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Dave Hutchison is an Assistant Professor of Finance at Central Michigan University. Contact him at hutch1de(at)mich.edu , replacing (at) with @.

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As the banking system has become less governed by the regulatory structure and more so by the forces of market competition, carefully constructed models of economic or market value have become more important. These models are used for many purposes, including the measurement of product level and business line profitability, interest rate risk modeling, and valuation modeling used in acquisition analysis. Although banks have always employed models of economic or risk-adjusted value even if only implicitly (when evaluating the “spread” on a loan or security, for instance), formal models have evolved from relatively simple pool-level funds transfer pricing (FTP) models to full blown value-added models and sophisticated stochastic models of market value and equity duration. Yet, the economic value and interest rate risk of some components of a bank’s business are not easily modeled nor well understood, particularly among small to medium sized banks. For instance, retail deposit markets, characterized by sluggish responses of both prices and quantities to changing market conditions, have historically been quite vexing, particularly when measuring the duration of the balance sheet.

Considered in this article are the economic merits of traditional practitioner models of retail deposit economic value and interest rate risk in light of some recent academic advances in value and duration modeling. A fundamental objective of this work is to illuminate the economic distinctions between retail and other banking markets and to describe with simple illustrative models how these distinctions impact value and duration analysis. Although more sophisticated, commercially-available value-added and asset/liability models have become more common, most depositories still depend on traditional modeling techniques. Even among those institutions using more sophisticated methods, frequently the models are a “black box” not well understood by the analysts using them. As will be shown, many of the problems encountered by practitioners result from the inappropriate application of traditional valuation and duration tools that were built for highly competitive markets, such as the bond market. In addition, the nature of credit risk and the role of deposit insurance in deposit valuation, also poorly understood, will be discussed. Finally, unresolved issues for future research are addressed.

To view the Table and Figures associated with this article go to http://www.westga.edu/~bquest/2005/bank/deposits.xls (This is an Excel document.)

Structural changes in the U.S. banking industry, most importantly the declining scope of government regulation and the increasing significance of market competition, have caused many banks to think more critically about the efficient deployment of capital. Increasingly, models of economic profit or “value-added” are being used to measure risk-adjusted income in order to provide product managers with market-based pricing signals and to allocate risks internally in efficient ways. In addition, these models are being integrated into valuation models used in mergers and acquisition analysis. In more sophisticated value-added systems, banks employ capital allocation and funds transfer pricing (FTP) models to hypothetically charge asset-generating business lines for funds used and to credit the deposit unit for funds gathered, and more generally to measure risk-adjusted economic income. The capital allocation model “assigns” a product-specific amount of equity capital to the business unit, generally based on value-at-risk, that is, the maximum loss associated with a product within some probabilistic bounds. On the asset side of the balance sheet, equity allocation reflects primarily credit risk. On the deposit side, a small amount of equity capital is usually allocated to reflect operating risks such as fraud. The business line receives an equity charge equal to the bank’s cost of equity capital per unit of capital assigned.

The FTP model provides the debt capital component of the funding charge for assets generated or, in the case of deposits, the credit for debt capital provided. Since deposit market equity allocations are typically small, FTP is the driver of the deposit unit’s perceived profitability. FTP is typically a “maturity-matched” debt capital markets rate which is a proxy for the marginal borrowing rate of the bank as a whole. Yield curves commonly chosen to represent FTP rates include the LIBOR/swaps curve and the bank’s senior unsecured borrowing curve. On the deposit side, the FTP rate net of the equity capital charge and the rate being paid to depositors (and other deposit costs including capital charges associated with physical assets) measures economic profitability or net income. The capitalized value of the economic net income of a deposit base over time is often used to value a deposit franchise for branch or bank acquisition purposes. For interest rate risk management purposes, typically the FTP model is tied to the bank’s asset/liability management function via the maturities assigned to deposits within the FTP system. A duration model then determines the bank’s deposit market interest rate risk exposure based on the assumed deposit maturity structure.[2]

Perhaps the most fundamental difference between banks and other financial firms is that under deposit insurance, banks issue a class of liabilities for which most balances are fully insured by the U.S. government. The resulting market structure creates several complications for the implementation of internal profitability and duration models. First, deposit insurance separates the deposit investor from the credit risks of the bank, which are assumed by the FDIC. In essence, when a bank issues a deposit it engages in two transactions: it issues a risk-free (government insured) liability to a depositor and it purchases an insurance contract from the FDIC to cover the credit risks associated with the priority position of the deposit claim. Thus, the economic value of a deposit depends upon the market yield on a comparable risk-free claim, as well as the pricing of deposit insurance relative to the market pricing of credit risk. Second, for small depositors, bank search and switch costs, convenience value, information costs, and simply limited alternatives make adjusting to changing market conditions difficult. Not surprisingly, retail deposit markets are characterized by sluggish behavior in both interest rates and deposit issuance in response to changing conditions in the financial marketplace. By definition, competitive markets respond instantaneously and completely to changing circumstances and, therefore, there is no comparable competitively priced instrument to be used as a reference for deposit profit.

To the extent that a capital allocation model is employed, it is typical for a small amount of capital to be assigned to deposits, primarily to reflect some product-specific operational risks. Thus, the capital allocation has a small impact on the perceived deposit spread and little impact on pricing behavior. The typical internal profitability model for deposits is driven primarily by FTP. It is most common for banks to use one FTP curve to charge “users” of funds and credit “suppliers” of funds, so that the economic value of deposits will be measured relative to an FTP curve that reflects a proxy for the marginal subordinated borrowing rate of the bank. Note that under deposit insurance, the FDIC assumes the role of creditor, and it is the market price of the credit risk assumed by the FDIC that should be reflected in the FTP rate. The consequences of this have not been well understood, nor are they easily measured. This will be addressed in more detail below.

Given a FTP curve, the bank must determine the maturity of the stock of deposits in order to assign a crediting rate. Time deposits, such as fixed rate consumer CDs, are assigned a rate corresponding to the term of the deposit. Demandable (“indeterminant maturity”) accounts, such as demand deposits and money market deposit accounts (MMDAs), are considered somewhat more problematic. These are markets for which the sluggishness of deposit interest rates and volumes is the most pronounced. From a traditional FTP or equity duration perspective, it is not obvious what maturity to assign to these deposits. Should checking account dollars that are on the one hand demandable at par, but on the other hand very price-inelastic, be treated as overnight or longer-term money? In the context of balance sheet duration, Kaufman (1984) has stated:

"A number of bank deposit accounts, such as demand deposits, savings, NOWs, SNOWs, and MMDAs, do not have specific maturity dates.....What are the durations of such deposit accounts?.....If a bank's deposit rates lag increases in market rates, all deposits will not leave the bank immediately.....It may be possible to assign accurate probabilities to the timing of net deposit outflows, depending on the difference between the market and deposit rates....If interest rates increase it is then possible to value these deposits at less than their par value......The correct duration awaits further research."

Much of the difficulty experienced by bankers and bank economists in measuring value and duration results from the use of analytic tools poorly designed for these markets.  Standard valuation/duration models, indeed, virtually all of finance theory, implicitly assume a competitive market in which a shock to current market interest rates impacts only the economic value of the existing assets and liabilities of the institution. Future bank activity is implicitly assumed to be competitively priced (zero net present value), or at a minimum it is assumed that the profitability of future lending and deposit business is unrelated to current levels of interest rates. In this framework, maturing deposits essentially are assumed to fully re-price to competitive market rates. Thus, determining the value and duration of deposits is simply a matter of determining the maturity of the current deposit liabilities and discounting them at competitive market rates before and after an interest rate shock.

However, because demandable deposits can be redeemed at par at any point in time, they effectively mature and are implicitly re-priced continuously.  In the traditional valuation framework, the duration and interest rate risk of these deposits is, therefore, zero and their contribution to the value of the firm negligible. Yet, as Kaufman’s remark demonstrates, neither demandable deposits quantities nor rates respond fully to changing market yields, and thus their behavior is inconsistent with the traditional valuation model.  Because deposit interest rates do not fully respond to changing market rates, a shock to current market interest rates impacts the profitability of deposits over time, and therefore, the value of the bank.  Conceptually, if we treat demand deposits as continuously-maturing financial contracts, although the current set of contracts has zero duration and a negligible impact on the value of the firm, the existence of today’s deposit base is indicative of economically profitable future deposit issuance.  From this perspective, it is the economic value of the deposit franchise , i.e., the economic value of deposit issuance over time, and its sensitivity to movements in current interest rates that we should be measuring.  Valuation models that assign a fixed maturity to the stock of deposits at best capture only a portion of the economic value of the franchise, and cannot reliably be used to measure the duration of the balance sheet or the value of a deposit franchise, whether the existing franchise or a potential deposit acquisition.

Note that this source of value and risk is not limited to demandable deposit markets.  Any market in which quantities display a degree of insensitivity to movements in comparable market interest rates is a candidate for franchise value interest rate risk exposure.[3]  Virtually all retail markets will display some of this behavior, reflecting what might be best called “relationship assets”.  Measuring the value of a deposit market franchise and its sensitivity to market interest rates is a very difficult problem.  Measuring the impact of interest rates requires modeling not only changes in discount factors, but also interest-rate-dependent spreads and deposit volumes.[4]  Essentially, we need to forecast deposit issuance over time as a function of interest rates,  and we need a valuation model in which to find the present value of profits.  This entails modeling deposit demand as well as modeling the joint time series behavior of competitive market and deposit interest rates.  The model must be constructed in such a way that a reasonable measure of interest rate risk or duration can be defined. [5]

Consider a simple deposit market in which identical banks price deposits to preserve market share, and further assume that the market is static (no growth).  Thus, we can think of deposit pricing as preserving each bank’s existing stock of deposits.  Further suppose that deposit rates respond to changes in short-term competitive market rates according to:

Rd(t) = a + bR(t),

where Rd(t) = the deposit rate and R(t) = the short-term competitive market rate. It has been well documented that deposit rates are sluggish in response to changes in market interest rates, so that b < 1. A shock to interest rates impacts the value of the deposit franchise through discount rates and through changes in the competitive market-deposit market rate spread. Suppose that a = .005, b = .8, and that competitive market rates of all maturities are 5 percent. The slope coefficient of .8, is reasonably consistent with some academic results for MMDAs.[6]  The prevailing deposit spread is .5 percent.  If we assume that interest rates follow a random walk (the implicit assumption in most standard duration models), then the expected future spread is .5 percent over time, and we can find the present value of this spread simply by discounting the spread using a discount rate that reflects the risks of the deposit franchise.[7]  Under our deposit demand assumptions, the value of the deposit franchise can be found using the formula for the present value of a perpetuity. Using a risk premium of 3 percent in order to account for risks associated with future deposit volumes and spreads, the value of the deposit franchise would be .005/.08 = 6.25 percent of deposit balances.  If interest rates moved upward by 1 percent, the value of the franchise would become .007./.09 = 7.78 percent, and the percentage change in the value of the franchise would be 1.53 percent/6.25 percent = +15.51 percent.  Relative to the stock of deposits, the change in market value due to the deposit franchise is 1.53 percent.  Using a common measure of duration, such as modified McCauley’s duration (defined to be the percentage change in value divided by the change in interest rates), the deposit liabilities have an estimated duration of 1.53 years, which can be compared to the results that would have been obtained using the estimated “maturity” approach common to many bank market value models.

The relationship between the results obtained in this simple model and the results of typical bank models will depend upon the bank’s perception of the inelasticity of the deposit market, and how that translates into account “maturity”.  As has been noted, it is a stylized empirical fact that many retail deposit rates, interest bearing checking accounts, money market accounts, and even CDs, respond less than fully to market rate movements.  Thus, there is franchise value interest rate risk in virtually all retail deposit markets.  These risks are a matter of degree that depends on the size of the market and the responsiveness of rates and balances.  But in many cases, whether bank interest rate risk models capture any or all of these franchise risks depends upon whether the bank perceives the account to have a fixed maturity and the maturity assumed for those accounts deemed not to. If the account were a checkable account, in which deposit balances are typically very interest rate-inelastic, a “decay” or deposit “attrition” model might assign a maturity of 3-5 years to the account.  On the other hand, an account that behaves similarly to the one in this simple example might be assumed to be very short-term, since the deposit rate is reasonably responsive to short-term market interest rates.  If, for instance, the deposit balances were treated as 3 month liabilities at their current rate of 4.5 percent, then a 1 percent interest rate shock impacts the value of the deposit liabilities by less than .25 percent of the outstanding balance, and, therefore,  greatly understates the impact of franchise value risk in this illustration.  On the other hand, if the deposit balance is treated as a four year bond at 4.5 percent, the change in value is approximately 3.5 percent of the account balance, which greatly overstates the impact on the value of the firm.

Although the deposit attrition approach overestimates the interest rate risk of the deposit market in this illustration (due to the relative sensitivity of the deposit interest rate), this is a byproduct of the modeling assumptions. In fact, there need be no relationship between estimated deposit attrition and interest rate risk properly measured. Consider a market in which jobs and employees turn over quickly, and, therefore, so do deposits. A bank might find that, although individual deposit accounts turn over quickly in such a market, the total volume of deposits is relatively steady, even with very sluggish deposit interest rates.  In such a market, the bank’s interest rate risk exposure will be very high, yet maturity (duration) as estimated by attrition will be small.

In large part, the difference between franchise value interest rate risk and the interest rate risk or duration of demandable deposits as estimated by banks is due to the focus placed on the existing balance sheet under traditional interest rate risk models. Banks implicitly recognize a portion of the franchise risk when they estimate a longer-term duration for the demandable deposit liabilities currently on the balance sheet.  Note, however, that an appropriate measure of market duration should be based on forecasts of total market demand and the impact of interest rate shocks on market spreads.  Although it may be argued that basing today’s measures of interest rate risk on forecasts of future business is speculative, we have already done so when we estimated the attrition of the existing stock of balances, and there are very good reasons to believe that these estimates are of no higher quality than total market demand estimates.

Modeling the value and interest rate sensitivity of the deposit franchise is a complex exercise.  In the model above, a very simple interest rate dynamics and a static market for deposits was assumed.  In particular, assumed was a random walk process for interest rates.  Under the random walk hypothesis, a shock to interest rates today is permanent in the sense that it is embedded in all forecasts of future rates.  In more sophisticated models of the term structure, interest rates are frequently modeled as mean-reverting.  Under mean reversion, interest rates will tend to gravitate toward long-run mean values and, therefore, interest rate shocks are expected to decay over time.  To the extent that rate surprises decay (rates revert to the mean), this simple model of franchise value is likely to overstate the impact of an interest rate shock, given that deposit rate spreads are driven by the general level of interest rates.

To view the Table and Figures associated with this article go to http://www.westga.edu/~bquest/2005/bank/deposits.xls (This is an Excel document.)

In order to address the impact of interest rate dynamics on deposit franchise value, a simple model of U.S. Treasury bond rates was constructed using constant maturity Treasury interest rates from the Federal Reserve Board of Governors.  In the spirit of “one factor” term structure models, we estimated maturity-specific, linear regression models of longer-term treasury rates as a function of the “short” rate, assumed to be the 3 month Treasury bill rate.  Models were estimated for 6 month, 1, 2, 3, 5, 7, 10, 20, and 30 year rates.  Since the 20 year bond series began in October of 1993, we used monthly data from October 1993 to March of 2003 to estimate these relationships.  Then we took the full 3 month rate data set from January 1982 until March 2003 and estimated a simple first order autoregressive model (AR(1)) for the short rate, allowing for the possibility of mean reversion in interest rates.[8]  These results are described in Table 1. Note that our AR(1) model implies a long-run mean value for the short-term Treasury rate of 3.414 percent.  In addition, a 1 percent shock to the short rate starting from the long-run mean value will have an economic “half-life” of about 40 months.

Using these results, we then found the value of the deposit franchise, per dollar of initial deposits, as the present value of the short Treasury rate/deposit rate spread over time, again discounted at a constant premium over the current Treasury yield curve.[9]  In Figure 1, we display the value of the deposit franchise per dollar of outstanding deposits for a range of short rates based on the dynamics of the short rate from our AR1 model.  As before, the deposit rate is assumed to equal .005 + .8R(t).  In addition, we have graphed the value of the franchise fixing the short rate at its initial value (the “random walk” forecasting assumption).  This allows us to focus on the effects of the dynamics of the short rate on franchise value.  Figure 1 strongly suggests that the modeling of interest rate dynamics is very important to the estimated value of the deposit franchise and its interest rate risk.  Note that over a sizable portion of the interest rate range, the estimated value of the deposit franchise under constant rates is more than twice the estimate under mean reverting rates.  Importantly, the estimated sensitivity of the deposit franchise to interest rate changes is generally between 3.5 and 4 times as great under the constant rate assumption as under the estimated mean reversion. For comparison with standard banking practices, we computed the modified duration of a $1 liability with the same value sensitivity (in percentage terms) as the deposit franchise.  Under the random walk hypothesis, duration values ranged from approximately 2.5 years for low rates to approximately 2 years for higher rates.  Not surprisingly, under the estimated AR1 rate dynamics the deposit franchise value had a much a much smaller duration of approximately .5 years across the interest rate range.

Go to http://www.westga.edu/~bquest/2005/bank/deposits.xls

In Figure 2, we replicate this analysis using deposit rate sensitivity parameters a = .0075, b = .4.  These coefficients are more representative of less rate-sensitive interest-bearing checking accounts.  Franchise values are much higher in this case, reflecting larger spreads (and the fact that no attempt has been made to address deposit service costs).  Again, the impact of market interest rate shocks on deposit value is much greater under the random walk hypothesis than mean reversion.  Under the random walk, duration values ranged from approximately 7 years to 5.5 years, whereas under mean reversion values ranged from approximately 1.5 years to 1 year.  As this case illustrates, the less sensitive deposit rates are to movements in competitive market rates, the more important competitive market rate dynamics will be to value and duration modeling.

Go to http://www.westga.edu/~bquest/2005/bank/deposits.xls

So far our simple models have assumed a static deposit market.  However, deposit markets generally grow over time, reflecting growth in nominal income and wealth. In order to address the impact of market growth on deposit franchise value, we measured the value of the deposit franchise using rate sensitivity parameters a = .005 and b = .8, and assuming a 4 percent deposit grow rate.   The results are presented in Figure 3 along with the franchise value in the static market case. Not surprisingly, the value of the franchise is much greater when we incorporate market growth. Perhaps more importantly, the interest rate risk exposure of the franchise changes markedly. In this case, the absolute change in the value of the franchise per dollar of initial deposits is much greater when the market grows at 4 percent.[10]

Simple attrition-based models of deposit duration account for neither the partial response of deposit rates to movements in competitive market rates, nor exogenous account turnover and market growth.  More sophisticated FTP/ALM models address some, if not all, of these issues.  For instance, one approach to dealing with the relative sluggishness of deposit rates is to assign a “blended” FTP rate, in which a portion of the deposit balances are assumed to be fixed rate instruments and the remainder floating rate instruments.  Based on a deposit rate response parameter of 40 percent as in the example above, such a system would assign a fixed maturity FTP rate to 60 percent of the “core” deposits and 40 percent of the deposit base would be considered floating rate.[11]  The treatment of account attrition and replacement is then addressed through the maturity assigned to the fixed rate portion of the deposit balances.  In some models, account balances are assumed to be replaced as they leave the bank and,  therefore, a long maturity is assigned to the fixed rate balances.  In other cases, fixed maturity deposit balances are assumed to decay over a window that is typically 5 to 10 years.  Whether the FTP model is consistent with a model of franchise value depends on the consistency of the maturity assumption with the assumptions regarding deposit demand implied by the franchise value model, and the dynamics of interest rates.  If, for instance, it is assumed that deposits are replenished, and that the fixed rate portion of the deposit base is a very long-term instrument, then the interest rate risk exposure estimated under the FTP/ALM model will be very close to that resulting from a franchise value model in which deposit demand is assumed to be static and rate shocks are persistent. However, it is more common for banks employing these methods to assume that deposit balances decay.  This amortization assumption often reflects the perspective of the traditional duration framework, which focuses on the existing balance sheet.  An argument in support of amortization can be made based on “market obsolescence”.  In this argument, potential structural changes in the market can be expected to result in new deposit products and/or changes in the relationships between competitive market interest rates, bank rates, and deposit demand.  This is an important point that has not been addressed in academic work on models of franchise value.  However, rather than an ad-hoc adjustment to a poorly designed duration framework, conceptually, the right approached to this issue is to address the impact of potential structural change on the present value of future deposit demand.

“High end” FTP/duration systems typically employ very sophisticated models of interest rate dynamics and valuation methods.  One popular approach is the options-adjusted spread (OAS) model, originally created to value mortgages whose embedded prepayment option makes cash flow very interest rate sensitive, yet not amenable to standard bond option pricing techniques.  In OAS models, stochastic interest rate paths are generated based on the dynamics of interest rates implied by an arbitrage-free model of the term structure.[12]  The rate-sensitive cash flows associated with mortgages or deposits are estimated along each rate path and discounted back to the present using discount rates that are a fixed spread (the options-adjusted spread) to the risk-free term structure.  The average of the present values associated with each rate path is considered to be the economic value of the mortgage asset or deposit liability.[13]  Although these models have sophisticated interest rate dynamics, the quality of the time series modeling of rate-sensitive deposit market cash flows relative to a full-blown model of franchise value varies.  Better models capture the impact of interest rate dynamics on deposit interest spreads using estimates of the relationship between bank and competitive market rates from either bank- specific or industry-wide data.  However, the time series behavior of deposit quantities in these models often reflects the shortcomings of other methods.  OAS analysis was developed to value mortgage instruments and portfolios of mortgages, rather than a business franchise.  Thus, OAS models are often coupled with deposit attrition models that reflect behavioral assumptions regarding the existing deposit base rather than future deposit market demand.  As a result, these models suffer from many of the same shortcomings as the simple traditional models discussed above.[14],[15]

The discussion so far has been focused on what might be called the “time value” component of deposit market value and interest rate risk.  At this point, nothing has been said about credit risk and its impact on deposit value.  Further complicating the understanding of deposit market value and risks is the separation of credit risk from the deposit liability that results from deposit insurance.  When deposits are issued, the bank effectively engages in two distinct transactions.  It issues a liability that is credit risk-free, and it purchases an insurance policy from the FDIC. Obviously, the bank may profit from either. Given that more than 90 percent of U.S. banks have been paying no deposit insurance premium for several years, it is clear that banks have been profiting from deposit insurance.  Academic work to date has separated the two sources of value, and recent work on the duration of retail deposits has addressed the time value issue, implicitly ignoring the value of deposit insurance.  One of the shortcomings of the academic approach is that deposit profitability and, thus, the bank’s deposit pricing problem is couched in terms of the Treasury rate-deposit rate spread.  Bank pricing, on the other hand, should reflect the value of deposit insurance as embodied in bond market credit spreads.  Not surprisingly, banks recognize the value of deposit insurance indirectly through FTP.  Banks typically use either the LIBOR/Swaps yield curve or the senior unsecured borrowing curve, both of which reflect credit risk, as the basis for FTP.  In theory, the crediting curve should reflect the credit risk exposure assumed by the FDIC given its priority position.  Unfortunately, this yield curve is not directly observable.[16]  I n practice, the FTP curve is chosen to be a readily observable yield curve that is a proxy for the marginal cost of unsecured bank borrowing.

In addition, the separation of the credit risk from the deposit liability implies that the credit risk and time value components of the deposit crediting rate need to be determined independently.  Banks typically credit deposits with yields that reflect the estimated term of the liability. Thus, a 5 year CD will receive the 5 year rate from the FTP curve, under which it is assumed that the credit risk premium is locked in for 5 years. If, for instance, the FDIC re-priced deposit insurance fully (i.e., to be consistent with credit risk premia in the bond market) once per year, the credit risk premium component of the deposit crediting rate should come from the one year credit spread.  In theory, the FDIC can re-price deposit insurance continuously, and of course member banks can choose to terminate coverage at any time.  However, the FDIC’s pricing of deposit insurance is currently based on a reserve standard, in which deposit insurance premia are essentially fixed until the insurance fund reaches a particular level. T hus, the FDIC’s pricing practices are retrospective (reflecting past period’s bank failures) and need not track current market pricing of credit risk.  In addition, pricing to a reserve standard over time implies that the FDIC premium recovers realized losses, but no credit risk premium.  Recent academic work suggests that realized credit losses account for no more than 40 percent of the total credit spread observed in the corporate bond market.  In many respects, the credit component of the FTP/valuation problem is like that of the time value component discussed above.  Just as the response of bank deposit rates to changes in competitive market rates is sluggish and incomplete, so is the FDIC’s response to changes in the market price of credit risk.  Currently, there is virtually no academic work on the value of deposit insurance that is directly applicable to this particular FTP problem, and this is certainly an area for future consideration.

Traditional valuation and interest rate risk models built primarily for use in highly competitive financial markets, are often inappropriately applied in retail financial markets, such as markets for small bank deposits.  Shocks to current market interest rates impact the profitability of retail banking markets, thereby impacting bank franchise value.  Because demandable deposits balances implicitly mature and re-price continuously, it is the franchise value interest rate risk in these markets that should be incorporated into bank FTP/ALM practices.  Many bank models, reflecting traditional duration tools, incorrectly focus on estimates of the “maturity” (attrition) of such deposits.

The above analysis demonstrates that the implicit (and poorly understood) assumptions regarding interest rate dynamics and market demand found in common bank models are likely to be very important when measuring value and interest rate risk.  By their nature, these assumptions are most often ad hoc, and it is highly recommended that such assumptions be reviewed and addressed up front.  Important issues, such as the impact of market “obsolescence” on the value of deposit markets, have not been addressed in the literature and provide an opportunity for future research.

Finally, the impact of deposit insurance on deposit franchise value and interest rate risk is not well understood.  Banks implicitly recognize the value of deposit insurance when they choose FTP curves that reflect the marginal cost of bank borrowing.  However, the “right” yield curve is not directly observable.  The separation of the pricing of deposit insurance from the pricing of the deposit liability under deposit insurance implies that the valuation of deposits should reflect the pricing practices of the FDIC as opposed to the term of the liability as is the standard approach among banks.  However, deposit insurance rates respond sluggishly and incompletely to changes in the competitive market pricing of credit risk.  Thus, the deposit insurance valuation problem resembles the demandable deposit valuation problem.  There has been little work applicable to this set of problems, and future research in this area could prove quite valuable.

Elton, E., M. Gruber, D. Agrawal, and C Mann, 2001, “Explaining the Rate Spread on Corporate Bonds”, Journal of Finance 56, pages 247-277.

Hutchison, D., and G. Pennacchi, 1996 "Measuring Rents and Interest Rate Risk in Imperfect Financial Markets”, Journal of Financial and Quantitative Analysis, September 1996, pages 399-417.

Hutchison D., 1995 "Retail Deposit Pricing: an Intertemporal Asset Pricing Approach", Journal of Money, Credit, and Banking, February 1995, pages 217-231.

Jarrow, R, and D. van Deventer, “The Arbitrage-Free Valuation and Hedging of Demand Deposits and Credit Card Loans”, Journal of Banking and Finance 22, March 1998, pages 249-272.

Judge, G., W. Griffiths, R. Hill, and H. Lutkepohl, 1985, The Theory and Practice of Econometrics, Second Edition, John Wiley and Sons, New York.

Kaufman, G., 1984, "Measuring and Managing Interest Rate Risk: A Primer", Economic Perspectives, Federal Reserve Bank of Chicago, 8, 16-29.

 

 

[1] Special thanks go to Darrell VanAmen, Treasurer Home Street Bank, Ron Mishler and Mike Goad, formerly Treasurer and Senior ALM Manager Old Kent Financial Corporation, and Bob Ziska, First Manhattan Corporation., for many fruitful banking discussions.

[2] Some banks do not use FTP assumptions in their ALM modeling, but it is considered economically correct as well as a “best practice” for ALM processes to reflect the assumptions of the internal profitability system.

[3] An obvious candidate on the asset side of the balance sheet is the market for credit card receivables.  Perhaps less obvious are markets such as the market for consumer CDs, in which the level of profitability can change markedly even though rates are relatively responsive to changes in competitive market conditions.  Hutchison (2003) suggests that for banks with large CD bases, franchise value is likely to be significant.

[4] Of course, there are many instruments in the competitive markets whose cash flows are also interest rate-dependent.  True floating rate instruments periodically re-price based on competitive market rates and can be treated as short-term instruments for duration purposes.  Many options-embedded instruments such as callable bonds can be priced with standard option pricing techniques such as lattice methods.  Other interest-sensitive instruments such as mortgages, whose cash flows are “path dependant”, are more difficult to model.  Techniques such as option adjusted spread models, designed for mortgages, have been adapted for use in deposit valuation modeling in more advanced FTP and asset/liability models.  (See the discussion below. )

[5] As Jarrow and Van Deventer point out, the value of the deposit franchise is just the present value of the future deposit cash inflows and outflows.  However, bankers typically view value in terms of the spread between deposit rates and competitive market rates, and the simple models used in this paper approach franchise value in terms of the present value of rate spreads over time.

[6] See, for instance, Hutchison and Pennacchi (1996).  Note that the models in this and following sections are meant only as illustrations. Modeling the time series behavior of bank and competitive market rates as well as the demand for deposits and the valuation framework are quite complicated both theoretically and empirically.

[7] A random walk is a time series for which the expected future value of the series or “best forecast” is just the current value of the series.  Note that the risks associated with the deposit franchise

[8] In an AR(1) model, next period’s interest rate is a linear function of the current rate, plus a random error term: r(t+1) = a + br(t) + e(t).  When ?b < 1, r(t) will tend to a long-run mean value of a/(1-b).

[9] It may be argued that deposit profitability should be measured relative to the marginal cost of funding rather than Treasury rates.  Implicitly we are assuming that deposit insurance has zero net present value.

[10] An upward shock to interest rates impacts franchise value in two ways.  First, holding discount rates fixed, franchise value increases as spreads widen.  Second, higher discount rates reduce the value of future deposits and franchise value holding spreads constant. In our illustration, the spread effect dominates.  Depending on the model, rapid growth could result in the discounting effect dominating because when growth is rapid more of the franchise value is the result of longer-term cash flows, whose present value is quite sensitive to the level of interest rates.

[11] Core deposits in this context are deposits net of seasonal balances.  For simplicity we have ignored seasonal balances in our models.

[12] Most commonly, rates paths are based on the “risk-neutral” probabilities associated with the model.

[13] In mortgage markets, such as the market for mortgage-backed securities in which market data are readily available, prices are used in OAS models to compute the option-adjusted spread.  The spread is often used as a “rich/cheap” index.

[14] To illustrate, the Quantitative Risk Management (QRM) deposit FTP model marries a sophisticated OAS framework to user -defined deposit market withdrawal functions.

[15] To the best of this author’s knowledge, the only commercially available model of deposit franchise value and duration based on modern asset pricing techniques is the proprietary KRM model developed by Professor Robert Jarrow.

[16] Alternatively, the difference could be captured through capital allocation. If the FTP curve used to credit the deposit unit represents a lower priority position than that of the FDIC, then in theory a capital charge should be applied to the deposit unit.