A cross-sectional investigation of the net interest margins of commercial banks

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FACULTY WORKING
PAPER NO. 1293

A Cross-Sectional Investigation of the Net
Interest Margins of Commercial Banks

Morgan J. Lynge,Jr.

College of Commerce and Business Administration
Bureau of Economic and Business Research
University of Illinois, Urbana-Champaign

BEBR

FACULTY WORKING PAPER NO. 1293
College of Commerce and Business Administration
University of Illinois at Urbana-Champaign
October 1986

A Cross-Sectional Investigation of the Net Interest
Margins of Commercial Banks

Morgan J. Lynge, Jr. , Associate Professor
Department of Finance

ABSTRACT

Recent research investigating the interest rate risk exposure
o-f cornfnerciai banks has declared banks to be well hedged, i.e.
they will be little a-f-fscted by changes in market rates of
interest. These studies examine time series data -for a sample o-f
commercial banks and -find that the measure o-f income ar net
interest income does not vairy with interest rates over time.
This paper examines a sample of banks cross— secti onal 1 y to
investigate the range of interest rate risk exposure among banks
of different sizes and in different markets. The data for 19S4
and 19S5 show that, an average, banks have positive gaps
between rate sensitive assets and liabilities, but that a
significant range of gap positions exists. Empirical results
indicate that balance sheet measures such as gap Brs not
reliable measures of interest rate risk in that they a.rs not
closely related to subsequent changes in net interest margins.

A CROSS-SECTIONAL INVESTIGATION OF THE NET INTEREST
MARGINS OF COMMERCIAL BANKS

I. INTRODUCTION

The volatile economic and financial environment of the last decade
has given rise to an increased awareness of and concern about the
degree to which financial institutions are exposed to interest rate
risk. While this concern has had its greatest focus on savings and
loan associations, all financial intermediaries are potentially sub-
ject to the effects of widely varying interest rates. In this paper
the interest rate risk, exposure of commercial banks is investigated.
Bank net interest margins (NIMs) are examined as a measure upon which
the ex post outcomes of interest rate movements are reflected.

Banks, as financial intermediaries, issue liabilities with differ-
ent characteristics than the assets they acquire. One dimension of
these differences is term to maturity with the classic description
being that banks borrow (issue liabilities) short and lend (acquire
financial assets) long. To the extent that this characterization is
true, banks therefore assume both liquidity and interest rate risk in
performing this term structure intermediation. If the opposite cha-
racterization were the case (i.e., borrow long and lend short) banks
would no longer be exposed to liquidity risk, but would still have
interest rate risk. The increase in the use of variable rate assets

(and to a much lesser extent liabilities) has no effect on liquidity
risk, but alters the focus of interest rate risk exposure from term to
maturity to the time that must elapse before a variable rate asset
(liability) may be repriced when market rates of interest change. The

-2-

recent removal of Regulation Q interest ceilings on deposit liabilities
has increased banks ' potential exposure to the effects of changing
interest rates.

To what degree are banks exposed to interest rate risk? Regulatory
efforts to avoid bank failure have been aimed primarily at asset
quality and capital adequacy rather than interest rate risk exposure.
However, there has been an increasing focus by managers and regulators
on measuring the interest rate risk exposure of banks. However, an-
ticipating the conclusion of this paper, the device often used to
measure interest rate risk, the gap between interest sensitive assets
and liabilities, may be a tool with little predictive ability. If the
gap measure is not closely associated with the ex post outcomes of
interest rate variation, than it should not be relied upon by managers
or by regulators, and a better measure needs to be developed.

In Section II measures of interest rate risk exposure are examined
and NIM is decomposed into its several elements; Section III provides
a description of the sample of commercial banks and the manner in
which balance sheet and income statement data are used; empirical
results are discussed in Section IV; and Section V contains conclu-
sions, implications and indicates further research needed.

II. INTEREST RATE RISK EXPOSURE AND NIM

As an intermediary, a bank operates in various types of markets.
In (retail) deposit markets a bank must make available deposit liabil-
ities that satisfy the liquidity or term preferences of its customers.
In loan markets borrowing customers also have specific maturity needs.
The balance sheet that results from this activity is likely to leave

-3-

the bank with a position that exposes it to interest rate risk. In
other cash markets, such as securities and purchased funds markets, a
bank has some discretion in issuing liabilities and acquiring assets
with desired maturities. In order to arrive at an overall desired
exposure to interest rate risk, a bank can manipulate discretionary
asset and liability maturities.

However, the achievement of a desired exposure via activity in
cash markets has costs. Purchasing funds at a specific maturity to
meet interest rate risk exposure objectives may not minimize the cost
of funds. In other words, the benefits of adjusting risk exposure to
the desired position must be compared to the costs of making the ad-
justment. In addition, banks with established channels for purchasing
funds and with borrowing customers with diverse maturity needs may be
able to adjust interest rate risk exposure easier or more cheaply than
banks without these conditions. Since large banks generally have more
diverse asset and liability markets, these banks may be expected to
adjust their exposure more quickly to desired levels. Graddy and
Kama (1984) have found evidence that this is the case.

This discussion leaves open the question of what a bank's desired
interest rate risk exposure is. An extensive literature has developed
that applies the concept of immunization to financial institutions
[Bierwag and Toevs (1982) and Kaufman (1984)]. Using information on
the durations of assets and liabilities a bank can establish an immu-
nized position that gives it zero exposure to movements in interest
rates. Whether or not this is the desired exposure, it establishes a
benchmark position against which departures from the immunized position

-4-

can be compared [see Bierwag, Kaufman, and Toevs (1983)]. If a bank
has confidence in its interest rate forecasts, nonimmunized positions
would be optimal.

Another issue that separates academic treatment of interest rate
risk from observed practice is the choice of the variable to be immu-
nized. For a bank that has the objective of maximizing firm value,
the strategy should be to immunize the market value of the firm from
changes in interest rates. Most banks seem to be concerned vd.th the
impact of interest rate risk on cash flows, such as measures of income
or net interest income. Since most banks do not have market traded
stock, and since most regulation is cast in terms of book value, this
may be a rational approach [Santomero (1984)].

Interest rate risk arises because, for a bank, as interest rates
change, the rates earned on assets held in the portfolio may change at
different times than rates paid on liabilities. This happens even if
asset and liability rates are perfectly correlated because of the con-
tractual characteristics of the assets and liabilities (term to matur-
ity or repricing intervals). In terms of interest flows, interest
revenues and interest expenses are not perfectly correlated, producing
variability in net interest income due to changes in market rates of
interest.

With a focus on net interest income (Nil) many banks measure the
degree of interest rate risk exposure by relating the dollar amounts
of assets and liabilities whose returns or costs will change if market
rates of interest change. This relationship may be the difference

-5-

between these quantities, called the gap [Toevs (1983)], or the ratio
of these quantities, called the gap ratio, as shown in (1) and (2):

$GAP = $RSA - $RSL (1)

GAP RATIO = $RSA/$RSL (2)

where $RSA and $RSL indicate the dollar amount of rate sensitive
assets and liabilities. The term "rate sensitive" must be specified
and usually means the asset (liability) either matures or can be re-
priced within a specified time period, often one year. The interpre-
tation given to these measures is that a $GAP of zero (GAP RATIO of 1)
indicates a hedged position, that is Nil will not change as interest
rates change. Any $GAP that is nonzero (GAP RATIO not equal to 1)
represents a balance sheet position that is exposed to interest rate
risk, i.e. , Nil will vary as interest rates change.

These measures of interest rate risk exposure omit the considera-
tion of other factors impacting on the level or variability of Nil.
Most bank annual reports present an ex post analysis of variances in
Nil by calculating the impact on Nil of (1) changes in the volume of
earning assets and interest bearing liabilities and (2) changes in the
mix of earning assets and interest bearing liabilities as well as (3)
changes in interest rates. Impacts of (1) and (2) on Nil are not
handled in the $GAP or GAP RATIO measures.

In the cross sectional analysis below. Nil will be converted to net
interest margin or NIM which is NII/EA where EA is earning assets. The
definition of NIM can be expanded to illustrate the influences of

-6-

additional variables besides market rates of interest. The definition
of NIM is:

MM = ^^^ = I'^t Income - Int Expense _ rEA - ilBL .„.

EA " EA " EA ^^^

where

r = average interest rate earned on earning assets;
i = average interest rate paid on interest bearing liabilities;
EA = average earning assets; and
IBL = average interest bearing liabilities.
Equation (3) can be rewritten as:

r EA - i IBL r EA - i.IBL,

^TTM ss ss.LL LL ...

"^" EX * E5 <*'

where the s subscript represents assets and liabilities that mature or
are repricable in some short term period and their associated rates;
the L subscript represents the remaining earning assets, interest
bearing liabilities, and their associated average rates. Over some
short time horizon, allowing only interest rates to change, a bank's
NIM will change only due to changes in the first term of (4),
Equation (4) can be manipulated to become (5):

GAP GAP IBL IBL

where GAP and GAP. are as defined in (1) for short term and long term

S Li

earning assets and interest bearing liabilities respectively. Equa-
tion (5) expresses a bank's NIM as a function of its balance sheet
gaps for short term and long term assets and liabilities, each

-7-

expressed as a percentage of earning assets, the extent to which its
earning assets are funded by interest bearing liabilities, and the

interest rates and interest rate spreads it experiences. If GAP is

s

zero, NIM can still be affected by any change in the spread (r -i ) or

s s

by a change in the funding of earning assets by short term IBL.
Flannery and James (1984a and 1984b) and Tarhan (1984) use measures
similar to GAP /EA to proxy the* rate sensitivity of a bank's balance
sheet position, although each chooses a different scaling variable.

III. SAMPLE DATA AND METHODOLOGY

The data used in the empirical analysis is for a sample of banks
drawn from the Call and Income Reports of all insured commercial banks.
The sample consists of 404 banks drawn randomly from each of the five
size groups shown below (using end of year 1984 total asset size).

Sample Banks as

Size

Number of

a

% of

All Banks

Class

Asset Size Range

Sample Banks

in

this

Size Class

SIZE 1

> $1 billion

52

19%

SIZE 2

$300 mil - $1 bil

57

11

SIZE 3

$100 - $300 mil

92

6

SIZE 4

$50 - $100 mil

105

4

SIZE 5

$25 - $50 mil

98

3

The empirical work below assumes that bank managers establish a
balance sheet position at the beginning of a period based on the
bank's market position, forecasts of interest rate movements, and the
resulting desired exposure to interest rate risk. Therefore, balance
sheet variables measuring exposure to interest rate risk such as
measures of gap or funding are calculated as of the beginning of the
period being examined. NIM is calculated as the realized value for

-8-

the period. The sample data are for four six-month periods over the
two years 1984 and 1985.

The question of what specific balance sheet items are considered
as "short" remains unresolved. The measures of interest rate risk
exposure should be related to the specific planning horizon of the
management of the bank. For example, if the planning horizon is three
months, then $RSA and $RSL in equations (1) and (2) should be assets
and liabilities which are potentially repricable within the next three
months. All other balance sheet items are, by definition, long; a
change in interest rates during the next three months will have no
impact on the interest revenue or expense generated over the next
three months by these existing "long" assets or liabilities.

If one does not know the relevant planning horizon of individual
banks, one year is often assumed to be the cutoff point for defining
short assets and liabilities. In earlier work this assumption was
required by the availability of bank balance sheet data. Flannery and
James (1984a and 1984b) and Tarhan (1984) use a one year horizon to
construct their interest rate risk exposure measures. Since 1983,
banks have been required to report maturity and repricing data for
selected assets and liabilities on Schedule RC-J of the call report.
The selected assets include almost all of a bank's earning assets.
Selected liabilities reported in RC-J exclude many deposit accounts
for which maturity or repricing dates are undefined or uncertain. How
to account for liabilities like NOW and super NOW accounts, MMDAs , and
even passbook savings accounts have provided empirical fog over the
measurement of interest rate risk. Flannery and James (1984b) infer

-9-

the effective maturities of demand, savings, and small time deposits

by using market data on bank, stock prices. Their results indicate

that these items behave more like "long" liabilities in that when

market interest rates change, the bank's effective cost of funds from

these liabilities changes by only a small amount.

Because of the results of Flannery and James (1984b), "short"

liability measures used here include only the Schedule RC-J liability

items. In the empirical section some estimates are obtained using a

GAP which includes super NOWs and MMDAs as short term interest sensi-
s ^

tive liabilities. To anticipate the results, little explanatory power
is gained by using this alternate measure of gap. A one year horizon
is only a crude measure of interest rate sensitivity since it weights
balance sheet items that reprice in 30 days equally with those that
reprice in 350 days. With Schedule RC-J data it is possible to calcu-
late a less crude gap measure by weighting the dollar amount of assets
(liabilities) in each maturity or repricing bucket by the average
maturity for the bucket to obtain a weighted average gap measure.
This alternate gap measure is also used in the empirical work.

This study uses six-month periods as the assumed planning horizon
of sample banks. Therefore, four six-month periods are examined for
the two-year period 1984-1985. During this two-year period interest
rates exhibited a variety of behaviors (see Chart 1). For the first
eight months of 1984 short term interest rates rose. Over the next
five months, until February 1985, rates fell to levels below those in
January 1984. Early 1985 saw a slight rebound in rates followed by
another decline until about June 1985. The last six months of 1985

-10-

where characterized by relatively flat rates. Long term rates fol-
lowed a similar but less volatile pattern. Thus this two year period
allows the examination of NIMs during rising, falling, and relatively
stable interest rate periods.

Ordinary least squares is used to identify cross-sectional differ-
ences in bank behavior among banks of different sizes during periods
of different interest rate movements. Much of the recent literature
examining bank reactions to different interest rate movements con-
cludes that commercial banks are relatively well hedged, that is,
their exposure to interest rate risk is small [Flannery (1981),
Flannery and James (1984a, 1984b), Hanweck and Kilcollin (1984),
Mitchell (1985)]. In this study this conclusion is tested for banks
of different sizes and with different balance sheet positions. While
it may be the case that the banking system is hedged in the aggregate,
it remains an open question as to the range of interest rate risk
exposure being assumed by individual banks.

IV. EMPIRICAL RESULTS

The average values reported in Table 1 provide a partial descrip-
tion of the sample of commercial banks used for the empirical work.
For the four six-month periods, NIM declined until the last half of
1985. The short gap position of the banks (defined over the tradi-
tional 12 month horizon here) varied considerably over the sample
period. Whether these variations are due to managerial choice or due
to changes in nondiscretionary balance sheet items is not clear. On
balance the sample banks have net $RSA positions, or positive gaps at
the short end. The share of the sample banks with negative gaps is

-11-

signif leant but decreasing. This is, perhaps, a reflection of an in-
creasingly held view that interest rate declines cannot continue, and
an increase in rates is near. Sample funding ratios, the percentage
of earning assets funded by interest bearing liabilities, are rela-
tively constant but decline somewhat at the end of 1985.

NIM performance and balance sheet positions vary considerably
among the different size classes of commercial banks. Size groups 3
(assets of $100-$300 million) and 4 (assets of $10-$100 million)
earned the highest NIMs in 1985 and 1984 respectively. These results
are understandable by examining the relative balance sheet positions
for these two size groups. Size 4 banks were positioned with larger
positive gaps to benefit from the market rate rises in 1984, but these
same positions caused them to be hurt (relative to size 3 banks) by
the market interest rate declines in 1985.

The largest banks earn the smallest NIMs which is consistent with
the view that these banks operate in larger geographic markets and
deal with larger borrowing customers, all of which leads to competi-
tive pressures that shrink spreads that can be earned. The smallest
banks, about whom regulatory concern is often great, have average
short gaps that seem unremarkable compared to other banks, but the
standard deviations of these short gasps are 40 percent to 80 percent
larger than those of Size 1 banks. The fact that the small bank
sample has larger percentages of banks with negative gaps in three of
the four periods further demonstrates the greater diversity of small
bank balance sheet positions. Conventional wisdom assigns these small
banks the greatest difficulty in altering interest rate risk exposure
to desired levels by transactions in the cash markets.

-12-

A. Estimates of Earning Rates and Spreads
Following the spirit of the statistical cost accounting literature
[Hester (1966) and Rose and Wolken (1986)], equation (6) is estimated
for the total sample of banks and for each size group subsample.

GAP GAP IBL IBL

In this form a^ and a^ are estimates of r and r, respectively, and
12 s L

a„ and a, are estimates of ( r -i ) and (r^-i ) respectively. Both the
34 ss LL

short and long term rates earned should reflect the levels and move-
ment of market interest rates over the 1984-85 period. Since NIM is
affected by changes in spreads, estimates of a and a will be exam-
ined to see how spreads have changed and how changing spreads will
have affected bank NIMs. In estimating equation (6) average balance
sheet data for each six-month period are used, and the six month
planning horizon is assumed. NIM is the actual value realized for the
six-month period.

Coefficient estimates for equation (6) are shown in Table 2.
Estimates of a, and a^ using the total sample reflect the rising rates
in the first half and the first several months of the second half of
1984. A downward sloping yield curve is evident in these estimates of
r and r. for 1984. Most of the rates are lower in 1985 and the yield

S Li

curve is upward sloping. Estimates of ( r -i ) are not significantly
different from zero in 1984, and are barely significant in 1985. How-
ever, these estimated spreads mirror the movements of NIM, rising over
the first three periods and then falling in the last half of 1985. For
the total sample of banks, a larger spread was earned on the long terra

-13-

portion (maturity or repricing of over six months) of the balance
sheet. Spreads of 350 to 400 basis points of asset returns over
liability costs are estimated.

When examining the estimated coefficients for subsamples segmented
by size, it is noted that small banks (SIZE 5) tended to earn higher
estimated average rates on short asset than large banks and lower
estimated average rates on long assets. The pattern of the estimated
spread coefficients showed small banks earning significant and larger
spreads on short assets, with the spread increasing as market interest
rates fell in late 1984 and most of 1985. On the other hand, the
largest banks earned the largest spreads on long terra balance sheet
positions. The implications of these estimated rates and spreads are
that small banks find positive spread opportunities in both short and
long balance sheet positions; large banks have smaller (and sometimes
not significantly different from zero) spreads from their short bal-
ance sheet positions, but greater spreads from long term positions.
These differences in short and long margins leaves large banks with
smaller NIMs when compared to small banks.

B. Change in NIMs
Equation (5) indicates the ex post relationship between NIM and
gap, earning rates, spreads, and funding ratios. To examine the rela-
tive importance of various balance sheet positions and their changes,
equation (7) is estimated:

°*^s EA IBL

-14-

Here the focus is on the change in NIM that occurred for each six-
month period and its relationship with the gap position at the begin-
ning of the six-month period, the change in the volume of earning
assets (relative to total assets), and the change in the funding ratio,
both changes measured over the six months.

If the movement in NIM is dominated by movements in market interest
rates, b, , b^ and b-, should be small or zero, and h^. should be positive
during periods of rising rates (since the sample is net asset sensi-
tive) and negative during periods of falling rates. If the different
individual bank gap positions or changes in their earning asset and
interest bearing liability mixes have significant impacts on NIM, then
b, , b„ or b^ will have coefficients significantly different from zero.

Table 3 presents average values for the change in NIM and the inde-
pendent variables of equation (7). The change in NIM column is the

average change from the previous period's NIM. GAP /EA is measured as

4
of the beginning of each six-month period using a 12-month horizon;

the other change variables are the change from the beginning to the
end of each six-month period. From the last half of 1983 to the first
half of 1984 the average NIM of these banks rose. It then fell in
each of the next two six-month periods, and finally rose slightly in
the last half of 1985. The short term gap position of the banks was
positive throughout this period, but shifts in the short gap are evi-
dent. The reduction in the average short gap by the beginning of the
second half of 1984 suggests a belief that interest rates would fall,
which did happen. An increase in the short gap by the beginning of
the next two six-month periods suggests a forecast of rising interest
rates, which did not occur.

-15-

The change in the Ea/TA ratio captures the effect of mix changes on
NIM. If this ratio increases, the asset portfolio consists of rela-
tively more earning assets which should have a positive impact on NIM.
For the total bank sample, the average value of this measure was nega-
tive in two of the four periods, causing a drag on NIM. The change
in IBL/EA captures changes in the way that the earning assets are
funded. If this ratio falls in value, a relatively larger share of
earning assets is being funded by liabilities on which no interest is
paid. A decline in this ratio would have a positive impact on NIM.
For the total bank sample this ratio showed decreases in three out of
four periods, providing a boost to NIM.

Table 3 also shows average values for banks with negative GAP

s

separately from those with positive GAP . The number of banks with

s

GAP < 0 declined considerably in 1985 from 1984. The negative gap
banks had a poorer change in NIM performance in 1984 and a superior
change in NIM performance in 1985 when compared to banks with positive
gaps. Holding other things constant, a bank NIM would perform better
if its gap is positive during rising rate periods and negative during
falling rate periods. The results here do not fit this expected pat-
tern, implying that other things were not constant. It is clear from
the average values in Table 3 that negative gap banks had significantly
different changes in the EA/TA and IBL/EA ratios than did positive gap
banks.

Table 4 presents estimated coefficients for equation (7) separately
for the total sample, for negative gap banks, and positive gap banks.
The estimated constant terms for the total sample have the hypothesized

-16-

signs, positive when rates are rising and negative when rates are
falling, but are statistically significant in only two of the four
periods. Only one-third of the estimated coefficients other than the
constant term are significant, indicating little ability for this set
of independent variables to explain changes in NIM.

For the total sample the coefficients of the gap measures, GAP /EA,
are positive for both 198A periods and negative for both 1985 periods.
However, the 1984-2 period coefficient is not significantly different
from zero. Since the total sample is characterized by a positive gap
position, this is the expected result with the gap associated with NIM
increases when rates rose in 1984-1 and with NIM decreases when rates
fell in 1984-2 and 1985-1. The 1985-2 gap coefficient indicates that
the positive gap was associated with NIM declines during this rela-
tively flat rate period.

During the first three six-month periods the coefficients on
A(EA/TA) are negative but not significant. Perhaps the positive in-
fluence on NIM from a higher proportion of total assets as earning
assets is buffered during a period of falling rates by the lower earn-
ing rates on the added earning assets. This buffering could cause
this volume effect to be reduced in magnitude.

For the total sample the coefficient on A(IBL/EA) is significant
only in the 1985-2 period. The interpretation of the negative coef-
ficient in 1985-2 is of a declining NIM in the case of an increase in
the proportion of earning assets funded by interest bearing liabili-
ties, even though liability rates are falling.

-17-

When the total sample is divided into negative gap and positive
gap subgroups, the number of significant coefficients remains unimpres-
sive. For the banks with positive gaps, the gap coefficients have the
expected signs but only two of the four coefficients are significantly
different from zero. For the negative gap banks, the gap coefficient
is significant only in the 1985-2 period. Few of the remaining coef-
ficients for the A(EA/TA) and the A(IBL/EA) variables are significant,
especially for the negative gap subgroup.

In an attempt to increase the explanatory power of the gap measure,

GAP was defined in two alternate ways: (1) the IBL component of
s -^ s

GAP was defined to include super NOW and MMDA liabilities, and (2)
s

weighted average gap measures were used. Neither of these alternative
specifications of GAP improved the explanatory power of equation (7).

V. IMPLICATIONS AND CONCLUSIONS

The research reported in this paper has attempted to measure the
interest rate risk exposure of commercial banks in recent years. An
emerging view that banks are well hedged and thus immune to changes in
interest rates is tested. The emerging view is generated by a time
series examination of the response of bank revenues, expenses and
profits to changes in interest rates. An alternative approach, used
here, is to examine a cross-section of banks for periods of time with
both interest rate increases and interest rate declines.

Average sample data indicate that many individual banks are not
well-hedged, and a variety of balance sheet positions exists among
different banks. However, empirical results indicate that differing
gap positions do not have a clear-cut and dominant impact on the

-18-

changes in net interest margins experienced by individual commercial
banks. Other facts, such as changes in balance sheet mix and changes
in the way earning assets are funded, do have some influence on bank
net interest margins, but the explanatory power of this set of vari-
ables is low. A gap measure by itself appears to be unable to provide
much information about a change in a bank's NIM in the next period.

Several possible reasons for the lack of close association between
gap measures and NIMs are possible. As certain off-balance sheet
items increase in amount, the interest rate sensitivity of the bank is
less accurately characterized by a balance sheet-based measure.
Interest rate swaps, for example, alter the interest rate sensitivity
of a bank's cash flows, but this influence is not captured in a gap
measure. However, this error in measurement should apply only to the
(usually larger) institutions engaging in these swaps and probably has
little impact on the usefulness of gap measures for smaller banks.

The more likely reason for the lack of a strong, measurable rela-
tionship between a bank's gap and its change in NIM is the inaccuracy
of the gap measures in proxying the desired degree of exposure. In
addition, a particular gap measure value is valid only at the point in
time at which the balance sheet is constructed. Balance sheet values
can change daily, destroying the predictive ability of a gap value
that is several weeks or several months old. It is difficult to cap-
ture the effects of a dynamic process with static measure.

In attempting to measure the interest rate risk in the banking
system by looking at balance sheet measures or gaps, an accurate

-19-

picture of exposure to risk would not be obtained. Whether for exam-
ination purposes or for determining appropriate variable insurance
premiums, current gap measures are inappropriate indicators of risk
without taking other factors into account.

-20-

ENDNOTES

The Federal Savings and Loan Insurance Corporation has proposed
variable insurance premiums based on a measure of interest rate risk,
exposure for insured savings and loan associations.

2
A bank would choose the position that would benefit it from the

expected interest rate movement, rather than an immunized position

that would snelter it from the effects of interest rate movements.

3

The buckets or maturity ranges in Schedule RC-J of the call

report are (1) immediately adjustable, (2) two days to three months,
(3) over three months to six months, (4) over six months to one year,
(5) over one year to five years, and (6) over five years. The first
four buckets are used to calculate the weighted average gap measures.

4
Equation (7) was estimated using a short gap position defined for

a six month horizon. The results of using GAPg defined in this way

differed little from those reported in Table 4.

-21-

REFERENCES

Bierwag, G. 0. and Alden L. Toevs , "Immunization of Interest Rate Risk
for Depository Financial Institutions," Proceedings of a Conference
on Bank Structure and Competition, Federal Reserve Bank of Chicago
(1982), 327-346.

Bierwag, G, 0., George G. Kaufman, and Alden Toevs, "Duration: Its
Development and Use in Bond Portfolio Management," Financial
Analysts Journal, 39 (July/August 1983), 15-35.

Flannery, Mark J., "Market Interest Rates and Commercial Bank Profit-
ability: An Empirical Investigation," Journal of Finance , 36
(December 1981), 1085-1011.

Flannery, Mark J. and Christopher M. James, "The Effect of Interest

Rate Changes on the Common Stock Returns of Financial Institutions,'
Journal of Finance, 39 (September 1984a), 1141-53.

, "Market Evidence on the Effective Maturity of Bank

Assets and Liabilities," Journal of Money, Credit and Banking, 16
(November 1984b, Part 1), 435-445.

Graddy , Duane B. and Adi S. Kama, "Net Interest Margin Sensitivity
Among Banks of Different Sizes," Journal of Bank Research, 14
(Winter 1984), 283-290.

Haley, Charles W. , "Interest Rate Risk in Financial Intermediaries:
Prospects for Immunization," Proceedings of a Conference on Bank
Structure and Competition, Federal Reserve Bank of Chicago (1982),
309-326.

Hanweck, Gerald A. and Thomas E. Kilcollin, "Bank Profitability and
Interest Rate Risk," Journal of Economics and Business, 36
(February 1984), 77-84.

Hester, Donald D. and John F. Zoellner, "The Relation Between Bank
Portfolios and Earnings: An Econometric Analysis," Review of
Economics and Statistics, 48 (November 1966), 372-386.

Kaufman, George G. , "Measuring and Managing Interest Rate Risk: A
Primer," Economic Perspectives, Federal Reserve Bank of Chicago
(January/February 1984), 16-29.

Mitchell, Karlyn, "Interest Rate Risk at Commercial Banks: An Empiri-
cal Investigation," RWP 85-06, Federal Reserve Bank of Kansas City
(July 1985).

Rose, John T. and John D. Wolken, "Statistical Cost Accounting Models
in Banking: A Reexamination and an Application," Staff Study 150,
Board of Governors of the Federal Reserve System (May 1986).

-22-

Santomero, Anthony M. , "Modeling the Banking Firm," Journal of Money,
Credit and Banking, 16 (November 1984, Part 2), 576-602.

Tarhan, Vefa, "The Response of Bank Stock Returns to Money Supply

Announcements," Proceedings of a Conference on Bank Structure and
Competition, Federal Reserve Bank of Chicago (1984), 402-423.

Toevs , Alden L. , "Gap Management: Managing Interest Rate Risk in

Banks and Thrifts," Economic Review, Federal Reserve Bank of San
Francisco (Spring 1983), 20-23.

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TABLE 1

SELECTED VARIABLE MEANS

Time period:

1984-1 1984-2 1985-1 1985-2

TOTAL

NIM

4.745%

4.697%

4.531%

4.573%

(404)1

GAPs/EA2

0.1438

0.1225

0.1447

0.1651

IBLg/EA

0.4359

0.4493

0.4464

0.4263

% GAPg<0

17.08%

17.82%

11.83%.

9.41%

SIZE 1

NIM

4.192%

4.315%

4.297%

4.280%

(52)

GAPg/EA

0.1312

0.1281

0.1485

0.1661

IBLg/EA

0.5085

0.5196

0.5077

0.4894

% GAPg<0

7.69%

5.77%

5.77%

5.77%

SIZE 2

NIM

4.554%

4.606%

4.546%

4.455%

(57)

GAPg/EA

0.1238

0.1204

0.1462

0.1731

IBLg/EA

0.4402

0.4644

0.4557

0.4349

% GAPs<0

15.79%

12.28%

5.26%

5.26%

SIZE 3

NIM

4.744%

4.675%

4.736%

4.775%

(92)

GAPg/EA

0.1298

0.1148

0.1486

0.1833

IBLg/EA

0.4471

0.4437

0.4346

0.4077

% GAPs<0

18.48%

17.39%

8.70%

6.52%

SIZE 4

NIM

4.978%

4.894%

4.506%

4.677%

(105)

GAPg/EA

0.1553

0.1226

0.1463

0.1539

IBLg/EA

0.4044

0.4226

0.4242

0.4066

% GAPg<0

15.24%

19.05%

12.38%

13.33%

SIZE 5

NIM

4.902%

4.766%

4.483%

4.499%

(98)

GAPg/EA

0.1628

0.1271

0.1356

0.1540

IBLg/EA

0.4181

0.4366

0.4427

0.4257

% GAPg<0

23.47%

26.53%

21.43%

12.24%

Sample sizes.

GAPg and IBLg are beginning of period positions and are defined
over a 12 month horizon.

TABLE 2

ESTIMATED COEFFICIENTS FOR EQUATION (6)

NIM = ajGAP /EA] +a^[GAP /EA] +a„[IBL /EA] +a,[IBL /EA]
Is zL Js 4L

a.

^3

R

1984-1 TOTAL

0.11551
(0.0060)

0.10117
(0.0059)

-0.00087
(0.0040)

0.03955
(0.0019)

0.34392

SIZE 1

0.10843
(0.0157)

0.13266
(0.0160)

-0.00138
(0.0065)

0.04742
(0.0065)

0.56203

SIZE 5

0.10807
(0.0106)

0.08939
(0.0108)

0.00759
(0.0078)

0.04032
(0.0030)

0.36771

1984-2 TOTAL

0.13086
(0.0064)

0.12505
(0.0069)

0.00387
(0.0040)

0.03448
(0.0019)

0.35077

SIZE 1

0.09921
(0.0180)

0.13778
(0.0189)

0.01323
(0.0068)

0.05403
(0.0074)

0.43630

SIZE 5

0.12200
(0.0130)

0.10816
(0.0139)

0.02121
(0.0081)

0.03237
(0.0035)

0.27702

1985-1 TOTAL

0.11090
(0.0057)

0.11358
(0.0061)

0.00759
(0.0038)

0.03933
(0.0017)

0.31213

SIZE 1

0.09902
(0.0137)

0.15504
(0.0152)

0.00891
(0.0056)

0.05711
(0.0057)

0.62515

SIZE 5

0.09610
(0.0127)

0.08801
(0.0129)

0.02567
(0.0084)

0.03643
(0.0034)

0.12440

1985-2 TOTAL

0.10832
(0.0063)

0.11210
(0.0065)

0.00717
(0.0042)

0.04055
(0.0019)

0.26967

SIZE 1

0.08715
(0.0152)

0.14417
(0.0180)

0.01546
(0.0068)

0.05863
(0.0064)

0.48540

SIZE 5

0.10600
(0.0133)

0.10460
(0.0133)

0.02874
(0.0095)

0.03486
(0.0035)

0.14799

Standard errors in parentheses. R is adjusted R-squared.

GAPg , IBLg , and EA are average values for each six month period.

TABLE 3

SELECTED VARIABLE MEANS

NUMBER

CHANGE

OF

IN NIM

BANKS

(basis pts)

GAP /EA
s

A(EA/TA)

A(IBL/EA)

1984-

-1

TOTAL

404

13.15

0.14376

0.01749

-0.00999

GAPg<0

69

11.21

-0.07228

0.01697

-0.004^5'

GAPs>0

335

13.55

0.18826

-0.01760

-0.01113

1984-

-2

TOTAL

404

-10.64

0.12251

-0.00275

-0.00212

GAPg<0

72

-25.53

-0.08776

-0.00189

-0.00619

GAPs>0

332

-7.40

0.16811

-0.00294

-0.00124

1985-

-1

TOTAL

404

-15.98

0.14472

0.00468

0.00763

GAPs<0

48

1.54

-0.08246

0.00508

-0.00179

GAPs>0

356

-18.34

0.17535

0.00462

0.00890

1985-

-2

TOTAL

404

2.38

0.16489

-0.00100

-0.00007

GAPs<0

38

33.26

-0.08894

-0.00046

0.00431

GAPg>0

366

-0.83

0.19117

-0.00106

-0.00052

GAP is defined over a 12 month horizon,
s

All changes are from the beginning to the end of the indicated six
month period.

TABLE 4

ESTIMATED COEFFICIENTS FOR EQUATION (7)

ANIM = b^ + b, [GAP /EA] + b^[A(EA/TA)] + b-[A(IBL/EA)
0 1s I J

0

R

1984-1 TOTAL

0.00045 0.00856 -0.01375 0.01259 0.07074
(0.00058) (0.06269)* (0.01434) (0.00769)

GAP <0
s

0.00183 0.01003 0.00755 0.02577 -0.01281
*(0r.00130) (0.01405) (0.02862) (0.02366)

GAP >0
s

-0.00076 0.01406 -0.02503 0.00846 0.09017
(0.00082) (0.00368)* (0.01697) (0.00865)

1984-2 TOTAL -0.00158 0.00357 -0.01517 -0.01820

(0.00044)* (0.00229) (0.01638) (0.01134

0.00467

GAP <0
s

-0.00165 0.01497 -0.03188 -0.05704 0.01935
(0.00143) (0.01313) (0.05028) (0.03084)*

GAP >0
s

-0.00068 -0.00063 -0.00960 -0.01044 -0.00664
(0.00063) (0.00313) (0.01739) (0.01228)

1985-1 TOTAL -0.00013 -0.01015 -0.01462 0.00915 0.04260

(0.00047) (0.00236)* (0.01458) (0.01011)

GAP <0
s

-0.00069 -0.00369 -0.04400 0.00515 -0.04612
(0.00147) (0.01314) (0.05700) (0.02903)

GAP >0
s

0.00029 -0.01234 -0.01106 -0.00983 0.04186
(0.00063) (0.00303)* (0.01509) (0.01083)

1985-2 TOTAL 0.00083 -0.00349 0.02175 -0.01943 0.03545

(0.00042)* (0.00194)* (0.01330) (0.00867)*

GAP <0
s

0.00553 0.02554 -0.12737 0.00177 0.13047
(0.00161)* (0.01409)* (0.05296)* (0.02928)

GAP >0
s

-0.00021 0.00077 0.03052 -0.02478 0.05631
(0.00052) (0.00233) (0.01329)* (0.00879)*

Standard errors in parentheses. * indicates coefficient is signifi-
cant at the 5 percent level. R^ is adjusted R-squared.

GAP is defined over a 12 month horizon,
s

HECKMAN

BINDERY INC.

JUN95

Bound . To -Plcas^ N.MANCHESTER,
INDIANA 46962