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IZVESTIYA TSKhA, special issue, 2013
OPERATIONS RESEARCH APPLIED TO ATTRACTING INVESTMENTS IN AGRO-INDUSTRIAL COMPLEX
N.M. Svetlov, A.S. Arkhipova
(RSAU-MTAA)
Abstract: Substantiation is provided for the possibility of using computer simulation in order to address the demand for information emerging when risks of investment portfolio assuming shared investments in real projects, are analyzed. A set of models, including simulation models of cash flow and an investment portfolio, allows to study statistical characteristics of investment projects' economic effect and to estimate expected volumes of investments in real projects when state support is rendered. The model's empiric base comprises materials of the project feasibility study, data on relevant price variations and aggregated price indices. Instrumental methods based on proposed models ensure making decisions about capital investment as well as about the type and amount of state support aimed at improving investment attractiveness of the agro-industrial complex.
Key words: investment risk estimation, portfolio investments, cash flow, investor's behavior, Markowitz model, computer simulation.
Introduction
A weak point of risk management in Russian agro-industrial complex is that the demand for information does not commonly meet the sufficient supply. This feature is of dualistic nature. On one hand, risk management applications of the data available from regular accounting and statistics, if possible at all, often require either developing original approaches or even special dedicated research. On the other hand, as a risk manager has made a decision on data sets to use, a lack of algorithms and, a fortiori, software that would suit to these specific data becomes evident.
The scope of the study presented in this paper is the above mentioned weakness, limited to the case of making decisions aimed at optimizing investors' risk in order to make a specific investment area (agro-industrial complex in our case) more attractive. The toolset we develop allows a risk manager to satisfy a substantial part of their information demand using readily available data and uniform algorithms.
Specifications of an information system aimed at the risk analysis in investment projects are based on the analyst's demand for information. The practice of making investment decisions suggests that the essential economic dimensions of a project are the net present value (NPV) of the cash flow resulting from the project and the internal rate of return (IRR), which indicates the relative efficiency of the invested capital (providing acceptable reservations) [4, p. 299-300]. Given that the data on the stochastic properties of project parameters are available, an opportunity arises to simulate variational series of both NPV an IRR. As soon as such series are obtained, the indicators commonly used in project risk management, such as: net present value at risk, expectation value of NPV, probability of negative value of NPV, variance of IRR, correlation between IRRs of different projects exposed to the same stochastic factors can be assessed.
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For the purpose of satisfying the demand for information that emerges due to project analysis needs, computer simulation can be applied. Specifically, A. Bykova [1] elaborated the methodology of computer simulation of project cash flows. However, the framework of [1] is not sufficient to meet the demand for information that emerges in case of combining real and portfolio investments. Our paper serves to develop a framework of computer simulations so that projects exposed to the same risk factors could be analyzed simultaneously. We believe that this framework can be used by various participants of project analysis procedures because:
1) it enables an analyst to perform a complex evaluation of project risks in interconnection with the effect of simultaneous implementation of other projects;
2) it helps an investor to reasonably include real investment shares in the investment portfolio considering interrelations between the risk and profitability of different projects and securities;
3) it enables a researcher to simulate investors' behavior in the capital market, particularly in order to substantiate the efficiency of governmental policies aimed at attracting capital.
Methodology
In connection with above mentioned role of the analytical framework we have been developing, the demand for specific information should be met:
1) of the analyst: in the expectation value of NPV, NPV variance, and probability of negative NPV;
2) of the investor: in the expectation value of IRR, IRR variance, probability of IRR being lower than the opportunity cost of capital (which is equal to the probability of negative NPV), and the correlation of IRR of different projects, which is necessary to minimize the risk of the portfolio;
3) of the researcher: all the data needed for both the analyst and the investor.
Figure 1 below presents the aggregated view of the analytical process that generates
the required data.
The basic formal framework for modeling the investor's behavior is the classic model of investment portfolio developed by H. Markowitz [6]. Despite significant limitations [2], the formalism based on this model covers a wide range of important practical cases.
For the purpose of our study, we extend the Markowitz model intoducing variables that denote shares of the capital stock invested in real sector projects. The normality of distribution of each project's IRR is essential for the validity of such extended model. It should be tested prior to its composition [2]. The complete model is defined as follows:
min j ° JxixJ
x,, iel 2 iel jel
i' el' i' eI' (1)
Z x, = 1,
iel
bx.„ ,, c.', i' e I',
i i
x ...0, i e I,
i ' '
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Fig. 1. A chart of information flows facilitating simulation of an investor's behavior in presence of governmental financial support
where I' is a set of securities with normally distributed income; I" is a set of real projects with normally distributed IRR; I is I' U I"; x, x,, xt, and xi„ are the shares of the corresponding (7th, j i'* 7'"th) security or project in the portfolio, providing that i e I, j e I, i' e I' and i" e I"; rH is Pearson's pairwise linear correlation coefficient between the normalized
th tn
income from the i and j security or project; ct and cj are standard deviations of the normalized income from the corresponding securities or projects; ^ is the expectation value of normalized income from i th security or project; p is the target expectation value of normalized income from the portfolio; b is a total worth of the portfolio; c^ is a present value of the total cost of project i".
For the members of I", the expectation value of IRR, its standard deviation and correlation coefficients are derived from simulated project cash flows. Following the approach developed in [1], one has
CFpk = Xp1k ^ Xpfk,
f eF\{1}
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where p e P, k e K f e F, Kp is a set of time periods that covers the lifetime of projectp; F is a set of cash flow components, which consists of 1 for revenues, 2 for material costs, 3 for managerial costs, 4 for labor costs and 5 for taxes; xpjk is a value offth component of the cash flow generated by projectp in the period k; P is a set of projects under consideration.
Each f th component of a cash flow can be envisioned as a time series consisting of random values. The final judgment on the project risk depends on each of these values. In this respect, computer simulation of the project cash flow requires information about statistic distributions of each value in each time series. We restricted our study by two cases of distribution laws: normal and gamma.
The normal distribution is the most common, as it emerges in every probabilistic situation where Lyapunov's central limit theorem applies. As far as under the normal distribution the probability of any negative value is strictly non-zero, this distribution can at best approximate the empirical distribution of cash flow components, which are all nonnegative in reality. A. Orlov [7] points out that a maintainable model of a true statistic distribution of demand for some commodity is commonly the gamma distribution. Assuming that some vicinity of actual demand is characterized by (nearly) linear relation between the demand and the price, the probability distribution of this price is also gamma. Insofar, even in case no empirical evidence of a specific distribution of cash flow components is present, we can rely on a theoretical judgment in our belief that cash flow components representing costs are distributed according to gamma law in case when the in-kind project purchases are fixed. The same extends to revenues in case when the sales in kind are fixed. Following this reasoning, we hereinafter accept the rather restrictive assumption that amounts in kind the project deals with are certain, while prices are stochastic.
The parameters of the normal distribution are the expectation value and standard deviation of the random value. As for the gamma distribution, its parameters are functions of the same moments. In presence of risk, the values of cash flow components found in business plans are commonly considered expectation values. As for standard deviations, none of their proxies can normally be found in business plans, with rare exceptions. So far, the only general way to fill this gap in information base of project risk management is computer simulations.
Following the above made assumption about the certainty of non-price sources of cash flow components' variation, a calculation of standard deviation for each component in a specific time period is based on:
- either price time series or price variance data in case of a cash flow component that is caused by the single commodity;
- time series of a suitable price index otherwise.
In presence of trends in the time series, the trend component should be removed from the time series variation prior to calculating the standard deviation of the price or price index. Otherwise risks would be overestimated, especially if substantial inflation is observed.
Computer simulations setting
The empirical part of our study benefits from the data of three agro-industrial investment projects submitted to Krasnodar regional Department of Food and Agriculture:
1) Slavyansky (rice processing);
2) Fishery (growing and processing fish);
3) The village of Voroshilov (milk processing).
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We presume gamma distribution of managerial costs, labor costs and taxes. Assuming this distribution law for the remaining two components of cash flows causes computational problems, as it often happens with gamma distributions having low asymmetry. The reason is large magnitude of / in probability density of gamma distribution B"
p(x)=—— xa-VBx, x > 0. Large P suggests minor difference between gamma and normal r(a)
distribution. For this reason, we hypothesize normal distribution for revenues and material costs. In both cases, the emerging probability of negative values of cash flow components appears ignorable.
The variance of cash flow components in each time period is calculated using one of the following formulae:
= Dfx*, f=i pe{2;3}' or (2) Df = Dpf yf, (f = 25, p e P) v (f = 1, p = 1),
where xpfk is the value (in thousand rubles) of cash flow component f in period k caused by project p; y^ is projected sales (in thousand tons) of the commodity forming the corresponding f-component of cash flow of project p in time period k; Dx is a variance of xpjfk; Dpf is a trend-free variance of the price index that corresponds to /-component of cash flow of projectp; Df is a trend-free variance of price of the commodity forming the corresponding /-component of cash flow of project p. Indices: f e F, p e P, k e Kp, where, just as in the previous section, Kp is a set of time periods covering the lifetime of projectp; F is a set of cash flow components and P is a set of projects.
Table 1 provides point estimates of the variance of prices for project outputs. These estimates are used in calculations of the variance of inflows forming cash flow component f = 1 of projects p = 2 and p = 3 (whereas the prices of rice are not available). Price indices engaged in modeling the remaining cash flow components are shown in Table 2.
Table 1
Consumer prices of outputs of the analyzed projects, rubles per kg
Output Years Trend-free variance Dpf
2004 2005 2006 2007 2008
Live and refrigerated fish 58.48 68.27 73.94 82.93 99.67 244.27
Pasteurized milk 25.00 - 16.91 22.32 23.77 12.71
Source: [5], calculations by A.S. Arkhipova.
The following calculations illustrate how the data of Table 2 are used in determining variance of each cash flow component in each time period, using Slavyansky project (p = 1) as the case study.
a) The revenue x112 for time period 2 (second quarter of the first project year), as shown in the business plan, is 18.26 million roubles. Its variance is D11-x1212, where D11
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Price indices used in the simulation of cash flows
Values Years Variance Trend-free variance Dpf
2002 2003 2008 2009
Polished rice consumer price index (p = 1, f = 1) 0.9997 1.012 1.01 0.99 0.000124 0.000121
Real wages index (p = 1; 3, f e {4; 5}) 1.1765 1.1254 0.93 1.14 0.011448 0.010105
Industrial commodities producer price index (p = 1; 3, f e {2; 3}) 1.394 1.546 2.85 2.75 0.366276 0.010772
Source: [5], calculations by A.S. Arkhipova.
is the variance of polished rice consumer price index. Hence, we have 18,26 • 0,000121 = = 0,041.The variance of revenue for other time periods is calculated in the same way, using the corresponding value of revenue.
b) The variance of material costs for time period 2 is calculated using the industrial commodities producer price index variance as follows:
D12 x222 = 20,0282 • 0,010772 = 4,053.
c) The variance of managerial costs for time period 2 is calculated in a similar way:
D13 X232 = 2,069• 0,010772 = 0,026.
d) The variance of labor costs for time period 2 is calculated using real wages index variance:
D14 xf42 = 9032 • 0,010105 = 8783,3.
e) Calculation of the variance of tax payments for time period 2 also uses the real wages index variance. We found this index the most relevant among available ones, because the consolidated social tax, which depends on wages, commonly makes a substantial part of overall taxes in agro-industrial complex, whilst we have no evidence that amounts of other taxes correlate with some other official price index stronger than with real wages index. Insofar we have
D15 X252 = 384,92 • 0,010105 = 1595,9.
Notations used in formulae above follow formula in the beginning of this section. The results of the similar calculations are presented in Table 3.
Upon computing the variance values, a random number generator was engaged to form ten thousand random quarterly time series of each cash flow component for each project (150 thousand series in total). Each uniformly distributed random number
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Variance DXpK of cash flow components in selected time periods (the case of Slavyansky project, p = 1)
Value f Quarters of project lifetime
1 2 9 10 13 14
Polished rice sales (f = 1)
Inflow, million rubles 1 0 18.26 28.0 28.0 30.0 30.0
Variance of inflow, squared million roubles 1 0 0.041 0.095 0.095 0.109 0.109
Material costs (f = 2)
Outflow, million roubles 2 0 20.028 19.8 20.13 19.8 20.1
Variance of inflow, squared million roubles 2 0 4.053 3.9 4.1 3.9 4.1
Managerial costs (f = 3)
Outflow, million roubles 3 1.613 2.069 2.297 2.297 2.297 2.297
Variance of inflow, squared million roubles 3 0,026 0.026 0.026 0.026 0.026 0.026
Labor costs (f = 4)
Outflow, thousand roubles 4 243 903 993.3 993.3 1072.8 1072.8
Variance of inflow, squared thousand roubles 4 636.1 8783.3 10627.8 10627.8 12396.3 12396.3
Taxes (f = 5)
Outflow, thousand roubles 5 87.7 384.9 917.4 917.4 1018.9 1018.9
Variance of inflow, squared thousand roubles 5 82.9 1595.9 9066.4 9066.4 11183.0 11183.0
Source: calculations by A.S. Arkhipova.
uxpJk (where s = 1;104) produced by the generator is a percentile for corresponding gamma or normal distribution with the expectation value either x ^ orypjk, depending on the nature of the specific cash flow component, and with the standard deviation equal to a square root of the corresponding value from Table 3. The monetary values in each time series are deflated to quarter 1 (inflation has been set aside) but not discounted regarding to opportunity cost of capital.
In the simulations, it is provided that usp 2k = usp 3k = usp 4k = usp 5k. The meaning of this condition is that the four cash flow components of five are exposed to the same risks and vary simultaneously. This condition is an important difference of the proposed modeling framework from the above mentioned [1]. It enables a researcher to measure (subject to the model assumptions) the correlation between IRR of different projects.
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Finally, variational series of ten thousand stochastic NPV and IRR values are computed for each of the three projects. These series are stored in the output database for the consequent statistical processing. Thus, an analyst or a potential investor is provided with the data that would present a comprehensive picture of the investment risk caused by price uncertainty. These data are sufficient for computing different point or interval estimates of any distribution moments.
Simulations of project cash flows in presence of governmental financial support
Within the frameworks of cash flow simulation we express risk in the probability of financial failure of a project, i.e. the probability of negative project NPV. Information on this probability is required by the project risk manager. Information demand due to the research aimed at political advice concerning investment attractiveness can be effectively satisfied by the explicit relation between governmental support and this probability. To satisfy this demand, we need to account for the probability of negative NPV in presence of such support with respect to its specific rule(s). In particular, if this probability is targeted, the simulation would serve to determine the amount of funds that, given the specific rule of support, provides exactly £T04 cases of negative NPV of ten thousand, where £ is the targeted probability of negative NPV.
In case of the three studied projects, the quantitative risk measures in the absence of governmental support, obtained from the performed simulations are presented in Table 4. The Fishery project is found to be the least risky, still demonstrating a very high risk. The Village of Voroshilov project displays extreme risks, which are clearly unacceptable for investors. Notably, the original business plans give no idea about such severe risks. Apparently, the original risk analysis either has not been performed or has proven completely wrong.
Table 4
Estimates of project risks from computer simulations
Value Project
Slavyansky Fishery The Village of Voroshylov
IRR in business plan, % 7.38 6.85 6.44
Average IRR throughout simulations, % 7.70 7.01 6.81
Standard deviation of IRR from simulations, % 4.18 2.13 4.80
Probability of negative NPV according to simulations, % 38.5 33.27 44.61
Source: calculations by A.S. Arkhipova.
The data of Table 5 reflect the effect of governmental financial support on the project risk. The modeled support scheme is that the government provides insurance payments free of charge, so that 100% of negative NPV caused by price risk is repaid from governmental funds provided the payment does not exceed a specified ceiling. To make it simple, we
IRR and its standard deviation under the specified levels of governmental financial support
Project Probability of negative NPV in presence of insurance No insurance
0 0.1 0.2 0.3 0.4 0.5
IRR
Slavyansky 0.07681 0.07681 0.07680 0.07680 0.07680 0.07680 0.07677
Fishery 0.07443 0.07426 0.07406 0.07381 0.07355 0.07327 0.07010
The Village of Voroshilov 0.08143 0.08087 0.08012 0.07926 0.07826 0.07717 0.06811
Standard deviation of IRR
Slavyansky 0.04176 0.04176 0.04176 0.04176 0.04176 0.04176 0.04177
Fishery 0,02127 0.02127 0.02127 0.02127 0.02128 0.02128 0.02130
The Village of Voroshilov 0.04636 0.04642 0.04651 0.04662 0.04674 0.04687 0.04804
Average insurance payment, million rubles
Slavyansky 4.00 3.84 3.64 3.41 3.17 2.90 -
Fishery 10.61 10.20 9.68 9.07 8.44 7.73 -
The Village of Voroshilov 101.08 96.70 90.80 84.00 76.21 67.79 -
Average insurance payment, % to project investments
Slavyansky 29.0 27.8 26.4 24.7 23.0 21.0 -
Fishery 0.7 0.7 0.6 0.6 0.6 0.5 -
The Village of Voroshilov 30.7 29.3 27.5 25.5 23.1 20.6 -
Source: calculations by A.S. Arkhipova and N.M. Svetlov.
assume that the insurance payment arrives at the end of project lifetime, however, any other scheme can be simulated as well. Prior to further simulations, we compute the ceiling payment so to ensure the pre-defined probability of negative NPV after receiving insurance payment.
For all three projects, the state support simultaneously increases IRR and decreases (although hardly) its standard deviation. Slavyansky project, although not the least risky, is the least demanding in terms of state support in absolute figures. The Village of Voroshilov project demonstrates the largest growth of IRR and the largest decrease of its standard deviation. So, its attractiveness for investors improves greater than that of any other project. However, this outcome appears very costly for the government. In this regard, Fishery project seems to be the most responsive to governmental support, as the threshold
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probabilities of negative NPV can be achieved at the costs that are less than 1% of private investments in the project.
Notably, large decrease in the risk of a project's financial failure is associated with a very minor change in the standard deviation of IRR. This observation enables us to suggest that variance and standard deviation can be preferably used as ordinal risk measures, as their magnitude is scarcely informative.
Simulation of investor's behavior in the presence of governmental financial support
In addition to the probability of negative NPV, the cash flow simulatio provides the input data for portfolio modeling using Markowitz scheme. This stage of simulation addresses the investor's demand for information. Moreover, it is essential for the researcher whose aim is to inform the government about the investor's response to each scenario of support policy. Comparing portfolios formed under various levels and scenarios of state support enables the researcher to make judgments about the capability of each policy to attract private capital into politically important projects (e.g. from standpoint of national food security).
Markowitz modeling scheme receives from the cash flow simulation both mean and standard deviation of each project's IRR and correlation coefficients of IRRs across the performed simulations. The IRR is comparable to the normalized income from a security, thus taking place of where i" e I", in problem (1). Its standard deviation takes place of oi, i e I", and linear correlation between IRRs of two projects substitutes rp, where {i; j} c I''. Table 6 below presents the latter values obtained from cash flow simulations. Slavyansky and Fishery are the least correlated, so their simultaneous presence in a portfolio reduces overall investment risk greater than the presence of any other pair.
Table 6
Linear correlation between IRR of agro-industrial projects obtained from cash flow simulations
Slavyansky Fishery The Village of Voroshilov
Slavyansky 1 0.159 0.390
Fishery 0.159 1 0.332
The Village of Voroshilov 0.390 0.332 1
Source: calculations by A.S. Arkhipova.
In this study, a project's IRR and a security's normalized income is assumed to be orthogonal, so rj = 0 when i e I" and j e I'. However, it is possible to approach the values of rj by running special cash flow simulations, in which actual prices and price indices data are used to access IRR under the same conditions on which the normalized income of securities was observed. Such simulations are planned for the future.
After having solved the modified Markowitz model that simulates some scenarios of support policy, the optimal portfolio and its attributes are saved in the output database so they can be processed later on.
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Despite their extreme risk, the studied projects take a small share in the investment portfolio formed, for the most part, of a set of large companies' securities (Table 7). In our case, these companies are agrarian holdings: Razgulyai Group, Sinergiya, Rusgrain Holding and food industry companies: Krasny Oktyabr', Cherkizovo, Baltika and Vimm-Bill-Dann. The availability of the state support for real projects substantially increases their share, although they never dominate in the portfolio.
Table 7
Simulated 50 million roubles investment portfolio with 12% annual income under the specified levels of government financial support
Targeted probability of negative NPV, % Gross amount of government support, million rubles Gross investments in actual projects, million rubles Gross investments in securities, million rubles
0 2.343 16.423 33.577
10 2.204 16.152 33.848
20 2.022 15.813 34.187
30 1.826 15.402 34.598
40 1.616 14.958 35.042
50 1.402 14.469 35.531
No support - 9.913 40.087
Source: calculations by A.S. Arkhipova.
The data of Table 7 lead us to a conclusion that the projected scenario of state support meant for bringing the probability of negative NPV down to the targeted threshold (which is assumed to be equal for all three projects) significantly influences the portfolio in favor of supported agro-industrial projects. Their share in the portfolio increases from 19.8% up to 32.8%, making 13.0 point growth..The government support amounting (expectation value) to 2.343 million roubles per 50 million roubles of the investment portfolio attracts 6.510 million roubles of private capital in addition to 9.913 million roubles that would be invested in actual projects if no support is rendered.
Figure 2 demonstrates the amounts of attracted private investments and governmental financial support in connection with the targeted probability of negative NPV and expected income. As one can see from the chart, proposed partial compensation of investor's risk at the expense of governmental funds, tested by the instrumentality of the developed simulation framework, makes it possible to achieve the competitive portfolio income at the acceptable level of risks. The trade-off between the amount of attracted private funds and government expenses is up to the decision maker, who takes into consideration both strategic priorities of governmental agro-industrial policy and the opportunity cost of government expenses.
Discussion and conclusions
The developed framework of cash flow and investment portfolio simulations proves its ability to provide valuable data for the purposes of project risk analysis and management, facilitating decision-making procedure when it comes to funding real sector projects under risky conditions (specifically, when price risk is the most important) and for forecasting
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Source: calculations by A. Arkhipova.
Fig. 2. Gross state support and amount of additionally attracted private funds depending on the targeted probability of negative NPV of agro-industrial projects (the portfolio is worth 50 million
rubles)
investors' response to government policies aimed at attracting private capital in a specific sector, e.g. agro-industrial complex.
Moreover, the application of this framework to the case of three agro-industrial projects that are suggested for implementation in Krasnodar area has shown that the compensation of negative NPV at the end of a project's lifecycle can influence investors' behavior so that attracted private funds exceed governmental expenses up to 2.7 times, subject to the set of securities considered in this study as alternative portfolio investments. The larger portfolio income the investor expects to receive, the greater is the effect of government support.
This result enables us to conclude that the government policies serving to attract private capital into agro-industrial projects via reducing investors' risks are capable to substantially improve the capital inflow into agro-industrial complex. For this reason, we believe that the specific forms, scales and targets of government support call for extensive research, which can largely benefit from the developed methodological framework.
Within the framework ofthis study, the applicability of one ofthe two above mentioned distribution probabilities to any cash flow component in each time period is hypothetic. Consequently, the validity of our conclusions is subjected to the validity of this hypothesis, which requires future testing in each application. However, in practical applications, when
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such testing is not possible, the decision maker can take the risk of unacceptability of this hypothesis. To provide the data for performing regular tests, the existing data gathering infrastructure of extension service needs to be extended. The collected data would be useful for many other analytical, risk-management and research purposes. For the moment it is not clear, though, whether such extension will repay its cost.
The restrictive assumption of certainty of all in-kind amounts throughout the project brings down the standard deviation of each cash flow component. In this regard, we rely on the general methodological standpoint of risk management, which suggests that the scope of unprejudiced risk management involves such risks that are amenable to elucidation, estimation and analysis (e.g., [8]). Insofar, the sources of variance of cash flow components other than prices fall into the category of risks that cannot be objectively analyzed given the existing level of methodology and information base. On the contrary, specific data sources on some or all cash flow components of some specific projects may exist and there is a chance they were not taken into consideration by our investigation. Using these sources to compute standard deviations does not require extensive modifications in the toolset we propose, providing a higher level of risk protection in comparison to the general situation.
Another open research question is approaching correlation between the normalized incomes of securities and real sector projects. Although it is clear theoretically how to measure this correlation, the empirical part of this study needs to be extended to obtain more accurate conclusions about investors' behavior both in the absence and presence of government financial support rendered to agro-industrial projects.
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ПРИМЕНЕНИЕ ИССЛЕДОВАНИЯ ОПЕРАЦИЙ
ДЛЯ ПРИВЛЕЧЕНИЯ ИНВЕСТИЦИЙ В АГРАРНО-ПРОМЫШЛЕННЫЙ КОМПЛЕКС
Н.М. Светлов, А.С. Архипова
(РГАУ-МСХА имени К.А. Тимирязева)
Аннотация: Обоснована возможность применения имитационного моделирования для удовлетворения информационной потребности, возникающей при анализе рисков инвестиционного портфеля, предусматривающего вложения во взаимосвязанные реальные проекты. Разработан комплекс имитационных моделей потоков денежных средств и инвестиционного портфеля, позволяющий определять статистические характеристики экономического эффекта инвестиционных проектов и оценивать вероятный объём инвестиций в реальные проекты в условиях их финансовой поддержки государством. Эмпирическая база имитационной модели образована проектно-сметной документацией, данными о вариации цен продукции, получаемой в результате проекта, а также индексами цен. Инструментальные методы, в основу которых положена разработанная модель, позволят принимать обоснованные решения о вложении капитала в инвестиционные проекты, о формах и размерах государственной поддержки, направляемой на повышение инвестиционной привлекательности АПК.
Ключевые слова: оценка риска проектов, портфельные инвестиции, поток денежных средств, поведение инвестора, модель Марковица, имитационное моделирование.
Светлов Николай Михайлович — д. э. н., проф. кафедры экономической кибернетики РГАУ-МСХА имени К.А. Тимирязева (127550, г. Москва, ул. Тимирязевская, 49. Тел.: (499) 976-03-45; e-mail: svetlov@timacad.ru).
Архипова Анастасия Сергеевна — аспирант кафедры экономической кибернетики РГАУ-МСХА имени К.А. Тимирязева. (e-mail: arkhipova@googlemail.com).
Prof. Dr. Nikolai Mikhailovich Svetlov - Ph.D. in Economic Sciences, professor of the Dept. of economical cybernetics, RSAU-MTAA (ul. Timiryazevskaya, 49, Moscow 127550, Russian Federation; phone +7(499)-976-0345; e-mail: svetlov@timacad.ru).
Anastasiya Sergeevna Arkhipova - post-graduate student of the Dept. of economical cybernetics, RSAU-MTAA (e-mail: arkhipova@googlemail.com).
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