A linear programming approach pdf 1

Journal of Banking and Finance 1 (1977) 277-296. © North-Holland Publishing Company

FINANCIAL INNOVATION

A linear programming approach
Moshe BEN-HORIM
University of Florida, Gainesville, FL3260I, U.S.A.

William L. SILBER
New York University, New York, NYIO006, U.S.A.

Introduction
Yhe analysis of the innovation of financial instruments and practices is not
nearly as well-developed as its counterpart in the real sector. The theoretical and
empirical studies on product and process innovation by Mansfield (l 968), Nelson
and Winter (1973), Schmookler (1966), and Schumpeter (1939) are well-known.
This paper is concerned with the microeconomics of financial innovation.
Drawing on the work of Silber (1975) which outlines the forces that induce
financial institutions to create new instruments or adopt new practices, an
empirical test of the theory of financial innovation is carried out within the context
of a linear programming model of commercial bank behavior.

Innovation has been given very specific and somewhat more general meanings.
Schumpeter (1939) related the term to the implementation of a new process or
method that alters the production possibilities of a firm. Mansfield (1968), Scherer
(1973), and Schmookler (1966), include both new processes and new products in
their analyses. The financial innovations discussed below fall largely into the new
product category.
There also has been considerable interdisciplinary work by behavioral scientists
and economists on the characteristics of the innovative firm, including studies by
Cyert and March (1963), Becker and Stafford (1967), and Knight (1967). Nelson
and Winter (1973) have carried that analysis one step further, towards an
'evolutionary theory' of innovation. Their approach stresses an incremental search
process that is triggered by a firm's rate of return falling below target levels. Our
approach in the financial sector parallels, with appropriate modifications, the
Nelson-Winter analysis in the real sector.
One final word of introduction concerns the definition of financial innovation.
When dealing with innovation in the real sector it is possible to lihait the scope by an
objective criterion: an innovation is a new product or process that qualifies for

278

M. Ben-Horim and W.L. Siiber, Financial innovation

patent protection. Economists who have studied real sector innovation, such as
Mansfield (1968) and Scherer (1973) have pointed out the dangers in relying on
patent data to delineate innovations. Indeed, Mansfield uses the designation as
recorded in trade journals to derive his list of innovations.
New financial instruments or practices are not afforded patent protection. Thus
we have no choice but to use the term financial innovation as it has been employed
with respect to specific developments, such as: the emergence of negotiable
certificates of deposit (CDs) in 1961 [Meigs (1966)]; Eurodollars in 1966 [Krooss
and Blyn (1971)]; bank-related commercial paper and loan repurchase agreements in 1969 [Kimbrel and Dill (1974)].
In the next section we summarize a theory of financial innovation that can be
applied to any financial institution. In the following section we set up a formal
linear programming model of commercial bank behavior with the objective of
testing the hypotheses concerning the innovative process. The LP model is then
simulated over the years 1952-1972 to see how well it anticipates the timing of the
commercial bank innovations during this period. The simulations are carried out
on data from the First National City Bank (used to represent money market banks)
and an aggregate of large New York City banks (to represent a leading sector of the
banking system).

The use of a linear programming (LP) model to analyze historical data differs
somewhat from its normal applications. The usual context of LP models is either
normative within a theoretical framework or as a practical tool for managerial
decision making. Our approach suggests that the LP model can be a useful tool
even for certain types of time series analysis.
2. A theory of financial innovation
Many have argued that financial innovation is largely a response to regulation.
The emergence of negotiable CDs, the development of the Eurodollar market and
the introduction of bank-related commercial paper are all credited to interest rate
ceilings under Regulation Q. The regulation theory of innovation has been
articulated most clearly (and rather elegantly) by Greenbaum and Haywood
(1971). While this hypothesis has merit, it is too narrow to properlY explain the
evolution of financial instruments. Regulation turns out to be just orie component
of a more general category of inn0vation-generating phenomena.
Specific examples of such factors are detailed in Silber (1975). For the purposes
at hand, we note that our basic hypothesis is that innovation of financial
instruments and practices occurs in an effort to remove or lessen the financial
constraints imposed on firms. Government regulation does, indeed, impose
constraints and thereby induces innovation. But the behavior of the financial firm
is constrained by other factors as well-including self-imposed constraints and

market-imposed constraints.
Financial institutions are assumed to maximize utility subject at least to the
balance sheet constraint that the sum of all assets minus liabilities and capital

M. Ben-Horim and W.L. Silber, Financial innovation

279

equals zero. There may be other explicit constraints built into the optimization
problem such as a target rate of growth for total assets, various regulatory
requirements (such as, reserves must equal at least x percent of total deposits in the
case of commercial banks) or self-imposed liquidity requirements specifying the
desired percentage of the total portfolio in some particular asset.
In addition to these explicit constraints on the firm's behavior, the markets
surrounding the financial firm define two sets of data: (1) the policy tools which the
firm can vary at its discretion in order to reach an optimum; and (2) the parameters
which the firm must accept as part of the optimization problem. The latter set of
data constrain the behavior of the firm.
New financial instruments or practices will be innovated when there is an
exogenous change in the constrained optimization of the firm that stimulates a

search for new policy tools. There are two types of changes which induce firms to
undertake the search costs required to modify its traditional policy tools. In one
case, exogenous changes in constraints force a reduction in the utility of the firm
and the firm innovates in an effort to return to its previous level of utility. In the
second case, innovation responds to an increase in the cost of adhering to a
constraint. In a programming context, this corresponds to an increase in the
shadow price (dual value) of the constraint. Both of these conditions create a strong
incentive to remove or modify the constraints. If set internally, the firm may simply
suspend or revise the constraint. If the constraint is imposed externally, e.g. by
market forces or by government regulation, the firm will attempt to circumvent the
constraint by altering the opportunity set it faces.
This constraint-induced innovation hypothesis requires further specification if
it is to be relevant operationally and if it is to be tested empirically. After all, the
financial firm is constantly responding to changing yields and risks, as well as
inflows and outflows of funds, by using its conventional policy tools. How are these
'normal' stimuli to be distinguished from those falling into the innovation
category ? The search costs inherent in reexamining the firm's policy weapons and
the nature of its financial assets and/or liabilities for potential innovation suggest
that this route will be chosen only when, for example, the 'normal' cyclical increase
in the shadow price of a constraint becomes 'abnormal,' or if there is a secular

uptrend in the shadow price of a constraint. The term 'abnormal' is best
understood in an historical context. In particular, a firm sets it goals (and 'normal'
policy reactions) in terms 0fits historical experience. It then reevaluates its position
when conditions change significantly.
The constraint-induced innovation hypothesis can now be given a time
dimension. As the cost of adhering to a constraint rises over time (or as the financial
firm experiences continued decreases in utility over time) it will undertake or
intensify the search for new financial instruments and/or practices. The sharper the
rise in the shadow price (or the reduction in utility) the greater will be the
innovative effort. We expect, therefore, a time lag between the initial stimulus to
innovate and the actual innovation. The time lag should be shorter, however, the

280

M. Ben-Horim and W.L. Silber, Financial innovation

greater the change in initial conditions (as well as previous experience with
innovative practices).
This brief outline of a behavioral theory of financial innovation directly lends
itself to empirical verification. A simple linear programming model of a financial

institution's portfolio allocation can be specified. Using historical data, the LP
model can be solved period by period. The shadow price of the constraints are
derived as a by-product of the optimization problem. Our hypothesis suggests that
the time series of the derived shadow prices should rise prior to the introduction of a
new financial instrument and drop immediately thereafter.
The attempt to match peaks in shadow prices with the introduction of new
financial instruments or practices could be unsuccessful because of the rigid nature
of the LP model. A sensitivity analysis will be performed in order to evaluate the
magnitude of this problem. Another way of putting it is as follows. In some cases we
can expect a single constraint to impose a dominant limitation on the objective
function. Removal (or ease) of such a constraint might enable the firm to increase
its objective function (e.g. profits) to a great extent before it interacts with another
constraint of the model. In some situations, however, we expect several constraints
to form a'bottleneck' such that the removal (or ease) of a dominant constraint will
not enable the firm to increase its objective function significantly because other
constraints (forming the 'bottleneck') will soon interact with the objective function
and prevent it from a further increase. Initially, these latter constraints may have a
zero dual value. Bank management is presumably aware of the situation, and will
not direct its innovative efforts towards the removal of the first constraint only, but
rather towards the removal of all the constraints forming the 'bottleneck.' A

sensitivity analysis is required in order to identify the 'bottleneck' constraints, and
to follow the changes in their dual values after the innovation.
The LP model is not capable of testing the reduction in utility aspect of the
innovation hypothesis. We will see how far the programming approach takes us in
explaining the timing of commercial bank innovations during the 1952-1972
interval. We will then turn briefly to some tests of the utility or adversity
explanation of bank innovation.
3. The model

Linear programming models for commercial bank asset selection are known in
the literature in various degrees of detail and sophistication depending upon
objectives set forth and the assumptions made by the authors. The model outlined
in this section is rather simple. It is designed to approximate a one period asset
allocation approach. Unlike some of the linear programming models for bank
asset allocation which are designed to provide bank management with quantitative.tools for solving the funds allocation problem, 1 the model used in this study
1Kalman J. Cohen and Frederick S. Hammer (1972).have developed a highly sophisticated linear
programming model for bank asset management. The model has been put to work by large banks to
determine optimal allocation of funds to the various assets and to determine the profitability of various

M. Ben-Horim and W.L. Silber, Financial innovation

281

is limited in its objective, hence we make several assumptions which greatly
simplify the structure of the LP model.
The first simplification is made possible by assuminga one period (year) model
where no reallocation of funds is allowed within the period. We further assume that
the level and composition of the liabilities and capital funds are exogenously
determined in each period. They are set equal to their actual levels on the balance
sheet. Similar assumptions are made by several authors who presented bank asset
selection models in recent years. 2
Assets are divided into five major categories as follows: (1) cash; (2) federal
government securities and securities of federal agencies (to be called 'governments'
hereafter); (3) state, local and other securities (to be called 'investments' or
'municipals'); (4) loans; (5) other assets (including bank premises).
The other assets category includes such assets as bank premises and
equipment, customers acceptances, federal funds sold, securities purchased under
agreement to resell and others. Because of the heterogeneity of this class of assets,
the great variance in their return and particularly because of the difficulty in
determining movements in their level, it was decided to set the value of this class of

assets equal to its actual value in each period. This assumption hampers the
usefulness of the model as a tool for determining optimal asset allocation, but has
only very limited effect on the estimation of the liabilities and capital shadow
prices.
We now turn to a detailed description of the model. The following is a list of the
variables used. Each variable is assigned a name and a sequential number:
Assets

CASH1
GI/2
MUN3
LOAN4
OTAST5

--Reserves, float, due from banks and other cash items
--U.S. government and federal agencies securities
--State, municipal and other securities
--Loans
---Other assets

funds sources. Several factors, however, make such a model impractical for this study. First, to employ
such a model one needs to have a fairly detailed set of data including (for example) a breakdown of the
loan portfolio into a joint distribution of class and maturity. Furthermore, Cohen and Hammer's model
utilizes many constraints whose parameters are to be specified by management. As we shall see, it is
quite difficult to estimate such parameters and a reduction in the number of parameters needed to be
estimated this way is desirable. Yet another reason why a substantial simplification is needed is that our
model is to be simulated on data starting in the early 1950s, an era in which the theory (let alone practice)
of bank asset selection was well behind a model like that of Cohen and Hammer. Finally, it is believed
that a simple model like the one suggested in the following pages can simply'do the job,' namely, identify
the major shadow price trends, which is the primary objective of the study.
2For example: Dudley A. Luckett (1970) develops an asset selection model and assumes
predetermined liability level and structure (p. 421, fn. 7). Mingo and Wolkowitz (1974) assume
exogenously determined deposits (p: 3). David Walker (1972) develops a way of predicting deposits for
period t based on previous deposit growth, but then states that '... these values (the predicted values) of
DD, (demand deposits in period t) and TSDt (time-and-saving deposits) will be assumed to be actual
levels. This implies that actual levels and values that are predicted from the regression equation are the
same.' (p. 2060)

282

Liabilities
DD6
TD7
CD8
OLIAB9
Capital
CAPSTIO
DEBll
OCAP12
TCP13

M. Ben-Horim and W.L. Silber, Financial innovation

- - D e m a n d deposits
- - T i m e and savings deposits excluding certificates of deposit
Certificates of deposit
- - O t h e r liabilities

Capital stock
--Debentures
- - O t h e r capital
- - T h e sum of CAPS T1 O,DEB11, OCAP12 and ca, where ea is the
current period's retained earnings

The entire LP model is presented in table 1. Equation (1) is the objective function
where ri (i =2, 3, 4) is the revenue of the ith asset expressed in percent and ci (i
= 6,..., 12) is the cost of the ith source of funds. The assumption is that banks are
profit maximizers. While utility maximization would have been more realistic, for
our purposes this seemed to be an unnecessary complication.
The first constraint, equation (2), is the availability of funds constraint to assure
that total assets equals the sum of the liabilities and capital accounts. Inequality (3)
specifies a minimum level of cash which relates to both the size and the composition
of the deposits. The parameter ~1 is the sum of the reserve requirement on demand
deposits, float, and interbank balances.a ~t2 is the reserve requirement against time
and savings deposits and 0ca is the reserve requirement against certificates of
deposits.
Constraint (4) sets a minimum level of the U.S. government bond portfolio
('go vernments') over and above the pledged U.S. government securities (ex).4 This
minimum is related to the size as well as the composition of the deposits. While
specifying fl~ and f12 in constraint (4) causes no difficulty when employed by
management in solving its own LP model, a great deal of difficulty arises when it is
to be simulated on historical data. The difficulty, of course, is to determine the
precise self-imposed minimum level that management of a given bank (or banks)
imposed on its asset allocation. The problem of estimating fl~ and f12was, therefore,
approached in two different ways.
The first approach is to impose a constraint which will be invariant throughout
the entire period, and is determined by an historical standard. Imposing an
historical standard requires that we identify a 'normal' period where, on average,
banks were holding the desired level of liquidity in the form of governments.
Unique economic conditions significantly affected bank behavior and balance
sheet allocation during the 1930s and 1940s: the Great Depression was
3Cohen and Hammer (1972, p. 405).
4Constraint on the minimum government to deposit ratio is imposed by Cohen and Hammer (1972).

Table 1

(1)

M a x z=

r2G V2 + r3MUN3 + r4LONS4

- c 6 D D 6 - c~TD~ - c s C D s - C 9 0 L I A B 9 - c l o C A P S T I O - c

I tDEBI1 - c t 2 O C A P I 2

s.t.

(2)
(3)
(4)
(5)
(6)
(7)
(s)
(9)
0o)
(tl)
02)
03)
(14)
05)
06)
07)
(18)

CASH 1 + G V 2 + M U N 3 +
CASH I
GV2
MUN3
MUN3

LONS4+OTAST5

DD6TDT- CDs- ~t D D 6 - % TD~ -~3CDs
-~tDD6-~2TD7
- ?t D D 6 - 71TD~
-?2DD6
~2TD~

OLIABg-

CAPSTIO-

DEBII-

OCAPI2

_~o

:~

_~o

R,

OCAPI2 + TCPI3=~3
- ~p~TCPI3 ~_0
-~p2 TCPI 3 _'~0

"P~
r~
~"

~o

LONS4
CAPSTIOMUN3+

DEBII -

LONS4+OTAST5
LONS4
OTAST5

= e4

DD6 •
TD~

=£6

CDs
OLIAB9
DEBI1

OCAP12

~"

=e9

('~
~.

=Elo

~.

=~H

"~

= £8

CAPST10

.

FO
O0

284

M. Ben-Horim and W.L. Silber, Financial innovation

characterized by many bank failures and an abnormal demand for liquidity
resulted; the 'war years' beginning in 1940 were atypical with respect to bank
holding of governments in connection with the financing of World War II. To get a
reasonable estimate of what may be considered an appropriate normal ratio of
governments to deposits, we thus have to refer back to the 1920s. While there may
be reservations regarding the relevance of the 1920s for establishing bank portfolio
policies of the 1950s or 1960s, it seems to be a reasonable place to start, and it
provides the best historical yardstick that can be employed.
Initial results produced fll and f12 (the ratios held for demand and time deposits)
equal to 0.186 and 0.095 respectively and a weighted average (~) of0.173. 5 As part
of the sensitivity analysis of the model, we also simulate on substantially different
values of fll and 82 to determine the effect of such a change on the results. For
example, in one of these runs 81 and 82 are set equal to 0.120 and 0.060 respectively
throughout the 1952-72 period.
Another approach to the determination of the 8 parameters assumes that the
ratio of governments to deposits of an individual bank is constrained primarily by
current actual ratios of governments to deposits at other comparable banks. This
approach takes into account changes in bank management attitudes towards the
governments-to-deposit ratio. To get such an estimate for First National City
Bank (FNCB) we calculate the actual ratio of governments to deposits at four large
New York City banks (excluding FNCB). We then find the minimum ratio across
banks.
This ratio is subject to significant cyclical fluctuations (when loan demand is low
more funds are invested in governments). In 1958, for example, the ratio went up
from 0.164 to 0.185. In 1961 the ratio increased from 0.123 to 0.143. In the 1952-55
period, however, the ratio was higher than the 0.173 which was estimated via our
previous method. Since many authors also report that the government bond
portfolio was in excess of liquidity needs in those years, we set ~ = 0.173 for the
1952-55 period while for subsequent years it was determined by the minimum of
comparable banks. The parameter values produced via this procedure appear in
table 2. The alternative estimates of the vectors 81 and 82 provide for a shift of these
parameters over a wide enough range to allow us to determine the extent to which
the results obtained by the simulations are sensitive to the specific assumed values
of fll and 32.
Constraints (5) and (6) impose maximum and minimum ratios of municipals to
deposits. Several reasons justify the minimum constraint. First, some of the
municipals are pledged against state and local government deposits. Second,
5To get estimates of unpledged and pledged U.S. government securities at large banks in the 1920s, we
used balance sheet data of national banks as published in the Annual Reports of the Comptroller of the
Currency. Unfortunately, the amount of pledged government securities is available only for the year
1921. Other detailed balance sheet data are available for the rest of the 1920s, so that the amount of
pledged governments for each year of the 1920s had to be approximated. The method of estimation is
explained in detail in Ben-Horim (1976).

M. Ben-Horim and W.L. Silber, Financial innovation

285

Table 2
The parameters ~, fll and f12 (FNCB).

Year

~

fll

f12

1952-55
1956
1957
1958
1959
1960
1961
1962
1963
1964
1965
1966
1967
1968
1969
1970
1971
1972

0.173
0.165
0.150
0.140
0.125
0.115
0.110
0.100
0.090
0.080
0.070
0.065
0.055
0.050
0.040
0.035
0.035
0.030

0.186
0.180
0.170
0.150
0.135
0.135
0.130
0.115
0.110
0.100
0.080
0.080
0.070
0.060
0.040
0.038
0.038
0.032

0.095
0.090
0.085
0.075
0.068
0.068
0.065
0.058
0.055
0.050
0.040
0.040
0.035
0.030
0.020
0.019
0.019
0.016

municipals serve as secondary reserves and therefore are used for liquidity. The
rationale for imposing a maximum constraint such as (5) is that the investment
portfolio is regarded as a residual item on the bank's balance sheet while the bank's
primary objective is to make loans. 6 During the 1952-72 period the ratio of
municipals to deposits in F N C B as well as in other money market banks fluctuated
between 6 and 13 percent so that Yl and Y2 were assumed to equal 0.13 and 0.06
respectively. 7
Constraint (7) is a market demand restriction on loans: the constraint simply
restricts the bank from lending out more than what is demanded by the bank's
customers, s Given the difficulty in estimating the loan demand (Lo), we set loan
demand equal to the actual loans made (LA)in every period. It is clear that under all
circumstances Lo > LA, and that in some periods L o is equal to LA. In the next
section where the simulation results are discussed, we examine what might have
changed if loan demand is assumed to be greater than LA.
6See for example Paul Nadler (1963): 'there are many reasons then why a bank prefers to lend out all it
has over and above the amount that must be tied up in plant and equipment and primary and secondary
reserves. The investment of an aggressive bank, other than the investment part of secondary reserves,
are truly considered a residual account, receiving funds only when loan demands are not strong enough
to use up all the money not tied up in reserves.'
VMaximum and minimum constraints on the municipals portfolio are imposed in David Walker's
(1972) recursive programming model, except that Walker's constraints are determined from more
detailed data such as investments and loans outstanding and maturing during a given period.
SA similar maximum restriction on the loan portfolio is suggested by Cohen and Hammer (1972) and
by David Walker (1972).

286

M. Ben-Horim and W.L. Silber, Financial innovation

Constraint (8) defines a new variable TCP13 (total capital) which is set equal to
the sum of the beginning of the period's capital accounts and the period's retained
earnings. This variable is then used in constraints (9) and (10), both of which
impose maximum ratios to capital: constraint (9) sets a maximum ratio of 'risk
assets' to total capital (TCP13) and (10) imposes a maximum ratio of loans to
capital. 9 The reasons TCP13 is used in these constraints is that when we want to
measure the pressure that exists on the bank to raise additional external capital we
have to measure the pressures that exist without the capital which was actually
raised during the period. An exception is the undivided profits of the period on the
assumption that management is able to predict its end of period value at the
beginning of the period.
To determine the parameters ~bl and ~b2 of (9) and (10) for the simulation of
FNCB data we computed the actual ratio of'risk assets' to capital and loans-tocapital for four large NYC banks. Both ratios, but particularly the loans to capital
ratio show cyclical fluctuation: they tend to decrease during recessions and
increase during expansions. We thus employ the following technique to determine
the vector ~bi : we use either the actual maximum ratio (across the four banks) or the
maximum in past years (starting in 1952). For example, ~bl for 1959 is 8.3 because
this was the maximum (across the four banks) observed in that year. In 1960, the
maximum was 7.7. Since a higher ratio (8.3) was observed previously the parameter
q~l for 1960 is set equal to 8.3. The values of ~b2are determined the same way except
that when the estimate derived is less than 7.0 we set ~b2 = 7.0 because this was the
parameter used by the Comptroller of the Currency in evaluating capital adequacy
of banks. The vectors ~1 and ~b2 appear in table 3.
The remaining constraints (11)-(18) set 'other assets,' deposit liabilities and
capital accounts equal to their actual levels in the current period. The dual values of
constraints (12) through (18) are our main concern. They indicate the value to the
bank of an additional dollar of deposits and capital. This summarizes the linear
programming model to be used here. Additional details and further justification
for the parameters and constraints are found in Ben-Horim (1976). 1°
4. Simulations of the LP model: First National City Bank
This section summarizes the empirical results of the linear programming model
as simulated on data of First National City Bank for the period 1952-72. Data
sources and their definitions as used in the simulations are detailed in the
9'Risk assets' is defined to include total assets less cash and governments.
10The use of a relatively simple LP model raises the question of whether it is possible to translate input
costs directly to the dual values of the constraints. While this is possible to some extent, the interaction of
the constraints, especially the possibility of bottlenecks, makes it impossible to infer when the shadow
prices of any particular constraint becomes relevant, thereby stimulatinginnovation. This is illustrated
in the next section with respect to the interaction of the capital constraint and the governments
constraint.

M. Ben-Horim and W..L. Silber, Financial innovation

287

Table 3
The parameters ~b~ and ~b2 for FNCB.
Year

~bl

~b2

1952
1953
1954
1955
1956
1957
1958
1959
1960
1961
1962
1963
1964
1965
1966
1967
1968
1969
1970
1971
1972

8.3
8.3
8.3
8.3
8.3
8.3
8.3
8.3
8.3
8.5
8.8
9.0
9.1
10.0
10.0
11.1
12.5
12.5
12.5
12.5
14.3

7.0
7.0
7.0
7.0
7.0
7.0
7.0
7.0
7.0
7.0
7.0
7.0
7.0
7.7
8.3
9.0
10.0
11.1
11.6
12.0
12.8

Appendix. The shadow prices are plotted graphically both for an initial set of
assumptions as well as for the sensitivity experiments. Separate graphs are
presented for the shadow prices of deposits and capital. Since the results turned out
to be quite invariant under alternative parameter specifications only a representative set of the sensitivity-simulations will be presented. The key innovations
during the 1952-1972 period that should be traced by shadow prices are: CDs in
1961; subordinated debentures, authorized in 1963 and issued in volume in 1965;
Eurodollars in 1966; and bank-related commercial paper and loan repurchases in
1969.
The initial simulation (Model 1) used the parameters for the capital ratios as
listed in table 3 above, the government bond ratios were set at the historical values
from the 1920s, the mirrimum and maximum ratios for municipals were set as
described above, and the interest rate and cost figures in the objective function were
derived from published data (see the Appendix). Figures la and lb plot the 3-year
moving average of the shadow prices. Moving averages are presented in these
figures as well as in all subsequent figures in order to smooth normal cyclical
variations. 1
11The raw data are available on request. The normal cyclical drop in loan demand creates variability
in the annual shadow prices which masks somewhat the peaks in the overall trend. Presumably, bank
management is aware of these cyclical movements and they are ignored in the innovation process, hence
can be ignored here.

288

M. Ben-Horim and W.L. Silber, Financial ~,,ovation
4.0

• TD
ADD

(a)
3.0

O CD

¢,
• ~.

0.

2.0

0

#, 1.o

0.0

-1.0
52

56

56

60

62

64

Year

F i g . la. Deposit shadow prices F N C B

68

68

70

72

Model 1

35.0

O DEB

(b)

•

CAPST

25.0

t.
¢,j

15.0

0

.~

5.o
o---o---o--o-..~-.o
-5.0

-15"O2

,•

I

56

I

58

I

60

6

~

I

64

i

66

I

68

I

70

I

72

Year

Fig. lb. capital shadow prices FNCB Model 1

The rising shadow prices on all deposits in figure 1a between 1954 and 1960,'tells
the story' of the pressure to innovate the negotiable CD. The major source of the
rising value of deposits is the increased interest rate spread between earning assets
and sources of funds. The shadow price trend does less well in anticipating the 1966
innovations but confirms the 1969 pressures quite accurately. Figure lb plots the
capital and debenture shadow prices. There is a modest reflection of the pressure to
issue debentures during the 1963-65 period.
One problemwith this initial simulation is its 'conversatism' with respect to the
government bond constraint. By setting the minimum ratio of governments at
levels derived from the 1920s the model does not take account of bank
management's decision to reduce this ratio as the 1950s progressed under the

289

M. Ben-Horim and W.L. Silber, Financial innovation

pressure of rising loan demand. Imposing high minimum holdings of governments
reduces the allocation to the loan portfolio. This produced relatively low shadow
prices of deposits. Moreover, by imposing large holdings of governments and
thereby preventing loans from expanding, the capital adequacy problem that
developed between 1963 and 1965 failed to emerge from the model. This is the
nature of the bottleneck problem referred to above.
Our second set of simulations (Model 2) reduces the government-to-deposit
constraint by one-third, approximating the actual ratio of the early 1960s. This
produces the shadow prices plotted in figures 2a and 2b. The results tell the same
story as presented in the first simulations, only better. Deposit shadow prices trace
the appropriate path, including a respectable upturn in 1966. The capital shadow
4.0
• TD

(a)

A DD

3.0

O CD

._u
~2.0

o
03

1.0

0.0

--1.0
52

I

54

56

58

60

62

64

66

68

70

72

I
68

,~
0

72

Year

Fig. 2a. Deposit shadow prices FNCB Model 2

35.0
O DEB

(b)

• CAPST

25.0

15.0
"7-.

5.0
03

-5.0

-15.0
52

,~4

i
56

,
58

I
60

,
62

|
64

r~6

Year

Fig. 2b. Capital Shadow prices FNCB Model 2

!

290

M. Ben-Horim and W.L. Silber, Financial innovation

prices move sharply higher between 1963 and 1965, describing the pressure to
expand capital as a result of increased allocations to loans.
Other simulations of the model were also carried out with similar results. The
capital ratios, ~bi and tk2,were varied, as were the maximum and minimum ratios of
municipals to deposits. The values of fll and f12 in the governments-to-deposit
constraint that are recorded in table 2 were substituted for the purely historical
values. Finally, the bank-customer relationship was simulated in the model by
increasing the loan rate by 20 percent. The robustness of the model under such
sensitivity experiments lends considerable credibility to the results.

5. Simulations of the LP model: Large New York City banks
The pressures to innovate felt by First National City Bank should also have been
present for other banks with similar characteristics. The Federal Reserve's
classification entitled 'Large New York City Banks' is ideal from this viewpoint.
The model as discussed above can be simulated on this set of data with relatively
minor modifications. In some of the parameter derivations we used 'comparable
bank ratios' to (partially) constrain the behavior of an individual bank. This is
clearly not directly applicable when using an aggregate. Nevertheless, since the
derived parameter values were varied over a reasonably wide range, the choice of a
particular value does not appear crucial. The one change in initial specification
concerns the capital ratios, 4)i and ~b2. We assume that the 'average' large New
York City Bank (LNYCB) is constrained by the previous year's loan to capital
ratio of all LNYCB.
The simulation experiments reported in figures 3a, 3b, 4a and 4b correspond to
those reported in the previous set of figures. The results for LNYCB are quite
similar to those presented for First National City Bank. Once again there is less
4.0
eTD

(a)

A DD
3.0

-g

O CD

2.0

1.0

0.0

--0.1

52

i

I

I

I

,

I

I

I

i

I

54

56

58

60

62

64

66

68

70

72

Year

Fig. 3a. Deposit shadow prices LNYB Model 1

M. Ben-Horim and W.L. Silber, Financial innovation

291

35.0
0 DEB

(b)

• CAPST

25.0

~
u 15.0
O

.= 5.0

O')

o o___~

o---o o o ~

--5.0

- 15.0

I

52

54

t

56

58

I

60

6J2
Year

64

66

I

I

I

68

70

72

Fig. 3b. Capital shadow prices LNYB Model 1
4.0
•TD

(a)

A DD
3.0

OCO

20
O.

O

.~ 1.0
¢/3

0.0

-1.0
52

,

,

,

,

54

56

58

60

_

,

62

_

64

66

,

68

I

7~

72

"70

72

Year

Fig. 4a. Deposit shadow prices LNYB Model 2
35.0
O DEB

(b)

• CAPST

25.0
.u
~. 15.0
O
¢-

m

5.0

-5.1

-15.1

•54

i

56

58

I

60

;2

I

Year

64

66
i

Fig. 4b. Capital shadow prices LNYB Model 2

i

68

I

292

M. Ben-Horim and W.L. Silber, Financial innovation

'explanatory power' for the 1966 innovations but even here there is a brief upturn in
the shadow prices coincident with the innovation. Thus, the model generates
shadow prices for large money market banks which confirms the pressure to
innovate felt by an individual bank. The model does not, of course, permit us to
identify the particular institution that is the innovator. This is left to the behavioral
scientists.
6. A note on adversity-induced innovation
The shadow price approach to financial innovation has essentially focussed on
the utility (profit) opportunities that banks perceived over time. Rising shadow
prices imply increased profit opportunities that could be exploited by altering the
constraints faced by the bank. Another explanation of innovation focusses on
adversity-that innovation is stimulated by decreases in utility (profitability).
These two theories are not, of course, mutually exclusive.
In an effort to evaluate the extent to which 'adversity' contributed to bank
innovations during the 1952-72 period we assumed that a fully specified bank
utility function includes stockholders' wealth as a major argument. Further we
assume that stockholders form their opinion of the value of bank's stock based on
the bank's profit, growth,'soundness' and so on. The behavior of bank stock prices
can then be regarded as a reflection of investor evaluation of bank utility. Table 4
presents the price earnings (P/E)ratio as well as price dividend (P/D)ratio for New
York City banks, for (Moody's) industrials, and the ratio of the former to the latter.
One relationship that emerges is a decline in the stock market's relative
valuation ofcommercial bank stocks from 1952 through 1960. This is illustrated in
columns (6) and (7) of table 4. Commercial banks were, therefore, made painfully
aware of the continued slippage in investor valuation of bank management
practices. This seems to qualify as an adverse experience and helps explain the CD
innovation.
While the profit opportunity approach as presented above explains the timing of
all the 1960s innovations, the crude measures of adversity just presented helps
account for at least one of the period's innovations. Needless to say, these results
are highly tentative and must be subject to further investigation if the adversity
hypothesis is to be given equal weight in explaining the innovations discussed here.
7. SummaryPredicting the timing of innovative behavior is a difficult task. There has been
considerable empirical work in the real sector on this issue. In the financial sector,
except for a few somewhat general descriptions of the innovative process, rigorous
empirical investigations are painfully absent. The study presented here is a step
towards a formal empirical evaluation of the stimuli to financial innovation.
Basically, we assumed that innovations were a reaction to profit opportunities.
We then tried to estimate the profit opportunities and their changes over time by

M. Ben-Horim and W.L. Silber, Financial innovation

293

Table 4
Price earnings ratio and price dividend ratio of large NYC banks and Moody's industrials, and their
relationship, 1952-72. a
NYC banks

Industrials

Relative ratios

Year
(1)

PIE

P/D

PIE

P/D

PIE

P/D

(2)

(3)

(4)

(5)

(6)= (2)/(4)

(7)= (3)/(5)

1952
1953
1954
1955
1956
1957
1958
1959
1960
1961
1962
1963
1964
1965
1966
1967
1968
1969
1970
1971
1972

13.10
12.9
13.35
14.93
13.13
12.01
13.31
14.25
12.43
16.77
16.29
17.29
16.95
15.00
11.76
11.93
13.24
13.03
11.38
11.52
13.62

22.73
22.47
22.27
24.70
23.04
21.10
22.42
26.95
25.58
31.45
30.21
21.75
33.67
25.45
24.75
25.84
29.41
26.88
24.81
24.15
29.85

10.53
9.86
11.43
12.43
14.44
13.99
18.03
18.91
18.00
20.80
17.11
17.55
18.01
17.31
15.90
18.40
17.97
17.86
17.70
18.17
17.87

18.02
18.83
21.46
25.45
25.71
24.33
26.04
32.05
28.74
32.89
29.50
31.25
33.56
33.56
29.07
32.15
31.85
31.85
27.78
33.56
37.74

1.24
1.31
1.17
1.20
0.91
0.86
0.74
0.75
0.69
0.81
0.95
0.99
0.94
0.87
0.74
0.65
0.74
0.73
0.64
0.63
0.76

1.26
1.19
1.04
0.97
0.90
0.87
0.86
0.84
0.89
0.96
1.02
1.02
1.00
0.76
0.85
0.80
0.92
0.84
0.89
0.72
0.79

"Source:

Moody's Industrials Manual, 1975.

using a linear programming approach to bank asset allocation (with profit
maximization as the objective function). The shadow prices of the constraints were
used to measure these profit opportunities. The results obtained, while differing
somewhat from one version of the model to another, tend to support the view that
innovations were introduced coincident with or immediately following periods of
rising shadow prices.
There is much that can be done along these lines in the future. Other institutions
can be simulated and other time periods can be used. Given the reasonable degree
of success in this initial investigation, it appears that such additional research
efforts might be quite fruitful.

Appendix: Data sources and definitions
This appendix provides the sources and definitions of the data used in the
simulations.

294

M. Ben-Horim and W.L. Silber, Financial innovation

A. Revenue figures
a. Interest rates on government bonds. The rates are taken from the 'Money
Market Rates' of the Federal Reserve Bulletin. The maturity assumed is up to 5
years.
b. State and local government bonds. The interest rate on these securities is
estimated by the rate on 'Good Grade' municipal securities maturing within 2
years. The yields are taken from Salomon Brothers, An Analytical Record of Yields
and Yield Spread. The rates were then adjusted to a before-tax basis, because of
their tax-exempt property. The adjustment was made by dividing the tax-exempt
rate by (1 - t) where t is the marginal tax rate which was 52 percent until 1964 and
48 percent since 1965.
c. Interest rates on loans. The rate used is taken from the Operating Ratios,
Federal Reserve Bank of New York (for banks in the second district). In this
publication the net rate (after losses or recoveries) on loans of large New York City
banks is available since 1952.
d. Other assets. No yield is assumed on these assets. While this might effect
total profits, it will have no impact on the optimization process because other
assets are set equal to their actual balance sheet level.
B. Cost figures
a. Cost of demand deposits. Demand deposit cost is taken from Barro, R.J. and
Santomero, A.M., 'Household Money Holdings and the D e m a n d Deposit Rate,'
Journal of Money, Credit and Banking (May 1972), pp. 397-413.
The cost is available for the 1950-1968 period, and it was obtained by surveying
major commercial banks on the rates at which they have remitted service charges
as a function of demand deposit balances. The rate is an unweighted mean of those
banks from which information was obtained in the survey. The rate is an imputed
marginal cost, and is computed on the basis of household accounts. Since the cost
of demand deposits according to Barro and Santomero is very stable over the
period 1950-1968 with a small long run upward trend, an estimate for 1969-1972
was derived by running a simple regression analysis where the dependent variable
is the cost of demand deposits and the independent variable is time (years).
b. Cost of time and savings deposits. The cost of these funds has two
components: the interest rate paid to the depositors and the operating cost. The
interest rate component was taken from the Operating Ratios, Federal Reserve
Bank of New York. As for the operating cost component, it is only available since
1966 from the Functional Cost Analysis, Federal Reserve Bank of New York. The
cost for the years prior to 1966 was approximated in the following way. The
operating cost components of time deposits and the cost of d e m a n d deposits for
1966-1973 were taken from the Functional Cost Analysis publication. It was found
that the operating cost of time deposits averaged about 20.5 percent of the cost
demand deposits. We therefore used 20.5 percent of the cost of demand deposits in

M. Ben-Horim and W.L. Silber, Financial innovation

295

the years 1952-1965 as an estimate for the operating cost component in time
deposits.
c. Cost of CDs. The rate on prime commercial paper (4-6 months) as reported
by the Federal Reserve Bulletin (average figure for the year) is used to approximate
the cost of the (hypothetical) CDs prior to 1961. The commercial paper rate was
selected because it is regarded as the closest competitor of negotiable CDs.
The rate for the period since 1961 was obtained from the Federal Reserve Board.

C. Cost of debentures
The rate was approximated by Moody's rate on Aa corporate bond yields with
fifteen years maturity.

D. Cost of equity capital
The following formula was used to estimate the cost of equity capital: cost of
equity = (NOE/P) + gr, where NOE = net operating earnings (excluding extraordinary items) per share; p = price per share (the price used is the average of the high
and low during the year as reported by Moody's); g =earning retention rate; r
= rate of return on equity measured by the NOE divided by total equity funds.

E. Balance sheet data
a. Data for First National City Bank were taken from the annual issues of

Moody's Bank and Finance Manuals: 1952-1972.
b. Data for large New York City banks were taken from the Federal Reserve
Bulletin: 1952-1972.
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