Zero Discount Value of Gold in the Total Banking System

by Michael S. Rozeff
by Michael S. Rozeff
Recently by Michael S. Rozeff: The Zero Discount Value of Gold and Dethroning the Dollar

The U.S. banking system has many banks with large amounts of bad loans on their books. How do these bad loans affect the value of the dollar and gold? Specifically, how do they affect the Zero Discount Value (ZDV) of gold?

Zero Discount Value (ZDV) in review

An earlier article introduced the concept of gold’s Zero Discount Value (ZDV). Applied to the central bank whose only asset is gold and whose liabilities are currency and bank reserves, the ZDV is a value for gold such that every outstanding dollar liability in the central bank’s monetary base (currency plus bank reserves) is backed by an equivalent dollar’s worth of gold. It is what the dollar price of gold would be if the central bank’s liabilities were 100 percent backed or covered by gold.

To estimate the ZDV in this simple situation, in which no other assets than gold qualify as valuable assets, divide the monetary base by the number of ounces (oz) of gold that the bank holds. If, for example, 200 oz. of gold are held against 400,000 dollars of monetary base, then the ZDV is $400,000/200 oz. = $2,000 an oz. Only if gold is valued at $2,000 an oz. does every dollar that has been issued by the central bank correspond to one dollar’s worth of gold.

The market price of gold need not be the ZDV we estimate from central bank data. Gold has sold at a discount to ZDV for many years in the U.S., which is the main reason the term "zero discount" is used. However, there are market and arbitrage forces that move gold’s price toward the ZDV, if they are not thwarted. This statement is a special case of a proposition that applies to any enterprise whatsoever: Market forces tend to make the value of the outstanding liabilities equal the value of the outstanding assets, inasmuch as the cash flows or other returns of the assets are what give value to the liabilities and investors can usually find ways to buy either the assets directly or else buy the securities that represent them.

The statement that market value of liabilities equals market value of assets is so widely accepted as true that it is taken for granted. One can invest directly in the real assets of an enterprise (that is, in some replica or close substitute of them) or indirectly by means of the debts and stock that finance them. If the values of these two options are not in line, one invests in the less costly alternative. Possibly one arbitrages by selling or issuing the more costly alternative simultaneously. If the debts and stock have market values that are low compared to the market value of the associated real assets, then the tendency is for the real assets to be avoided or sold and the financial claims on them to be bought. Conversely, if the debts and stock have market values that are high compared to the market value of the real assets, the tendency is to buy the real assets directly and sell the financial claims. These actions align the market values on both sides of the balance sheet.

Gold is the real asset of the FED, and currency and reserves comprise its main liability. If the currency value is its face value and the face value is $400,000, then a 200 oz. holding of gold has a ZDV of $2,000 per oz. If the gold sells for less than this, there is a tendency to buy the gold instead of the currency, and vice versa. We observe that gold has in fact sold at a hefty discount to its ZDV for many years. The tendency to buy gold and sell the dollar has been seriously thwarted in the world’s monetary dealings, but not entirely so. Gold has shown a long-term tendency to rise as its ZDV has risen, even if the discount remains large. That tendency has been very far from being a smooth and continuous one. The market price depends on human recognition and action. It depends on many factors, including the actions of authorities, interventions, and sundry political matters. The result is a market price whose many ups and downs depend at times, sometimes long times, on factors other than convergence to ZDV. But still it is my judgment that ZDV exerts a very long-term pull or an attraction for gold’s price.

Bank Money and Bank Money Inflation

In addition to the central bank, the banking system has as its main component the many ordinary banks that make loans to the public and create bank deposits accordingly. Ordinary banks do not hold gold as an asset. Their loans are their main assets. What is the ZDV when we take these banks into account?

When a bank creates a mortgage loan or a business loan, it simultaneously creates a demand deposit or checking account in the name of the borrower, who then spends out of the account to buy a house or perhaps business inventory. Since checking accounts are used as money, the bank creates money when it creates loans. The accounting for this is a debit to a Loan account and a credit to a Deposit account. When loans are repaid, the borrower writes a check to the bank. The bank then credits the Loan account and debits the Deposit account.

We use demand deposits as money. We use currency as money. Time deposits are not used in everyday exchange, but yet time deposits are easily converted into demand deposits. If a bank certificate of deposit matures, we can instruct the bank to credit a demand deposit account. When it comes to getting gold’s ZDV, these distinctions among the various kinds of deposits are not relevant. What we want to know is what value of gold it takes to back up all deposits in full. I simply call all deposits bank money to distinguish them from the central bank’s money, which is the monetary base consisting of currency plus bank reserves.

The backing of deposits is defined as the value of the bank’s assets that can be used to extinguish the deposit liabilities. Good loans are defined as loans that pay off the promised amounts. Good loans back deposits in the sense that when these loans are paid off, they provide their promised amounts of payments by borrowers to the bank. These payments then shrink deposits by the extent of the loans being paid off.

Bad loans are loans that fail to provide the full amount of the promised payments. Any losses in value of bad loans below the promised payments mean that borrowers have not collected enough dollars from their customers or jobs to write checks to the banks and reduce deposits. The dollars remain in the system as deposits. How so? If a borrower has bought a house on a mortgage loan that he cannot repay, he has written a check to the house’s owner. That seller then has those funds on deposit in his account. They will only be offset when the borrower pays off the bank loan. If he is unable to do this, then bank deposits or bank money do not shrink. But since the bad loan has reduced or no market worth, we see that bad loans reduce the loan backing of the still outstanding dollar deposits that were created against them.

Banks are supposed to write the bad loans off. This requires them to credit the Loan account to reduce it and debit an Equity account, which reduces it. When many loans go bad and reduce Equity drastically, the bank owners and/or managers have to get more equity capital somehow if the bank is to survive. If they do not or cannot, the bank fails and its creditors, the depositors, lose some or, in the worst case, all of their deposits.

Deposit insurance is a bank asset and a method to counteract the effect of bad loans. The extent to which it backs deposits is an important element that I discuss below. Until that discussion commences, it is convenient to carry this analysis forward assuming that there is no deposit insurance. Since I conclude later that deposit insurance does not substantially alter the situation, this assumption is warranted.

Suppose a bank has a simple balance sheet with $200 of good loans and $200 of deposits. The ratio of the market value of the deposits to the loan assets is 1. This indicates a viable or sound bank, that is, a bank with enough backing for deposits to reduce them when the loans are paid off. Now suppose that $40 of the $200 in loans are a total loss. The ratio of deposits to loans is $200/$160 = 1.25. This signifies that even if the loans are fully liquidated, the bank does not have enough bank money to pay off on its deposits.

A bank might have certain off-balance sheet assets to remedy such situations. It might also have off-balance sheet obligations that make the situation even worse. It might have a commitment by its owners to supply capital in such circumstances, or it might have lines of credit with other banks. It might have deposit insurance.

I define bank money inflation as an issue of bank money (deposits) not secured by additional assets of equivalent worth. In the preceding instance, there was no inflation when the deposit/asset ratio was 1. There was inflation when the bad loans produced a deposit/asset ratio of 1.25. Sufficient backing to the deposits means the same thing as no bank money inflation. Insufficient backing means inflation. As long as loan values keep pace with deposits, there is no bank money inflation, simply because good loans mean that loans are being repaid and that they are extinguishing the bank deposits and money as they are repaid. If the loan values are overstated, which has certainly happened in the past decade, then there is insufficient backing and there is bank money inflation.

Notice that bank money inflation does not refer to inflation of prices in the economy, whether of wholesale goods, consumer goods, stocks, bonds, labor, commodities, interest rates, or real estate. Analyzing how this vast array of prices relates to bank money inflation and to central bank money inflation is another ball of wax. I steer clear of mixing up that analysis with the one at hand.

Individual banks within the banking system can always inflate by making bad loans. If the bank’s loans are good loans, it is not inflating money. If the loans are bad loans, then it is inflating money. Critical to bank money inflation occurring is the nature of the loans the banks make. Are they good loans or are they bad loans? That is what determines the extent of bank money inflation.

Inflation (of bank money) is not an economy-wide phenomenon unless banks in general are creating loans whose values fail to keep pace with deposit liabilities. This can occur in a central banking and government-influenced system, even when banks compete with one another in making loans. A government might, for example, subsidize or use its powers to encourage the economy-wide expansion of an industry to which banks make loans that ultimately become bad loans due to overbuilding. The FED’s creation of monetary base can influence interest rates and create bank reserves that induce banks to make what turn out to be bad loans. I’ve discussed these issues at length in an earlier article. It seems to me that these kinds of actions are exactly what caused the present credit debacle, and I’ve argued that case in many articles. The government and the FED stimulated bank lending that gave rise to bad loans and the concomitant bank money inflation. Many observers saw this happening while it happened and others predicted it would happen. Warnings filled the air, but the authorities caused the inflation anyway.

Zero Discount Value with Bank Money

There are two layers involved in the banking system. There is the central bank that produces base money and there are the ordinary banks that produce bank money. Gold backs the monetary base, and loans back the bank money or deposits. If the bank money is fully backed by good loans, does this alter the ZDV? The answer we shall find is that it does not. If the bank money loses value because the banks experience bad loans, does that affect the ZDV? We shall find that it does. In this case, if the deposits are not covered by bank loans, they have to be covered by gold.

For purposes of thinking about the price of gold, which is my objective in all of this, I suggest we obtain a ZDV for the total system. I will sketch out how to do this by consolidating the banks and the central bank. I show that the ZDV for the total system cannot be any lower than the ZDV for the central bank alone. A chain is no stronger than its weakest link. Even if the banks make sound loans and produce no bank money inflation, the currency is still subject to the inflation produced by the central bank. This means that sound bank loans cannot lower the ZDV. Second, if the banks make unsound loans and produce bank money inflation, then the total ZDV must be higher than the ZDV of the central bank alone.

Suppose that the banks have Assets of 10, consisting of Reserves of 1 and Loans of 9. If these are in trillions, they are nearly the same as in the U.S. banking system. The Reserves are held as deposits at the central bank. The Liabilities are Deposits of 10. Equity is 0.

The central bank has Assets of gold, or G, which is a certain number of ounces of gold. Its liabilities are Currency of 1 and Reserves of 1. The Reserves are the deposits of the banks. This fifty-fifty split between currency and reserves is roughly the current situation at the FED. The ZDV of the central bank is (R + C )/G = (1 + 1)/G = 2/G. With gold later to be taken as 261.5 million ounces and the bank’s numbers expressed in trillions, the central bank’s ZDV is $2 trillion/261.5 million oz. = $7,648 per oz. This is actually quite close to the FED’s ZDV at present, which I estimate to be $7,456.

We consolidate the two balance sheets in order to obtain a useful picture of the total banking system. The Reserves disappear from the consolidated balance sheet, because they are an asset of the banks and a liability of the central bank. The combination has no net asset or liability arising from bank reserves.

In actuality, the reserves help the central bank control or influence the maximum amount of bank lending and deposit creation. That is their main role. Competition among individual banks by the production of bank notes and money is thereby replaced by a centralizing influence and a single form of bank money throughout the whole system. Consolidating the balance sheets does nothing to change this reality. It simply allows us to gauge values in an otherwise complex system.

The combined entity has two assets: Loans (L) of 9 and Gold of G ounces. Its Liabilities are Deposits (D) of 10 and Currency (C) of 1.

In order to measure a total ZDV in this situation, we need to incorporate Deposits and Loans of the banks. We need to use the idea that good loans back deposits and bad loans do not.

Consider the case first where all loans are good loans. Bank Reserves identically equal Deposits minus Loans, when all loans are good loans. In that case, ZDV = (D – L + C)/G. The numerator of the ZDV when all loans are good has Deposits minus Loans plus Currency. The denominator is G ounces of gold. The term D – L is the net deposit liabilities of the ordinary banks.

Gold still has to cover the issue of Currency. Since all the loans in L are good, they all subtract from Deposits, and that leaves D – L = R to be covered by gold too. The system ZDV equals the central bank ZDV.

In this particular example, total system ZDV = (10 – 9 + 1)/G = 2/G. The system ZDV is identical to the FED’s ZDV. The reason for this is that Deposits minus Loans equal Reserves, and that is because there are no bad loans.

The total system Zero Discount Value has to equal the central bank’s Zero Discount Value when the banking system’s net liabilities of D – L equal its Reserves. This occurs only when the system’s loans are good loans, that is to say, their market values equal their accounting values or values carried on the books of the banks.

The intuition of the unchanged ZDV in the good loans case is this. The central bank base money inflation gives a certain ZDV of gold. If the derivative bank money that banks then produce is backed up by sound loans, the inflation situation is not made worse. That is, there is no further bank money inflation, for loan repayments are capable of shrinking the bank money supply. We get bank money inflation, as shown earlier, if and only if the banks make loans that go bad. In that case we should find that the ZDV rises above the ZDV using only the central bank balance sheet, because more net deposits and thus money are being backed by the same amount of gold.

Bad Loans and the ZDV

Now we are in a position to evaluate the ZDV of gold when the banking system produces bad loans. The intuition in this case is that since bad loans cannot cover the deposit liabilities as fully as when they are good loans, the system’s net deposit liabilities rise relative to the same amount of gold held. Consequently, the money falls in value relative to gold or gold’s price rises in terms of this money.

To model this case, I modify the Loans (L) to be L – hL, where h is a positive number that provides a "haircut" to Loans. The number hL measures the loss in value of the bank loans. These loans may be carried on the books at face value, but their real market values are less. This is what justifies replacing L by L – hL, where h < 1. Then we find

ZDV = (D – (L – hL) + C)/G = (D – L + hL + C)/G = (R + hL + C)/G.

Hence, we obtain an important result: When bank loans are bad, the system’s ZDV has to be above the central bank’s ZDV alone. If loans are bad in amount hL, then G has to cover that amount of deposits in addition to covering R and C. R of these deposits have always to be covered by gold because every dollar of these deposits that total R in amount has been made through a FED loan whose excess earnings revert to the Treasury, so that they lack asset backing other than gold.

With a 10 percent loan loss, h = 0.1. I use the numbers (in trillions) that are close to those of the U.S. system, with D = 10t, L = 9t, and C = 1t. G = 261.5 million oz. Then ZDV = (10 – 9 + hL + 1)/261.5 = (2 + hL)/261.5 = (2 + 0.1(9))/261.5 = $11,090 per oz.

Looking at a range of h values that are less than 1, we get a range of total system ZDV values of gold:

In a previous article, I was critical of an estimate of $30,000 per oz. of gold. This analysis shows that to get such an estimate, one must assume that bank loans have lost 65 percent of their value. If real estate values have fallen by roughly 30 percent and affected total loan values by the same degree, then the estimates of ZDV are still very large. But since there are many good business and other loans, a loss estimate of 10–20 percent may be more realistic. Whatever estimate of loan losses one chooses, the ZDV ratio provides a way of translating it into a gold price estimate.

The large amount of bad bank loans in the U.S. banking system indicates a very serious bank money inflation and points to a much lower value of the dollar and a much higher price of gold. Before this bad loan debacle, the ZDV of gold of the central bank already was substantially above gold’s market value. The FED’s rush to supply Reserves raised it further, sending it above $7,000. When we bring bad loans into the picture, the ZDV is even higher.

I recognize that some loans can be structured and be so good that h < 0. The bank may have arranged its duration in such a way that when interest rates change, the bank becomes even more solid. However, for the system as a whole, this case is not typically relevant and surely not relevant at this time.

The FED once was restricted to issuing currency with a 40 percent backing of gold. If that has any relevance to what our society considered to be a reasonable amount of fractional-reserve lending at the central bank level, then the above ZDV values can be multiplied by 0.4 to obtain more conservative numbers. They are still very high, ranging from $4,436 to $9,943 in the event of a 50 percent haircut.

A feature of this model is that the ZDV is very sensitive to the destruction of loan values. A 10 percent drop in loan value (h = 0.1) caused the ZDV to rise from $7,648 to $11,090. That’s a whopping 45 percent increase. The reason for this is that the banking system is highly leveraged to gold. The coefficient of h is L/G, and the loans are very high compared to the number of gold ounces. Hence, a small decrease in loan values indicates a much larger loss in the value of the dollars whose backing is gold.

When loan values are impaired but the loans remain on the balance sheet, Deposits minus Loans no longer equal Reserves. If D = 10 and L = 0.9(9) = 8.1, then their difference is 1.9; but R = 1. This difference is what causes the system ZDV to go up. Banks have a hole on the asset side of their balance sheets. There is legal and regulatory forbearance, which is a postponement of action to remedy a problem of obligation. The situation is as if the FED were supplying phantom or shadow reserves. The effect of the bad loans on ZDV is somewhat the same as if the FED had actually created Reserves in even larger amount than they have. Deposit money stays in the economy while the real loan values decline.

The problem I raised at the outset was how the Zero Discount Value of gold might be related to the bad loan problems evident in banks. My way of solving this problem is to define a Zero Discount Value for the total banking system that consolidates the central bank and the member banks. We discover that when bad loans occur, the system ZDV has to be higher than the central bank’s ZDV alone.

The fractional-reserve central banking system has great problems. It pays to pin down what these problems are. Bank money inflation does not follow automatically from the fractional-reserve creation of money by free market banks not under the control or influence of a central bank. Free market banks are monitored by those who use their notes as money. The market punishes banks that inflate and rewards those that do not. Bank money inflation results from the fractional-reserve creation of money when bad loans result from the central bank’s fractional-reserve creation of bank reserves followed by deposit and loan creation. A key question is whether banks are necessarily induced to make bad loans when they find that they have excess reserves created by the central bank. In a previous article exploring this question, I argue strongly that the central bank’s provision of reserves does induce the system to make more loans that eventually go bad. In the same article, I point out that frequently government (as distinct from the central bank) gets into the act by encouraging banks to lend into certain industries and activities that eventually do not pay off, such as housing and railroad building.

Capital Infusions

Banks with bad loans have been raising funds by selling new equity and debt to the public and the government. They have raised something like $900 billion dollars in the last two years or so. Nearly all of this has been in the form of debt, not equity. About $200 billion have been used to sustain dividend payments, which reduce equity.

These capital infusions are not a free market phenomenon. A substantial portion of them came under a brand new FDIC program (Temporary Liquidity Guarantee Program) that fully guaranteed newly-issued senior undescured debt of FDIC insured banks, financial holding companies, bank holding companies, and savings and loan holding companies. A substantial amount (over $300 billion) still exists under this program which has recently been renewed for six more months.

The FDIC’s program was for up to $1.4 trillion. The FDIC could never have paid off on such a huge amount. It cannot pay off on the ordinary deposits it has insured, much less new debt of these companies. These guarantees are a fiction.

The financial system was given a reprieve due to a rush of government guarantees, some of which facilitated capital infusions that back deposits. They bought some time.

These desperation moves also revealed that the government-backed, government-run, government-regulated, government-insured, and government- manipulated banking system cannot stand on its own two feet. It is extremely untrustworthy. It remains alive today only because the American people retain confidence in "the government" and government guarantees. The system will collapse the moment that this confidence collapses, which will be when people at large realize that the guarantees mean little. In the meantime, the banking system is being transformed more and more into a government enterprise. The guarantees are a sign of that as are government’s direct infusions of capital. The absorption of the mortgage business is another sign of that. The regulation of executive pay is yet another.

At some point, the U.S. system will cross over into the existing Chinese communist banking system which is a sta te-run affair. All such systems collapse, although sometimes the news of the collapse is withheld from public attention.

Deposit Insurance

Deposit insurance is a bank asset that backs deposits. It therefore mitigates a rise in the ZDV. This means that the total system ZDV is an upper bound. The lower bound is the central bank’s ZDV.

Deposit insurance encourages the central bank to produce base money and the banks to produce bank money via loans, because they have a backup credit insurance policy that is typically underpriced to banks. Because it is underpriced insurance, deposit insurance encourages bad loans and inflation because the banks act as if taxpayers will bail them out and make all deposits good despite loans going bad.

In the U.S., the Federal Deposit Insurance Corporation (FDIC) assesses banks with insurance fees. The fiction is maintained that the banks co-insure each other. As long as failures are few and loans are good, this fiction can be maintained. This system can survive if bank loan risks are independent of one another and not too large. The banks together build up an insurance fund asset that stands behind deposits, in which case inflation is mitigated when loans go bad in amounts that threaten deposits.

But this system does not work if many kinds of loans go bad at the same time as in a widespread recession, for then the insurance fund is insufficient. That is currently the case.

The FDIC protects about one-half of bank deposits. If one believes that only the other half is subject to lower loan backing, then one can easily modify the ZDV model by reducing the haircut factor accordingly. But where in fact is such backing to come from? Who is going to pay for it? Who is going to pay for the insurance of deposits? Who is going to remedy the hole on bank balance sheets due to trillions of dollars of bad loans?

The FDIC fund is almost broke. The FDIC will assess banks with higher fees. That has to be a trivial amount compared to the amount of bad loans. The FDIC will borrow billions from the Treasury. How long will it be before it collects enough fees from banks to repay such loans? It appears that taxpayers will be making good the bank deposits for a long time to come. However, the taxpayers are in large part the same people who are the depositors! They cannot back up their own deposit accounts. The idea that the Treasury and thus taxpayers save their own deposits is also a fiction.

As long as the FDIC has only to deal with isolated bank failures spread over time, it can go on. In times like the present when failures are widespread and pervasive due to bad loans that are worth much less than deposits, the entire insurance scheme is revealed as a fiction or a fraud. People who believe that their deposits are insured are not seeing that in their role as taxpayers, they are being made to insure their own deposits.

The FDIC often merges bad banks into good banks. The insured depositors do not lose. The bad loans are either absorbed and worked out or written off. In either case, loan values remain below deposit values. Such mergers do not magically create value. The inflation does not disappear. The money is still in the system and supported by lower loan values.

It seems that no matter how one looks at this, the deposits remain alive in the economy while the bad loans mean that the backing has fallen. If there were truly an exogenous deposit insurer, who paid the banks compensation for their bad loans, the bank money inflation would be mitigated. There is no such sugar daddy. The banks have not put enough money into the FDIC piggy bank over the good years to pay for the lean years. The taxpayers can’t bail themselves out.

I conclude that, although the Zero Discount Values for gold seem high, they are accurately reflecting the facts of the case.

October 27, 2009

Michael S. Rozeff [send him mail] is a retired Professor of Finance living in East Amherst, New York. He is the author of the free e-book Essays on American Empire.

Copyright © 2009 by LewRockwell.com. Permission to reprint in whole or in part is gladly granted, provided full credit is given.