcase.

The manager is worried about robbery and buys a $25,000 vault. That leaves the bank with $9,975,000 of reserves, sitting safely in the vault. The bank's capital is still $10 million. Its assets are made up of $9,975,000 of reserves, (vault cash,) and a vault worth $25,000. It has no liabilities. And so, $9,975,000 + 25,000 - 0 = $10 million. The bank has a capital ratio of 100 percent. The bank's leverage is zero.

After operating for a year, things are a bit bleak for the bank. The bank manager earned his $75,000 and the $100,000 in rent was paid. Ignoring the depreciation of the vault, the bank has zero revenue and costs of $175,000. It lost $175,000. The payments, of course, came out of the vault cash. Currency was pulled out of the vault to pay the salary and rent. At the end of the year, the bank's assets are $9,800,000 in reserves and a vault worth $25,000. It still has no liabilities. The bank's capital is $9,825,000. That is, $9,800,000 + $25,000 - 0 = $9,825,000. The bank's capital ratio is still 100 percent and its leverage is zero.

Obviously, the entrepreneur had something else in mind than renting a store, buying a vault, and paying someone to watch his money. No, the entrepreneur hoped to make money. So, let us wind back the clock, and find a different manager.

It would be possible to imagine that after purchasing the vault, the manager immediately lends out all $9,975,000. Suppose he lends at 3%. After all the loans are made, the bank's assets are $10 million--$9,975,000 in loans and a vault worth $25,000. It has no liabilities. The bank's capital is $10 million. The bank's capital ratio is still 100 percent. The bank's leverage is zero. The bank also has zero reserves. The vault is empty.

After a year, the bank is doing a bit better. All the loans were repaid with interest, and all the funds were immediately lent back out. The bank earned interest income of $299,250 (.03*$9,975,000). The costs were the $100,000 in rent and the manager's salary of $75,000 (continuing to ignore depreciation of the safe.) The bank earned a profit of $124,250.

The manager could turn this over the the entrepreneur. If that were done, then the bank's assets would be the $25,000 vault, and $9,975,000 in loans (the funds are lent back out as they are repaid.) The bank still has no liabilities, so its capital remains $10 million and its reserves remain zero. The bank has a capital ratio of 100 percent and no leverage.

There are some problems with the imaginary scenario of the bank lending out everything and leaving the vault empty. Loan customers appear, borrow money for a time, repay loans, perhaps on an installment plan. Even if all the money was immediately lent for the full year, the bank would have trouble making periodic rent and salary payments. So, the bank must keep some reserves. The amount of the reserves would naturally vary depending on when loans are repaid and when new loan customers appear. And then there must be provision for the payment of costs. Suppose that on average, the bank keeps $100,000 in the vault--not always, but that is what the average turns out to be. Then the bank's lending is, on average, $100,000 less.

And so, the banks assets would be $10 million. On average, it would have $9,875,000 lent out. On average, it would have reserves of $100,000 in a $25,000 vault. Its liabilities would remain zero. Its capital ratio is 100% and its leverage is zero. On average, it has $100,000 in reserves. While its reserve-asset ratio would average one percent, reserve ratios are usually defined relative to deposits. Since this bank has no deposits (and really isn't a bank,) the reserve ratio is undefined.

Taking into account the bank's reserves, its profit would be $3,000 less. It earns no interest on the funds left in the vault. Suppose that instead of paying the $121,250 profit to the entrepreneur, all of the profits are retained and are lent out as well. Then the bank's capital increases. The bank's capital will be $10,121,250, the initial investment by the entrepreneur plus the profit. Its assets would be $10,096,250 in loans and $100,000 of reserves in a $25,000 vault. It would have no liabilities. Its capital to asset ratio is 100 percent. It has no leverage, and it has expanded lending by amount of profit. It has $100,000 in reserves.

When the entrepreneur checks up on his manager, he should be happy, right? His investment has grown. He has earned a profit. Sadly, for the manager, that is not true. The entrepreneur is very disappointed in his 1.2 percent rate of return. He says, "I told you to start a bank. You know, a financial intermediary."

And so, let's start again. The entrepreneur chose a different manager, one who understands banking to be financial intermediation.

So, the manager has $10 million in currency in the rented office. But he finds depositors. He offers 1/4 percent interest on transactions (checking) accounts. He is obligated to pay those depositors back "on demand," (whenever they like.) Further, he has agreed to provide them payments services, managing checks and electronic payments for them. Various customers are willing to lend the bank a total of $20 million on those terms.

He offers 1/2 percent interest for "savings accounts." He also promises to pay those depositors back "on demand," (whenever they like.) However, there are no payments services associated with those accounts. Various customers are willing to lend the bank a total of $40 million on those terms.

And finally, he offers 1 percent interest for certificates of deposit. These have specific terms to maturity, perhaps a year, but maybe one month, three months or six months. Various customers are willing to lend the bank a total of $30 million on those terms.

While the various depositors give the manager checks or make electronic payments, he cashes them all, and has it all delivered to the bank. And so he has a huge amount of reserves. He has the initial $10 million provided by the entrepreneur, and $90 million provided by various classes of depositors. Total reserves are $100 million. And that is the sole asset of the bank so far. Total assets are $100 million. Liabilities, however, are now 90 million. The bank's capital is $100 million - $90,000, or $10 million.

The banks capital ratio is 10 percent, that is, the $10 million net worth divided by the $100,000 in assets. The bank's leverage is 9, which is the $90 million in deposits divided by the $10 million in capital.

What about reserve ratios? The bank now has several classes of deposits, and it is conventional to express reserves as a fraction of deposits. Monetary theorists look at the ratio between reserves and transactions deposits. Transactions deposits serve as medium of exchange as does currency. The reserve ratio for this bank is 500%, $100 million of reserves divided by 20 million in transactions deposits. (Current U.S. banking regulation requires that banks hold reserves equal to a fraction of transactions accounts. After some deductions, it is 10 percent.)

Rothbardian legal theory insists that bank should be required to hold at least 100 percent reserves against all deposits payable on demand. Many economists count savings accounts as part of the money supply because they are highly liquid. The ratio between reserves and savings and transactions accounts together for this bank is 167 percent. And, for completeness, the ratio between all deposits and reserves for this bank is 111%.

So, the banks capital ratio is 10 percent and its reserve ratio is 500 percent. The bank is leveraged by 9 but has reserves equal to its total assets. Once the manager buys the vault to store all of this currency, the reserves are no longer equal to assets and capital. And the reserve ratios are all slightly lower, but all remain well above 100 percent.

How does this bank fare after a year? Was leverage a great source of profit? On the contrary. Along with the $100,000 rent and the managers $75,000 salary, the bank now has $550,000 in interest expense. Total costs are $725,000, even ignoring depreciation of the vault. The bank has no revenue and so, after one year, it suffers a loss of $725,000.

After that year, the bank's assets are $99,275, 000, which is the $25,000 vault and the remaining vault cash, $99,250,000. Assuming that all of the interest to depositors was paid to them, and they took it out of the bank, then liabilities remain $90 million. The bank's capital is $9,275,000. It is the initial investment of the entrepreneur minus the bank's loss--minus his loss.

The banks capital to asset ratio has fallen, it is now $9,275,000/$99,275,000 or 9.34 percent. The bank's leverage is now increased from 9 to 9.7. The reserve ratio (for transactions deposits) is now slightly lower, 496 percent. Still, all the reserve ratios are well over 100 percent. The bank is solvent. At this rate, it will be many years before the manager runs through all of the bank's capital, and it fails, unable to cover costs and perhaps, repay all the depositors.

Naturally, the entrepreneur will be even more unhappy with this manager. Like the first manager, he lost money, but "leveraging" the investment just made the losses worse.

Last but not least, let's try again. The manager has the $10 million of currency in the rented office. The manager again has the bank borrow $90 million of deposits. Now the bank has $100 million in reserves. But this clever manager lends all of the funds out at 3 percent interest. He still purchases a vault, but it isn't clear why, since it stays empty.

After buying the vault and making the loans, the banks assets are $100 million, $99,975,000 in loans and a vault worth $25,000. The banks capital is $10 million. That is the $100 million in assets less the $90 million in liabilities. The bank's capital ratio is 10 percent, the $10 million in capital divided by the $100 million in assets. The banks leverage is 9. That is the $90 million in liabilities, the deposits, divided by the $10 million in capital.

The bank has no reserves, having spent a little on the vault and lent nearly all of it out. The reserve ratio (for transactions deposits) is zero, as are the other reserve ratios. The bank has 10 percent capital and zero percent reserves!

How do things work out for the bank over the year? Its interest income was $2,999,250 (.03*$99,975,000.) Its interest costs were only $550,000. (.0025*20 million + .005 * 40 million + .01 * 30 million.) When combined with the rent of the building and manager's salary, the total cost (ignoring depreciation of the vault) were again $725,000. The profit for the bank was $2,274,250.

While the profit was only 2.27 percent of total assets ($2,274,250/100 million) it as 22.74 percent of the entrepreneur's investment ($2,274,250/10 million.) By borrowing through deposits, the manager has "leveraged" the entrepreneur's investment.

It would be possible, of course, for the bank to pay out all of the profit to the entrepreneur. (And perhaps he would reward this successful manager with a big bonus!) If the depositors receive their interest and take it out of the bank, then the bank begins the new year as it was before. It has $100 million in assets, $90 millions in deposits, and $10 million in capital, ready to continue on.

But can the bank operate with zero reserves? Just as before, the bank is going to make loans at various times and receive loan repayments. It will need funds to pay the rent and the manager's salary. And now, it has to worry about the deposit side of the business. CD and saving account deposits come at various times and depositors may withdraw money. The transactions deposit business creates changes in reserves any time the bank's customers receive payments on net from customers of other banks. It also creates a need for reserves when its customers on net make payments to other banks.

Suppose that the bank finds that it can operate with $600,000 in reserves on average. Now the $25,000 vault is put to use! (By having access to the payments system, the bank doesn't need to make payments with currency, and most of its reserve needs are better handled with clearing balances at the central bank. Still, because its customers may need currency from time to time, and especially because customers who are retail businesses need currency to make change, vault cash is necessary.)

If the bank keeps $600,000 in reserves on average, then its lending will be slightly less. It would lend on average $99,375,000. Its total assets would remain $100 million, divided among the slightly smaller amount of loans, the $25,000 vault, and the $600,000 of reserves, at least some of which is kept in the vault. Capital is unchanged and so the capital to asset ratio remains 10 percent and the leverage remains 9.

However, the bank now has a reserve ratio (for transactions accounts) of 3 percent. It's reserve ratio for all deposits payable on demand (transactions and savings accounts) is 1 percent. And its reserve ratio for all deposits is .67 percent.

Assuming that reserves pay no interest, then bank's revenue is slightly reduced, to $2,981,250. Subtracting off the costs, that leaves a profit of $2,256,750. This profit is about 2.3 percent of total assets, but 22.6 percent on capital--on the entrepreneur's investment.

Suppose the bank retains the profit rather than paying it out to the entrepreneur. Capital is now $12,256,750. Assuming the bank pays interest to depositors, but continues to borrow $90 million, the bank's total assets are $102,256,750. Assuming it continues with its $25,000 vault and keeps $600,000 in reserves, the banks total lending will now be $101,631,250.

The bank's capital ratio is now $12,256,750/102,256,750 or approximately 12 percent. The leverage of the bank is $90 million/ $12,256,750 or 7.3. The bank as increased its capital and reduced its leverage even though it expanded its lending. It's reserve ratios remain the same, 3 percent against transactions accounts, one percent against all demand accounts (transactions plus savings accounts) and .67 percent against all deposits.

Should the bank maintain its leverage and attract more deposits? Perhaps, but hopefully, the purpose of this exercise has been achieved. Capital and leverage are not the same things as reserves and reserve ratios. And they aren't very closely related!


  1. Excellent post! I'm routinely surprised by how few people truly understand banking. Thank you for the comprehensive overview of reserves, capital and leverage.

  2. I think a lot of the problem comes from legally, reserves and capital are the same if they are certain kinds of capital. If the discount window and/or federal funds rate is low enough, the bank can use that instead of actually keeping enough reserves.

    This however makes the system brittle when the rates rise.

  3. Doc:

    I don't think that is correct. Why do you say that legally reserves and capital are the same if they are certain kinds of capital.

  4. Fabulous. Probably the best in class way to explain these terms to a newbie.

  5. in your example it seemed that the hypothetical bank only made loans from deposits placed in the bank and equity; but my understanding is that banks create their own deposits when a loan is created: i.e. the deposit is the value of the principal of the loan and placed as a liability, which is counterbalanced by the loan itself as an asset.

  6. Excellent post Sir, very clearly illustrated! Thank you.