Donald J. Smith

An Economic Theory of a Credit Union

THE majority of research to date on CUs has been empirical (cf. Cargill [1] and Kidwell and Peterson [7]), yet there is serious need to develop a theoretical framework of CU behavior that incorporates their unique characteristics. A CU is essentially a financial intermediation cooperative. However, the standard theoretical treatments of financial intermediaries (cf. Meyer [8]) and cooperative enterprises cannot be directly applied to model credit union behavior. There are two principal characteristics of CUs that prevent this: First, in a CU (and cooperatives in general) the members are both the owners of the organization and the consumers of its output or suppliers of its input. One cannot simply assume that the members seek to maximize the profit generated by their transactions with the CU irrespective of the price and quantities of those same transactions, thus models of a financial firm based on profit maximization cannot be directly translated to a CU environment. Second, in a CU the membership provides both the demand for and supply of loanable funds. The CU then intermediates between its member-savers and member-borrowers. This heterogeneity is an inherent source of conflict between members. Clearly, a CU cannot simultaneously maximize its dividend rate for savers and minimize its loan rate for borrowers. Since most theoretical models of cooperative enterprises assume a homogeneous member objective, they are not generally applicable to CUs. There are two basic requirements for a framework to model CU behavior. First, the specification of the objective function should focus on the value of CU participation to the members. This value should include the prices and quantities of transactions as well as any profit that results. Second, the analysis should explicitly consider the possibility of conflict among members, and the resolution of that conflict being a preference to either the borrowers or savers. The existing literature on CUs contains a wide variety of objective functions. Hempel and Yawitz [5] ignore the owners-are-consumers issue and simply contend that CUs, like other financial intermediaries, should maximize profit. Most writers, however, recognize that profit-maximization would be a somewhat incongruous objective for an organization that typically labels itself not-for-profit. Murray and White [9] use cost minimization subject to an output constraint. Keating [6] employs the managerial discretion approach by maximizing the managers utility function subject to minimum member benefit constraints. Taylor [11, 12] suggests that the CU should minimize the difference between its average loan rate and savings rate paid. Smith [10] argues that the CU should

Credit Union Rate and Earnings Retention Decisions Under Uncertainty and Taxation

This paper presents a model of credit union loan and deposit rate setting when net income flows are uncertain and subj ect to taxation. Optimal rates are chosen to maximize the expected va lue of a performance measure based on a comparison of the credit unio ns rates to alternative rates, subject to a probabilistic constraint on the net change in capital reserves relative to a capital adequacy standard. Taxation will alter the end-of-period trade-off between th e change in capital reserves and the immediate distribution of surplu s, and would likely affect credit unions in a nonuniform manner and p erhaps be regressive in nature. Copyright 1988 by Ohio State University Press.

Recent Innovations in Interest Rate Risk Management and the Reintermediation of Commercial Banking

0 A dominant theme of commercial banking in the 1980s has been the search for off-balance sheet, feebased income to improve return on equity. As money center and large regional banks recover from the burdens of the international debt and energy loan crises, new product lines are being sought which meet those criteria. One promising line is Interest Rate Risk Management (IRRM). Commercial banks have become market makers in IRRM products such as forward rate agreements and interest rate swaps, caps, collars, and floors. These products are often versions of, and companions to, instruments that are used to manage a firms foreign exchange risk exposure. The movement toward market making in IRRM products represents a new form of bank intermediation, a form distinct from the classic function of transforming household savings into corporate borrowings. In this new role commercial banks intermediate be-

The Borrower's Choice between Fixed and Adjustable Rate Loan Contracts

Previous research indicates that key variables in the choice between fixed and price index-linked debt are the covariances between inflation and real income and between inflation and the real value of the asset financed by the debt. This model extends those results to adjustable rate loan contracts and examines the impact of covariance between the real interest rate and, in turn, real income and real asset values. Positive (negative) covariance between those terms shifts preference toward the adjustable (fixed) loan contract. Copyright American Real Estate and Urban Economics Association.

Default Risk and Innovations in the Design of Interest Rate Swaps

The emergence of an active interest rate swap market has transformed the nature of corporate debt issuance and risk management. Many firms nowadays routinely use swaps to adjust their ratio of fixed to floating rate debt when there is a change in managements view on interest rates. For instance, if it is felt that market rates have bottomed, a firm could raise that ratio by entering a swap to pay a fixed rate and receive the prevailing level of some reference rate, such as LIBOR (London Interbank Offer Rate). There is, however, default risk on the swap. In this example, the risk is that the counterparty defaults when the fixed rate on a replacement swap is higher than the one originally contracted. Potential default risk at origination is bilateral in that each party to the agreement must consider the riskiness of the other. At any point in the lifetime of the swap, the actual default risk is unilateral in that the swap would have positive economic value to only one of its counterparties.

Moving from an Efficient to a Behavioral Market Hypothesis

Behavioral finance typically is introduced in investments courses in the context of the efficient markets hypothesis (see, e.g., the widely used textbooks by Bodie, Kane, and Marcus [2002] and Reilly and Brown [2003]). This note offers a diagrammatic approach to “position” visually behavioral finance between the information available to market participants and their investment decisions.

Mind the Gap: Using Derivatives Overlays to Hedge Pension Duration

Recent legislation and accounting rule changes motivate defined-benefit pension plans to manage the interest rate risk arising from volatility in their liabilities, as measured by either the accumulated benefit obligation (ABO) or the projected benefit obligation (PBO). For either measure, asset portfolios comprising equity and fixed-income bonds usually have much lower average durations than do liabilities. This article discusses how interest rate derivatives overlay strategies can be used to reduce or eliminate the negative duration gap. A theoretical model is developed to show how to calculate the ABO and PBO measures and their duration statistics. Recent legislation and accounting rule changes—in particular, the U.S. Pension Protection Act of 2006 and Financial Accounting Standard (FAS) No. 158—motivate sponsors of defined-benefit (DB) pension plans to manage the interest rate risk arising from volatility in their plans’ liabilities, as measured by either the accumulated benefit obligation (ABO) or the projected benefit obligation (PBO). ABO, a measure of the sponsor’s current legal liability, is the present value of retirement benefits based on current wages. PBO is a larger amount because it is based on the estimated future wage level at the time of retirement. In the past, the plan sponsor recognized a funding deficit on its balance sheet only if the fair value of plan assets was less than the ABO liability. Now, under FAS No. 158, PBO is used to determine the funding status of the DB pension plan. In practice, the interest rate risk of an asset or liability is measured by its duration statistic, which is a measure of the change in value given a change in interest rates. The essence of the risk management problem facing the typical DB pension plan is that the average duration of its asset portfolio—which is usually invested about two-thirds in equity and one-third in fixed income—is much less than the estimated duration of either its ABO or PBO liability. Thus, a significant negative duration gap exists: Lower interest rates increase asset values much less than they increase liabilities. In this article, we develop a theoretical model (based on a representative employee) to demonstrate how the ABO and PBO liability durations are estimated. A promising method to decrease the interest rate risk facing a DB pension plan is a derivatives overlay strategy that reduces or eliminates the negative duration gap without changing the asset portfolio. Derivatives—in particular, interest rate swaps or options on swaps (“swaptions”)—transform the risk profile of the overall plan while leaving the existing asset allocation (i.e., investments in equity and fixed income) intact. For example, we show that a receive-fixed interest rate swap has a positive duration. The plan manager can choose the requisite notional principal on the swap to close the negative duration gap fully or partially. We present numerical examples to illustrate this calculation. Another derivatives overlay strategy is for the DB pension plan to buy a “receiver swaption.” The plan pays the premium and has the right to enter into an interest rate swap as the receiver of the fixed rate. If interest rates fall, the value of the swaption goes up, thus offsetting the increase in the plan’s liability. A related strategy is for the plan to enter into a “swaption collar” whereby a “payer swaption” is sold to provide the premium to offset the cost of the purchased receiver swaption.

Valuing Interest Rate Swaps UsingOvernight Indexed Swap (OIS) Discounting

The role of LIBOR in interest rate swaps and other financial derivatives is to be the effective “riskless” rate, based on the premise that while banks that could borrow in the market at LIBOR flat were not completely risk-free, the rate corresponded to a high credit quality, approximately AA. The 2008 financial crisis left most banks financial weakened, including the largest banks, which provide the quotes from which LIBOR is computed. LIBOR spiked upward following the Lehman bankruptcy and was well above other “riskless” rates, notably the overnight indexed swap (OIS) rate. Since that time, much of the over-the-counter (OTC) interest rate derivatives market has shifted over to discounting at OIS rates. Since these are lower than LIBOR, one result is that when the floating leg of a LIBOR-based swap is repriced, it will not be valued at par with OIS discounting. This issue is becoming increasingly important, as swaps and other interest rate derivatives are transitioning to central clearing. In this article, Smith clarifies the issues and works through some examples to illustrate the size of the effects involved.

Bond portfolio duration, cash flow dispersion and convexity

Immunization is a well-known fixed-income strategy to lock in a target rate of return over a known investment horizon. This is accomplished by structuring the bonds so that the duration of the portfolio matches the time horizon and then rebalancing the portfolio to maintain the match as time passes and yields change. The structural risk to the strategy can be measured by the cash flow dispersion or by the convexity of the immunizing portfolio. The general relationship between the duration, cash flow dispersion and convexity statistics for any date in the current period is derived in the article. Although both statistics measure the risk, convexity is significantly easier to implement in practice.

Synthetic Floating‐Rate Debt: An Example of an Asset‐Driven Liability Structure

An asset‐driven liability (ADL) structure is analogous to a liability‐driven investment (LDI) strategy. In both cases, the intent is to reduce the risk arising from a mismatch of assets and liabilities by aligning the interest rate sensitivity of cash flows on both sides of the balance sheet. Increasingly, defined‐benefit pension plans have adopted LDI strategies that reduce their equity assets and increase the average duration of their debt assets to better match the typical long duration of their retirement obligations to its employees. To illustrate the concept of ADL, the authors use the example of a corporate issue of traditional fixed‐rate debt that is transformed into synthetic floating‐rate debt using an interest rate swap (in which the corporation receives the fixed rate on the swap and pays at money market reference rate like three‐month LIBOR). The use of such long‐term, floating‐rate debt reduces interest rate risk when the firm has operating revenues that are positively correlated to the business cycle. However, a problem arises in that there is limited demand for such debt securities from institutional investors, many of which, because of LDI guidelines, prefer long‐term, fixed‐rate securities. Derivatives provide a way of resolving this mismatch between issuer and investor interests. In the article, the authors present a detailed example of the cash flows on the “receive‐fixed” interest rate swap (and its valuation for financial reporting) to show how the synthetic ADL debt structure obtains the desired outcome.