A multicriteria methodology for bank asset
liability management
Kyriaki Kosmidou1,2, Constantin Zopounidis1
1
Technical University of Crete
Dept. of Production Engineering and Management
Financial Engineering Laboratory
University Campus
73100 Chania, Greece
2
University of Crete
Dept. of Economics
University Campus
74100 Rethymno, Greece
E-mails: kosmidou@dpem.tuc.gr, kostas@dpem.tuc.gr
Abstract :
The aim of this paper is to present an Asset Liability Management (ALM) technique,
which combines a goal programming model with a simulation analysis to determine the
balance sheet of a bank for the year 2000. To attain this goal, we analyzed the 1999
balance sheet of a Greek commercial bank facing conflicting goals such as returns,
liquidity, solvency, and expansion of deposits and loans under uncertainty. An optimizer
was embedded in a simulation model to obtain different optimal solutions for a set of
interest rate scenarios, while a sensitivity analysis explored the effects of alterations in the
order of goal priorities.
Keywords: Asset and liability management, banking, goal programming, optimization,
simulation analysis
1
1. Introduction
Bank asset and liability management is defined as the simultaneous planning of all asset
and liability positions on the bank’s balance sheet under consideration of the different
bank management objectives and legal, managerial and market constraints, for the
purpose of mitigating interest rate risk, providing liquidity and enhancing the value of the
bank (Gup and Brooks, 1993).
Nowadays, the growing internationalization, the globalization of financial markets, the
increasing competition in the national and international banking markets and the
introduction of complex products have increased volatility and risks. The great and fast
availability of all kinds of different information due to the development towards an
“information society” has eliminated any delays between the occurrence of an event and
the impact on the markets. Consideration of uncertainties is critical in financial planning.
Investors often seek to develop long-term strategies that hedge against uncertainties. But
evaluating long-term investment strategies requires several components that are not now
commonly available.
There must be a way to generate scenarios that is logically
consistent and based on sound economic principles.
Moreover, parameters of the
scenario generator must fit past data and trends. Thus, the stochastic model, which will be
implemented, should take into account changing economic conditions, such as the
deregulation of interest rates and currencies.
All the above drove banks to seek out greater efficiency in the management of their
assets and liabilities. Thus, the central problem of ALM revolves around the bank’s
balance sheet and the main question that arises is: What should be the composition of a
bank’s assets and liabilities on average given the corresponding returns and costs, in order
2
to achieve certain goals, such as maximization of the bank’s gross revenues? This need
has led banks to determine their optimal balance among profitability, risk, liquidity and
other uncertainties. The optimal balance between these factors cannot be found without
considering important interactions that exist between the structure of a bank’s liability
and capital and the composition of its assets. ALM is heavily dependent on the movement
of interest rates in the market. The history of ALM suggests that it is very important for a
financial institution to measure, manage and control interest rate risk.
Many are the studies that have been developed concerning the bank asset liability
techniques.
1.1 Previous Research
Looking to the past, we find the first mathematical models in the field of bank
management. Asset and liability management models can be deterministic or stochastic
(Kosmidou and Zopounidis, 2001).
Deterministic models use linear programming, assume particular realizations for
random events, and are computationally tractable for large problems. The deterministic
linear programming model of Chambers and Charnes (1961) is the pioneer in ALM.
Chambers and Charnes were concerned with formulating, exploring and interpreting the
use and construction which may be derived from a mathematical programming model
which expresses more realistically than past efforts the actual conditions of current
operations. Their model corresponds to the problem of determining an optimal portfolio
for an individual bank over several time periods in accordance with requirements laid
down by bank examiners which are interpreted as defining limits within which the level
of risk associated with the return on the portfolio is an acceptable one.
3
Cohen and Hammer (1967), Robertson (1972), Lifson and Blackman (1973), Fielitz
and Loeffler (1979) have realized successful applications of Chambers and
Charnes’model. Even though these models have differed in their treatment of
disaggregation, uncertainty and dynamic considerations, they all have in common the fact
that they are specified to optimize a single objective profit function subject to the relevant
linear constraints.
Eatman and Sealey (1979) developed a multiobjective linear programming model for
commercial bank balance sheet management considering profitability and solvency
objectives subject to policy and managerial constraints.
Giokas and Vassiloglou (1991) developed a goal-programming model for bank asset
and liability management. They supported the idea that apart from attempting to
maximize revenues, management tries to minimize risks involved in the allocation of the
bank’s capital, as well as to fulfill other goals of the bank, such as retaining its market
share, increasing the size of its deposits and loans, etc. Conventional linear programming
is unable to deal with this kind of problem, as it can only handle a single goal in the
objective function. Goal programming is the most widely used approach that solves largescale multi-criteria decision making problems.
Apart from the deterministic models, several stochastic models have been proposed
since the 1970s. These models, including the use of chance-constrained programming
(Charnes and Thore, 1966; Charnes and Littlechild, 1968; Pogue and Bussard, 1972),
dynamic programming (Samuelson, 1969; Merton, 1969,1990; Eppen and Fama, 1971),
sequential decision theory (Wolf, 1969; Bradley and Crane, 1972) and stochastic linear
programming under uncertainty (Cohen and Thore, 1970; Booth, 1972; Crane, 1971;
Kallberg et al. 1982), presented computational difficulties. The stochastic models, in their
4
majority, originate from the portfolio selection theory of Markowitz (1959) and they are
known as static mean-variance methods. Pyle (1971) and Brodt (1978) adapted
Markowitz’s theory and presented an efficient dynamic balance sheet management plan
that considers only the risk of the portfolio and not other possible uncertainties or
maximizes profits for a given amount of risk over a multi-period planning horizon
respectively.
Wolf (1969) proposed the sequential decision theoretic approach that employs
sequential decision analysis to find an optimal solution through the use of implicit
enumeration.
An alternative approach in considering stochastic models, is the stochastic linear
programming with simple recourse. Kusy and Ziemba (1986) employed a multi-period
stochastic linear program with simple recourse to model the management of assets and
liabilities in banking while maintaining computational feasibility. Their results indicate
that the proposed ALM model is theoretically and operationally superior to a
corresponding deterministic linear programming model and that the computational effort
required for its implementation is comparable to that of the deterministic model. Another
application of the multistage stochastic programming is the Russell-Yasuda Kasai model
(Carino et al., 1994), which aims at maximizing the long term wealth of the firm while
producing high income returns.
Mulvey and Vladimirou (1992) used dynamic generalized network programs for
financial planning problems under uncertainty and they developed a model in the
framework of multi-scenario generalized network that captures essential features of
various discrete time financial decision problems.
5
Finally, Mulvey and Ziemba (1998) present a more detailed overview of various asset
and liability modeling techniques, including models for individuals and financial
institutions such as banks and insurance companies.
Moreover, over the years, many models have been developed in the area of financial
analysis and financial planning techniques. Kvanli (1980), Lee and Lerro (1973), Lee and
Chesser (1980), Baston (1989), Sharma et al. (1995), among others have applied goal
programming to investment planning.
Booth et al. (1989), Giokas and Vassiloglou
(1991), Seshadri et al. (1999) presented bank models using goal programming. These
studies focus on the areas of banking and financial institutions and they use data from the
bank financial statements.
Taking into consideration all the above, the purpose of this paper is to develop a goal
programming system into a stochastic environment, focusing, mainly, on the change of
the interest rate risk. Taking into account the financial statements of a Greek commercial
bank for the year 1999, a goal programming system is developed in order to determine the
assets and liabilities of the bank for the period 2000. The objectives used are based on
liquidity, solvency and average yield of assets and liabilities. Moreover, ALM is
associated with the changes of the interest rate risk and specifically with the bond interest,
deposit interest and loan interest, since the loans and deposits constitute the major
accounts of the bank’s balance sheet and the profitability sources of the banks. Thus, a
simulation analysis is performed to generate interest rate scenarios and develop optimal
ALM strategies along these scenarios, while a sensitivity analysis explores the effects of
alterations in the order of goal priorities. This system provides the possibility to the
administrative board and the managers of the bank to proceed to various scenarios related
6
to their future economic process, aiming mainly to the management of the risks, emerged
from the changes of the market parameters.
The rest of the paper is organized as follows. The next section outlines the
methodology used and presents the application of this methodology in a commercial bank
of Greece. Section 3 presents the results of this analysis. Finally, the conclusions of the
paper as well as future research perspectives are discussed in the last section.
2. Applying the Goal Programming Model
The present paper, using data from a commercial bank of Greece, presents an ALM
methodology in a stochastic interest-rate environment in order to choose strategic
directions in bank’s financial plan.
More precisely, the goal programming model of this study was developed in terms of a
one-year time horizon (1999). The model used balance sheet and income statement
information for 1999 to produce a future course of ALM strategy for the year 2000. As
far as model variables are concerned, we used variables familiar to management and
facilitated the specification of the constraints/goals. For example, goals concerning
measurements such as liquidity, return and risk have to be expressed in terms of utilized
variables.
The variables used in the specification of the model were taken directly from the 1999
financial statement of a commercial bank of Greece. 42 structural variables were used, of
which 22 correspond to assets (Xi, i=1,…,22) and 20 to liabilities (Yj, j=1,…,20), as they
are presented in Table 1.
Insert Table 1
7
2.1 Constraints and goals
Before proceeding to the goal programming formulation it would be appropriate to
describe the constraints and goals that were used.
Certain constraints are imposed by the banking regulation on particular categories of
accounts. For example, the total loans (X8+X9+X10) granted are expected to maintain at
least the previous year’s level (7,632,392) and cannot rise by more than 38% in relation to
these levels, as follows:
X 8 + X 9 + X 10 ≥ 7,632,392
(1)
X 8 + X 9 + X 10 ≤ 1.38 × 7,632,392
(2)
Similarly, the following constraints state that the total deposits are not expected to
increase by more than 28% above the previous year’s levels (12,348,981) and cannot be
lower than that.
Y4 + Y5 + Y6 + Y7 + Y8 ≥ 12,348,981
(3)
Y4 + Y5 + Y6 + Y7 + Y8 ≤ 1.28 × 12,348,981
(4)
Since the major part of the capital of the commercial banks is consisted of the share
capital the variable Y19 is selected for the development of the asset liability management
model.
Y19 ≥ 1,052,384
(5)
Moreover, the ratio retained earnings to total assets Y20 indicates the profitability of the
total assets. In the present paper this ratio is set equal to 2.27%, which is the average
growth rate of the ratio retained earnings to total assets.
Y20 ≥ 2.27% × ∑i =1 X i
22
(6)
8
The following constraints are derived from the obligation of the bank to reserve a
specific amount of its deposits in a special interest-bearing account at the Bank of Greece,
as well as in interest-bearing government bonds. Moreover, a percentage of private
deposits is directed towards loans for public sector corporations.
Y4 + Y5 + Y6 + Y7 + Y8 − 1.99( X 8 + X 9 + X 10 ) = 0
(7)
Y4 + Y5 + Y6 + Y7 + Y8 − 2.29( X 4 + X 5 + X 11 + X 12 + X 13 ) = 0
(8)
Y4 + Y5 + Y6 + Y7 + Y8 − 5.67 X 3 = 0
(9)
The constraint
∑
22
i =1
X i − ∑ j =1 Y j = 653,116
20
(10)
defines the equality relationship between assets and liabilities and net worth (the amount
653.116€ refers to the amount of capital that is assumed stable).
The following constraint assumes that the total assets are expected to increase not
more than 30% above the previous year’s levels.
∑
22
i =1
X i ≤ 1.30 × 17,327,046
(11)
The goal constraint
Y19 − 0.3349Y20 − 0.08(0.2 X 4 − 0.5 X 8 − 0.7 X 9 − 0.5 X 10 − 0.2 X 11 − 0.4 X 12 − X 13 ) − d 1+ + d 1− = 0
(12)
involves the solvency goal which is related to the risk exposure of the bank. The solvency
ratio is used as a risk measure and is defined as the ratio of the bank’s equity capital to its
total weighted assets. The weighting of the assets reflects their respective risk, greater
weights corresponding to a higher degree of risk. According to the proposal of the
Commission of the European Communities, this ratio must be greater than or equal to 8%
in order to guarantee the required solvency.
9
The following constraint defines the liquidity goal, specified as the ratio of liquid
assets to current liabilities which is used as a liquidity risk measure. According to the
Bank policy this ratio should be approximately 0.60 and not higher than 0.60, indicating
that at least half of the total capital of the bank should be derived from the liquid current
data of the bank and not from the deposits in order to avoid the liquidity risk.
∑
21
i =1
X i − 0.6∑ j =1 Y j − d 2+ + d 2− = 0
18
(13)
The constraint
Y4 + Y5 + Y6 + Y7 + Y8 − d 4+ + d 4− = 1.28 × 12,348,981
(14)
defines the goal for the growth of the deposits (28% higher than the previous year’s
deposits), reflecting the management decision to maintain the forecast for deposit growth
in the overall economy.
Taking into account the historical data of the previous years of the bank, we assume that
the average growth rate of the ratio deposits to total assets should be at least 73.31%.
Y4 + Y5 + Y6 + d10− − d10+ = 73.31% × 17,327,046
(15)
Similarly, the following constraint specifies the goal for the increase of the loans
granted which is set at 38% above the previous year’s level.
X 8 + X 9 + X 10 − d 3+ + d 3− = 1.38 × 7,632,392
(16)
The constraint
∑
22
i =1
RiX X i − ∑ j =1 R Yj Y j − d 5+ + d 5− = 30% × 17,327,046 + 653,116
20
(17)
defines the goal for the overall return of the selected asset-liability strategy over the year
of the analysis. This goal is set at 30% and is defined on the basis of the returns for all
assets RX and liabilities RY.
10
Finally, it should be noted that the above goal programming model incorporates also
goals reflecting that variables such as cash, cheques receivable, deposits to the Bank of
Greece and fixed assets, should remain at the levels of previous years.
X 1 − 0.01 × 17,327,046 + d 6− − d 6+ = 0
(18)
X 2 − 0.004 × 17,327,046 + d 7− − d 7+ = 0
(19)
X 3 − 0.14 × 17,327,046 + d 8− − d 8+ = 0
(20)
X 22 − 0.015 × 17,327,046 + d 9− − d 9+ = 0
(21)
2.2 Mathematical formulation
As was already mentioned the major advantage of goal programming technique is its
great flexibility, which enables the decision maker to incorporate easily numerous
variations of constraints and goals.
Taking into account the constraints and goals as were described above as well as the
preferences of the banking managers, the proposed goal programming formulation can be
expressed as follows:
10
10
k =3
k =3
Min z = ∑ d k+ + ∑ d k− + 2d 2+ + 3d1−
(22)
subject to
X 8 + X 9 + X 10 ≥ 7,632,392
(23)
X 8 + X 9 + X 10 ≤ 1,38 × 7,632,392
(24)
Y4 + Y5 + Y6 + Y7 + Y8 ≥ 12,348,981
(25)
Y4 + Y5 + Y6 + Y7 + Y8 ≤ 1.28 × 12,348,981
(26)
Y19 ≥ 1,052,384
(27)
11
Y20 ≥ 2.27% × ∑i =1 X i
(28)
Y4 + Y5 + Y6 + Y7 + Y8 − 1.99( X 8 + X 9 + X 10 ) = 0
(29)
Y4 + Y5 + Y6 + Y7 + Y8 − 2.29( X 4 + X 5 + X 11 + X 12 + X 13 ) = 0
(30)
Y4 + Y5 + Y6 + Y7 + Y8 − 5.67 X 3 = 0
(31)
∑
i =1
X i − ∑ j =1 Y j = 653,116
(32)
∑
i =1
X i ≤ 1.30 × 17,327,046
(33)
22
22
22
20
Y19 − 0.3349Y20 − 0.08(0.2 X 4 − 0.5 X 8 − 0.7 X 9 − 0.5 X 10 − 0.2 X 11 − 0.4 X 12 − X 13 ) − d1+ + d1− = 0
(34)
∑
X i − 0.6∑ j =1 Y j − d 2+ + d 2− = 0
i =1
21
18
(35)
X 8 + X 9 + X 10 − d 3+ + d 3− = 1.38 × 7,632,392
(36)
Y4 + Y5 + Y6 + Y7 + Y8 − d 4+ + d 4− = 1.28 × 12,348,981
(37)
∑
(38)
22
i =1
RiX X i − ∑ j =1 R Yj Y j − d 5+ + d 5− = 30% × 17,327,046 + 653,116
20
X 1 − 0.01 × 17,327,046 + d 6− − d 6+ = 0
(39)
X 2 − 0.004 × 17,327,046 + d 7− − d 7+ = 0
(40)
X 3 − 0.14 × 17,327,046 + d 8− − d 8+ = 0
(41)
X 22 − 0.015 × 17,327,046 + d 9− − d 9+ = 0
(42)
Y4 + Y5 + Y6 + d10− − d10+ = 73.31% × 17,327,046
(43)
Xi ≥ 0, Yj ≥ 0, d k+ ≥ 0, d k− ≥ 0 , for all i=1, 2, …, 22, j=1, 2, …, 20, k=1, 2, …, 10
(44)
The objective function involves the minimization of the deviations d+ and d– from the
target values of goals, where d+ denotes the over-achievement of a goal and d– the underachievement. The deviations corresponding to different goals are weighted in the
12
objective according to the significance of the goals. It should be mentioned that the above
goal programming formulation is based on the version that gives first priority level to the
solvency goal, second priority level to the liquidity goal and third priority level to the rest
goals (version 1). More precisely, the selected weighted scheme assigns higher weight to
under-achievement of the solvency goal ( d 1− ), considering that it is achieved with a
priority rank 3/2 higher than the priority rank that is imposed to the over achievement of
the liquidity goal ( d 2+ ) and three times higher than the priority rank of the remaining goals
( (d k+ + d k− ), ∀k = 3,..,10 ).
Once the optimal solution z* of the goal programming problem (22)-(44) is obtained, a
post-optimality stage is performed to investigate the sensitivity and the robustness of the
optimal solution that was obtained from the above goal programming formulation. This is
achieved through the investigation of the existence of sub-optimal solutions that
correspond to objective function values lower than z* + k(z*), where k(z*) is a small
portion of the optimal solution z*. In this case study k(z*) is set equal to 5% of z*. This
additional constraint is incorporated into the initial goal programming formulation and the
new goal programming formulation is solved 42 times. Each of the 42 obtained solutions
corresponds to the maximization of the asset and liability variables. The final ALM
solution is specified as the average of the 42 solutions obtained during the post optimality
analysis.
3. Simulation Analysis and Results
The major unknown element in the above goal programming formulations which is of
interest to the bank’s managers is the return of the assets and liabilities used in the goal
constraint (38). These involve the bonds’ interest rates, the interest rates of the loans
13
granted and the interest rates of the deposits to the bank. To cope with the uncertainty on
these parameters a scenario analysis approach is employed. This analysis involves the
consideration of 2,500 scenarios on the aforementioned uncertain parameters. The
scenarios are generated at random as follows. Initially, 50 scenarios are generated for the
bonds’ interest rates. The bonds’ interest rates are generated as normally distributed
random variables with appropriate mean and standard deviation so that they range
(approximately) between 10% and 13%. 50 scenarios are also generated for the interest
rates of the deposits at the bank. Similarly to the scenarios for the bonds, the deposits’
interest rates RD are treated as normally distributed random variables with appropriate
mean and standard deviation so that they range (approximately) between 3.5% and 7%.
On the basis of the deposits’ interest rates, the loans’ interest rates RL are specified as:
RL=RD+S, where S is the spread between RL and RD. The spread is defined as normally
distributed random variables with mean and standard deviation so that it ranges
(approximately) between 3% and 4%.
The goal programming formulation (22)-(44) is solved for each of the 2,500 interest
rate scenarios and 2,500 different solutions are obtained. Each of these solutions is then
evaluated along all scenarios. This evaluation leads to the calculation of the expected
present value and the corresponding risk of the return (standard deviation) among the
solutions. An interactive technique through the set of non dominated solutions was
performed. This analysis concluded 207 solutions, non-dominated by any other solution
in terms of their expected present value and risk. Each of these solutions can be
considered as ALM strategies to implement during the year 2000. For comparison reasons
the actual strategy (AS) that the bank followed during the year 2000 is also considered
along the same dimensions. Table 2a presents the results (expected present value, in euro)
14
for AS and for 11 (out of the 207 non-dominated solutions) of the non-dominated
identified solutions (ND1, ND2, …, ND11), that are similar to the actual strategy of the
bank (in terms of the expected present value and risk)1. It should be noted that in the
present paper, the selection criterion of these 11 non-dominated solutions was based on
their expected present value. Taking into account a different selection criterion we could
have probably ended to the presentation of a different set of 11 out of 207 non dominated
solutions.
A sensitivity analysis was carried out, exploring the effects of alterations in the order
of goal priorities. As was expected, changes in the order of priorities, by giving first
priority level to the liquidity ratio and second to the solvency ratio (version 2), had no
effect on the results, since the optimal solution of the model (version 1) achieves the two
relevant goals.
Only variations affecting the order of the loans and deposits goals
produce a different optimal solution. Reordering the priority levels (version 2) produces
the optimal solution in Table 2b for AS and for 11 of the non-dominated identified
solutions (ND1, ND2, …, ND11) (Kosmidou and Zopounidis, 2004).
However, the
comparison of the solution of the second version of the problem to that of the original
indicates that the optimal values of the variables change only marginally.
This is
explained by the fact that the original solution does not deviate much from the target
values of the loans and deposits goals.
Insert Table 2a and Table 2b
1
We present only 11 out of the 207 non dominated solutions due to the saving of space.
15
Assuming that the decision maker choose the solutions ND1, ND2, ND3 of version 1 and
the solutions ND1, ND2, ND3 of version 2 as the most preferred ones, based on the
expected value and standard deviation, Table 3 presents the final values of all decision
variables based on the selected solutions for both versions.
The following sets of
solutions could be considered as a base for the final decision.
Insert Table 3
If we analyze the content of the above Table 3 and compare it with the actual results of
the bank’s financial statement we conclude that the values of the variables X2, X3 do not
differ significantly from those of the actual strategy.
This is due to the restriction
imposed, that the variables of fixed assets, cash, cheques receivable and deposits with the
Bank of Greece should remain at the levels of previous years. Although variable X4 of
the solution ND1 does not vary significantly from the AS, the values of X4 of the other
solutions in both versions differ significantly from the AS. Similarly, the values of X8 for
the solutions ND2 (version 1), ND3 (version 1), ND1 (version 2) and ND3 (version 2) have
not significant differences with those of the AS. The above results clearly indicate that
the main source of funds for the bank is the accounts of loans and deposits. The values of
X9, X10, Y1,…, Y8, concerning the loans and deposits variables, differ significantly from
those of the AS.
Moreover, the performance of the solutions obtained through the
proposed goal programming model either outperform or not the actual strategy of the
bank, both in terms of their expected present value and the risk evaluated through all the
interest rates scenarios considered in the simulation analysis. This is due to the fact that
several restrictions were imposed on the loans and deposits goals during this research.
16
Based on the historical data of the financial statements of the bank it was assumed that the
total deposits and the total loans were not expected to increase by more than 28% and
38% respectively above the previous year’s levels. Moreover, since ALM deals with
uncertainty, it was necessary to perform a simulation analysis. Thus, the consideration of
scenarios on loans and deposits interest rates contributes to the selection of the optimal
solution for the bank. With the introduction into the monetary union, the commission and
interest rate income from loans and deposits has been reduced due to the common
currency. Thus, the bank should change its policy and find new income resources in
order to sustain the desirable income levels of deposits and loans and consequently of its
assets.
4. Conclusions
This paper has presented the problem of bank ALM. The problem was handled
through a goal programming model, in which goals secondary to the objective function
were included as additional hard constraints. This model addresses the multiobjective
nature of the problem, as it allows the incorporation of several objectives. The objectives
used are based on liquidity, solvency and average return of assets and liabilities. A postoptimality analysis is performed to investigate the sensitivity and the robustness of the
optimal solution. Moreover, a simulation analysis on interest rate scenarios as well as a
sensitivity analysis in the order of goal priorities have been investigated to obtain a wide
range of non-dominated solutions.
Finally, as the number of solutions was relatively
large, a technique of interactive search through the set of non dominated solutions was
performed. Thus, from the 2.500 solutions that were obtained from the solution of the
17
goal programming model, we concluded to 207 solutions, non-dominated by any other
solutions in terms of their expected present value and risk.
Current trends in the sophistication of the data and the frequent fluctuations of the
market rates emphasize the need for all organizations to have an asset liability
management system which can give them an accurate representation of its current
position and the favorable scenarios for the future. Finally, a number of further
developments of the model can be explored and several features, such as bank
performance ratios, could be incorporated into the model to determine the favorable
alternatives in changing market environments. Moreover, the off balance sheet assets and
liabilities could be taken into account into the model. The consideration of derivatives
would be interesting in order to know how derivatives hedge the interest rate risk. Such
variations as well as the development of a decision support system for asset liability
management will be studied in future research.
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22
Table 1: The decision variables of the goal programming formulation
X1:
Cash
Y1:
Due to credit institutions
X2:
Cheques receivable
Y2:
Due to credit institutions with agreed maturity
X3:
Deposits to the Bank of Greece
Y 3:
Commitments arising out of sale and repurchase
transactions
X4:
Treasury bills and other securities issued by the Greek
State
Y4:
Deposits repayable on demand
X5:
Other Treasury bills and securities
Y5 :
Saving deposits
X6:
Interbank deposits and loans repayable on demand
Y6:
Deposits with agreed maturity
X7:
Other interbank deposits and loasn
Y7:
Cheques and orders payable
X8:
Loans and advances to customers maturing within one
year
Y8:
Commitments arising out of sale and repurchase
transactions (customer amounts)
X9:
Loans and advances to customers maturing after one
year
Y9:
Dividends payable
X10:
Other receivables
Y10:
Income tax and other taxes payable
X11:
Securities issued by the Greek State
Y11:
Withholdings in favour of social security funds and other
third parties
X12:
Other securities
Y12:
Other liabilities
X13:
Shares and other variable-yield securities
Y13:
Accruals and deferred income
X14:
Investments in non-affiliates
Y14:
Accrued interest on time deposits
X15:
Investments in affiliates
Y15:
Other accrued expenses of the year
X16:
Other assets
Y16:
Provisions for staff retirement indemnities
X17:
Deferred charges
Y17:
Other provisions for liabilities and charges
X18:
Accrued income state bonds
Y18:
Loans of reduced indemnity
X19:
Accrued income other bonds
Y19:
Share Capital
X20:
Accrued income loans and advances
Y20:
Retained earnings
X21:
Other accrued income
X22:
Fixed assets
23
Table 2a: Results of the scenario simulation (version 1)
Solutions
AS
ND1
ND2
ND3
ND4
ND5
ND6
ND7
ND8
ND9
ND10
ND11
Expected present value
1,938,864.22
2,130,981.42
2,128,391.16
2,121575.94
2,114,888.59
2,113,781.52
2,111,739.58
2,107,943.52
2,107,422.41
2,104,687.38
2,103,863.46
2,103,381.86
24
Standard Deviation
55,437.14
55,004.64
44,105.87
43,862.38
43,633.00
43,515.20
42,837.61
42,560.53
42,531.65
42,462.88
42,164.79
42,137.06
Table 2b: Results of the scenario simulation (version 2)
Solutions
AS
ND1
ND2
ND3
ND4
ND5
ND6
ND7
ND8
ND9
ND10
ND11
Expected present value
1,938,864.22
2,130,947.93
2,128,422.47
2,121,607.22
2,113,233.20
2,112,101.98
2,111,768.84
2,107,974.04
2,107,453.12
2,104,718.17
2,101,786.31
2,101,280.91
25
Standard Deviation
55,437.14
55,007.54
44,103.41
43,859.93
43,582.24
43,463.85
42,835.52
42,558.45
42,529.57
42,460.81
42,108.90
42,079.55
Table 3: Results of the decision variables
Version 1
Variables
X2
X3
X4
X8
X9
X10
Y1
Y2
Y3
Y4
Y5
Y6
Y7
Y8
Y19
Y20
Version 2
AS
ND1
ND2
ND3
ND1
ND2
ND3
79,079.94
1,883,999.81
6,976,945.44
8,262,491.89
3,610,828.97
19,372.98
851,488.71
3,205,814.06
986,568.61
3,070,110.44
6,712,749.03
5,637,741.45
189,980.40
4,515,094.38
744,576.73
337,545.89
71,153.30
2,786,231.92
3,779,185.45
189,120.55
144,370.52
7,605,169.72
27,912.73
27,125.26
172,567.99
12,087,289.46
309,248.10
306,890.03
3,011,042.54
83,464.84
5,018,383.78
529,219.80
69,915.08
2,786,260.08
164,344.93
7,605,997.51
143,622.98
189,120.55
26,153.74
25,907.52
72,640.73
12,087,359.25
305,942.27
304,176.22
3,017,216.88
83,400.03
5,075,529.05
527,320.69
68,682.47
2,786,222.04
164,344.93
7,602,072.28
147,439.82
189,120.55
27,417.96
27,327.37
75,889.30
12,087,247.24
308,393.81
306,577.45
3,012,156.41
83,504.04
5,048,367.63
527,505.57
71,056.40
2,786,646.51
164,344.93
7,676,080.94
74,586.21
189,120.55
270,579.40
26,259.55
162,181.26
12,087,413.96
305,449.34
308,075.08
3,015,889.90
83,349.23
5,038,760.56
529,822.53
70,873.21
2,786,646.51
164,344.93
189,120.55
74,435.69
7,676,246.28
25,910.89
24,359.51
157,660.64
12,087,531.83
305,751.76
306,072.61
3,017,611.03
83,239.78
5,060,526.05
528,632.55
70,361.87
2,786,626.42
164,344.93
7,675,934.70
74,729.57
189,120.55
25,313.61
24,993.44
70,504.22
12,087,396.61
306,082.00
307,206.82
3,016,121.01
83,365.34
5,090,478.27
527,213.99
26