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83-3 A Series of Occasional Papers in Draft Form Prepared by Members of the Research Department for Review and Comment. Chicago 83-3 A PROPOSAL FOR FEDERAL DEPOSIT INSURANCE WITH RISK SENSITIVE PREMIUMS G. O. Bierwag and George G. Kaufman Draft March 16, 1983 A PROPOSAL FOR FEDERAL DEPOSIT INSURANCE WITH RISK SENSITIVE PREMIUMS G. 0. Blerwag and George G. Kaufman* *Bierwag is Professor of Finance and Economics at the University of Arizona, and Kaufman Is Professor of Finance and Economics at Loyola University of Chicago and Consultant to the Federal Reserve Bank of Chicago. This study was funded by the Federal Home Loan Bank Board and was undertaken as part of a task force established by the Federal Savings and Loan Insurance Corporation to prepare a report on deposit Insurance mandated by the Garn-St Germain Depository Institu tions Act of 1982. Sections of this paper appear In that report. We are thank ful to the other members of the task force (Fischer Black, Tim Campbell, Andrew Carron, David Glenn, Paul Horvitz, and Steve Naslund) as well as to the research staff of the FHLBB, particularly Jerry Hartzog, for many of the ideas, helpful comments, and assistance. a a . H /■?•: Background The primary purpose of deposit insurance is to guarantee the par value of deposits (including the promised interest return) to depositors so as to dis courage them from withdrawing their deposits from depository institutions, or "banks" in the general sense, when they believe that the institution may not be able to redeem the deposits at par. If successful, deposit insurance effectively quarantines individual Institutions that are experiencing actual or perceived financial difficulties. Large-scale deposit withdrawals will be prevented both at the financially troubled banks and from spreading to other, healthy banks. In the absence of such insurance, deposit withdrawals may spread to these banks, forcing them to sell assets hastily and possibly to encounter liquidity problems if the widespread sales temporarily depress the selling prices of the assets. When this occurs, the banks may be unable to redeem their deposits at par value and may be forced into bankruptcy. Because widespread failures of depository institutions may be expected to have adverse effects on aggregate levels of economic activity, deposit insurance produces externalities for the economy as a whole. Depositors are debt holders who are promised repayment at par value by the bank at the maturity of the deposit whether on demand, on demand subject to 30 days' advance notice, or on a particular future date. Similar to debt holders in any firm, depositors may expect to receive par value at maturity as long as the -2aggregate market value of the Institution's assets Is equal to or exceeds the aggregate market value of the deposits, that Is, as long as net worth Is equal to or greater than zero. (Unlike the debt of most firms, a large percentage of bank deposits have market values that must be maintained equal to their par values.) Depositors will experience losses only if the market value of assets is permitted to decline below that of the deposits so that net worth is negative. If this occurs and the bank is not declared insolvent, all depositors, in the absence of deposit insurance, will not be treated equally. front of financially troubled institutions. This accounts for the queuing in Some or all of the deposits with early maturity dates may receive par, while all those with later maturity dates are likely to receive less. In a world of perfect and costless information and no bankruptcy costs, depositors will not experience any loss if the institution is closed as soon as the market value of net worth equals zero.^ Deposit losses occur only in a world where the institution is not closed quickly enough. Thus, deposit losses are unlike losses resulting from "an act of God," such as hurri canes and floods, or "an act of man," such as fires and accidents, that occur pretty much independently of the actions of theiuinsurance firm. As a result, deposit insurance is different from flood, hurricane, accident, fire, and similar insurance. Federal deposit insurance was introduced in 1933 in large measure to compensate for the failure of the Federal Reserve to provide sufficient liquidity as the country's lender of last resort to prevent the widespread cumulative deposit runs on banks that brought most of them to the brink of insolvency before they were temporarily closed in about one-half of the states, including New York and Illinois, by their governors and finally throughout the country in March 1933 by President Roosevelt. 2 -3Why might institutions not be closed quickly enough to avoid losses to depositors even under Federal Deposit insurance? mary reasons: There appear to be three pri 1) detection failures, 2) contract failures, and 3) public policy. To shut down an institution when net worth reaches zero and before it turns negative requires timely and accurate information. Timely information requires frequent monitoring of the institution and accurate information requires adequate detection systems. Both are costly and banking is particularly susceptible to fraud, which makes timely detection difficult. Debtors or their agents do not always have sufficiently strong contracts to shut down a bankrupt firm quickly. Courts can rule to have the firm continue to operate even though its net worth will become more negative, increasing the losses to the debtholders. Lastly, it may not be in the public interest to close bankrupt firms unless they can be sold sufficiently quickly so that services would not be interrupted. This is particularly true for depository institutions, whose services must be produced on an uninterrupted basis for the economy to operate efficiently. Banking, in the generic sense, is in a somewhat different position with respect to speedy closure than most other Industries. It is regulated by govern ment agencies that have been granted 1) broad authority to monitor its operations frequently and to pursue detection of fraudulent and unethical operations and 2) strong contracts on behalf of depositors to terminate a bank's operations. (The power to close banks quickly was apparently not granted the state insurance agencies in the few states that had experimented with public deposit insurance before 1933.) Consequently, banks may be closed down more quickly than other firms with consequent smaller losses to depositors. It should be noted that closing an institution financially does not suggest closing the institution physically. Rather, it simply involves terminating the control over the institu tion by owners in a stock association and by management in a mutual association. -4 - The institution is then auctioned off to potential new owners. If the market value of net worth is zero but the institution has some going market value, it can be sold at a positive premium. If net worth is less than zero, as may occur for reasons discussed below, the institution can likely be sold only at a nega tive premium. But this premium should be no larger than the present value of the expected costs to the insurance agency of keeping the institution open. The institution need not and should not be closed physically during the ownership changeover. The deposit Insurance agency may be viewed as assuming the bankruptcy costs previously borne by the depositors. This makes its role somewhat different from private insurance firms that operate either by offsetting potential losses not under their control by potential gains of the same size, at minimum, or by pooling the cost of a potential loss not under their control among a large number of participants so that no one will suffer unduly in any one period. Except for detection failures, government deposit insurance agencies do not confront a poten tial loss beyond their control. To the extent there is a potential loss, it is attributable to a public policy decision not to close Insolvent depository institutions until their net worth reaches some negative value. This value may depend on a number of factors, including the number of institutions with negative or near negative net worth at the same time, the state of the economy or of particular sectors served by the troubled institutions, and the efficiency of the market in selling ownership of the troubled institutions without disruption in their services. The more important are these factors, the more negative may net worth be permitted to become before institutions are closed. Similarly, the greater the proportion of uninsured deposits at particular failing institutions, the later may the institutions be closed without cost to the agency. -5 - Sale of a closed Institution with zero or negative net worth nay require a pre mium paid by the Insurance agency to the new owners, but this Is little different from the financial assistance now provided to many falling Institutions in a merger. (When net worth of a mutually organized institution reaches zero, it may easily be reorganized as a stock institution.) Thus, the potential losses are quite different from the potential losses confronting most other insurance firms. There are a number of important and interesting implications of analyzing federal deposit insurance in this framework. One, the premiums charged institutions for insurance are based on a different standard. Generally, insurance premiums are related to the probability of an event occurring that gives rise to a loss and to the magnitude of the potential loss. The product of these two factors is the statistical or actuarial expected loss. In order to match benefits and costs correctly, the insurance premium charged each insuree is the actuarially fair value of the loss to the firm. Any smaller premium would encourage the insuree to take additional risks and any larger premium would encourage it either to be self-insured or to withdraw from the activity. For banking, it is possible for the insurance agency to estimate the probability of any individual bank experiencing zero net worth have argued, the potential loss is under its own control. but, as we Thus, except to the extent necessary to cover the insuring agency’s operating costs, the actuarially fair premium is related not as much to the magnitude of a loss beyond the control of the insurance firm as it is to the magnitude of the lors determined by the insurer as desirable for public policy purposes. One may question whether this cost should be borne only by the banks and their depositors of by all taxpayers. Two, to the extent that the insurance premium is not totally connected to a loss that is independent of the insurance company’s actions, it is possible to -6 - separate the question of the appropriate premium from the question of the appropriate size of the insurance fund; this is particularly so as the expected loss could be zero. (Until 1982, the only significant loss experienced by the FDIC from bank failure was in the case of the U.S. National Bank of San Diego in 1973, which was attributable to fraud and difficult to detect until after net worth was substan tially negative.) Thus, the premium can be viewed as a user tax, designed to encourage the banks to operate in economically and socially desirable ways. If bank bankruptcy costs are believed to be severe, in terms of losses from continued operation after net worth becomes negative, legal fees, adverse publicity, and so on, the premiums may be scaled to discourage, or at minimum not to encourage, risk taking. This would appear rational as the probabilities, if not the losses, of bankruptcy may be estimated. Such premiums will also produce the least distortion to an efficient allocation of banking resources. It may also be desirable to relate the premiums to the benefits accruing to the insured banks. By removing the cost of bankruptcy, deposit insurance (on all deposits) permits banks to borrow unlimited amounts at the risk-free interest rate.^ The difference between this rate and the higher deposit rate that banks would need to pay in the absence of deposit insurance represents the benefit. But this amount is a subsidy only if the insuring agency experiences losses. Otherwise, it reflects the externality associated with the transfer of the power *, to close failing banks promptly from depositors to the government or a reduction in agency costs (or costs of protecting rights of. creditors) stemming from improved contracting and monitoring. Three, the appropriate size of the insurance fund to meet depositor losses is obviously a function of public policy. For a given probability of bank fail ure, the more slowly failed banks are closed, the'larger is the insurance fund necessary. The same fund would suffice if the probability of failure Increased, * -7 - but the speed of bank closings also increased. Thus, the size of the fund may be determined by the needs of public policy or public policy may be shaped by the size of the fund. Four, to the extent that the magnitude of any loss is dependent on the ability of the insuring agency to close bankrupt banks quickly before net worth turns significantly negative, there is unlikely to be much of a role for private deposit insurance. It is unlikely that the government would grant sufficient authority to private insurers to close institutions as quickly as could govern ment agencies. Thus, potential losses would be greater without any offsetting benefits to the economy as a whole. Even if private Insurers were granted suf ficiently strong contracting powers, other difficulties would arise. Because it would be in their best interests to close institutions before net worth was completely exhausted so as to minimize their own losses, private insurers might be expected to attempt to cancel the Insurance coverage of nonfailed institutions as net worth declined towards zero. Thus, unlike a government insurer that may be expected to err on the side of closing institutions too late, private insurers may be expected to err on the side of closing them too early. Five, for the sake of both accuracy and maximizing the public's understanding of the system, it may be best to term the protection as deposit guaranty rather .than deposit insurance and to refer to the responsible agency as the federal deposit guarantor rather than insurer. -8 JuBtification for Risk Sensitive Premiums The provision of deposit insurance is of benefit to the banks, depositors, and the public as a whole. However, by permitting depository institutions to borrow some of their funds at the lower risk-free interest rate, deposit insurance, by itself, encourages institutions to increase their risk exposure in two ways,^ One, because many depositors are no longer interested in the financial strength of the Institution, the institutions are encouraged to reduce their ratio of capital to deposits. Two, because they do not have to pay correspondingly higher interest rates when they invest in higher risk asset structures, the institutions are encouraged to seek a greater rate of return than otherwise. The riskier the activity, the higher is the expected return required to compensate the investor for any potential loss. In the insurance literature, behavior induced by changed incentives under insurance is referred to as "moral hazard." The increase in risk assumed by the institution as a result of deposit insurance may not be desirable. It may be possible to reduce the institution's risk exposures by pricing the insurance premiums charged for the deposit insurance in particular ways.. This paper discusses the .theory of deposit insurance premiums, analyzes and evaluates alternative premium schemes, in particular with respect to their implications for the risk behavior of the institution, and notes some of the practical difficulties with each scheme. It provides readers with a number of options from which to select a premium structure either for now or for later. However, an explicit assumption in the remainder of this paper is that some form of risk sensitive premium structure is desirable. The introduction of deposit insurance, per se, in effect relaxes the market discipline on the institutions. As noted above, risk taking is not as heavily -9penalized. The greater is the proportion of insured deposits, the less is the market discipline. If savings and loan associations succeed in obtaining all their deposit needs in insurable amounts of $100,000 or less through offices of security dealers acting as agents— that is, in "brokering" their deposits— so that they will have no uninsured deposits at all, they will be immunized totally from restrictive market pressures, except for that arising from the potential loss of net worth. In theory, insurance premiums may be used to affect the behavior of the institutions under deposit insurance. This may be achieved by scaling the insurance premiums to the specific risk exposure of the individual institutions. Such a premium scheme effectively reintroduces the higher costs associated with higher risk and serves as a substitute for market discipline. Thus, if it is desirable to do so and if premiums can be imposed correctly, the moral hazard introduced by deposit insurance may be offset. But insurance premiums do not serve as surrogates for market discipline if the premiums are scaled to characteristics of the insured institutions other than risk, for example, to total deposits as is currently done.^ Moreover, when insurance premiums are related proportionally to deposits, they may, in fact, increase the risk exposure that the institutions are willing to incur. A number of studies of behavior under alternative tax structures have concluded that taxpayers, who wish to preserve their after-tax income levels, will increase the riskiness of their asset portfolios after the imposition of a proportional tax— which is analogous to a proportional insurance premium— on their assets in order to offset the cost of the tax or premium.^ -10As is argued in an earlier chapter, if the insurer can close a depository institution quickly at any time after net worth hits zero, the costs of deposit insurance are the sum of 1) the operating costs of adequate detection and monitoring of banks and 2) the losses to depositors of not closing the institu tions until they achieve some predetermined value of net worth below zero. As long as these costs are greater than zero, it appears to be both economically efficient and fair to charge the benefactors of the insurance in proportion to their contribution in causing insurance payouts. Although not the only bene factors, depository institutions are both the most immediately affected benefac tors and the benefactor with greatest control over the possibility of deposit losses. This suggests that, because the likelihood of payouts is dependent on the risk that institutions will experience reductions in their net worth to zero or below, the riskier is an institution, the relatively greater should be its insurance premium. If not, the more risky institutions would in effect subsidize the less risky institutions. Thus, it follows that efficient insurance premiums can serve a dual purpose. They can restore the effects of market discipline lost by the deposit insurance itself and they represent an equitable distribution of the costs of the insurance system. Scaling deposit insurance premiums to valid risk measures of the insured institutions in a way that makes them as risk averse as they would be in the absence of deposit insurance satisfies these criteria. Indeed, the failure to scale the premiums to risk would both encourage the institutions to seek greater -11risk exposure than they would in the absence of deposit insurance and make the burden of the premiums inequitable so that less risky institutions, that are responsible for little of the costs incurred by the insuring agency, in effect subsidize the more risky institutions. In addition, because banks are not sub ject to the usual disclosure regulations and the cost of information on risk exposure, much of which is not even currently prepared for internal bank manage ment use, is very high, public disclosure of the insurance premiums charged provides valuable information to the market. Because it leads to bank failures, bank risk is a major public concern, and influence over the risk exposure incurred by banks has been practiced by govern ments in all countries. The precise form of this influence can vary in many ways. Primarily, it can be exerted by regulation (administration) or by price. Most often governments have chosen to influence risk exposure by regulation and have established detailed regulatory procedures and processes to implement this influ ence. These include laws and regulations concerning permitted activities, strategies, and prices and reporting to monitor compliance and on-site examina tions to verify compliance. In part, governments have preferred to influence the risk assumed by individual institutions through regulation because of the substantial practical problems that are associated with structuring an effective explicit risk premium scheme. These problems are addressed later in the chapter. However, as banking has become more complex and diversified, the regulations have also become more complex and numerous. Moreover, as is the nature of regulation in a dynamic indusry, it has lagged behind the changes in the industry and has overreacted to temporary but dramatic and publicly visible events that adversely impacted the performance of the industry. Moreover, once imposed, regulations tend to be written in concrete and crumble only slowly as their reasons for -12existence change or disappear altogether. As a result, regulators, like generals, often find themselves prepared to fight the last war rather than the present one. The limitations and consequences of attempting to influence bank risk and performance by regulation in the United States have become particularly visible in recent years. They will not be repeated here. Suffice it to note that the dissatisfaction with the implications of influencing bank behavior by regulation has stimulated the search for alternative methods. banking is not unique. The unfavorable experience in In recent years, similar experiences in other industries have led to significant deregulation in the airlines, motor transportation, and communications, just to cite a few. It is in this setting that consideration is being given to using deposit insurance premiums to replace partially regulation in influencing the risk exposure and behavior of depository institutions. In other words, deposit insurance premiums are used to price regulation. Although a case could be constructed that, as debtors, depositors could control the riskiness of their banks through careful monitoring of their activi ties, it is clear that the riskiness of banks is most directly under the control of bank management and bank ownership. Moreover, banks benefit most directly by being able to offer insured deposits at the risk-free Interest rate regardless of the riskiness of their asset portfolios. Thus, the premiums should be levied directly on the insured institutions, although the true cost of the insurance will be borne in some unknown proportion by depositors, loan customers, and employees as well as the bank owners. It is insufficient to say that the premiums will be scaled according to risk. It is necessary to 1. identify the risks, 2. measure the risks accurately, -1 3 * 3. weigh the importance of the different types of risk and estimate the probabilities of each type of bank failure, 4. weigh the importance of the different exposures to the same type of risk and estimate the probabilities of each exposure for bank failure, and 5. estimate the impact on the bankfs risk management of both the relative size of the deposit insurance premiums and the absolute size of the premiums on each risk category. Banks may fail for a number of reasons. The most prominent are losses from: 1. default, 2. unfavorable interest rate changes, and 3. fraud and theft. Less important are losses from: 4. poor management in everyday operations, 5. poor management in exploiting newly permitted powers, and 6. expropriation of assets in foreign countries (political risk). These risks are, of course, not completely independent. Attempts by institutions to reduce their interest rate risk exposure by increasing emphasis on variable rate loans may increase their default risk exposure. For example, borrowers may encounter increased difficulties in meeting their higher interest payments required by variable rate loans as market rates of interest rise. Risk sensitive insurance premiums can be related either to the overall risk of the institution as measured by a single aggregate risk index or to each of the separate risk components enumerated above. tages. Each has its advantages and disadvan The most important advantage to a single risk measure is that risk pre miums structured to it are simpler to construct. The measure also incorporates any interdependencies that may exist among the individual risk components. On the -1 4 - other hand, a single measure does not allow the insuring agency the flexibility to either charge different premiums for different types of risks according to its evaluation of their relative importance or to change the relative premium charges on different risk types as their importance is considered to change. Premium structures related to the individual risk components would obviously permit this, but only at the cost of both greater complexity and inability to capture any interdependencies. In addition, it is necessary to assign relative weights to the individual risk components in order to sum up and obtain the total overall premium. A number of alternative potential premium structures are examined in the next sections. As discussed earlier, the greater the net worth of the depository institution, the smaller is the risk of bankruptcy as the larger are the losses that can be absorbed by the institution. Thus, the greater is the net worth for a given degree of interest rate and default risk exposure, the less risky is the insti tution and the smaller should be its insurance premium. This may be incorporated into the premium structure by treating net worth as an offset to or deduction from the premiums computed for the two types of risk exposures. This would make it comparable to a deductability clause in other insurance policies for which the insuree bears the cost of the first x dollars of losses and the insurer the cost of the remainder. capital. The insured bank bears the cost of losses charged to its The details of such a procedure are discussed at greater length later in the paper. Before considering^hese risks, it is appropriate to enumerate the criteria that an optimal risk sensitive deposit premium structure should possess. should: 1. have explicit objectives, 2. interfere minimally, if at all, with market mechanisms, 3. be theoretically sound, It -15- 4. be simple to understand, 5. be simple to compute, 6. be simple to implement, 7. be based on accurate and reliable risk data, 8. impose minimal additional reporting and compliance costs, 9. be efficient, and 10. minimize the need for supplementary nonprice regulation. The relative ability of alternative premium structures to satisfy these conditions is examined in the concluding section of this paper. The following sections analyze the theoretical pros and cons of possible risk sensitive premium structures. -1 6 - Single Aggregate Risk Premium Structures As noted, risk sensitive premium structures may be divided into two basic types: 1) those that are scaled to a measure of overall bank risk and 2) those that are scaled to individual risk components. Premiums scaled to single overall risk measures are examined in this section; premiums scaled to measures of the individual composite risks are examined in the next section. These sections dis cuss the theoretical underpinnings of each premium structure and the relative difficulties in implementing each structure in practice at this time and suggest possible ways of establishing a workable premium structure compatible with todayfs knowledge and information. Examinations Ratings Depository institutions receive ratings from their respective regulatory agency based on the periodic evaluation of, among other things, the quality of their asset portfolios, their asset-liability mix, compliance with regulations, internal management control systems, earnings, and capital based on on-site visi tations by examiners. Each of the regulatory agencies uses somewhat different examination techniques and categories, although the activities of the federal agencies are coordinated by the Federal Financial Institutions Examination Council. The Federal Home Loan Bank Board classifies insured member associations into four categories. It is thus simple in practice to scale the insurance premiums to these categories. Although simple in practice, several studies have shown that the examination g ratings have not proved empirically to be very accurate predictors of bankruptcy. They appear best at evaluating asset quality, management systems, and fraudulent practices, and weakest at evaluating interest rate risk. Moreover, because exami nation ratings are in measure subjective, it is unlikely that the large number of bank examiners in the field will produce consistent ratings for all institutions. -1 7 - Flnanclal Ratios Close relationships have been reported between a limited number of important financial ratios for nonfinancial firms such as the trend in earnings, earnings variability, liquidity, and debt to capital ratios, and both their marketdetermined default risk premiums on their debt 9 and their rates of bankruptcy. 10 One study finds a similar relationship for default risk premiums for commercial banks.^ It would be theoretically feasible to relate bank failures to a number of financial variables and to estimate statistically the relative importance of each of these factors. estimated weights. Insurance premiums could then be established from these If the number of statistically important financial ratios is limited, such a structure would be simple to implement. Unfortunately, the empirical evidence for such relationships appears to be considerably weaker for depository institutions than it is for nonfinancial firms. The regulatory agencies have attempted to construct early warning systems to provide advance notification of institutions that may encounter serious financial problems. These are based on a mix of examination reports and analysis of finan cial ratios. The most elaborate such system was developed by the Comptroller of the Currency for national banks. It uses a large number of financial ratios for each bank and compares each ratio with the average for that ratio for the insti- . tution s peer group. 12 Unfortunately, these systems have neither a sufficiently explicit analytical or conceptual framework nor measures on which to base insuree specific risk sensitive insurance premiums. 13 Past Loan and Security Losses Because losses on loans and securities are a major potential cause of bank failures, insurance premiums may be scaled to past losses if they are viewed as reasonably accurate predictors of future losses. A premium structure based on the experience of the insuree is common for most types of insurance. Drivers -1 8 wit h records of traffic violations and accidents are charged higher premiums than drivers with better experiences and homeowners with histories of fire and bur glaries are charged higher premiums than those with fewer past losses from these sources. A long history indicates that incidents of these types are highly autocorrelated among individual units so that units with poor experiences in the past tend to have similar poor experiences in the future. foretell future losses or reduced net earnings? But do bank loan losses A recent study found that the best predictor of next yearvs loan losses as a percent of assets was this year's loan losses.14 Loto losses are also greater the greater the percentage of gross interest revenues to loans, the percentage of loans in the portfolio, the percentage of business and consumer loans to total loans, and the size of the bank. The positive relationship with gross interest revenues reflects the fact that expected loan losses are impounded in the interest rate charged loan cus tomers in the form of default risk premiums. But, tying insurance premiums to actual loan losses has an important drawback; it is the unexpected loan losses, not realized loan losses, that are of danger to the solvency of the institutions. Banks with larger than average loan losses, however, tend to experience smaller, not larger, losses in the future. mean. There tends to be a regression towards the Similar studies have not been performed on security losses or losses from interest rate intermediation. Although not exactly the same as loan losses, the proportion of nonperforming, slow paying or scheduled loans appears to foretell loan losses and thus are some times also recommended as reliable measures of default risk^”* although at least one researcher is less sure of their predictive powers.1^ practically simple to implement and appears promising. This approach is -19Past Levels and Volatility of Earnings The lower are bank earnings, the slower is the growth in capital and the greater is the probability that a decline in earnings will need to be charged to capital* The more volatile are earnings, the greater is the probability of losses* Studies have found these two variables for nonfinancial firms to be highly signi ficant with market-determined default risk premiums and the incidence of default and to be, at least, promising for depository institutions.^ If further research supports such relationships, then insurance premiums may be scaled to them* Interest Rate on Uninsured Deposits Because uninsured depositors (those with balances well in excess of $100,000) and other creditors of depository institutions are not protected by insurance, they must evaluate the financial strength of their banks similar to any other borrower. The riskier they perceive the institution, the higher will be the interest rate that they will charge on the deposits and other funds they lend to the institution. Thus, rates on uninsured deposits and other funds incorporate a default risk premium just like rates on any other risky security. This premium may be viewed as the marketfs evaluation of the riskiness of the institution and be used to scale the insurance premium. Although theoretically appealing by its simplicity, this measure has two serious drawbacks. « One, most smaller institutions, and almost all savings and loan associations, have minimal or no uninsured deposits. This pattern is being reinforced by the ability of many institutions to collect all the funds they need t in amounts less than the $100,000 deposit insurance ceiling through the use of nationwide brokers. institutions. Thus, a default risk premium cannot be observed for most Two, until very recently uninsured depositors, particularly at larger institutions, were routinely made whole when their banks failed and exper- -20ienced no significant losses* Thus, these depositors did not expect losses and did not fully incorporate this possibility in the interest rates they charged on deposits. To the extent that there were default risk premiums, they were scaled to the expected response of the insurance agency in reimbursing all credits as much as to the riskiness of the institution. Differences in large CD and borrowing rates among individual institutions reflected primarily differences in market ability and location rather than differences in default risks. Market default risk premiums may assume additional meaning and be more useful for scaling risk sensitive insurance premiums if and when the insuring agencies act in ways that uninsured depositors perceive will result in losses to them. -21Interest Rate Risk This section discusses alternative premium structures scaled to the individual components of bank risk. Because deposit insurance covers losses from all causes of institution failure, insurance premiums could, in theory, be designed to cover each of these and, in time, should be so designed. But, in practice, in designing a structure de novo, it appears reasonable to consider only the most important causes. Both because it is difficult to design risk-scaled premiums for fraud and because all banks are bonded for at least part of such losses with private insurance, this cause will not be considered in this paper. of fraud is best left to on-site examinations. Detection We will focus only on premiums scaled to interest rate risk and to default risk. Interest rate risk has received considerable attention in recent years, deservedly as market rates of interest both rose unexpectedly to record highs and became highly volatile. Depository institutions offer customers a wide variety of different types of deposits, the interest rates on which differ and change at different times in line with changes in market rates of interest on similar securities. At the same time, the institutions extend a wide variety of loans and purchase a wide variety of investment securities with different interest rates that change at different times. If the interest rates received on their loans and investments do not change at the same time as the interest rates they pay on their deposits and other borrowings so that the institutions9 interest revenues, ceteris paribus, do not change at the same time as their interest pay ments, the institutions bear the risk of Incurring losses from unfavorable changes in market rates of interest. Their interest payments could rise relative to their interest revenues and they would incur losses. This is referred to as interest -22- rate risk. Like most risks, interest rate risk is a two edged sword. The insti tution may incur losses if interest rates change one way, but will achieve gains if rates change the other way. In a world of no regulatory or legislative constraints, banks can manage their Interest rate risk exposure to achieve their desired expected return-risk tradeoff. The greater the risk they are willing to assume, the greater are the returns that they may expect. However, some types of institutions may be con strained by regulation and/or legislation as to the types of the deposits and their interest rate sensitivities that they may offer and/or the loans they may extend in ways such that they are locked into minimum or maximum levels of Interest rate risk exposure. Thus, for example, to the extent, that savings and loan associa tions were for many years limited to offering primarily short-term deposits and extending primarily long-term, fixed contract rate residential mortgages so that their interest revenues were less sensitive to changes in market rates of interest than their interest payments, they were effectively locked into a minimum level of interest rate risk exposure below which they could not go. Because market interest rates increased more than expected for most of the last two decades, savings and loan associations suffered severe losses from this source of risk. Indeed, according to many analysts, interest rate risk has replaced default or credit quality risk as the major risk for thrift institutions. Thus, it appears appropriate to apply deposit insurance premiums to the interest rate risk exposure of the insured institution. The next section discusses a method for doing so. Measuring Interest Rate Risk Exposure To design a practical deposit insurance risk premium structured to interest rate risk exposure, it is necessary to measure interest rate risk. In addition, to satisfy the criteria cited earlier for an optimal premium structure, the -2 3 - measurement procedure must be both 1) theoretically sound and 2) relatively simple and costless to implement practically at this time. Because large losses from interest rate risk exposure are a relatively recent phenomenon, the theoretical determinants of this risk have only recently been explored. Although the process is not yet fully understood, enough is known to measure interest rate risk exposure for depository institutions on a theoretically reasonably sound basis. A rela tively simple theoretical model of interest rate risk is constructed in the appendix to this paper and can be described in words. Basically, an institution assumes no interest rate risk over the life of the longest term asset or liability on its books if its interest revenues change with changes in the market rate of interest at exactly the same time and by exactly the same amount as its interest payments. A number of researchers have shown that this condition occurs when a measure of the average life of an insti tution’s assets, termed duration, is equal to the average life or duration of its liabilities with an equal market value. Duration is computed by multiplying the length of time, in months or years, to the date each payment on a security is received or paid, both coupons and principal, by the present value of the cor responding payment, summing these numbers, and dividing by the current market price of the security. Similar to maturity, duration is denominated in units of time, months or years. The duration of an institution’s assets and liabilities is under its control, although more so for some of its balance sheet items than others. When an institution, whose balance sheet balances so that the present value of its assets is equal to that of its liabilities including net worth, sets the duration of its assets equal to that of its liabilities, changes in market rates of interest are passed directly through from borrowers to depositors and conversely. The institution is effectively a conduit; it does not engage in interest rate intermediation and is not affected by interest rate changes. -2 4 - When the durations of its assets and liabilities of equal market value are not equal, the future stream of a bankfs interest revenues will not match the future stream of its interest expenses. The greater the mismatch so that the duration of the assets is relatively longer or shorter than the duration of the liabilities, the greater is the risk exposure faced by the institution. The absolute difference between the durations of the two sides of the bank’s balance sheet indicates the degree of risk exposure. Moreover, this relationship is, at first approximation, linear so that a doubling of the mismatch, commonly referred to as*the asset-liability "gap," between the durations doubles the risk exposure. Thus, duration gaps are a theoretically sound measure of interest rate exposure at any moment in time. Although duration is a relatively simple computation for an individual fixed-coupon rate security, it is a more difficult computation for variable or floating coupon rate securities and the process becomes highly complex for the very large number of different types of securities on the two sides of bank balance sheets. Data must be manipulated for every security on a bank’s books. It is also difficult, given the extant technology and bank record maintenance systems, to project accurately interest revenues and expenses over the life of the assets and liabilities currently on the books of the institutions. Not only must changes in flows from variable rate securities be predicted, but assumptions must be made about the turnover of maturing assets and liabilities, including deposits that do not have specific maturity dates such as demand deposits, NOW accounts, and pass book savings, and about the interest rates on the replacement securities. Thus, simplified procedures must be used to put such a system into practice until the states of technology and bank record maintenance systems advance to the points where the required computations and estimates are simple and cheap. -2 5 It is possible to approximate the duration gap by comparing the change in market values of a bank's assets and liabilities, excluding futures contracts, for a given change in interest rates, (The theoretical justification for this approximation is developed in the appendix.) The greater the difference between the changes in market values of the two sides of the balance sheet for this change in interest rates, the greater is the institution's risk exposure. Thus, it is just necessary to take the market price of every item on the bank's books and subject it to an arbitrary interest rate shock. But banks do not typically main tain the market values of each of, their asset and liability securities. generally recorded only at book value. They are Thus, this procedure requires the institu tions to convert their balance sheet items from book to market values, that is, mark its assets and liabilities to market. To convert from book value to market value, it is necessary to know the maturity of the security as well as its current coupon or contract interest rate and any provisions for changes in this rate before maturity. Although banks have a large number and wide variety of different asset and liability items, they are grouped by like characteristics for both internal and external reporting and control systems. Thus, it should be possible, even given today's relatively primitive information systems used by most thrift institutions, to design a system that requires a reasonably smaller number of relatively homogenous groupings of assets and liabilities by type, remaining term to maturity, fixed coupon or con tract rate, and variable coupon rate characteristics. is shown in Table 1. One such possible grouping Although simple in terms of the information necessary to implement both the interest rate risk scaled premium structure described above and almost any meaningful price to market system, it may appear complex in terms of the amount of information required. As can be seen from Table 1, the combina -2 6 - tion of major loan, investment, and deposit groupings multiplied by the groupings of coupon or contract rates for both fixed and variable contracts results in a very large number of cells for which information needs to be provided. But a closer look should show that these data are not overly difficult to obtain from the internal systems currently in use at almost all depository institutions and, indeed, that they are necessary for the proper management of the institution. Thus, the need to provide this data for insurance premiums provides a desirable impetus for the development of reporting systems that will inform and educate internal management and should improve the quality of its operations. However, the actual groupings to be used in a system as is being discussed depends on the information that is available to institutions. In the best of all worlds, suf ficient information is available on each individual balance sheet item. A number of assumptions need to be made about the maturities of loans that are frequently prepaid or have variable contract rates and of deposits that do not have specific maturity dates. For example, for the sake of expediency, the table assumes that all residential mortgages with more than 12 years to maturity will be prepaid by the twelfth year, all savings and regular NOW accounts have a maturity of one year, and the new money market deposit accounts have a maturity of three months. (A more sophisticated scheme would specify the maturity of super NOW and MMD accounts equal to the time until the prevailing deposit rate may be changed, e.g., daily, one week, one month, etc.) The insuring agency will need to provide an interest rate value for each cell based on representative current market rates of interest for securities in that cell. securities this is not overly difficult. securities are readily available. For fixed-rate marketable Interest yield data for many types of For mortgages, it would require the construction of a yield series for fixed-rate mortgages with different terms to maturity. For other non-marketable securities, this presents a more, but not exceptionally diffi -2 7 - cult problem for the insuring agency. are more complex. For variable-rate securities, the problems The most difficult task is to estimate meaningful market yields for deposits subject to rate ceilings and associated with ••free" services such as check writing. But these are decreasing in Importance as deposit rate deregula tion proceeds. The optimal system would involve the projection of cash flows on both sides of the balance sheet based on the individual institution's management best estimates of the timing and magnitude of the repricing of variable rate loans and deposits, prepayment of loans, turnover of deposits, and so on. These projections would be updated each time it was necessary to measure risk exposure. Such a complete projected cash flow system is not available today to all but the very largest commercial banks. It is, however, the information system necessary in the future for management of all institutions to manage their institutions intelligently and thus may be expected to be adopted by most financial institutions as quickly as technology and costs permit. Using the simplifying assumptions discussed above, it is possible to compute changes in the aggregate market value of the securities in each cell in Table 1 or its equivalent for a given change in interest yields. This is done through the use of a typical bond pricing equation that relates the change in market price to the maturity of the securities in the particular group and the change in the respective interest rate. For the sake of simplicity, the assumed change in interest rates is standardized at 100 basis points. does not affect the results. This assumption The computed changes in the market values of all asset items are summed an? subtracted from the sum of the changes in the market values of all liability items. This difference is then divided by the initial market value of total assets and is multiplied by the factor ]Jl/i)/.0l], where i is the current market rate of interest on an intermediate-term, say a 10-year Treasury security. (These steps are demonstrated in the appendix.) The resulting -28- value provides the first measure of the mismatch gap and interest rate risk for the bank. At least two limiting characteristics to this procedure may be noted. One, all of the asset and liability items cannot practically be priced, even in a group. The omitted items include buildings, equipment assets obtained through foreclosure, and net worth. Thus, the net difference in the change in market values of the assets and liabilities computed as described above does not represent the complete impact of market interest rate changes on assets and liabilities. This problem requires further analysis. Two, some of the deposits, such as pass book savings, may be redeemed only at par value regardless of their current market value. Thus, a change in interest rates cannot legally affect the par value of these deposits. But, even if the interest rate risk for the bank were zero, the change in interest rates does affect the market value of the deposits. To main tain the par value of the deposits when interest rates change, the dollar value of this change must be transferred to net worth. This reduces net worth when interest rates rise and increases net worth when they decline. But, as shown in the appendix, when the duration gap is zero, such transfers are automatically self-reversing and do not hamper the ability of the bank to meet its deposit liabilities fully and on time, even when net worth is temporarily negative due to these transfers. As a result, nothing is gained by including the impact of these net worth changes in the measure of interest rate risk. This is less true when the duration gap is not zero and the bank actively assumes interest rate risk, but may still be omitted from the computation without much loss in the meaning fulness of the resulting risk index. It should also be noted that as time passes and interest rates change, the market values of the assets and liabilities change. In theory, even if the bank -29does not deliberately change its risk exposure, the risk measure should be computed continuously so as to prevent the value of the insurance premium from deviating very far from the current risk exposure of the bank. If this occurred, the risk would be mispriced and it would present the bank with incentives to change its risk exposure further to take advantage of the mispricing. In prac tice, because of high reporting costs, it would be difficult to justify computing a bank’s risk exposure and altering its insurance premium more than once or, at best, twice a year. Thus, it would be reasonable to develop an ongoing monitoring system that would identify evidence of apparent sufficiently dramatic changes in the bank’s risk exposure to warrant recomputing the risk more precisely and repricing the premium. In recent years, banks have been given permission to hedge their operations in the futures market. To the extent they have done so, this should reduce their exposure by reducing the size of the previously estimated gap. The second step in measuring overall interest rate risk exposure is thus to adjust the previous gap estimated by the value of the net hedge. the appendix. The necessary steps are shown in The value of the hedge can be computed in a manner similar to the previous computation of the change in the net value of the securities traded in the cash market on the banks’ balance sheets. The market value of the futures contracts is first determined for homogeneous groupings of contracts by the maturity of the contract and the term to delivery from interest rate factors pro vided by the insuring agency. Then, as before, the change in the market value of the contracts in each group for a standard 100 basis point change in interest rates is obtained with the use of a bond pricing equation. The resulting changes are summed, added to the net change in cash assets and liabilities, divided by the market value of the bank’s total assets, and, as before, multiplied by the factor l£l+i/.0l]. The resulting index represents the bank’s total estimated interest -3 0 rate risk exposure and is used to scale the insurance premiums. As noted earlier, this measure is approximately linearly related to risk, so that the premiums may be priced proportionately. A bank with twice the net gap of another bank would be charged twice the interest rate risk premium of the second bank. Net Worth Deductibility One additional adjustment is necessary. Because deposit insurance does not require payouts until net worth is at least zero, banks with equal interest rate exposures would not necessarily be equally risky to the insurance agency if they had different amounts of net worth. Banks with relatively larger net worths would be less risky than banks with smaller net worths. Moreover, owners, in the case of stock associations, and management, in the case of mutually organized associations, have less to lose in institutions with relatively smaller net worths and, similar to a gambler down to his or her last dollar, are more willing to plunge into riskier activities in order to increase earnings by a large amount. 18 In effect, net worth is analogous to a deductibility clause in regular insurance policies. The insurer pays only if the loss exceeds the amount of the deductible. Insurance firms generally permit the insuree to determine the amount of the deductibility it wishes to assume, and scale the insurance premiums accordingly. The larger the deductibility, the smaller the premium charged. Thus, it appears reasonable for the deposit insurance agency to permit banks a deduction or another type of adjustment for the value of their net worth relative to assets before determining their premium. How can this be done in practice? One possibility is to multiply the overall gap index computed above by the ratio of the market value of the institution’s assets to its net worth. The product of these two indexes may be considered the "effective” interest rate sensitivity index. The smaller is its adjusted net worth ratio, the greater is the effective interest rate sensitivity index, and -3 1 - the higher will be the institutions insurance premiums- Thus, the impact of greater interest rate risk exposure on insurance premiums can be offset by higher relative levels of net worth, and conversely. An institution whose interest rate gap is twice that of another institution but whose asset to net worth ratio is only half as large would post the same effective interest rate sensitivity index and pay the same insurance premiums. An example of the computation of the effec tive interest rate sensitivity index is provided in the appendix. This procedure has the advantage of being simple, easily understood by management, and clear in terms of what changes in net worth will do to the amount of the institution’s insurance premiums. Moreover, it maintains the linearity of the risk index described above so that an institution with an index value twice that of another institution is twice as exposed to interest rate risk as that institution. The premium structure for interest rate risk can be of two types. the premiums can be related directly to the interest rate risk measure. First, In this way, continuous variation in the interest rate risk implies continuous variation in the applicable premiums. Second, the premiums can be determined on the basis of the risk class into which an institution is classified. In this case, insti tutions are classified into groups, and any institution within the same group is charged the same premium. If interest rate risk can be measured accurately, then the premiums can vary continuously with the measure of interest rate risk. Any small change in the level of interest rate risk will imply a small change in the applicable premium. If the information upon which the interest rate risk measure is not completely accurate, because of the groupings of assets and liabilities in the calculation of the risk measure, it may be better to classify the institutions into risk classes. There are three difficulties with such a scheme, however. First, if -32the number of classes Is too few, the Intended effect of the premiums on risk taking may not result; two institutions in the same risk class may have vastly different risk exposures even though they are charged the same premium, and two institutions in adjoining risk classes with only slightly different risk expo sures may be charged vastly different premiums. Second, if there are too many Tisk classes, the probability of misclassifying an institution because of errors in measurement can increase. If premiums are determined on the basis of risk classes, the number of risk classes should be specified so as to minimize the amount of error and distortion of effects that can result from these extremes. Third, the existence of discrete risk classes may encourage the placing of banks in particular classes for reasons other than risk, e.g., political or societal reasons. Whichever of the premium structures selected, it would be advisable to allow for reassessments as more accurate information on the degree of risk exposure is obtained. If an institution believes that it is being charged an excessive premium because its measure of risk is too high or because it has been misclassified into a risk class that is too high, the burden of demonstrating the conten tion can be imposed on the institution. By making available more detailed information for the calculation of the risk measure, the institution may be able to demonstrate the inaccuracy. If so, a corresponding correction can be made. With provisions for rebates on this basis, the institutions have an incentive to provide full information for the determination of the risk measure. The FSLIC can indicate in detail the information that must be disclosed for the rebate to be effective. Provisions of this kind are not unusual in a regulatory setting. For example, under the Clean Air Act, firms in some industries may secure waivers from the requirement of installing certain kinds of pollution abatement equipment -33provided they can demonstrate that meeting the requirements would imply closure of the firm. The burden of the demonstration falls on the firm; it must provide detailed information to support the contended impact. In time, the required information reported to the FSLIC for use in the determination of interest rate risk exposure can be made more extensive. As com puter technology becomes more intesively used for record keeping and for finan cial control, the required information for determining risk can be more cheaply provided. Moreover, the institutions will have an incentive to provide this information under rebate provisions. -3 4 - Default Risk The more traditional risk incurred by depository institutions has been losses on their loans and investments from default, or default risk. To protect themselves against such losses, the institutions, similar to all Investors, have demanded higher interest yields on loans and investments subject to default risk than on securities comparable in all other respects but subject to no or less risk of default. The additional interest rates serve to compensate the lender for the greater likelihood of loss. Thus, the difference in yields between a security with default risk and a comparable security without this risk may be viewed as an insurance premium paid by the lender to itself, or a self-insurance premium. This difference is not income. For a bank, it should not be paid out as interest or dividends; it should be charged to a reserve account. Similar to any insurance premium on a long-lived asset, any one period premium by itself need not compensate for the entire loss. Rather, the sum of all the premiums paid over the life of the security should be sufficient, on average, to offset the magnitude of the loss. That is, the sum of the premiums represents the actuarially fair value of the loss expected over the period in which the security is held, obtained by multiplying the probability of losses of different magnitudes in each period by the magnitude of the loss. It follows that if the default occurs early in the overall investment period, the investor may not have collected sufficient premiums and is worse off than if the default occurs later. To reduce the chances of this occurring, investors diversify across a large number of different securities. The probability of all defaulting at the same time is small and the defaults in any given period should be, on average, no greater than the losses expected in that period. Unlike some other risks, however, default risk cannot be diversified away altogether. -3 5 - The difference between the market yield on a security subject to default loss and a comparable default-free security is referred to as the default risk premium. For marketable securities, the premium is determined by the market. This premium represents the weighted average of the default expectations on a particular security by individual market participants. But all individual inves tors may not be expected to evaluate the expected loss on a particular security equally. Those investors who evaluate the expected loss on this security equal to the market's default risk premium would expect to receive the risk-free return. Those who consider the security to be of higher credit quality and expect a smaller default loss would expect to receive a return greater than the risk-free return and find the security a good investment. Those who consider the security of lower credit quality would expect to receive a lower than risk-free return and would not purchase the security, Of course, expectations may not be realized, and actual default losses may be greater or smaller than the expected loss im pounded in the default risk premiums. How well do the market-determined default risk premiums compensate investors for the losses that they experience? There have been only a few studies that test empirically the efficiency of the market-determined default risk premiums. These are of two types. The first type relates this premium to the financial ratios that are generally used to measure the financial strength of the issuers, such as debt/equity, length of consecutive earnings, and variability in earnings. The studies find that these variables explain about 75 percent of the amount of the premiums and that the impact of each of the variables is in the direction expected from theory. 19 The second type of study relates the market default risk premiums to the actual default losses experienced by investors. These studies trace groups of -3 6 - corporate and municipal bonds through their lives. They find two things. One, the timing of defaults is not uniform but varies with the business cycle. They are lowest during periods of economic prosperity, higher during recessions, and much higher during major economic depressions. Two, over sufficiently long periods of time, differences between the yields realized on the securities and the yields promised at the time the securities were purchased approximated the default risk premiums. Thus, the average investor did not realize either more or less on securities subject to default risk than on comparable default-free securities. 20 On the whole, these studies confirm the economic content of the market’s default risk premiums. Moreover, another study finds a high correlation between the market default risk premiums on bonds of commercial banks and bank holding companies and the ratings assigned the banks by federal bank examiners. 21 Because bank examination is to a large extent an evaluation of the quality of the bank’s assets and the ratings are confidential, the finding also supports the economic meaningfulness of the market-determined default risk premiums. Because default risk premiums are related to the expected value of default losses and may be viewed as self-insurance premiums, it appears appropriate to scale deposit insurance premiums to them, even though the federal insurance agency’s losses are not totally actuarially related to the default losses and it is the unexpected losses, that are not impounded in the default risk premium, and not the expected losses, that are so impounded, that endanger the institutions and threaten losses to the insurance agency. As with interest rate risk, the insurance premiums primarily serve the purpose of controlling the risk exposure of the institutions as a substitute for market discipline. -37Unlike interest rate risk, default risk applies only to an institution's asset items. Loans and investments that have higher market-determined default risk premiums would be charged higher insurance premiums than loans and invest ments with lower risk premiums. A number of questions arise: 1) how large should the premiums be, 2) what should be the gradation in the premiums, 3) should the premiums be sensitive to intertemporal changes in the default risk premiums, and 4) how can default risk premiums be determined for nonmarketable securities? Size of the Premiums The magnitude of the insurance premiums charged has important implications for the willingness of the depository institutions to invest in securities with different risks of default. If the premiums charged are exactly equal to the market-determined default risk premiums, the average Institution should be indif ferent among securities with differing default risks. roughly the same yield on any of the securities. It would expect to realize If the premiums charged are larger than the market premiums, few institutions would invest in the risky securities as they would expect to realize less than the riskless return. Only those institutions that considered the security relatively more risky than the market as a whole and were successful in charging a higher interest rate would purchase the risky securities. If the premiums charged were smaller than the market premiums, most investors would expect to earn more than the risk-free rate and invest in the securities. But the insuring agency would collect less than the fair actuarial value of the expected default loss. However, we have argued earlier that the federal deposit insurance agencies are different from regular private insurance firms. They need not experience losses if they close institutions promptly when net worth becomes zero. Up to that point, any default losses are charged first to the depository institution's -38approprlate security loss reserve account and thereafter to net worth. Only if the insuring agency does not close the Institution when its net worth is depleted will the agency incur losses. However, the smaller the premium charged, the less is the disincentive for the institutions to assume riskier loans. Thus, the premium charged should be less than the market default risk premium on the par ticular security and it should be based- on the degree of risk averseness the insur ance agency wishes to impose on the institutions as a matter of public policy. Gradation of Premiums The previously cited empirical studies suggest that there is some evidence that investors are risk averse and charge a somewhat higher proportional default risk premium the riskier the security. If this is so, scaling the premiums proportionately to the market risk premiums would, on the one hand, have a neu tral impact on the default risk investment decision process of the institutions but, on the other hand, discourage slightly investment in riskier securities. Nevertheless, in the absence of well-defined, articulated, and justified economic or social objectives, it is most efficient to accept the risk preferences indicated by the marketplace. Sensitivity to Changes in Market Default Risk Premiums As discussed earlier, the incidence of default varies contracyclically. As a result, the market-determined default risk premium varies cyclically, declining in periods of prosperity and increasing in periods of recession as investors reevaluate the outlook for default. Should the Insurance agency charge a fixed annual premium based on the premium at the time the security is purchased or a variable premium based on the annual market premium? The market premium at the time an investment is purchased represents an average of the expected annual premiums over the remaining life of the security. It will differ ex-post only if -39the expectations of market participants are not realized. The changes in the default risk of the securities after purchase are independent of the actions of the depository institutions. Basing insurance premiums on the annual default risk premiums would either penalize or reward the Institutions for changes outside their control. Moreover, except for unexpected changes in credit quality, the average of the annual insurance premiums charged over the life of the security should equal the fixed annual insurance premiums based on the market-determined default risk premium at the time the security is purchfsed. Higher market-determined default risk premiums received on securi ties purchased in periods of recession should more or less average out for individual institutions with lower default risk premiums received in periods of economic prosperity. However, there may be some slippage for securities, such as residential mortgages, for which defaults tend to occur sooner than later and which are sold by the originating institutions after the first few years. These institutions would, in effect, pay a lower than otherwise insurance premium for the period they held the mortgages. Thus, it would appear both simple, fair, and efficient to scale the premium charged to the initial market premium at the time a security is purchased and maintain it at this level until the security matures or is sold. The insurance agency would absorb any opportunity losses from unexpected increases in the market default premium and benefit from any opportu nity gains from unexpected decreases in the market premium. need not affect the profitability of the agency. But as noted, these Even if it did, it would be reasonable to spread the costs of changes in the business cycle over the public as a whole rather than charge only the Institutions. Nonmarketable Investments Most of the loans extended by thrift Institutions are effectively nonmarketable. Thus, there is not a market-determined risk premium for each security in the -40institutions' portfolios not only currently, but also for many years to come. Moreover, thrift institutions are offering an increasing variety of loans, Including a range of new and highly complex variable rate and graduated payment type residential mortgages that include negative amortization for the first time and for which market default experience is negligible and the inclusion of pre payment (call) and due-on-sale (put) options makes it difficult to separate out default risk premiums from the overall premiums for all differences between these instruments and as comparable as possible default-free securities. Moreover, unlike most securities broadly traded on the markets, mortgages are amortized securities whose terms to maturity are far less representative of their average lives than these terms are for regular coupon securities. (durations) may need to be estimated. Thus, average lives In sum, comparable default-free, broadly traded securities from whidh market-determined default risk premiums may be com puted are not readily available and must be searched out or surrogate series developed. One possible comparable default-free residential mortgage security is the GNMA pass-through security. However, although widely traded for a number of years, reliable data have not been developed on Interest yields on these securities with assumed prepayment maturities of less than 12 years. It is recommended that monthly yield curve series be developed by the Federal Home Loan Bank Board for these securities for use as the reference default-free security. also necessary for estimating interest rate risk premiums.) (This series is It would be necessary to develop separate series for fixed rate, variable rate, and graduated payment securities. This will be particularly difficult for the variable rate securities, both because of their newness and because of the large number of different forms in which they are Issued. However, variable rate securities have many of the properties of shorter maturity fixed rate securities depending on how fre- -4 1 quently and by how much the contract Interest rate may be changed with changes in market rates of Interest. Although not easy, development of a number of yield curve series based on GNMA pass-through certificates is the best approach to obtaining default-free yields on a variety of residential mortgage loans typically extended by savings and loan associations. In the absence of such a series, the interest rate series for Treasury securities with terms to maturity up to 12 years developed for measuring Interest rate risk may be used. To use this series as the reference securities, however, it would be necessary to compute durations, for both the mortgages and the Treasury securities. Estimating market default risk premiums is considerably easier for comsumer and business loans that savings and loan associations may reasonably be expected to increasingly extend. Most of these loans may be compared with Treasury securities of comparable maturities. Approximate average lives or durations may be readily computed for amortized consumer loans, whose maturities are typically four years or shorter. The estimated default risk premiums may be expected to differ for similar loans extended by institutions in different sections of the country as regional economic conditions differ. 77 Diversification As discussed earlier, depository institutions can reduce the likelihood of experiencing large default losses in any one short interval of time by diversit fying their loans and securities across borrowers whose income flows are not, or * better yet negatively, correlated. Diversification may be across borrowers in different industry sectors and/or in different geographical sectors. Contrary to equity securities, the market, however, does not appear to reward diversification among debt securities by lowering the default risk premiums. Thus, because the -42insurance premiums are scaled to the market risk premiums > it appears reasonable to provide a credit against their insurance premiums for appropriately diversified institutions Two arguments may be made against such a provision. One, defaults by borrowers are not always independent regardless of how well the institution is diversified. As levels of economic activity deteriorate, increasingly more firms experience reduced sales and Incomes and find it increasingly more difficult to meet their debt obligations in time and in full. In severe depressions, such as in the 1930s, even the most ,,solid,, borrowers are likely to default. Because economic conditions do not change in lock-step in all industries or in all geo graphical areas, diversification can offset some of the effects of interdependence. But as economic conditions worsen, even diversification may not be sufficient to prevent substantial simultaneous bank losses. Two, depository institutions, and in particular savings and loan associations, are prohibited by extant or past legislation from significant diversification > across product or geographical lines. Until recently, the; were restricted pri marily to residential mortgages extended to local borrowers. Indeed, one study found an inverse relationship between permissible limited diversification and SLA profitability in the 1970s, so that institutions with greater asset diversification experienced lower not higher net profits.^ This constraint haS been relaxed by recent legislation and regulation and diversification may reasonably be expected ^ to increase as the institutions expand into newly authorized consumer and business i loans and commercial mortgages and into residential mortgages of distant borrowers through newly authorized branching across wider areas or purchases in the growing secondary market. -4 3 Diversification may be measured in a number of ways. One simple way is to compute the percentage of the dollar amount of total assets at the particular institution in each major balance sheet classification, square this number, and sum the squares. In mathematical terms, this procedure may be written as DI - T I K n*li n where: DI * diversification index Kq * percent of dollar amount of total assets in particular asset classification n, and T « total number of asset classifications. Technically, this index is referred to as the Herfindahl Index. It is familiar to some bankers because it is used by the U.S. Department of Justice to measure concentration in product markets in evaluating the implications of mergers and other acquisitions in its enforcement of antitrust legislation. 25 As a result, the index has also been adopted by the financial institution regulatory agencies in evaluating applications for merger and holding company acquisitions under their jurisdiction. The simplicity of the Herfindahl Index may be demonstrated by an example that assumes only two asset classifications. If all the assets in an institution were in one classification and none in the other, the index takes on a value of 1.0. This indicates total concentration, or no diversification whatsoever. If 75 percent of the dollar volume were in the first category and 25 percent in the second, the value of the index declines to .625. If an equal 50 percent were in each category, the index value declines further to .5. This is the minimum value for the two classification cases and indicates maximum diversification. Maximum diversification for any number of classifications is always shown by an index value of 1/T where T is the total number of classifications used. This would be -4 4 - the minimum index value and represent maximum diversification for that particular number of asset classifications. How would credit be given for diversification? A straightforward method would be to assign some weight to one minus the diversification index, where the index is computed for a given number of asset classifications for all institutions, and subtract this value from the premiums for default risk previously computed for the particular institution as described earlier in this section. Thus, the greater the diversification, the smaller the value of DI, the larger (1 - DI), and the greater is the credit given against the insurance premiums for default risk. The value of the weight given diversification and the number of asset categories to be used must be determined by the insurance agency on the basis of further research. -4 5 Monitoring Factors affecting the financial condition of depository institutions can change quickly, particularly if the dramatic interest rate swings of recent years continue. Thus, an institution's net worth may change quickly. Because the insurance agency's losses depend on the speed with which it can close the insti tutions after the target positive, zero, or negative net worth value is reached, it is Important for the agency to monitor the institutions frequently and accurately. This will require more frequent reporting by the institutions than is necessary to establish the annual or semi-annual insurance premiums, although in less detail. Such monitoring, however, is independent of the insurance premium structure adopted and is as necessary for flat premium or premiums scaled to deposit size as for risk sensitive premiums. However, -the riskier the insti- 26 tution, the more frequent need it be monitored. -4 6 - Conclusions and Recommendations Deposit insurance, per se, permits depository institutions to borrow insured deposits at the riskless interest rate, regardless of the riskiness of the insti tution. This reduces the market discipline on insured institutions and encourages them to increase their risk exposure both by reducing their net worth relative to deposits and by increasing their investments in risky assets and liabilities. The benefits of market discipline may be reintroduced by pricing the deposit insurance in such a way as to mimic market forces. Thus, the greater is the risk exposure of the institution, the more expensive should deposit insurance be to the institution. Conversely, the more expensive deposit insurance is made, the less likely is the institution to increase its risk exposure. This paper considered a large number of alternative deposit insurance premium structures that are designed both to serve as a surrogate for the disci pline of market forces to restrain risk seeking by insured depository institutions and to allocate the cost of deposit insurance equitably among institutions accor ding to their likely contribution to the operating costs and losses of the insur ance agency. Thus, this paper does not consider nonrisk sensitive premium structures, such as the current system of premiums scaled proportionately to deposits. Although these structures have the substantial advantages of being simple and immediately implementable in practice, they have the dual disadvantage of neither allocating the cost of the insurance equitably across institutions nor discouraging risk exposure. Indeed, some so-called flat premium structures may actually encourage additional risk exposure. institutions subsidize less risky ones. Such structures also have more risky The alternative structures are evaluated on the basis of their theoretical soundness, their ability to be implemented in practice either at this time or in the near future, and how well they satisfy a -4 7 - number of criteria cited earlier in this chapter that an optimal risk sensitive premium structure should possess. This risk exposure of depository institutions is not easily measured given today’s state of the art in both financial theory and institution information systems. Risk exposure may be measured either for the institution as a whole or for the individual components of risk. In today's environment, the most important risk components for depository institutions are interest rate risk and default risk. Single overall risk measures for the institution are both easier to obtain and tb implement quickly and cheaply given today's state of the art in information systems for depository institutions. They also interfere minimally with market forces and should minimize the need for supplementary nonprice regulation. However, they are both less precisely related to individual institution failure and less amenable to use as a lever for the insurance agency to affect the risk exposure of the institution through variable premium charges. On the other hand, although the principles are not difficult, meaningful empirical measures of interest rate and default risk exposure that can be implemented efficiently are difficult to obtain at this point in time. Two premium structures, one scaled to interest rate risk and the other to default risk, were developed in this chapter. Both are theoretically sound, have explicit objectives, are relatively simple to understand and minimize the need for supplementary nonprice regulation, but both are difficult and costly to compute because of the poor quality of the available data and thus are difficult to implement at this time. However, the state of the art in computer and information systems is advancing so rapidly that both measures should be feasible in a few years. In addition, it is necessary to combine the indices for the individual risk components into one overall index value to which to scale the deposit premiums. This requires that the insurance agency assign weights to the components. What -48should be these weights and should they be constant through time? One option is to determine the value of the weights on the basis of their contribution to the possibility of the failure of the institution and thereby to the costs and losses of the insurance agency. Another option is to base the relative weights on the relative importance assigned each risk component at the time by the insurance agency. This procedure permits the agency to change the magnitude of the component premiums without changing the magnitude of the total premium to the institution and improves its control over the particular type of risk exposure incurred by the institution. If, for example, the agency suddenly considered interest rate risk to be of greater concern than default risk, it could increase the relative weight assigned interest rate risk in the summation scheme. This would increase the risk premium applied against this risk without increasing the total premium charged and encourage the insured institutions to become more interest rate risk averse. Lastly, should the insurance agency allow any weight to the risk components that are not explicitly specified, such as management or political risk? If so, how? For all these reasons, it may be inadvisable to adopt risk measures that may be sophisticated by today’s standards but are likely to be significantly inferior to what should be possible just a few years in the future. It might be better to defer the introduction of such premium structures until then, so as not to lock in concrete an inferior structure. In the meaintime, it is recommended that, until more sophisticated information systems are available to all depository institutions, deposit insurance premiums be based either on simple, single over all risk measures for the institutions, such as variability in the earnings, a limited number of important financial ratios, or their past loan losses, or on a combination of simple interest rate risk measures, such as developed in this -49paper, and deposit size, such as the current system. The response of deposit institutions to the insurance premiums is dependent on both the relative magnitude of the premiums for different degrees of risk exposure (gradation) and the absolute magnitude of the premiums. For usual types of insurance, the size of the premiums needs to be at least sufficient to be equal to the actuarially fair value of the losses. different. But, as argued, deposit insurance is Federal deposit insurance agencies are empowered to close financially troubled institutions as soon as their net worths reach zero and thereby not experience any losses other than operating expenses and losses from detection failures. The closed institution is auctioned to the highest bidder at positive or negative premiums. However, it may, on occasion, be desirable to keep failed institutions open if a large number of institutions are failing simultaneously and sufficient potential buyers may be difficult to find. Thus, the potential losses of the federal deposit insurance agencies are primarily a matter of public policy. It follows that the size of the insurance funds is also a matter of public policy -and is not related to the magnitude of the expected losses of the Insured institutions. The size of the premiums then can be established primarily in a way to achieve the risk exposure that the insurance agency wishes to impose on the insured institutions. The question of how institutions respond to premiums of different magnitudes and different degrees of gradation has not been researched to date. need the premiums be to affect the risk strategy of the institutions? gressive” need the risk premiums be to do the same? How large How "pro These questions are analogous to the response of the households to different levels and degrees of progressivity of the personal income tax, which is one of the more controversial topics in poli tical economy today. It is obvious that at least partial answers to these -5 0 - questions must be obtained before a meaningful risk sensitive premium structure should be implemented. To the extent that insurance premiums do affect bank risk behavior in the hypothesized directions, a highly progressive nominal premium structure need not indicate a highly progressive de facto premium structure. The high rates will discourage the particular types of undesired behavior and would not be paid de facto. Lastly, although risk sensitive premiums may be expected to affect bank risk behavior, they cannot prevent risk behavior that is undesirable only in retrospect. These insurance premiums, like any other insurance premiums, are based on previous experience, and may not be appropriate if conditions change significantly. Thus, it is possible that a premium structure for, say, interest rate risk exposure based on the relatively tranquil period of the 1950s and 1960s would not have dis couraged banks sufficiently from incurring some of the risk exposure that they did in the 1970s and 1980s. retrospect. This exposure looks excessively risky primarily in Similarly, if interest rate volatility declines and predictability increases, insurance premiums based on recent years may discourage banks exces sively from incurring the degree of interest rate risk exposures appropriate for the new economic environment. HYPOTHETICAL GROUPING OF BALANCE SHEET ACCOUNTS (million dollars) Remaining Term to Maturity or to Earliest Repricing __________ Months___________ _______________________ Years__________________ 0-1 1-3 3-6 6-9 9-12 1 2 3 4 5 6 1 8 9 1 0 1 1 1 2 >12 ASSETS Cash, Demand Deposits Residential Mortgages!*3 Fixed Contract Rate >18 Variable Contract Rate2*3 <7 Z 7- 8 8- 9 9- 10 10- 11 11-12 1213151617>18 13 14 16 17 18 Table 1 <7 Z 7- 8 8- 9 9- 10 10- 11 11-12 12- 13 13- 14 15- 16 16- 17 17- 18 Remaining Term to Maturity or to Earliest Repricing __________ Months__________ ________________________ Years___________ ______ 0-1 1-3 3-6 6-9 9-12 1 2 3 ‘4 5 6 7 8 9 10 11 >12 12 Other Improved Real Estate Contract Rate Land Loans Contract Rate Unsecured Home Improvement Loans Contract Rate Consumer Loans Contract Rate Unsecured Construction Loans Contract Rate Table 1 Cont'd. Secured Home Improvement Loans Contract Rate Months 0-1 1-3 3-6 Remaining Term to Maturity or to Earliest Repricing Years 6-9 9-12 1 2 3 4 5 6 7 8 9 10 11 12 Secured Construction Loans Contract Rate Other Loans Contract Rate U.S. Treasury Securities Coupon Rate Tax-Exempt Securities Coupon Rate .ther Investments Coupon Rate Other Assets LIABILITIES Insured Deposits NOW Accounts^ Super NOW Accounts^ MMD Accounts^ MMCs Contract Rate Table 1 Contfd Federal Agency Securities Coupon Rate >12 Months 0-1 1-3 3-6 Remaining Term to Maturity or to Earliest Repricing Years 6-9 9-12 8 10 11 12 >12 SSCs Contract Rate Other Certificates Contract Rate Secured Other Borrowing Contract Rate Unsecured Other Borrowing Contract Rate Other Liabilities Contract Rate Net Worth6 Table 1 Cont’d Advances Contract Rate Notes ^-Includes pass-through certificates. ^Separate accounting for mortgages that may be repriced to current contract rates and those that cannot. ^All mortgages are assumed to be prepaid by end of twelfth year. 4Assumed maturity of 1 year. ^Assumed maturity of 3 months. ^Assumed maturity of more than 12 years. -5 6 - Footnotes Franco Modigliani and Merton Miller, "The Cost of Capital, Corporation Finance and the Theory of Investment," American Economic Review 48 (June 1958): 261-97. Paul M. Horvitz, "A Reconsideration of the Role of Bank Examination," Journal of Money, Credit and Banking 12 (November 1980, Part I): 654-9. O Milton Friedman and Anna Schwartz, A Monetary History of the United States (Princeton: Princeton University Press, 1963), pp. 324-32. O Stephen A. Buser, Andrew H. Chen and Edward J. Kane, "Federal Deposit Insurance, Regulatory Policy and Optimal Bank Capital," Journal of Finance 36 (March 1981): 51-60. W. F. Sharpe, "Bank Capital Adequacy, Deposit Insurance, and Security Values," in Risk and Capital Adequacy in Commercial Banks, ed. Sherman J. Maisel (Chicago: University of Chicago Press, 1981), pp. 187-202. 4Ibid. ^John H. Boyd, Jr., "Federal Insurance of Savings and Loan Deposits: Analysis and Reform Proposals," in A Study of FSLIC Risk Management in a Changing Economic and Regulatory Framework (Northwestern University, 1978). Buser, Chen and Kane, "Federal Deposit Insurance," pp. 51-60. Mark J. Flannery, "Deposit Insurance Creates a Need for Bank Regulation," Federal Reserve Bank of PhiladelphiaBusiness Review (January/February 1982): 17-27. Sharpe, "Bank Capital Adequacy," pp. 187-202. Robert C. Merton, "An Analytic Derivation of the Cost of Deposit • Insurance Guarantees: An Application of M o d e m Option Pricing Theory," Journal of Banking and Finance 1 (June 1977): 3-11. Thomas Mayer, "A Graduated Deposit Insurance Plan," Review of Economics and Statistics 47 (February 1965): 114-6. Kenneth E. Scott and Thomas Mayer, "Risk and Regulation in Banking: Some Proposals for Federal Deposit Insurance Reform," Stanford Law Review 23 (May 1971): 857-902. ^Buser, Chen and Kane, "Federal Deposit Insurance," pp. 51-60. "Federal Insurance of Savings and Loan Deposits." Boyd, ^J. E. Stiglitz, "The Effects of Income, Wealth, and Capital Gains Taxation on Risk Taking," Quarterly Journal of Economics 83 (May 1969): 263-83. B. Naslund, "Some Effects of Taxes on Risk Taking," Review of Economic Studies 36 (July 1968): 289-306. A. D. Roy, "Safety First and the Holding of Assets," Econometrica 20 (July 1952): 431-49. Evsey D. Domar and Richard Musgrave, "Proportional Income Taxation and Risk Taking," Quarterly Journal of Economics 58 (May 1944): 388-422. ®George J. Benston, "Bank Examination," The Bulletin of the Institute of Finance, Graduate School of Business Administration, New York University, Nos. 89-90 (May 1973): 1-73. Mark J. Flannery and Jack M. Guttentag, "Identifying Problem Banks," in Proceedings of a Conference on Bank Structure and Competition (Chicago: Federal Reserve Bank of Chicago, May 3-4, 1979), p. 1-32. Mark J. Flannery and Jack M. Guttentag, "Problem Banks: Examination, Identification and Supervision," in State and Federal Regulation of Commercial Banks, eds. Leonard Lapidus and others, (Washington: Federal Deposit Insurance Corp., 1980), pp. 171-226. -5 7 - L. Fisher, "Determinants of Risk Premiums on Corporate Bonds," Journal of Political Economy 67 (June 1959): 217-37. Richard R. West, "An Alternative Approach to Predicting Corporate Bond Ratings," Journal of Accounting Research 8 (Spring 1970): 118-25. Richard R. West, "Bond Ratings, Bond Yields and Financial Regulation: Some Findings," Journal of Law and Economics 16 (April 1973): 159-68. ^ W . H. Beaver, "Alternative Accounting Measures as Predictors of Failure," The Accounting Review 43 (January. 1968): 113-22. W. H. Beaver, "Market Prices, Financial Ratios and the Prediction of Failure," Journal of Accounting Research 6 (Autumn 1968): 179-92. Edward I. Altman, "Predicting Performance in the Savings and Loan Industry," Journal of Monetary Economics 3 (October 1977): 443-66. Edward B. Deakin, "Business Failure Prediction: An Empirical Analysis," in Financial Crises: Institutions and Markets in a Fragile Environment, eds. Edward I. Altman and Arnold W. Sametz (New York: John Wiley and Sons, 1977), pp. 72-88. ^Chayim Herzig-Marx, "Comparing Market and Regulatory Assessments of Bank Condition," in Proceedings of a Conference on Bank Structure and Competition (Chicago: Federal Reserve Bank of Chicago, April 28-9, 1977), pp. 89-112. ■^Robert a Mullin, "The National Bank Surveillance System," in Financial Crises: Institutions and Markets in a Fragile Environment, eds. Edward I . Altman and Arnold W. Sametz (New York: John Wiley and Sons, 1977), pp. 48-67. 13 Flannery and Guttentag, "Identifying Problem Banks," pp. 1-32. Flannery and Guttentag, "Examination, Identification and Supervision," pp. 171-226. ^Sherman J. Maisel, "The Theory and Measurement of Risk and Capital Adequacy," in Risk and Capital Adequacy in Commercial Banks, ed. Sherman J. Maisel (Chicago: University of Chicago Press, 1981), pp. 19-183. ^^Ibid. Deloitte, Haskins and Sells, ''Asset Composition Net Worth Index," (Washington, DC: Federal Home Loan Bank Board, 1980). ^George J. Benston and John T. Marlin, "Bank Examiners1 Evaluation of Credit: An Analysis of the Usefulness of Substandard Loan Data," Journal of Money. Credit and Banking 4 (February 1974): 23-44. ^Joseph p. Sinkey, Jr., Problem and Failed Institutions in the Commercial Banking Industry (Greenwich, CT: JAI Press, Inc., 1979), pp. 92-100. ^®J. E. Stiglitz and Andrew Weiss, "Credit Rationing in Markets with Imperfect Information,” The American Economic Review 71 (June 1981): 393-410. "^Fisher, "The Determinants of Risk Premiums," pp. 217-37. Ratings and Bond Yields," pp. 159-68. 20 West, "Bond Braddock W. Hickman, Corporate Bond Quality and Investor Experience (New Jersey: Princeton University Press, 1958), Thomas R. Atkinson, Trends in Corporate Bond Quality (New York: Columbia University Press, 1967). Harold G. Fraine and Robert H. Mills, "Effects of Defaults and Credit Deterioration on Yields of Corporate Bonds," Journal of Finance 16 (September 1961): 423-34. George H. Hempel, The Postwar Quality of State and Local Debt. (New York: National Bureau of Economic Research, 1971). -5 8 - 21 Herzig-Marx, "Assessments of Bank Conditions," pp. 89-112. 22 Tim S. Campbell and J. Kimball Dietrich, "The Determinants of Default on Insured Conventional Residential Mortgage Loans," (Working Paper, University of Southern California, September 1982). ^Maisel, "Measurement of Risk," pp. 19-183. 24 Deloitte, Haskins and Sells, "Net Worth Index." ^-’David S. Weinstock, "Using the Herfindahl Index to Measure Concentration," The Antitrust Bulletin 27 (Summer 1982): 285-301. Charles H. Berry, "Corporate Growth and Diversification," Journal of Law and Economics 14 (October 1971): 371-83. 26 U. Dothan and J. Williams, "Banks, Agency and Regulation," (Working Paper, Kellogg Graduate School of Management, Northwestern University, 1981). -5 9 - APPENDIX Interest Rate Risk Exposure 1. The Cash (Spot) Position A financial intermediary is exposed to interest rate risk when interest rate changes affect the market value of its cash assets and liabilities by different amounts. For example, if a general increase in interest rates results in a decrease in the market value of assets by 10 percent but decreases the value of its liabilities by 5 percent, the net worth of the intermediary relative to its assets must decrease. A continuous deterioration of the intermediaryfs financial position can make it unable to discharge its liability commitments and can result in insolvency and bankruptcy. Interest rate risk depends, therefore, upon the relative impact of interest rate changes on the intermediary's assets and liabilities. The impact of interest rate changes on the cash (spot) assets and liabilities of an institution may be measured by their respective durations. The duration of a set of securities is the average life of the securities, measured as an average of the length of time to the dates on which payments are received weighted by the present values of the respective payments. Mathematically, duration is defined most simply as N I tFt ------- t - i (i + D 1 __ — (Al) z t«l (1 + i)* where F^ is the cash flow occurring at time t In the future, i is the rate of Interest (yield to maturity), and N is the date of the last flow.' Redington showed that, when the initial present values of a financial intermediary's assets and liabilities are equal, the impact of subsequent interest -6 0 - rate changes on its net worth is determined by the difference between the durations of the institution's assets and liabilities (including net worth). as follows. This may be proven The present (market) value of the institution's assets (A) is the discounted value of its expected future income flows from the present to the last period N, or A N F A - I ---- ---t-1 (1 + (A2) Likewise, for its liabilities (L) L N F L - Z ---- ---t-1 (1 + i)* Initially, A = L. (A3) If interest rates change, then > A < L or A - L | 0. The impact of a change in interest rates on net worth may be written as A (A - L) Ai Equating with the flow equivalents from equations (A2) and (A3) and using calculus yields, at first approximation, A(A - L ) _ Ai N tF* N tF^ I -------I ----t-1 (1 + i)fc . t-1 (1 + i)C (1 + i) (1 + i) * Equation (Al) may be rewritten N tF^ N f£ E ---- ---- - D. T ---- ---t-1 (1 + i)C t-1 (1 + i)£ and substituting from Equation (A2) (A4) -6 1 A N tFt E t=l (1 + i)t Thus, Equation (A4) may be rewritten A(A - L) Ai DaA DlL = ‘ (1 + 1) + (1 + i) Remembering that A * L and collecting terms A(A - L) Ai (Da - Dl)A (1 + i) or A (A - L) - -(DA - D L)A -(1-^ ±) = ANW (A5) The difference between the durations of the assets and liabilities in Equation (A5) is the duration "gap," and can be written as Gap = Da - D^. (A6) The gap is scaled in years. If the asset and liability durations are equal and the assets and liabilities are both marked to market, the gap is zero and the intermediary is exposed to no interest rate risk. In effect, the intermediary is a conduit and any change in interest rates is passed through from one side of the balance sheet to the other on a one to one basis. A special and restrictive case of this is when the cash outflows and inflows are perfectly matched. If the duration of the assets exceeds that of the liabilities, the duration gap is positive and any increase (decrease) in interest rates reduces (increases) the value of the assets more than the value of the liabilities and, hence, decreases (increases) net worth. The duration gap can serve as an index of interest rate risk because it measures the relative impact of interest rate changes on the market values of the assets and liabilities. -6 2 - The larger the gap, the larger is the value of the risk index, and the larger is the change in net worth for any given change in interest rates* The calculation of duration is difficult and complex. to avoid these calculations. However, it is possible As is shown below, the duration gap can be approxi mated from relative changes in the market value of the assets and liabilities. It follows from before that, at first approximation, A (A7) Thus, the relative change in the price of a security can be calculated for any change in the yield to maturity if the duration is known. By rearranging terms in A7, it follows that D = - — A . (1 + .11 (A8) Ai Thus, we can approximate the durations by the proportional change in market price multiplied by an interest rate factor. By rearranging terms in Equation (5A), we can then approximate the duration gap as AL - AA . (1 + i) Gap = Da - D l - --- --------- £ — (A9) Although, as noted in the text, durations are difficult to compute, the gap may be approximated by computing the market values on the right side of Equation (A9). This may be done in several steps. 1. Assume the interest rates used to calculate the market value of assets and liabilities increase by a given amount. The corresponding difference in the changes of the market values of the liabilities and assets can be denoted as -6 3 (change in liabilities - change in assets), this difference is zero, all liability obligations can be discharged as scheduled. 2. Divide the difference in step 1 by the market value of assets to form the ratio: (change in liabilities - change in assets) assets In this way we can compare different Intermediaries having different Ib v s Is of assets. An institution which is twice as large as another may have this same ratio so that both would have the same degree of interest rate risk, 3. The given change in interest rates used in step 1 was arbitrary. In order to have an index of interest rate risk that tends to be insensi tive to this arbitrary change, we^multiply the ratio in step 2 by the ratio: one plus the level of interest rates given change in rates * The resulting index can be written as Change in _ Change in Liabilities Assets Assets One plus level of interest rates Change in rates This renders an index that is insensitive to the size of the change in interest rates because the larger we make the change in rates in the denominator of the latter ratio, the larger we make the numerator in the former ratio. These increments to the changes cancel out. For example, if we multiply the "change in rates" by, say, 10, we approximately mul tiply "change in liabilities - change in assets" by 10. The 10s cancel. The level of rates included in the formula indicates that the degree of -6 4 - interest rate risk generally changes with the level of rates. denominated in years. The gap is It is positive when the duration of assets is longer than that of the liabilities, and is negative when the duration of the assets is shorter than that of the liabilities. 2. The Futures Position In order to reduce its exposure to interest rate risk from increases in market rates, an institution can sell commercial paper, Treasury bonds, Treasury bills, GNMA certificates, or CDs in the futures market. position with a short futures position. It hedges its long cash In a short hedge position, the institution sells one of these instruments at a given price for delivery on a specific future date. As most futures markets require immediate settlement of daily gains and losses in prices, changes in interest rates that affect the price of open con tracts produce immediate cash gains or losses. If interest rates increase, the value of the instrument to be delivered in the future will decrease so that the institution can buy the instrument on the delivery date at a lower price than it has contracted forward to sell it. These future gains are posted immediately to the institution. Example: An institution sells a $100,000 Treasury bond contract in the futures market for delivery 90 days hence. The standardized Treasury bond sold at the exchange operated by the Chicago Board of Trade is an 8 percent, 20 year bond. If the market yield on this contract is 10 percent, the price is $82,844. If the next day interest rates increase to 10.102 percent, the futures price falls to $82,094. The value of the open contract increases by $750. This amount is credited to the institution. The profits in the futures market offset some or all of the decrease in the value of the institution's cash assets resulting from the increase in interest -65rates, and the institution has reduced its exposure to interest rate risk. interest rates decrease, the Implications are reversed. If The institution will suffer losses on sales of futures contracts, but the value of its assets will increase. It should be noted that the institutions must be prepared to meet possible cash losses if they utilize the futures market to reduce their interest rate risk. These possible losses can be met from cash reserves and/or from the sale of assets whose values have increased. The risk of an open futures position may also be measured by the change in market value for a given change in interest rates as described in Section 1. 3. Calculation of the Overall Index of Interest Rate Sensitivity Gap The calculation of the proposed overall index of interest rate sensitivity involved four steps: (1) the conversion of all cash and futures assets and liabili ties on the balance sheet from book to market values; (2) the calculation of changes in these values for a standardized change in the applicable market interest rates; (3) the calculation of the index of interest rate risk, using the formula devel oped in section 1 of this Appendix; and (4) this index is then multiplied by the ratio of assets to net worth to determine the effective interest rate sensitivity gapThe conversion of cash assets and liabilities from book to market value is accomplished in two steps. First, all of the assets, liabilities, and futures contracts are grouped into categories such as those suggested in Table 1 of the text. Second, the market valuation of the assets, liabilities, and futures con tracts within these groups is compute^ for market rates of interest which are provided by the insuring agency. Next, the changes in the value of the assets, liabilities, and futures contracts are evaluated for a given equal change in market rates of interest for -6 6 - each group, say, of 100 basis points. The changes are summed and divided by the market value of total assets as follows: changes in liabilities market value of total assets This sum is multiplied by one plus the level of interest rates change in interest rates to obtain equation A . The interest rate level in the formula is assumed to be an average rate, say, the 10 year Treasury rate. Last, the resulting index is multi plied by the initial market values of assets * net worth. 4. An Illustration of the Calculation of the Interest Rate Index The four steps in the calculation of the interest rate index are illustrated here for a hypothetical savings and loan association. A very simplified balance sheet at book values for this savings and loan is illustrated in Exhibit 1 . The market rates at which the assets, liabilities, and futures contracts are valued are shown in Exhibit 2 . FSLIC. These rates are provided the institution by the Exhibit 3 shows the computed market value of the assets, liabilities, and futures contracts. Note that net worth is lower than its book value. This decrease results primarily from the large- decreases in value of long-term low contract rate mortgages. Exhibit 4 shows the balance sheet of the hypothetical savings and loan after an increase in market rates of 100 basis points. worth declines. Exhibit 5 computes the index of interest rate risk. Its net For our hypothetical institution, the measure of interest rate gap is +1.86 years. This implies that the interest rate gap is positive so that the value of the assets changes more as a consequence of a change in interest rates than the value of the liabilities. This is consistent with the decline in net worth. Lastly, this gap is multiplied by the ratio of assets to net worth (85.00/4.23 * 20.09). The -6 7 - result ing effective net Interest rate sensitivity index is 37.37. This institution is exposed to greater interest rate risk than an institution having a smaller index, say, 30, and to lesser risk than an institution having a larger index, say, 40. In addition, as discussed in the text, the index is a linear measure of interest rate risk, so that the above institution is twice as risky as one whose index is 18.7 and only one-half as risky as one whose index is 74.7. -6 8 EXHIBIT 1 Balance Sheet at Book Value for a Hypothetical Savings and Loan Association (millions of,dollars) Assets Cash, Demand Deposits Treasury Securities, maturity 2 years at 11% coupon Residential Mortgages: 5 year maturity at 14% 25 year maturity at 14%* 25 year maturity at 10%* Other Loans, 2 year maturity at 15% 5.0 5.0 10.0 27.0 40.0 13.0 100.0 Liabilities Deposits and Savings Accounts: Passbook Accounts, (assumed 1 year maturity), at 5.5% NOW Accounts, (assumed 3 months), at 5.25% Super NOW Accounts, (assumed 3 months), at 11% CDs, 1 year maturity, at 6.5% CDs, 2.5 year-s maturity, at 6.75% MMCs, 6 months maturity, at 13% MMCs, 6 months maturity, at12% SSCs, 1.5 years maturity, at 12% Jumbo CDs, 6 months maturity, at 13.5% FHLB Advances, 1.5 years maturity, at 13% Net Worth 13.0 8.5 8.5 4.0 4.0 13.0 5.0 8.5 *7.0 10.4 81.9 19.1 100.0 Open Futures Contracts Sell for 3 month delivery Treasury security, 20 year, 8% GNMA security, 8% 5.0 5.0 loTo.- ♦Assumed to be prepaid at end of the twelfth year. -6 9 - EXHIBIT 2 Hypothetical Prevailing Market Rates of Interest* (Percent) Mortgage Loans 5 year maturities 25 year maturities 15 16 Other Loans 15 Passbook Savings CDs, 1 year maturity CDs, 2.5 years maturity NOW Accounts MMCs Jumbo CDs SSCs FHLB Advances 8 12 13 12 13 14 12 13 2 year Treasury rate 10 year Treasury rate 3 month GNMA futures rate 3 month Treasury futures rate 10 10 15 10 ♦These rates are provided by the FSLIC. -7 0 EXHIBIT 3 Balance Sheet at Market Value for a Hypothetical Savings and Loan Association (millions of dollars) Assets Cash, Demand Deposits Treasury Securities Residential Mortgages: 5 year maturity 12 year maturity at 14% 12 year maturity at 10% Other Loans Liabilities Deposits and Savings Accounts: Passbook Accounts, 5.5% NOW Accounts, 5.25% Super NOW Accounts, 11% CDs, 1 year maturity, 6.5% CDs, 2.5 years maturity, 6.75% MMCs, 6 months, 13% MMCs, 6 months, 12% SSCs, 1.5 years maturity, 12% Jumbo CDs, 13.5% FHLB Advances, 13% Net Worth Open Futures Contracts Treasury Bond GNMA Security 5.00 5.09 9.78 24.22 27.91 13.00 85.00 12.82 8.36 8.48 3.80 3.45 13.00 4.98 8.50 6.98 10.40 BU777 4.23 85.00 4.14 3.13 7.27 -7 1 EXHIBIT 4 Balance Sheet at Market Value for a Hypothetical Savings and Loan Association After a Market Rate Increase of 100 Basis Points (millions of dollars) Assets Cash, Demand Deposits Treasury Securities Residential Mortgages: 5 year maturity 12 year maturity at 14% 12 year maturity at 10% Other Loans Liabilities Deposits and Savings Accounts: Passbook Accounts, 5.5% NOW Accounts, 5.25% Super NOW Accounts, 11% CDs, 1 year maturity, 6.5% CDs, 2.5 years maturity, 6.75% MMCs, 6 months, 13% MMCs, 6 months, 12% SSCs, 1.5 years maturity, 12% Jumbo CDs, 13.5% FHLB Advances, 13% Net Worth Open Futures Contracts Treasury Bond GNMA Security 5.00 5.00 9.80 23.00 26.50 12.97 82.27 12.58 8.34 8.46 3.77 3.37 12.94 4.96 8.38 6.55 10.26 80.01 2.26 82.27 3.80 2.94 6.74 -7 2 - EXHIBIT 5 Calculation of the Effective Interest Rate Sensitivity Index 1. Change In the value of cash liabilities: (from Exhibits 3 and 4) -$0.76 2. Change In the value of cash assets: (from Exhibits 3 and 4) -$2.73 3. Change in value of open futures contracts: $0.53 4. Item 1 less the sum of Items 2 and 3: $1.44 5. One plus the level of interest rates (10%) divided by 100 basis points (1.10/.01) 6. Item 4, above, divided by market value of assets (1.27/85) .001694 7, Interest rate risk index (Item 5 multiplied by Item 6) +1.89 years 8. Market value of total cash assets to net worth ratio (from Exhibit 3) 20.09 . 9. Effective interest rate sensitivity index (Item 7 multiplied by Item 8) 37.37 110 -73Appendix Footnotes ^•Frederick R. Macaulay, The Movements of Interest Rates, Bond Yields and Stock Prices In the United States Since 1856 (New York: National Bureau of Economic Research, 1938), pp. 43-53. ^F. M. Redington, "Review of the Principle of Life and Office Valuations," Journal of the Institute of Actuaries 78 (1952): 286-340. 3Ibid. ^Michael H. 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