Interest rate derivatives and asset-liability management by commercial banks

New England Economic Review, Jan-Feb, 1995 by Katerina Simons

One refinement of a simple maturity gap measure calculates a sequence of periodic maturity gaps, such as a series of three-month gaps for five years. This method has the advantage of more precision, although periodic gaps may be difficult to interpret, especially if they result in a long sequence of alternating negative and positive gaps. On the quarterly Call Reports, banks are required to report the book value of all interest-bearing assets and liabilities, classified according to whether they mature or have interest rate reset dates within the next three months, three months to one year, one to five years, or more than five years. Accordingly, one can calculate the book value of the corresponding periodic gaps for all reporting banks on a quarterly basis.

Figure 1 shows two profiles of average periodic gaps (interest-earning assets less interest-bearing liabilities within the period, divided by total interest-earning assets) for all U.S. commercial banks with assets greater than $100 million. The first gap profile is for 1988 (the earliest year for which the classifications reported are consistent with the later periods) and the second is for 1993.

The profiles for both years show a negative gap for very short maturities (under three months) and positive gaps thereafter. The gaps have a characteristic humpback shape, reflecting the biggest asset sensitivity in the one- to five-year period. The 1993 profile has a smaller "hump" in that period relative to the 1988 profile, but a larger positive gap for the longest maturities. Both gaps imply that the average bank in both years issued shorter-term liabilities to fund longer-term assets. Thus, in both years the average bank would suffer a loss in interest income when interest rates rose, because the bank would have to pay higher interest on the funds it borrowed, while the interest it received on assets would remain the same.

Ideally, one would want to reduce the measure of interest rate exposure to one number, showing how net interest income would react to a given change in the market interest rate. To provide such an estimate, the concept of "duration" was developed (Macaulay 1938). Duration represents an account's weighted average time to repricing, where the weights are discounted cash flows. The duration gap is the difference between the duration of assets, weighted by dollars of assets, and the duration of liabilities, weighted by dollars of liabilities. The larger the duration gap, the more sensitive the bank is to the changes in the market interest rate. Box 2 shows a simple example of calculating duration gap.

However, duration gap is an accurate measure of the interest risk only if the term structure of interest rates shifts in parallel, or if any departures from parallel shifts are known in advance. To the extent these conditions are violated, as they often are, interest rate risk cannot be summed up simply in one number.

II. Managing Interest Rate Risk with Derivative Contracts

Traditionally, banks controlled interest rate risk by adjusting the maturity or repricing schedules of their assets and liabilities. For example, a bank wishing to lengthen the duration of its assets can add long-term government bonds to its securities portfolio. More recently, however, many banks realized that they could accomplish the same goal more cheaply and efficiently by entering into plain-vanilla swaps, where they pay a floating rate, usually denominated in London Interbank Offer Rate (LIBOR), and receive a fixed rate, usually the Treasury rate of equivalent maturity plus a premium. A liability-sensitive bank, on the other hand, can enter into a swap where it pays a fixed rate and receives a floating rate. The bank can also use a "basis" swap, where both sides pay floating rates but the index rates are tied to the bank's cost of funds and lending rate. Specifically, the bank would pay the prime rate and receive LIBOR.