Government debt as the integral portfolio of assets and liabilities generated by debt.
Rutkauskas, Aleksandras Vytautas ; Stasytyte, Viktorija ; Maknickiene, Nijole 等
Introduction
The adequate investment portfolio was selected to reach the main
objective of the paper, namely, to prepare the maximization scheme of
net utility for the debtor, generated by government debt, and using the
integral portfolio model of asset and liability management to apply the
scheme in Lithuanian conditions (Rutkauskas 2006).
In this paper, the debt category is analysed, which as a financial
instrument (Landon, Smith 2007; Martin 2009; Pan, Wang 2012) at its
basic content formation moment is contemporary with money as trade
tools' origin; it has invaluable merit in developing division of
labour as the most effective all-time economic means. Indeed, the
importance and evolution of division of labour problem achieved the key
attention of the scientific thought of economics since Plato to
Friedrich A. von Hayek (The Concise Encyclopedia of Economics ... 2013).
Intensive development of the trade, determined by the division of labour
necessity (Pridotkiene, Dapkus 2011; Bruneckiene, Paltanaviciene 2012),
has been the driver behind the abundance and improvement of financial
relations and instruments. The success of the most impressive
contemporary phenomenon--globalization --highly depends on the success
of division of labour from the territorial as well as technological
points of view, and on successful trading efficiency as well as
perfection of the attendant system of financial instruments (Stulz 2005;
De Santis, Gerard 2006; Mishkin 2007; Pekarskiene, Susniene 2011).
Etymology of debt states that the English word "debt"
came from Latin "ebere" (to owe) somewhere in the XVIII
century. However, there is no doubt that trading, which transformed 5000
years ago, has been using the idea of trust (credit--trust,
creditum--loan) in the sense that it is possible to trust the promise to
pay for goods after their delivery.
In finance, debt is a means of present use of the purchasing power
receivable by the debtor in the future, maybe even far before it has
been earned. Some companies and corporations use debt as part of their
overall corporate finance strategy (Bradley, Chen 2011; Norvaisiene
2012; Zhan, Zeng 2012).
Although in the act of debt formation the debtor is assumed to be
the primary side assuming the risk, however, a debt transaction can take
place only under the condition of a possible bilateral benefit (Bruche,
Naqvi 2010). In this paper, the main attention will be paid to the
borrower (debtor), attempting to not only realize benefit possibilities,
but also circumstances applicable for borrowing in situations when a
debt increase not only becomes risky but can also become less useful in
cases of a big guarantee, which is not only because the debt as such was
unsuccessful, but also because of its inadmissible enormous growth that
results in the loss of the possibility by a debtor to use it efficiently
even under standard borrowing conditions.
The paper reveals the attempts of the authors to ground the
management principles of the debt, the emerging of which is marked by
the possibilities of uncertainty, when the existence of uncertainty is
evident in forming costs of the debt, as well as in creating the value
using debt funds.
1. Debt growth rate and related problems
As division of labour is the most important economic tool in the
international context, the balance of needs and possibilities of all the
subjects is a particularly important instrument of economic development
management in a particular country. Only properly composed monetary and
fiscal policy could foster discussion about the guarantee for
sustainable economic growth and the most effective utilization of
national disposable resources. (Muscatelli et al. 2004; Kalyuzhnova,
Nygaard 2009; Canzoneri et al. 2010; Zvirblis, Buracas 2010; Bartolomeo,
Giuli 2011; Asici 2013).
However, in the paper, the authors confine themselves to the
creation of theoretical optimization model of government debt
acquisition means and forms of use. Also, the model will be applied
experimentally to Lithuanian conditions in order to maximize the utility
receivable using government debt, i.e. selecting the traditional
international financial institutions as the debt sources, but evaluating
the effect of debt use according to the government debt use
possibilities established in Lithuania.
Also, it is necessary to carefully evaluate the sufficient created
benefit of every debt unit in the future to prevent its total present
value (utility) from dropping below the taken amount of the present
value of debt. According to statistical data, if government debt equals
GDP level, the debt efficiency starts diminishing significantly.
Analysts often notice the presence of certain debt thresholds that
should not be exceeded.
The reasons for individual and household debts as well as borrowing
by a specific business unit are similar: to obtain a highly priced asset
for the use before its settlement, or to use a loan in order to gain the
purchasing power for implementation of a desired objective. The success
of borrowing and debt use is important not only to the above-mentioned
entities, but also for the entire country. However, government debts
became the permanent focus of attention for analyst and politicians
(Drudi, Giordano 2000; Balibek, Koksalan 2010). Government debt
management becomes one of the most important national development
problems in countries with high and developing level of economy (Qin et
al. 2006; Melecky 2012; De Mendonca, Machado 2013). Moreover, failed
foreign debt management cases create the environment beneficial for
regional or global crises. Although analysts have long been trumpeting
that at certain proportions a foreign debt results in the negative
effect of debt growth impact on the debtor (Mohd Daud, Podivinsky 2012),
still, the world inevitably sinks into the debt-caused non-existence
with heavily predictable and controllable results.
2. Waymarks to national debt management success
2.1. Government functions mostly realized using government debt
funds
While performing its purpose, a government must get involved in
many fields of state life and social activities, which are at the centre
of public attention. Management of the current situation in these fields
requires for funds that are possessed by the government in the form of
state budget. In Lithuania, the state budget is allocated to the
following fields: social security, education, health, economy, business
promotion, transport and communication, agriculture, environmental
protection, public order and security, defence, leisure, culture and
religion (2013 metu ...).
The funds borrowed by the government become part of the state
budget. Also, borrowed funds are usually used to repay previous debts
(for example, repurchase of government securities) and finance the
budget deficit. Thus, government debt actually contributes to the
financing of all the fields distinguished above. In the paper, however,
the authors will analyse only the part of the debt for t-year that is
used for t-year budget expenses and investments.
2.2. Problems with appraisal of public assets
Indeed, assets are the basic source of economic vitality and
development. In financial accounting, assets are economic resources. It
is usually assumed that assets represent value of ownership that can be
converted into cash although an asset itself is a resource that can be
controlled to bring the utility for its holder.
It is worth noticing that the concept of assets used in the title
of the paper differs from the one used in net debt calculation: the net
debt is calculated as gross debt minus direct values of financial
assets' debt instruments (see Table 1). According to economic
conception, an asset is a piece of property, using which an economic
benefit may be derived during a certain period of time. Thus,
borrower's assets, generated by debt, are the volume of debt
directly fallen into one's property.
Gross debt evaluation is usually based on the sum of total debt,
which consists of liabilities according to all debt instruments. A debt
instrument is defined as a financial claim that requires payments of
interest and/or principal of the debtor to the creditor at a date, or
dates in the future. Financial assets corresponding to debt instruments
(column b, Table 1) show the way, in which indebted funds reach the
debtor accounts. These accounts serve for the debtor to use the economic
funds.
3. Debt optimization. What is it?
3.1. Peculiarities of debt optimization
While analysing debt management, scientific literature mainly
focuses on cost of debt minimization (Lim 2011; Chen 2012). In case of
every country, cost ambiguity, different debt service plans appropriate
for both debt sides--the creditor and the debtor--as well as
uncertainty, which accompanies all debt service process, points out the
importance of debt service cost minimization. However, emphasis on the
mentioned aspects alone does not consider the reasons behind borrowing
and the ways debt utility success or failure could also influence the
effect generated by debt.
If types of borrowing would automatically suggest the efficiency of
debt, such problem-solving of debt management as well as debt
optimization could be reasoned. But real estate debt bubbles have shown
that activity absorbing the borrowed funds has caused these
uncertainties, which to the great extent contributed to the continuing
world economic crisis (Dubinskas, Stunguriene 2010; Afonso, Jalles
2013).
Since any business associates its development possibilities with
borrowing possibilities, debt analysis will not be complete without
combining debt objectives and cost of debt possibilities. Certainly,
taking into account probable success and failure of activities that
require borrowing, the additional possibilities of value creation would
emerge, and in turn, the possibilities to gain additional benefit for
the creditor as well as for the debtor. Practically such possibilities
are considered in all particular borrowing cases, but the unique
theoretical viewpoint on debt management should still be formed.
3.2. Is borrowing a self-regulating process?
There has never been any doubt that the proper amount of borrowing
stimulates economic growth, and also can become a condition of wealth
growth. But many papers on highly developed economies referring to
statistical data and other theoretical tests (Cecchetti et al. 2011)
predicate the thresholds amounting to 85 percent of GDP to household and
government debt and 90 percent of GDP to national business, the
overstepping of which with debt growth becomes dangerous for economic
growth rate. Also, it has been confirmed, that these thresholds should
be precisely measured. It is stated that if debt oversteps the mentioned
thresholds, other conditions remaining the same, the economy growth
rates decrease.
Debt management strategy, which was based on facts requiring the
broader viewpoint, states that one shouldn't overdraft the a priori
established debt growth norms. The necessity of such viewpoint is also
discussed in debt management strategy (Public Sector Debt Statistics
2011) proposed by the IMF (International Monetary Fund).
4. The methodology for formulation of tasks on general debt
management optimization and their solution
In this chapter, the authors will recall the promise already
declared in the abstract of the paper--to present the government debt
optimal management possibility, based on the maximization of the present
value of the difference between the effect generated from the debt
obtained in a particular year (hereinafter--t year) and costs generated
by debt servicing.
Section 4.1 describes the logics behind the determination of the
present value of debt servicing costs and possible effect of the present
value of debt use, which are depicted in Schemes 1 and 2, respectively.
In turn, it is worth noticing that seeking for the adequate effect
of debt use as well as debt servicing cost evaluation, it is necessary
to invoke the stochastic assessment ideology and technique. It is clear
that analyzing the possible effects of debt use the avoidance of the
recognition of stochastic nature of these processes would be
unacceptable. This remark equally concerns the debt servicing costs,
when the interest on borrowed funds is often linked with stochastically
changing global financial parameters and also when the violation of debt
conditions traditionally changes the parameters of costs.
Besides, the lack or absence of statistical observations, data and
etc. is often observed in the attempts to reveal the possible stochastic
consistent patterns in debt management problems. The expert evaluation
based on the informative expert assessment principles will be used while
analyzing particular situations in the paper.
4.1. Formulation of an optimization task
The projected government debt volume [S.sup.t] for t-years must be
composed (see Scheme 1) of borrowing volumes according to every
borrowing tool [S.sup.t.sub.1], [S.sup.t.sub.2], ..., [S.sup.t.sub.I]
such as [[summation].sup.I.sub.i=1][S.sup.t.sub.i] = [S.sup.t] and debt
must be used (see Scheme 2) for investment in K public activity sectors
[V.sup.t.sub.1], [V.sup.t.sub.2], ..., [V.sup.t.sub.K] such that
[[summation].sup.K.sub.k=1][V.sup.t.sub.k] = [V.sup.t] = [S.sup.t].
Unfortunately, the determined comparison possibilities of the borrowed
and used sum ends here, because cost of debt service formation as well
as investment efficiency achievement in various public activity sectors
evidences that described processes, their relationships and interactions
are characterized by stochastic nature. On the other hand, the systems
of developed stochastic process analysis and management allow expecting
success during public debt management analysis performed using
multicriteria stochastic optimization and also checking the emerging
sustainability conception.
Thus, the emerging debt service costs as well as the resulting
effects of investment of borrowed funds can be identified with the help
of specialized stochastic models. It can be stated that using historical
data, simulation options and expert assessments, one can create
uncontroversial system of stochastic models, allowing to form the
positive and practically-confirmed stochastic optimization criteria and
debt management system.
The adequacy and consistency of the system is guaranteed by the
fact that at this stage the focus is not on the problem related to
formation of strategic principles for public debt management, but simply
on the marginal optimization problem, attempting to determine the ways
to optimize additional conditional net effect, i.e. to maximize the
benefit of the difference between the generated benefit and incurred
costs for borrowed marginal relative unit for each analysed country.
The sequence of formation of Schemes 1 and 2 is fully explained at
the beginning of the chapter. However, it can be repeated that the
present value PV([S.sup.t]) of the servicing costs St of the debt
obtained in t year becomes a stochastic value due to the uncertainty of
discount rate in the time interval [t, t + [[tau].sup.-]], as well as
because of a possibly real ambiguity of the interest rate for the same
period. In this step, the selection of the adequate stochastic
dependencies in Schemes 1 and 2 was performed using the method of
stochastically informed expertise (Rutkauskas 2012b).
Further (Scheme 2), completely analogically to the present value of
the cash flow generated by debt servicing, the present value created by
the use of debt obtained in the year t will be presented. While debt
servicing of the year t went into the time interval [t, t +
[[tau].sup.-]], the obtained effect is evaluated in the interval [t, t +
[[tau].sup.+]].
Probably, explanation of the Scheme 2 does not need arguing that
turning of debt S* into the present value PV([V.sup.t]) of the created
effect requires the description of the investigated processes with
regard to uncertainty. Of course, it is the practical problem of high
complexity, seeking to obtain the adequate solution for the raised
problem. The existing methods of stochastically informed expertise
(Rutkauskas 2012b), the techniques of stochastic optimization as well as
the methods of stochastic evaluation of losses incurred by the
environmental or social components, allow expecting for the success.
4.2. Applied optimization criteria
It is necessary to choose a combination of borrowing tools and
investments into specific activities. This combination should give the
maximum of utility function U:
U(npv(ef), P{[zeta] > npv(ef)}, rnpv(ef)}) = npv(ef) x P{[xi]
> npv(ef)}/rnpv(ef) => max. (1)
Here: npv(ef)--the present value of effect possibilities generated
by the debt; P{[zeta] > npv(ef)}--the guarantee for the possibility
of the present value; rnpv(ef)--the riskiness of the possibility.
Detailed description of solution possibilities of the formulated
problem is presented in the next chapter.
5. The essence of adequate portfolio model and its suitability for
the formation of government debt-related integral asset and liability
portfolio
5.1. The scheme for formation and use of an adequate portfolio
The concept of portfolio is used in various fields of research and
practical activity. This concept is used in various perceptions even in
fields of investment and finance. The traditional case of investment
portfolio perception as a set of homogeneous securities that belongs to
one subject equals the sum of respective number's random variables,
and it is being substituted with a set of non-homogeneous securities
that belong to one subject. The variety of relations among changing
securities becomes especially complex. Merely the entirety of
non-homogeneous securities in the portfolio can create a hardly solved
chain of interactions. Thus, it is hardly a surprise that the technique
used for portfolio management is getting complex continuously and
quickly. A portfolio becomes an especially important instrument of
systemic analysis, which according to its nature is intended for solving
the complex stochastic systems, and, what is especially important, for
optimal allocation of resources among the subsystems interacting under
conditions of uncertainty.
The detailed information about the adequate portfolio and its
application possibilities can be found in publications by authors
(Rutkauskas, Stasytyte 2011; Rutkauskas 2012a).
In this paper, the portfolio will be perceived as an integral
portfolio of assets created due to the funds borrowed by the government
and liabilities emerged in relation to that borrowing. It is clear that
to achieve the integral effect of borrowing and debt management one
should invoke the technique adequate for informative supply of decisions
and search for solutions.
In the presented experiment, the possibilities of adequate
portfolio (Rutkauskas 2006)--the portfolio adequate for the stochastic
nature of investment assets--will be used. This will allow evaluating
borrowing and the use of the received debt according to its efficiency
as well as reliability. Traditionally, the portfolio will be presented
as means of asset and liability management.
5.2. The anatomy of the adequate portfolio
In order to reveal the contents and possibilities of the adequate
portfolio, it should be treated as natural follow-up of the modern or
Markowitz portfolio.
Simplifying the Markowitz portfolio, it can be interpreted as
follows: having n investment assets [A.sub.1], [A.sub.2], ...,
[A.sub.n], that form a property of a subject and generate income for
this subject, expressed in random values
[a.sub.1]([[alpha].sub.1],[[sigma].sub.1]),
[a.sub.2]([[alpha].sub.2],[[sigma].sub.2]), ...,
[a.sub.n]([[alpha].sub.n],[[sigma].sub.n]). Here,
[[alpha].sub.i],[[sigma].sub.i] are respectively the mean value
[[alpha].sub.i] of the random value [a.sub.i] and standard deviation
[[sigma].sub.i] of the random value [a.sub.i]. A subject can evaluate
how one should distribute the capital intended for investment among the
separate assets, i.e. how one should choose the proportions [w.sub.1],
[w.sub.2], [w.sub.3], ..., [w.sub.n]([n.summation over (i=1)][w.sub.i] =
1), according to which the whole capital is allocated among the assets.
For simplified perception, it is possible to say that there is a great
unit of money (ex., 1 million) and thus wi will describe the parts of
this unit. In order to determine the best diversification possibilities
of investment capital, it is worth analysing the distribution of all the
possibilities of the possessed capital among the assets:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (2)
To find the best variant of investment capital diversification, one
needs just to revise all the possibilities of structural allocation,
i.e. to demand that structural complexes {[w.sup.j.sub.i]}, i = 1, 2,
..., n; j = 1, 2, ..., m would in reality reflect all the possibilities
of capital allocation among the selected investment assets. Practically,
the evaluation of capital possibilities is performed using the following
calculations:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], (3)
here ([n.summation over (i=1)][w.sup.j.sub.i] = 1) for every j = 1,
2, m.
[S.sup.j], j = 1, 2, ..., m--are the values of differently
diversified portfolios, obtained as functions of assets and allocation
coefficients. These values are stochastic variables with their
parameters--mean value, standard deviation, variation, quartiles,
deciles and other quintiles, etc., which, in turn, depend on the
probability distributions of asset possibilities and their
interdependencies.
In graphical analysis the sets of possible values of a portfolio
are usually analysed. In the case with the Markowitz portfolio, the
obtained system (3) is analysed, where every value of a set of values
{[S.sup.j]} of the portfolio is described by its mean value and standard
deviation.
Graphically, this situation is presented in Figures 1a and 1b. In
Figure 1a all of the possible values are depicted, while in Figure
1b--only the efficient values, i.e. those that have maximum mean values
for the selected standard deviation level.
The standard deviation-mean analysis and decision-making
methodology plays an especially important role in recognizing and
quantifying the investment possibilities as stochastic values or
processes.
However, analysts as well as practitioners are actually interested
not only in mean values of portfolio possibilities, but also in
constructive characteristics of various situations such as median, mode,
various quintiles, etc., or simply in the probability distribution of
every [S.sup.j]. The primary objective of the adequate portfolio is to
form the so-called efficient surface, analogous to the efficient
frontier in the modern portfolio case. For this purpose, the
"standard deviation-percentiles" (virtually there can be any
quintiles) bunch of portfolios, or the set of possible values is formed
(Fig. 1c), along with the respective bunch of efficiency lines (Fig.
1d). Every selected point [[xi].sub.p] on "standard deviation-the
percentile of p level" efficient frontier possesses the following
characteristic (probability):
P{[xi] > [[xi].sub.p]} = p,p = 0; 0,01; 0,02; ..., 1. (4)
[FIGURE 1 OMITTED]
This circumstance indicates that if percentile efficient frontiers
are raised to the level of respective percentile's value on the
applicate axis, then an efficient surface appears with analogous
characteristics as efficient frontier in the plane "standard
deviation-mean value" (Fig. 2b).
However, for convenience of presentation, the bunch of efficient
frontiers presented in Figure 1d should be rotated in order to put it in
the first quadrant of the plane (a, p). If in Figures 2a and 2b the
schematic views are presented, then in Figure 3 the surfaces of real
calculations are depicted, when assets were assumed to be three Normal
probability distributions [N.sub.1]([[alpha].sub.1] = 0,062;
[[sigma].sub.1] = 0,022); [N.sub.2]([[alpha].sub.2] = 0,07;
[[sigma].sub.2] = 0,023); [N.sub.3]([[alpha].sub.3] = 0,13;
[[sigma].sub.3] = 0,03).
[FIGURE 2 OMITTED]
5.3. Formation of the utility function for the adequate portfolio
In order to disclose the commensuration process of profitability,
risk and reliability in more details while forming utility function,
first of all, it is advisable to present the expressions of utility
function in two two-dimensional planes: profitability-risk and
profitability-reliability. The detailed analysis of such functions is
presented by Rutkauskas (2006, 2012a), Rutkauskas, Stasytyte (2010).
After investigating the versions of utility function in
profitability-reliability and profitability-risk planes, it must be
analysed how the combination of these functions into a single network
could produce a three-dimensional utility function, described by the
profitability of the general possibility of a portfolio, the reliability
of that possibility and the risk faced by investor in case the
possibility happens. For this reason a threeparametric utility function
in profitability-risk-reliability space is constructed (Fig. 4). The
composed utility function, approaching the set of values of the adequate
portfolio, indicates the portfolio value with the highest utility, and,
in turn, the portfolio itself. It is worth noticing that if the set of
possibilities of adequate portfolio is an intersection network of
survival functions and izoguarantees, then spatial utility function is a
network of intersection of profitability-risk and
profitability-guarantee utility functions. Graphical view of such a
utility function is formed using analytical expression:
U = exp(e/r) x g, (5)
here: U--utility level of possibility; e--profitability; r--risk;
g--guarantee.
[FIGURE 3 OMITTED]
[FIGURE 4 OMITTED]
Such specification of utility function and decision-making
procedure is analytically meaningful because in such a manner the
complex stochastic programming problem is being solved using imitative
technologies and graphical decision-making means.
Consequently, the logics of the adequate portfolio formation, which
serves as the base for the analysis of guarantee of every profit
possibility, being described as a probability that the profitability
(return) on investment will not be lower than the certain level,
presents the full disclosure of the interaction of guarantee of
profitability and risk, as a measure for interaction of variability
pertaining to profit possibilities with utility function of an investor.
6. Expert formation and solutions of adequate portfolio of
government debt generated liabilities and assets
6.1. Prerequisites for formation of optimized portfolio
In scientific literature, M. Melecky (2012) attempts to reveal how
the government debt portfolio should be formed in order to minimize the
cost of debt. It is clear that minimization should be adequately
perceived. In government debt strategy formation, the evaluation of
reliability pertaining to cost of debt possibilities cannot be avoided.
Of course, the volume of cost of debt possibilities and the reliability
of these possibilities should be commensurated. Thus, the content of
adequate investment portfolio is oriented towards such decision while
developing the government debt portfolio (Rutkauskas 2006).
As it was stated at the beginning of the paper, along with debt
liabilities, the debt-generated assets will be analysed as certain
processes that generate certain values using government debt funds by
developing these values or ensuring possibilities to avoid losses, i.e.
allowing to retain the possessed possibilities. Loss avoidance using
investment or operating assets is a broadly used concept in
environmental protection, as well as in life and non-life insurance or
in any other activities. The funds borrowed by the government are
usually used to ensure the quality of the core functions of the
government.
However, the evaluation of loss or damage derived from the
insufficient quality of the most often discussed government
functions--defence, education, transportation, public health, social
security, legal and judicial functions--is not a simple solution of the
problem, especially when the functions should be evaluated. Taking into
account that such evaluations are almost not collected and there are no
such statistics, the expert valuations should be applied.
In the research, the functions that are usually performed using
budget financing in Lithuania were divided into three groups:
The first group--education and science, economics, business
promotion, agriculture;
The second group--social security, health, public order and
security of the society;
The third group--environmental protection, defence, culture,
religion, leisure.
According to the opinion of specialists of these activities, only
the first group can be currently purposefully credited with the
evaluated effect that can be determined by the marginal financing volume
of the government debt. The second, as well as the third group can
responsibly operate the categories of avoidable loss or damage that can
be revealed under shortage of financing. According to the special
projects prepared for every group an internal group structure is already
fixed and efficiency indicators determined
--[a.sub.1]([[alpha].sub.1],[s.sub.1]),
[a.sub.2]([[alpha].sub.2],[s.sub.2]) and
[a.sub.3]([[alpha].sub.3],[s.sub.3]). These are stochastic values
showing the generalized effect of marginal investment unit on the entire
group, where [[alpha].sub.i], [s.sub.i], i = 1, 2, 3 are the mean values
and standard deviations of the effect.
In 2011-2012 in Lithuania, the government securities were the main
debt instruments together with loans and deposits. The possessed
information about debt instruments in many countries for a long time
allows to reasonably enough determine the indicators of debt servicing
of borrowed marginal unit according to every debt instrument. As well as
in the case of assets, the fixed structure of the used instruments in
every mentioned group of three instruments, and the indicators of debt
servicing of the borrowed marginal unit were
formulated--[l.sub.1]([[beta].sub.1],[[delta].sub.1]),
[l.sub.2]([[beta].sub.2],[[delta].sub.2]),
[l.sub.3]([[beta].sub.3],[[delta].sub.3]). Debt servicing indicators
were also projected as random values, where
[[beta].sub.i],[[delta].sub.i] are their mean values and standard
deviations.
Expert valuations were performed using stochastically informed
expertise method (Rutkauskas 2012b).
6.2. Optimization of the government debt generated integral asset
and liability portfolio
The idea of optimization - to select such borrowing proportions
[[omega].sup.l.sub.1], [[omega].sup.l.sub.2], [[omega].sup.l.sub.3]
([[omega].sup.l.sub.1] + [[omega].sup.l.sub.2] + [[omega].sup.l.sub.3]
=1) and such proportions of borrowed funds distribution among the assets
--[[omega].sup.a.sub.1], [[omega].sup.a.sub.2],
[[omega].sup.a.sub.3]([[omega].sup.1.sub.1] + [[omega].sup.a.sub.2] +
[[omega].sup.a.sub.3] = 1) that the present value NPV([D.sub.t]) of the
debt [D.sub.t] for the analysed year is the maximum measured according
to the adequate utility function, i.e. according to the function in
which the effect and reliability of possibilities is taken into account.
With the help of the possessed data and stochastically informed
expertise (Rutkauskas 2012b), the following values of [a.sub.i] and
[l.sub.i] indicators were selected:
[a.sub.1]([[alpha].sub.1],[s.sub.1]), here [[alpha].sub.1] = 1,461;
[[sigma].sub.1] = 0,012,
[a.sub.2]([[alpha].sub.2],[s.sub.2]), here [[alpha].sub.1] = 1,320;
[[sigma].sub.1] = 0,044,
[a.sub.3]([[alpha].sub.3],[s.sub.3]), here [[alpha].sub.1] = 1,061;
[[sigma].sub.1] = 0,045,
[l.sub.1]([[beta].sub.1],[[delta].sub.1]), here [[beta].sub.1] =
1,546; [[delta].sub.1] = 0,170,
[l.sub.2]([[beta].sub.2],[[delta].sub.2]), here [[beta].sub.1] =
1,202; [[delta].sub.1] = 0,058,
[l.sub.3]([[beta].sub.3],[[delta].sub.3]), here [[beta].sub.1] =
1,019; [[delta].sub.1] = 0,007.
Here [[alpha].sub.i] and [[beta].sub.i] are the mean values of
random variables, [[sigma].sub.i] and [[delta].sub.i]--standard
deviations. In the particular case, the utility function was selected as
follows:
U = exp{[n x p]/r}, (6)
here n--possibility, p--the reliability of possibility n, r--the
risk, U--utility.
In Figure 5, the anatomy of decision search is presented: a--the
general view of possibilities, b--the utility function, c--the general
view of the set of possibilities and utility function, d--determining
the particular possibility, e--the particular solution.
[FIGURE 5 OMITTED]
Conclusions
1. The management of government borrowing process usually does not
cover all moments of use of the received debt. While fostering the
government debt management strategies, probably the most important
problem is the efficient use of the borrowed funds, at the same time
seeking the optimization of the borrowing effect itself.
2. Borrowing and debt utilization processes are linked by the
common objective--to obtain the highest gross debt utilization effect,
along with the set of impacts on financial system, raised by the time
and risk. Thus, integrated borrowing and debt utilization management has
clear advantages.
3. In analytical research works, there are no more or less
universal or thorough methodology on quantitative evaluation of losses
incurred by the society, environmental protection or business, if the
objective resources do not reach the required standards or norms. At
least expert systems must be oriented towards the solution of such
problems.
4. Orientation towards the optimization of annual government debt
effect gross present value should become the core attitude while
formulating strategic provisions pertaining to the government debt
management.
5. Borrowing expenses and preconceived (projected) evaluations of
debt management must be named according to their extent and reliability.
Caption: Fig. 1. Initial steps of transition from Markowitz to
adequate portfolio: a) the set of values of the Markowitz or
"mean-standard deviation" portfolio; b) the set of values of
the efficient frontier of "mean-standard deviation" portfolio;
c) the set of values of the "percentiles-standard deviation"
portfolio; d) the efficient frontiers of the bunch of
"quintiles-standard deviations" portfolios
Caption: Fig. 2. Schematic view of efficient surface formation: a)
rotation of efficient frontiers; b) raising of efficient frontiers
Caption: Fig. 3. The possibility surface of adequate portfolio and
investor utility function (Rutkauskas, Stasytyte 2011): a) efficient
surface (geometrical view) of the adequate portfolio; b) the view of the
utility function
Caption: Fig. 4. Utility surface approaching the surface of
possibilities (Rutkauskas 2006)
Caption: Fig. 5. The anatomy of decision search: a)
three-dimensional surface; b) utility function; c) possibility surface
and utility function--three-dimensional view; d) possibility surface and
utility function--the tangency point; e) the information about optimal
solution
doi: 10.3846/16111699.2013.815129
Acknowledgements
The research was financed by The Research Council of Lithuania
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Aleksandras Vytautas Rutkauskas (1), Viktorija Stasytyte (2),
Nijole Maknickiene (3)
Vilnius Gediminas Technical University, Sauletekio al. 11, LT 10223
Vilnius, Lithuania
E-mails: (1) ar@vgtu.lt (corresponding author); (2)
viktorija.stasytyte@vgtu.lt; (3) nijole.maknickiene@vgtu.lt
Received 22 February 2013; accepted 11 June 2013
Aleksandras Vytautas RUTKAUSKAS is a Professor and the Head of the
Department of Finance Engineering at Vilnius Gediminas Technical
University. His research interests are: investment portfolio management
in capital and exchange markets, risk and uncertainty, sustainable
development, integrated value and risk management
Viktorija STASYTYTE holds a PhD in Economics. She is an Associate
Professor in the Department of Finance Engineering at Vilnius Gediminas
Technical University. Her research interests are: capital markets,
investment portfolio management, risk management, sustainable
development.
Nijole MAKNICKIENE holds a Master degree in Physics. She is a PhD
student at the Department of Finance Engineering of Vilnius Gediminas
Technical University. She is a Senior Manager at the Laboratory of
Business Projection and Environmental Economics and an Assistant at the
Department of Finance Engineering of Vilnius Gediminas Technical
University.
Table 1. Calculation of net debt
Gross debt (gross Financial Net debt
value of liabilities assets obtained
in the form of debt using debt means
means)
a b C = a - b
SDRs (Special Monetary gold
Drawing Rights) and SDRs
Currency and Currency and
deposits deposits
Debt securities Debt securities
Loans Loans
Insurance, pension Insurance, pension
and standardized and standardized
guarantee schemes guarantee schemes
Other accounts Other account
payable receivable
Total gross debt Total Total net
financial assets debt
corresponding to
gross debt
Scheme 1. Digest on the formation of servicing components and their
present values pertaining to the debt obtained in the year t, or the
formation logics of the present value P([S.sup.t]) of debt servicing
Debt extent of the year t
Years Debt extent according to every debt tool Total
t [S. [S. ... [S.sup.t. [I.
sup.t. sup.t. sub.I] summation
sub.1] sub.2] over (i=1)]
[S.sup.t.
sub.i] =
[S.sup.t]
t year's debt service extent of the year t to the year t +
[[tau].sup.+]
t [S.sup. [S.sup. ... [S.sup. [I.
t+0. t+0. t+0. summation
sub.1] sub.2] sub.I] over (i=1)]
[S.sup.t+0.
sub.i] =
[S.sup.t+0]
t + 1 [S.sup. [S.sup. ... [S.sup. [I.
t+1. t+1. t+1. summation
sub.1] sub.2] sub.I] over (i=1)]
[S.sup.t.
sub.1] =
[S.sup.t+1]
t + [S.sup. [S.sup. ... [S.sup. [MATHEMATICAL
[[tau]. t+[tau]-. t+[tau]-. t+[tau]-. EXPRESSION
sup.-] sub.1] sub.2] sub.I] NOT
REPRODUCIBLE
IN ASCII]
Present values of the debt service extent of the year t
t + PV PV ... PV([S.sup. [MATHEMATICAL
[[tau]. ([S.sup. ([S.sup. t+[tau]-. EXPRESSION
sup.-] t+[tau]-. t+[tau]-. sub.I]) NOT
sub.1]) sub.2]) REPRODUCIBLE
IN ASCII]
... ... ... ... ... ...
t + 1 PV([S. PV([S. ... PV([S. [I.
sup.t+1. sup.t+1. sup.t+1. summation
sub.1]) sub.2]) sub.2]) over (i=1)]
PV([S.sup.
t+1.sub.i]) =
PV([S.sup.
t+1)]
t + 0 PV([S. PV([S. ... [MATHEMATICAL [I.
sup.t+0. sup.t+0. EXPRESSION summation
sub.1]) sub.2]) NOT over (i=1)]
REPRODUCIBLE PV([S.sup.
IN ASCII] t+0.sub.i]) =
PV([S.sup.
t+0)]
The total present value of debt service payments of years t
PV([[tau]-.summaion over ([tau]=0)] [MATHEMATICAL
[V.sup.t+[tau].sub.i]) = EXPRESSION
PV([S.sup.t.sub.i]), i = 1, 2, ..., I NOT
REPRODUCIBLE
IN ASCII]
Scheme 2. Public debt utilization and the created present value
of the year t
Public debt utilization of the year t
Years Utilization according to public sectors
1 2 ... k Total
t [V.sup.t. [V.sup.t. ... [V.sup.t. [V.sup.t] =
sub.1] sub.2] sub.2] [K.summation
over (k=1)]
[V.sup.t.
sub.k] =
[I.summation
over (i=1)]
[S.sup.t.
sub.i] =
[S.sup.t]
The effect of the debt for the year t used in the public sector
t [V.sup. [V.sup. ... [V.sup. [K.summation
t+0. t+0. t+0. over (k=1)]
sub.1] sub.2] sub.k] [V.sup.t+0.
sub.k] =
[V.sup.t+0]
t + 1 [V.sup. [V.sup. ... [V.sup. [K.summation
t+1. t+1. t+1. over (k=1)]
sub.1] sub.2] sub.k] [V.sup.t+1.
sub.k] =
[V.sup.t+1]
t + [V.sup. [V.sup. ... [V.sup. [K.summation
[[tau]. t+[tau]+. t+[tau]+. t+[tau]+. over (k=1)]
sup.+] sub.1] sub.2] sub.k] [V.sup.
t+[tau].
sub.k] =
[V.sup.
t+[tau]+]
The present values of effects of funds borrowed in the year t
t + PV([V.sup. PV([V.sup. ... PV([V.sup. [K.summation
[[tau]. t+[tau]+. t+[tau]+. t+[tau]+. over (k=1)]
sup.-] sub.1]) sub.2]) k PV([V.sup.
t+[tau]+.
sub.k]) =
[PV.sup.
t+[tau]+]
... ... ... ... ... ...
t + 1 PV([V.sup. PV([V.sup. ... PV([V.sup. [K.summation
t+1. t+1. t+1. over (k=1)]
sub.1]) sub.2]) k PV([V.sup.
t+1.sub.k]) =
[PV.sup.t+1]
t + 0 PV([V.sup. PV([V.sup. ... PV([V.sup. [K.summation
t+0. t+0. t+0. over (k=1)]
sub.1]) sub.2]) sub.k]) PV([V.sup.
t+0.sub.k]) =
[PV.sup.t+0]
The total present value of debt effects generated by the debt of the
year t
t [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE [K.summation
IN ASCII] over (k=1)]
PV(V.sub.K]) =
PV(V.sup.t])
