Modeling risk situations in the economy laboratory work. Theory of risk and modeling of risk situations. The concept of risk. Criteria for risk classifications. Accounting for risk in investment ~ projects
THEORY OF RISK AND MODELING OF RISK SITUATIONS
LECTURE 1
- The concept of risk. Criteria for risk classifications.
- Mathematical Apparatus for Modeling and Studying Risk Situations.
- Basic concepts of game theory. Classification of games.
1. The concept of risk. Criteria for risk classifications.
CONCEPT OF RISK
Any sphere of human activity, especially economics or business, is associated with decision-making in conditions of incomplete information.
Sources of uncertainty can be very diverse: instability of the economic, political situation, uncertainty of the actions of business partners, random factors, that is, a large number of circumstances that cannot be taken into account (for example, weather conditions, uncertainty in demand for goods, not absolute reliability of production processes, inaccuracy of information, etc.). Economic decisions, taking into account the above and many other uncertain factors, are made within the framework of the so-called decision theory - an analytical approach to choosing the best action (alternative) or sequence of actions. Depending on the degree of certainty of possible outcomes or consequences of various actions faced by a decision maker (DM), three types of models are considered in decision theory:
the choice of decisions under conditions of certainty, if for each action it is known that it invariably leads to some specific outcome;
decision choice at risk, if each action leads to one of the many possible particular outcomes, and each outcome has a calculated or expertly estimated probability of occurrence. It is assumed that the decision maker knows these probabilities or they can be determined by expert assessments;
the choice of decisions under uncertainty, when one or another action or several actions result in many particular outcomes, but their probabilities are completely unknown or do not make sense.
The difference between risk and uncertainty refers to the way information is specified and is determined by the presence (in the case of risk) or absence (in the case of uncertainty) of the probabilistic characteristics of the uncontrolled variables. In the noted sense, these terms are used in the mathematical theory of operations research, where they distinguish between decision-making problems at risk and, accordingly, under conditions of uncertainty. If it is possible to qualitatively and quantitatively determine the degree of probability of a particular option, then this will be a risk situation.
A risk situation is a type of uncertainty when the occurrence of an event is likely and can be determined.
That is, in a risk situation, it is objectively possible to assess the likelihood of events arising from the joint activities of production partners, counter-actions of competitors or opponents, the impact of the natural environment on the development of the economy, the introduction of scientific achievements, the transition to a new level of technology, etc.
For risk about the situation are characteristic:
-presence of uncertainty(the random nature of the event, which determines which of the possible outcomes is realized in practice);
-availability of alternative solutions;
-outcome probabilities and expected outcomes are known or can be determined;
-loss probability;
-the likelihood of additional profit.
In conditions market economy risk is the key to entrepreneurship. The problem of risk and profit is one of the key economic activity, in particular in the management of production and finance.
In this context, it is appropriate to recall that in V. Dahl's explanatory dictionary, "risk" means "to go at random, to do the wrong thing, at random, to dare, to go at random, to do something without the right calculation, to be exposed to chance, to act boldly, enterprisingly, hoping for luck". "Risking" means "courage, boldness, determination, enterprise, action at random, at random."
In the dictionary of the Russian language S.I. Ozhegov "risk" is defined as "danger, the possibility of danger" or as "action at random in the hope of a happy outcome."
Note an interesting paradox. Expressions such as “He who does not take risks does not win”, “Risk is a noble cause”, “There is no business without risk”, etc. have long been known. - a big benefit”, etc. At the same time, the expressions “risk step”, “risky event” contain a clear connotation of disapproval. Recommendations and instructions to “avoid risk”, “reduce risk to a minimum” are widely popular.
Thus, "risk" is defined, on the one hand, as "the danger of something", on the other hand, as "an action at random, requiring courage, determination, enterprise, in the hope of a happy outcome."
An entrepreneur who knows how to take risks in time is often rewarded. risk in entrepreneurial activity naturally associated with management, with all its functions - planning, organization, operational management, use of personnel, economic control. Each of these functions is associated with a certain measure of risk and requires the creation of an adaptive management system. That is, a special risk management is also necessary, which is based on the knowledge of the economic essence of risk, the development and implementation of a strategy for dealing with it in business. In the conditions of market relations, the problem of accounting and risk assessment acquires independent and applied significance as an important part of the theory and practice of management. Most management decisions are made under conditions of risk.
Risk is an activity associated with overcoming uncertainty in a situation of inevitable choice, during which it is possible to quantitatively and qualitatively assess the probability of achieving the intended result, failure and deviation from the goal.
A quantitative assessment of the degree of risk, as well as the possibility of constructing confidence intervals for a known probability, make it possible to influence the considered economic process with greater reliability in order to increase profits and reduce risk.
To understand the nature of entrepreneurial risk, the relationship between risk and profit is of fundamental importance. The entrepreneur is willing to take risks in the face of uncertainty, since along with the risk of loss, there is the possibility of additional income. Although it is clear that profit is not guaranteed for the entrepreneur, the reward for his time, effort and ability can be both profit and loss.
You can choose a solution that contains less risk, but the resulting profit will also be less. And at the highest risk, profit has the highest value.
Taking risks, the entrepreneur gets a chance to make super profits and at the same time gets the opportunity to be at a loss. The desire to "earn" is contrary to the goal of "security". Incomes above the usual, average rate are achieved, as a rule, as a result of risky actions. It has been proven in economic theory and practice that a certain amount of risk is a necessary condition for generating income.
Along with this, there is an inverse relationship between the level of risk and liquidity.
The higher the level of liquidity (of the firm's assets, etc.), the lower the level of risk.
High return on assets can be achieved by minimizing inventories, which is fraught with disruption of operational processes and means the risk of loss of liquidity. And excessive thrift inevitably threatens the turnover and profitability of assets.
CRITERIA FOR RISK CLASSIFICATIONS
The qualification system of risks includes groups, categories, types, subtypes and varieties of risks.
By the nature of the consequences, that is, depending on the possible result (risk about event) risks can be divided into two large groups: pure risks and speculative risks.
Ø Pure risksmeans the possibility of obtaining a negative or zero result. The peculiarity of pure risks (they are sometimes called statistical or simple) is that they almost always incur losses for entrepreneurial activity. Their causes can be natural disasters, accidents, illness of company executives, etc.
Ø Speculative risks expressed in the possibility of obtaining both positive and negative results. A feature of speculative risks, which are also called dynamic or commercial, is that they carry either losses or additional profit for the entrepreneur. Their reasons may be changes in exchange rates, changes in market conditions, changes in investment conditions, etc.
According to the sphere of origin, which is based on the spheres of activity, the following are distinguished: types of risks: production risk, commercial risk, financial risk.
Production risk - this is the risk associated with the failure of the enterprise to fulfill its plans and obligations for the production of products, goods and services, other types of production activities, as a result of the impact of both the external environment and internal factors.
Commercial risk is the risk of loss in the process of financial economic activity. The reasons for commercial risk may be a decrease in sales volumes, an unforeseen decrease in purchase volumes, an increase in the purchase price of goods, an increase in distribution costs, loss of goods in the circulation process, etc.
financial risk- this is the risk associated with the inability of the company to fulfill its financial obligations. The causes of financial risk may be a change in the purchasing power of money, failure to make payments, changes in exchange rates, etc.
Depending on the main cause of the risks, they are divided into the following categories Key words: natural risks, environmental risks, political risks, transport risks, commercial risks.
To natural-natural risks include risks associated with the manifestation of the elemental forces of nature: earthquake, flood, hurricane, tsunami, fire, epidemic, etc.
Environmental risks are the risks associated with environmental pollution.
Environmental pollution is classified as follows: natural environmental pollution is caused by natural phenomena, usually catastrophes (floods, volcanic eruptions, mudflows); Anthropogenic pollution occurs as a result of human activities.
An environmental risk may arise during the construction and operation of an object and be an integral part of industrial risk.
Political risks - these are the risks associated with the political situation in the country and the activities of the state. Political risks arise when the conditions of the production and trade process are violated, which are not directly dependent on the economic entity.
Political risks include:
uthe impossibility of carrying out economic activities due to hostilities, revolution, aggravation of the internal political situation in the country, nationalization, confiscation of goods and enterprises, the introduction of an embargo, due to the refusal of the new government to fulfill the obligations assumed by its predecessors, etc .;
uthe introduction of a deferment (moratorium) on external payments for a certain period due to the onset of emergency circumstances (strike, war, etc.);
uunfavorable change in tax legislation;
uprohibition or restriction of the conversion of the national currency into the payment currency.
Transport risks - these are the risks associated with the transportation of goods by transport: road, sea, river, rail, air, etc.
Commercial risks means the uncertainty of the results from this commercial transaction.
On a structural basis commercial risks are divided into property, production, trade, financial.
è Property risks - these are the risks associated with the probability of loss of the entrepreneur's property due to theft, negligence, overvoltage of the technical and technological systems, etc.
Property risk is the probability of loss by the enterprise of part of its property, its damage and shortfall in income in the process of carrying out production and financial activities.
The group of property risks can be divided into the following subspecies:
Risk of loss of property as a result of natural disasters (fires, floods, earthquakes, hurricanes, etc.);
The risk of loss of property due to the actions of intruders (theft, sabotage);
Risk of loss of property as a result of accidents at work;
Risk of loss or damage to property during transportation;
The risk of alienation of property due to the actions of local authorities or other owners.
In addition, for a particular manufacturing company, there is a risk of losing any particular type of property, such as computer equipment or certain types of raw materials, materials and components.
The level of these risks can be reduced by insuring certain types of property, as well as by establishing strict property liability of financially responsible persons at the enterprise, ensuring the organization of protection of the company's territory, developing and implementing organizational, technical, economic and other measures to prevent risks or minimize them.
è Production risks - these are the risks associated with a loss from stopping production due to the influence of various factors, and above all with the loss or damage of fixed and working capital (equipment, raw materials, transport, etc.), as well as the risks associated with the introduction of new equipment into production and technology.
è Trading risks- risks associated with loss due to delayed payments, refusal to pay during the period of transportation of goods, non-delivery of goods, etc.
è Financial risks associated with the probability of loss financial resources(i.e. money).
Financial risks are divided into two kinds: risks associated with the purchasing power of money and risks associated with investing capital (investment risks).
The risks associated with the purchasing power of money include: types of risks: inflationary and deflationary risks, currency risks, liquidity risks.
inflation risk is the risk that, as inflation rises, cash incomes depreciate in terms of real purchasing power faster than they grow. In such conditions, the entrepreneur bears real losses.
deflationary risk is the risk that, as deflation increases, the price level will fall, economic conditions for business will worsen, and incomes will decline.
Currency risksrepresent a risk of currency losses associated with a change in the exchange rate of one foreign currency against another, in the course of foreign economic, credit and other foreign exchange transactions.
Liquidity risks - these are the risks associated with the possibility of losses during the implementation valuable papers or other goods due to a change in the assessment of their quality and use value.
Currency risk includes three types of risks: economic risk, transfer risk, transaction risk.
è Economic risk for an entrepreneurial firm is that the value of its assets and liabilities can change up or down (in local currency) due to future changes in the exchange rate. This also applies to investors whose foreign investments - stocks or debt - generate income in foreign currency.
è Translation riskhas an accounting nature and is associated with differences in the accounting of assets and liabilities of the company in foreign currency. If there is a fall in the exchange rate
è the foreign currency in which the firm's assets are denominated, the value of those assets decreases. It should be kept in mind that transfer risk is an accounting effect but little or no reflection of the economic risk of the transaction.
è More important from an economic point of view is transaction risk, which considers the impact of a change in the exchange rate on the future flow of payments, and hence on the future profitability of the entrepreneurial firm as a whole.
è Transaction risk- is the probability of cash foreign exchange losses on specific transactions in foreign currency. This risk arises from the uncertainty of the future value of a foreign exchange transaction in the national currency. This type of risk exists both when concluding trade contracts, and when obtaining or granting loans. It consists in the possibility of changing the amount of receipts or payments when recalculated in the national currency.
In addition, a distinction should be made between the foreign exchange risk for the importer and the risk for the exporter.
Transaction risk for the exporter - this is the fall in the foreign exchange rate from the moment the order is received or confirmed until payment is received and during negotiations.
Transaction risk for the importer - this is the increase in the exchange rate in the period of time between the date of confirmation of the order and the day of payment.
Thus, when concluding contracts, it is necessary to take into account possible changes in exchange rates.
Investment risks include the following subtypes of risks: the risk of lost profits, the risk of reduced profitability, the risk of direct financial losses.
Lost profit risk - this is the risk of indirect (collateral) financial damage (lost profit) as a result of the failure to carry out any activity (for example, insurance, hedging, investing, etc.).
Return risk may arise as a result of a decrease in the amount of interest and dividends on portfolio investments, on deposits and loans. Yield downside risk includes the following varieties: interest rate risks and credit risks.
Risks of direct financial losses include the following varieties: stock risk, selective risk, bankruptcy risk, and credit risk.
uExchange riskThis is the danger of losses from exchange transactions.
uselective risk - this is the risk of incorrect choice of types of capital investment, type of securities for investment in comparison with other types of securities when forming an investment portfolio.
uBankruptcy risk represents a danger as a result of the wrong choice of capital investment, the complete loss of the entrepreneur's own capital and its inability to pay for its obligations.
From the point of view of duration in time, entrepreneurial risks can be divided into short term and permanent.
The short term ones are risks that threaten the entrepreneur for a known period of time (for example, transport risk, when losses may occur during the transportation of goods, or the risk of non-payment for a specific transaction).
To constant risks include those that continuously threaten business activity in a given geographic area or in a particular sector of the economy (for example, the risk of non-payment in a country with an imperfect legal system or the risk of building collapses in an area with high seismic hazard).
Since the main task of an entrepreneur is to take risks prudently, without crossing the line beyond which the bankruptcy of the company is possible, it is necessary to single out tolerable, critical and catastrophic risks.
Tolerable risk- this is the threat of a complete loss of profit from the implementation of a project or from entrepreneurial activity in general. In this case, losses are possible, but their size is less than the expected business
arrived. Thus, this type of entrepreneurial activity or a specific transaction, despite the likelihood of risk, retains its economic feasibility.
The next degree of risk, more dangerous than acceptable, is critical risk. Critical Risk associated with the risk of losses in the amount of the costs incurred for the implementation of this type of entrepreneurial activity or a separate transaction.
Wherein first degree critical risk is associated with the threat of obtaining zero income, but with compensation for the material costs incurred by the entrepreneur.
Critical risk of the second degree associated with the possibility of losses in the amount of full
costs as a result of the implementation of this entrepreneurial activity, that is, the loss of the intended revenue is likely and the entrepreneur has to reimburse the costs at his own expense.
Catastrophic refers to the risk , which is characterized by danger, the threat of loss in an amount equal to or greater than the entire property status
entrepreneur. As a rule, such a risk leads to the bankruptcy of the company, since in this case it is possible to lose not only all the funds invested by the entrepreneur in a certain type of activity or in a specific transaction, but also his property. This is typical for a situation where an entrepreneurial firm received external loans for the expected profit. When this risk occurs, the entrepreneur has to repay loans from personal funds.
2. Mathematical apparatus for modeling and research of risk situations.
The role of a quantitative assessment of economic risk increases significantly when it is possible to choose the optimal solution from a set of alternative solutions. The optimal solution provides the highest probability of the best result at the lowest cost and loss in accordance with the tasks of risk minimization and programming.
The use of economic and mathematical methods makes it possible to conduct a qualitative and quantitative analysis of economic phenomena, to quantify the significance of risk and market uncertainty, and to choose the most effective (optimal) solution.
Mathematical methods and models make it possible to simulate various economic situations and evaluate the consequences of choosing decisions, without costly experiments.
As mathematical means of decision-making under conditions of uncertainty and risk, we will use the methods of mathematical game theory, probability theory, mathematical statistics, the theory of statistical decisions, and mathematical programming.
Many financial transactions (venture investment, purchase of shares, selling transactions, credit transactions, etc.) are associated with a rather significant risk. They require to assess the degree of risk and determine its magnitude.
Entrepreneur risk quantitatively characterized by a subjective assessment of the probable (that is, expected) value of the maximum and minimum income (loss) from a given investment of capital. At the same time, the larger the range between the minimum and maximum income (loss) with an equal probability of their receipt, the higher the degree of risk.
The degree of risk is the probability of a loss occurring, as well as the amount of possible damage from it.
The choice of an acceptable degree of risk depends on the preferences of the head of the enterprise. Leaders of the conservative type are not prone to innovation, they usually try to
walk away from any risk. Agile leaders tend to take riskier decisions if the risk is voluntary. In a difficult situation, such leaders are focused on more risky decisions, if they are confident in the professionalism of the performers.
The manager's willingness to take risks is usually formed under the influence of the results of the implementation of past similar decisions taken under conditions of uncertainty.
Losses dictate prudent policies, while success encourages risk taking.
Most people prefer low-risk options. At the same time, the attitude to risk largely depends on the amount of capital that the entrepreneur has. In the course of evaluating alternative solutions, the manager has to predict possible results. In this case, the decision is made under conditions of certainty, when the manager can accurately assess the results of each alternative solution.
Risky decisions are those decisions that involve obtaining some result with a certain degree of probability. This happens in conditions of uncertainty, when the factors requiring analysis and accounting are very complex, and there is no reliable or sufficient information about them. Then it is impossible to be sure of achieving certain results. Uncertainty is also characteristic of many decisions made in rapidly changing circumstances. This situation is quite familiar to Russian entrepreneurs. Determining the choice, the manager considers a new project
in relation to other options and to already established activities of firms. In order to reduce risk, it is desirable to choose the production of such goods (services), the demand for which changes in opposite directions, that is, with an increase in demand for one product, the demand for another decreases, and vice versa.
Unfortunately, not every risk can be reduced through diversification. The fact is that entrepreneurship is affected by various macroeconomic factors, such as the expectation of a rise or crisis, the movement of bank interest rates, etc. The manager cannot reduce the risk caused by these processes by diversifying production. Making managerial decisions at the enterprise
implies a close linkage of all types of risk. However, the best forecasts of a manager may not come true due to unexpected and unforeseen circumstances beyond the control of the firm itself (economic conflicts, sudden changes in customer tastes, actions of competitors, strikes, unexpected government decisions).
Therefore, in the event of adverse events, various opportunities are provided to reduce the negative consequences at the expense of reserve funds, production capacities, raw materials, finished products; financially secured plans for the reorientation of activities are being developed.
It is possible to significantly reduce the risk through qualified work on forecasting and intra-company planning, self-insurance and insurance, transferring part of the risk to other persons or organizations through hedging, futures transactions, redemption of options.
To quantify the magnitude of the risk, it is necessary to know all the possible consequences of any individual action and the likelihood of the consequences themselves.
Probability means the possibility of obtaining a certain result. In relation to economic problems, the methods of probability theory are reduced to determining the values of the probabilities of the occurrence of events and to choosing the most preferable event from possible events based on the largest value of mathematical expectation.
Risk is an action in the hope of a happy outcome on the principle of "lucky or not lucky." The entrepreneur is forced to take risks due to the uncertainty of the economic situation. The greater the uncertainty of the economic situation, the greater the degree of risk.
The uncertainty of the economic situation is due to the following factors: lack of complete information, chance, opposition.
Lack of complete information about the economic situation and the prospects for its change makes the entrepreneur look for an opportunity to acquire the missing additional information, and in the absence of such an opportunity, start acting at random, relying on his experience and intuition.
The uncertainty of the economic situation is largely determined by the factor of chance. Accident- this is what happens differently under similar conditions, and therefore it cannot be foreseen and predicted in advance. The mathematical apparatus for studying random variables is given by probability theory. Probability allows you to predict random events. It gives them a quantitative and qualitative characteristic. At the same time, the level of uncertainty and the degree of risk are reduced.
The uncertainty of the economic situation is largely determined by the counteraction factor. To counteractions relate catastrophes, fires and other natural phenomena, wars, revolutions, strikes, various conflicts in labor collectives, competition, changes in demand, accidents, thefts, etc. The entrepreneur, in the course of his actions, must choose a strategy that will allow him to reduce the degree of opposition, and consequently, reduce the degree of risk. The mathematical apparatus for choosing a strategy in conflict situations is given by game theory.
The degree of risk is measured by two criteria:
Average expected value,
Fluctuation (variability) of the expected result.
RISK MEASURE
The most widely held view is that measure of risk of some commercial (financial) decision or operation, the standard deviation (positive square root of the dispersion) of the value of the indicator of the effectiveness of this decision or operation should be considered.
Indeed, since the risk is due to the non-determinism of the outcome of the decision (operation), then the smaller the spread (dispersion) of the result of the decision, the more predictable it is, i.e. less risk.
If the variation (variance) of the result is zero, there is no risk at all. For example, in a stable economy, transactions in government securities are considered risk-free.
Most often, the indicator of the effectiveness of a financial decision (operation) is profit.
Let us consider, as an illustration, the choice by some person of one of the two options
investment at risk.
Let there be two projects BUT And IN , in which the said person may invest funds.
Project BUT at some point in the future provides a random amount of profit.
Assume that its mean expected value, the mathematical expectation, is t A from
dispersion . For the project IN these numerical characteristics of profit as random
values are assumed to be equal respectivelym BAnd . RMS
deviations are equal respectivelyS A And S B.
The following cases are possible:
1) T A = m B, S A < S B, choose a project BUT ;
2) T A > m B, S A < S B, should choose a project BUT ;
3) T A > m B, S A = S B, choose a project BUT;
4) TA > m B , S A > S B ;
5) TA < m B , S A< S B .
In the last two cases, the decision to choose a project BUT or IN depends on the attitude towards the risk of the decision maker.
In particular, in case 4) the project BUT provides a higher average profit,
however, it is also more risky. The choice is determined by which additional
the value of the average profit compensates for the given increase in risk for the decision maker.
In case 5) for the project BUT The risk is lower, but the expected return is also lower.
The subjective attitude to risk is taken into account in the Neumann-Morgenstern theory.
Consider an example of choosing an investment option.
Example.Let there be two investment projects. The first with a probability of 0.6 provides a profit of 15 million rubles, but with a probability of 0.4 you can lose 5.5 million rubles. For the second project, with a probability of 0.8, you can make a profit of 10 million rubles. and with a probability of 0.2 to lose 6 million rubles. Which project to choose?
Solution.
Both projects have the same average profitability equal to 6.8 million rubles:
0,6*15 + +0,4(-5,5) = 0,8*10 + 0,2(-6) = 6,8.
However, the standard deviation of profit for the first project is 10.04 million rubles:
1/2 = 10,04;
and for the second - 6.4 million rubles:
1/2 = 6,4.
Therefore, the second project is more preferable.
Although the standard deviation of the effectiveness of the solution is often used
as a measure of risk, it does not accurately reflect reality. There are situations in which options provide approximately the same average profit and have the same standard deviations of profit, but are not equally risky. Indeed, if risk is understood as the risk of ruin, then the amount of risk should depend on the amount of the initial capital of the decision maker or the company that he represents. The Neumann-Morgenstern theory takes this circumstance into account.
3. BASIC CONCEPTS OF GAME THEORY. CLASSIFICATION OF GAMES.
Game theory is a theory of mathematical models for making optimal decisions under conditions of uncertainty, opposing interests of various parties, conflict.
Mathematical game theory is an integral part of operations research.
Operations research tasks can be classified according to the level of information about the situation that the decision maker has.
The simplest levels of information about the situation are deterministic (when the conditions under which decisions are made are fully known) and stochastic (when
many possible variants of conditions and their probability distribution are known).
In these cases, the problem is reduced to finding the extremum of the function (or its mathematical expectation) under given constraints. Methods for solving such problems are studied in the courses of mathematical programming or optimization methods.
Finally, the third level is indeterminate, when many possible
options, but without any information about their probabilities. This level of information about the situation is the most difficult. This complexity turns out to be fundamental, since the very principles of optimal behavior may not be clear.
Game theory is a theory of mathematical models of decision-making under conditions of uncertainty, when the decision-making subject (“player”) has information only about the set of possible situations, one of which he is actually in, about the set of decisions (“strategies”) that he can accept, and about the quantitative measure of the “gain” that he could get by choosing this strategy in a given situation.
Establishing the principles of optimal behavior under uncertainty, proving the existence of solutions that satisfy these principles, indicating algorithms for finding solutions and constitute the content of game theory.
The uncertainty that we encounter in game theory can have various origins. However, as a rule, it is a consequence of the conscious activity of another person (persons) defending their interests. In this regard, game theory is often understood as the theory mathematical models making optimal decisions in conflict situations.
Mathematical "game theory" is a theory of mathematical models for making optimal decisions in conflict conditions.
Thus, game theory models can, in principle, meaningfully describe very diverse phenomena: economic, legal and class conflicts, human interaction with nature, the biological struggle for existence, etc.
All such models in game theory are called games.
Conflict situation - a situation in which two (or more) parties pursue different goals, and the results of any action of each of the parties depend on the actions of partners.
A game- a mathematical model of a conflict situation.
win(payment) - the outcome of the conflict.
Zero sum game - a game in which the gain of one of the players is equal to the loss of the other.
movein game theory is called the choice of one of the options provided by the rules of the game.
personal moveis called a conscious choice by one of the players of one of the moves possible in a given situation and its implementation.
Random moveis called a choice from a number of possibilities, carried out not by the decision of the player, but by some mechanism of random selection.
Player strategy - a set of rules that determine the choice of his actions for each personal move, depending on the situation.
The Purpose of Game Theory– determination of the optimal strategy for each player.
The mathematical description of the game is reduced to listing all the players acting in it, indicating for each player all his strategies, as well as the numerical payoff that he will receive after the players choose their strategies. As a result, the game becomes a formal object that lends itself to mathematical analysis.
Games can be classified according to various criteria.
Firstly , non-cooperative games, in which each coalition (the set of players acting together) consists of only one player. The so-called cooperative theory of non-cooperative games allows temporary association of players in coalitions during the game, followed by the division of the resulting gain or the adoption of joint decisions.
Secondly, coalition games, in which the decision makers, according to the rules of the game, are united in fixed coalitions. Members of the same coalition can freely exchange information and make fully coordinated decisions.
By winning the game can be divided into antagonistic and games with non-zero sum.
By the nature of obtaining information - for games in normal form(players receive all the information intended for them before the start of the game) and dynamic games (information comes to the players in the process of game development).
By the number of strategies - final And endless games.
LITERATURE
Balabanov I.T. Risk-management. - M.: Finance and statistics, 1996. - 192 p.: ill.
[ 2 ] . Dubrov A.M., Lagosha B.A., Khrustalev E.Yu. Modeling risk situations in economics and business. Tutorial. - M.: Finance and statistics, 2000. - 176 p.: ill.
Petrosyan L. A., Zenkevich N. A., Shevkoplyas E. V. Game theory. Textbook. - St. Petersburg: BVH-Petersburg, 2012. - 432 p.: ill.
Tapman L.N. Risks in the economy. Textbook for universities. - M.: UNITI-DANA, 2002. - 380 p.
Shapkin A.S., Shapkin V.A. Theory of risk and modeling of risk situations. Textbook. M .: Publishing and Trade Corporation "Dashkov and K 0", 2005. - 880 p.
The book reveals the essence of risk management, its organization, strategy, techniques, methods of risk reduction, including insurance.
The tutorial discusses approaches to accounting for uncertainty and risk factors in economic practice, as well as mathematical models used for these purposes. Analyzed are situations that arise in conditions of uncertainty and lack of information when making managerial decisions. The content is illustrated by applied problems with solutions.
The textbook is intended for both initial and in-depth study of game theory. A systematic study of mathematical models of decision-making by several parties in a conflict has been carried out. A consistent presentation of a unified theory of static and dynamic games is presented. All main classes of games are considered: finite and infinite antagonistic games, non-cooperative and cooperative games, multi-stage and differential games. To consolidate the material, each chapter contains tasks and exercises of varying degrees of complexity.
The textbook is intended for students, graduate students and teachers of economic universities and faculties, students of business schools, heads of enterprises and organizations.
The textbook outlines the essence of uncertainty and risk, classification and factors acting on them; methods for qualitative and quantitative assessment of economic and financial situations under conditions of uncertainty and risk are given.
TEST QUESTIONS.
1. What is risk?
2. How do the concepts of "risk" and "uncertainty" differ?
3. What is a "risk situation"?
4. Economic consequences of risky situations. Give examples.
5. Define economic risk. Give examples of economic risks.
4. Give examples of classifications of economic risks.
6. Describe the relationship between the risk and profit of financial transactions.
7. Is the concept of economic risks associated exclusively with those
risks, the occurrence of which leads to monetary damage?
8. What is the degree of risk?
9. What are the main factors of uncertainty in the economic situation?
10. What is a measure of risk? How is it measured? Give examples.
11. Formulate the basic concepts of game theory.
12. What are the features of the classification of games. Give examples of games.
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Introduction
1.1 Introductory remarks
1.4.2 Risk management system
Chapter 2. Modeling the process of managing the operational risk of credit institutions
2.1 Mathematical statement of the problem
2.2 Loss modeling
2.3 Modeling dependent structures of random variables. Copula functions
2.4 Modeling loss rates
2.5 Stochastic Monte Carlo approximation of a random
2.6 Calculating risk capital 66
Chapter 3. Implementation of the operational risk management system
3.1 Development and implementation of an operational risk management system
3.2 Calculation of risk capital
3.3 Assessing the cost-effectiveness and sustainability of the model
Conclusion
List of used literature
Applications
Introduction
mathematical operational risk economic
Economic and mathematical modeling is now at a stage when a qualitative leap is ripe. All over the world, a huge number of different models have accumulated. Whatever area of economics we take, there will always be a whole range of mathematical, computer, verbal and meaningful models, one way or another related to it. Hundreds of scientific journals monthly publish descriptions of new models, or modifications and developments of old ones.
All of them, although they are called models of the economy, are actually models of one of its areas, they explain one thing. Each of them contributes to the system of knowledge about the economy. A feature of the process of understanding, cognition by a person of complex phenomena is their simplification, reduction to a simple image. Therefore, since knowledge is infinite, the creation of models also seems to have no limit.
Within the framework of mathematical economics, with the help of formal means, the study of complex economic mechanisms already encounters significant difficulties. Models are no longer as beautiful and complete as in classical cases, although they consider the most common or most economically feasible combinations of simple mechanisms.
From a practical point of view, any, even a very large amount of information in itself has no value. Data in its purest form is not the kind of knowledge that is called "power". Information becomes power when it allows foreseeing the future, i.e. answer the main question when choosing a solution: “What will happen if?” To answer this question, in addition to data, it is necessary to have a model of the real world.
Where do models come from and why are they practically absent in banking management systems? In the banking business, the process of creating adequate models is complicated by two objectively existing factors. The first is that from the point of view of management, the bank is an extremely complex object, consisting of many different subsystems, between which there are a large number of heterogeneous links. The activity of the bank consists of a number of business processes, which significantly depend on the set external factors: legislative, economic, social, political.
In cybernetics, objects such as a bank are called complex systems, and methods of their study - methods of system analysis. The most significant results in this area are associated with operations research, an approach based on the use of quantitative mathematical methods to evaluate decisions. However, the use of quantitative methods is possible only if the researcher has adequate mathematical models, which are precisely absent in banking.
The second factor is manifested in the fact that in banking (especially in the transition to a market economy) it is impossible to conduct targeted experiments that precede the formation of a hypothesis and allow it to be tested in practice. The accumulation of personal experience by analysts is hampered by the dynamic change in the situation typical of modern Russia.
Most of all, financial science is associated with the analysis of the profitability of investment activities. In addition to measuring profitability, bank analysts also deal with the uncertainty of income generation; risk analysis is associated with this uncertainty. The lack of development of these issues in our practice explains the need to study foreign experience in terms of its application in Russia.
The set of indicators, methods and calculation models used in assessing the profitability of a particular banking strategy is the subject of new, dynamically developing scientific areas - financial mathematics and financial analysis, formed at the intersection modern theory finance and a number of mathematical disciplines, such as: econometrics, probability theory, mathematical statistics, operations research, the theory of random processes.
The main goal of banking is profit maximization; an almost equivalent task is also the minimization of banking risks. The decline in the rate of return from banking operations, the reduction of the client base and the decrease in turnover on customer accounts lead to the fact that the ratio between the bank's profit and its operating costs becomes extremely unfavorable. Thus, a situation is created when banks are forced to look for ways to reduce costs and minimize risks. And this, in turn, makes banks pay special attention to the financial analysis and methods of managing their resources.
The ability to take reasonable risks is one of the elements of the culture of entrepreneurship in general, and banking activity in particular. In market conditions, each of its participants accepts certain rules of the business game and, to a certain extent, depends on the behavior of partners. One of these rules can be considered the willingness to take on the risk and take into account the possibility of its implementation in their activities.
One of the main types of risks of credit institutions is the operational risk due to the uncertainty of the state and functioning of their internal and external environment. Losses from the occurrence of operational risk events can lead to significant direct and indirect losses, ruin of companies and even death of people. The high-profile bankruptcies of recent years, which were caused, among other things, by errors in the organization of the operational risk management system, testify to the scale and insufficient elaboration of the issues of assessing, preventing and minimizing losses from the occurrence of events related to operational risk. Lack of representative statistical information, heterogeneous and individual for each credit institution profile of operational risk makes it impossible to use generally accepted methods and models of measurement and management financial risks used in risk management theory to analyze and manage operational risk.
The need to reserve capital for operational risk (inclusion of operational risk in the calculation of capital adequacy ratio H1) became a reality for Russian commercial banks already in August 2010, as this reflects the strategy for the development of the banking sector and the course of the Central Bank of the Russian Federation to introduce risk-based approaches to assessing credit organizations.
Thus, the tasks of building an effective system for measuring, forecasting and minimizing the operational risk arising in the course of the activities of credit institutions determine the relevance of the study.
The purpose of the study is to develop methods and models for the comprehensive management of the operational risk of credit institutions. In accordance with this goal, the following tasks were set and solved in the work:
1. Conduct a study of existing models and methods for analyzing and managing financial risks in relation to the specifics of operational risk.
2. Develop a comprehensive classification of events and operational risk factors, taking into account the specifics of the activities of credit institutions.
3. Develop mathematical tools necessary for the analysis, measurement and management of operational risk, including:
· set and implement the task of mathematical modeling of random processes of losses, taking into account the presence of the effect of correlations between them;
· develop and programmatically implement a stochastic algorithm for modeling the total amount of losses with a given structure of dependencies and calculating the amount of risk capital to cover them (taking into account the presence of various insurance coverages and risk measures).
4. Develop a software implementation of modeling the process of managing the operational risk of a credit institution, assess the sensitivity of the implemented methods to various disturbances of input parameters.
5. Determine the economic efficiency of the implemented operational risk management model. Develop guidelines for organizing the operational risk management process in credit institutions.
The object of the thesis research is the operational risks arising in the course of the current activities of credit institutions. The subject of the thesis research is economic and mathematical methods and models of the operational risk management process as an element of the risk management system of a credit institution.
The theoretical and methodological basis of the study were the works of domestic scientists in the field of insurance business, financial and actuarial mathematics, game theory, probability theory and mathematical statistics, extreme value theory, random processes, numerical methods, risk management.
The scientific novelty of the study lies in the development of an integrated approach to managing operational risk based on the synthesis of the following problems of economic and mathematical modeling: analysis of the processes of losses, assessment of the total amount of losses, calculation of the amount of risk capital to cover them. The subject of protection is the following provisions and results containing elements of scientific novelty:
1. The problem of mathematical modeling of random processes of occurrence of losses of credit institutions associated with operational risk has been posed and solved, which allows for a more accurate assessment of the magnitude of operational risk, in comparison with existing calculation methods.
2. A probabilistic modeling of the aggregate amount of losses has been implemented, taking into account the presence of correlations between them, which makes it possible to more accurately assess the total amount of losses, to reasonably reduce the estimated amount of required risk capital to cover them.
3. A software implementation of stochastic modeling of the sums of random processes (losses) with a predetermined structure of dependencies and calculation of the amount of capital to cover them, taking into account the presence of various insurance programs and risk measures, has been developed. The sensitivity of the developed methods to various perturbations of the input parameters was assessed.
4. The economic efficiency of applying the developed integrated model of operational risk management in credit institutions in comparison with existing methods and models of analysis and management of operational risk (in terms of saving the amount of risk capital) has been proved.
The first chapter discusses the features of simulation modeling of banking processes, the model of the functioning of the bank, the concept of risk in banking, the classification of banking risks and the risk management system.
In the second chapter, the problem of mathematical modeling of the processes of the onset of losses of credit institutions associated with operational risk is posed and solved. Mathematical models have been implemented and: methods for estimating, measuring and forecasting the total amount of aggregated losses, calculating and coherent distribution of risk capital, a mechanism for supplementing own data by mapping information on losses of external organizations, taking into account the effect of the time structure of money and the presence of a significance threshold, when modeling the amount of losses. In the third section of the chapter, the main facts of the copula theory necessary for modeling dependent random processes are presented, and correlation measures that are invariant to monotone transformations are discussed. An algorithm for stochastic modeling of random processes with known distribution functions and a predetermined dependence structure, using the Gaussian copula, has been implemented. Using the theory of copulas, an algorithm for generating dependent processes is implemented that simulates the frequency of occurrence of losses. Section 2.5 describes a stochastic Monte Carlo model, developed and implemented in MATLAB, for estimating the probability distributions of the total losses of a credit institution for the general case, using Gaussian and Student's t-copulas and fast Fourier transform. This model formed the basis of the AMA model, the results of which are discussed in the third chapter. As an alternative to the Basel II quantile function VaR for calculating the amount of capital to cover operational risk, Section 2.6 proposes the use of coherent risk measures. A measure (Expected ShortFall - ES) is considered, which satisfies the subadditivity condition and allows obtaining results that are more resistant to various extreme distributions of loss values. The problem of coherent distribution of risk capital between lines of business and/or subdivisions of a credit institution has been posed and solved. The result obtained is that, in terms of non-atomic game theory, the principle of coherent distribution of risk capital can be uniquely determined through the Aumann-Shapley vector, which always exists and belongs to the core of the game.
In the third chapter, the main stages are developed - the implementation and information support of the system of integrated management of the operational risk of a credit institution. The key points of the creation of internal regulations and methodologies that regulate the process of managing operational risk, which are subject to mandatory coverage in accordance with the requirements of the Central Bank of the Russian Federation and the Basel II recommendations, are given. In addition to calculating quantitative indicators of operational risk, it is recommended to monitor qualitative indicators of operational risk that best characterize the main areas of the credit institution's activities that are subject to operational risk. Section 3.1 develops a comprehensive scorecard (KIR - Key Risk Indicators) for medium-sized credit institutions.
As a demonstration of the developed quantitative methods for managing operational risk, in the second part of the third chapter, a simplified implementation of the AMA model is considered using the example of calculating the CaR value for a medium-sized credit bank. A comparison was made of risk capital values calculated on the basis of different approaches and for different risk measures and significance levels. Section 3.3 analyzes the sensitivity of the implemented model for various perturbations of the input parameters. The estimated economic effect from the introduction of the developed models and methods for managing the operational risk of credit institutions was assessed in comparison with existing approaches.
In conclusion, the main results and conclusions of the study are formulated.
Chapter 1. Analysis of existing mathematical models of the bank
1.1 Introductory remarks
As mentioned above, the main goal of banking is profit maximization; an almost equivalent task is also the minimization of banking risks. This means that the policy of a commercial bank should be based on a thorough assessment and simulation of various situations, an analysis of many factors that affect the amount of profit. These factors determine the level of banking risk; the task of the bank is to minimize it.
Bank profitability \u003d Profitability of credit resources + Return on investments:
where is the share of the th and th type of resources,
DB - profitability of the bank,
KR - credit resources,
Central Bank-investments in securities.
Investors acquire assets, such as stocks, bonds, or real estate, with the aim of generating income either from selling them at a higher price, or in the form of dividends, coupon interest, or rental payments. Lenders lend money in the hope of earning an income in the form of interest payments when the borrower repays the loan in full. Thus, lenders and investors have a common goal - to receive income or interest as a result of investment or lending activities.
The decline in the rate of return from banking operations, the reduction of the client base and the decrease in turnover on customer accounts lead to the fact that the ratio between the bank's profit and its operating costs becomes extremely unfavorable. Thus, a situation is created when banks are forced to look for ways to reduce costs and minimize risks. And this, in turn, makes Russian banks pay special attention to financial analysis and methods of managing their resources.
The most important rule on which risk decision-making strategies in business are based:
Risk and return move in the same direction: the higher the return, the higher the risk of the operation, as a rule.
If banks want to raise additional funds, they must demonstrate to their customers that they fully consider the risk-return ratio.
It is this thesis that is currently used in a number of major foreign banks.
Under the conditions of a planned economy, the understanding of risk and uncertainty as integral components of socio-economic development, as the most important scientific categories that require a comprehensive study, was excluded. The formation of market relations in Russia and the corresponding economic mechanisms led to the return of the concept of risk to the theory and practice of managing economic objects at all levels and forms of ownership.
Much attention is paid to the modeling of banking processes abroad. The idea of bank portfolio management or end-to-end balance sheet management originates in modern portfolio theory (portfolio theory), developed in the mid-1950s. The first attempts to apply modern portfolio theory to banking were in the form of linear and quadratic models of mathematical programming. Although these models were quite slender in the classical sense, they were too limited and complex for practical use. Their main value lies in the ability to penetrate into the full management of the balance sheet. It is useful as an aid to understanding how to manage a banking portfolio and risk.
Portfolio management concepts are illustrated using a linear programming model. Of course, in order to demolish reality to a two-dimensional problem, we had to seriously simplify the formulation of the problem.
Let's represent the bank's balance sheet in the following simplified form:
where the Central Bank is securities,
KR - loans,
DV - demand deposits,
SD - term deposits,
K is capital. Egorova N.E., Smulov A.S. Enterprises and banks: interaction, economic analysis and modeling.-M.; Delo, 2002. P.61.
Let us designate the profit on securities and profit on loans as Pcb and Pkr, respectively. The costs of attracting deposits and capital are assumed to be zero. Hence, the income or profit of the bank Pr is given by the equation:
We also give a classification of analytical programs of banking activities:
1. Level in the organizational structure of the bank: top management, middle level, performers.
2. Type of analyzed transaction: credit transactions, securities, currency transactions, other transactions.
3. Type of problem being solved: monitoring, analysis, optimization, modeling, forecasting, planning, control.
4. Analysis time lag: this moment, short-term estimates, medium-term estimates, long-term estimates.
1.2 Features of simulation modeling of banking processes
The need to use simulation modeling is primarily due to the peculiarities of the Russian market. A distinctive feature of the Russian financial market is its "subjectivism", extreme dependence on non-economic factors and, as a result, a high degree of uncertainty, which makes it difficult to make informed financial decisions.
This uncertainty is created by:
1. instability of the external environment of Russian banks, lack of clearly established rules and procedures for organizing various sectors of the financial market (institutional aspect);
2. the lack of a sufficiently developed apparatus for predicting the macroeconomic situation in uncertain conditions and analyzing the multiplicity of factors (instrumental aspect);
3. the impossibility of taking into account and formalizing all connections to build an economic and mathematical model that adequately reflects the structure of the financial market (cognitive aspect);
4. inaccessibility of reliable information - the absence of a single information space "bank - client - financial market - state" (information aspect);
5. inadequate reflection of the real financial condition of the bank in the financial statements (balance sheet, etc.) and, thus, the lack of financial transparency in the bank (accounting aspect). The use of traditional means of supporting management decisions and forecasting in these conditions is difficult, and the more valuable is the possibility of using the simulation method. Emelyanov A.A. Simulation modeling in risk management. - St. Petersburg: St. Petersburg Academy of Engineering and Economics, 2000. P.132.
Many modern software products designed specifically for predicting the situation in the financial market. These include tools for technical analysis of the stock market, expert systems and statistical packages. These products are intended primarily for decision makers in the government debt market.
The practice of using forecasting tools by banks and investment companies in trading on the securities market shows that the forecast is not always reliable even from the point of view of the trend. One of the reasons for this is the limited period of statistical observations.
In turn, simulation modeling is a tool that can be used to cover all areas of the bank's activities: credit and deposit, stock, work with foreign exchange assets. The Bank Simulation Model (BMI) does not predict market behavior. Its task is to take into account the maximum possible number of financial factors of the external environment (foreign exchange market, securities market, interbank loans, etc.) to support financial decision-making at the level of the head of the bank, treasury, asset and liability management committee.
In this sense, the MBI is closely related in its functions to the developed Western automated banking systems (ABS), which are used by large international commercial banks.
Modeling processes in a bank allows you to simulate the registration of banking transactions and take into account the information that the transaction contains. The use of this construction ideology is fully justified not only from the point of view of imitation of real financial flows in the bank, but also from the point of view of the practical applicability of the simulation results in the activities of the financial manager of the bank.
Indeed, the balance sheet is a secondary result decisions taken. Both in practice and in the IMB, the manager, when making a decision on a transaction, assesses its risks and consequences for the bank not at once, but throughout the whole life cycle deals.
Simulation models are an integral part of modern banking management. Asset and liability management, planning of large-scale operations requires reliable analytical techniques.
Simulation modeling systems are widely used for the analysis, forecasting and study of various processes in various areas of the economy, industry, scientific research, both purely theoretical and practical.
The use of such systems is most effective and justified for long-term forecasting and in situations where it is impossible or difficult to conduct a practical experiment. Simulation modeling is an information technology that works with a simulation model and allows you to evaluate its parameters (and therefore efficiency) on an accelerated time scale.
simulation model -- software, which allows you to simulate the activity of any complex object. Sometimes the simulated objects can be so complex, and have so many parameters, that creating a simulation model in a standard high-level programming language can take too long to justify the results. Emelyanov A.A. Simulation modeling in risk management. - St. Petersburg: St. Petersburg Academy of Engineering and Economics, 2000. P.24
There are many tasks and situations that require the use of simulation technologies. These include modeling scenarios for the bank, "testing" certain decisions, analyzing alternative strategies, and much more. A qualified specialist is able to bring dozens of typical and particular problems that require analytical techniques. These include both classical banking planning tasks and tasks of "home" origin, for example, coordinating schedules of obligations and receipts. Simulation models make it possible to make both approximate estimates and an express audit of decisions made, as well as detailed numerical forecasts and calculations. Rapid analysis of the situation based on a compact model of medium complexity is a valuable opportunity for any bank manager.
Simulation models make it possible to link the activities of all departments of the bank into a single whole. On this basis, it becomes possible to effectively organize the entire system of operational and strategic planning commercial bank. Thanks to the use of streaming approaches, information about the activities of the bank and its services becomes concise and easy to read. It lends itself to quantitative and qualitative (meaningful) analysis. A simulation model based on one of the expert packages is a reliable benchmark for bank management. The streaming "picture" of the bank's activities greatly facilitates both operational management and long-term planning of the bank's work.
Simulation models can be embedded in the basis of the expert complex of a commercial bank. In this case, the simulation model created on the basis of one of the expert packages is connected by data exchange channels with other specialized software packages and spreadsheets databases. Such a complex can operate in real time. In terms of its capabilities, it approaches large expensive systems for automating bank management.
Optimization models, including multicriteria ones, have a common property - a well-known goal, to achieve which one often has to deal with complex systems, where it is not so much about solving optimization problems, but about researching and predicting states depending on the chosen control strategies. And here we are faced with difficulties in implementing the previous plan. They are as follows:
1. a complex system contains many connections between elements;
2. the real system is influenced by random factors, which cannot be taken into account analytically;
3. The possibility of comparing the original with the model exists only at the beginning and after the application of the mathematical apparatus, since the intermediate results may not have analogues in the real system. Emelyanov A.A. Simulation modeling in risk management. - St. Petersburg: St. Petersburg Academy of Engineering and Economics, 2000. P.58.
Due to the various difficulties that arise in the study of complex systems, practice required a more flexible method, and it appeared - simulation modeling (Simulation modeling).
Usually, a simulation model is understood as a set of computer programs that describes the functioning of individual blocks of systems and the rules of interaction between them. The use of random variables makes it necessary to repeatedly conduct experiments with a simulation system (on a computer) and subsequent statistical analysis of the results obtained. A very common example of the use of simulation models is the solution of a queuing problem by the Monte Carlo method.
Thus, work with the simulation system is an experiment carried out on a computer. What are the benefits?
1. greater proximity to the real system than mathematical models;
2. the block principle makes it possible to verify each block before it is included in the overall system;
3. the use of dependencies of a more complex nature, not described by simple mathematical relationships.
The listed advantages determine the disadvantages:
1. to build a simulation model is longer, more difficult and more expensive;
2. to work with the simulation system, you must have a computer that is suitable for the class;
3. interaction between the user and the simulation model (interface) should not be too complicated, convenient and well known;
4. The construction of a simulation model requires a deeper study of the real process than mathematical modeling. Emelyanov A.A. Simulation modeling in risk management. - St. Petersburg: St. Petersburg Academy of Engineering and Economics, 2000. P.79.
The question arises: can simulation modeling replace optimization methods? No, but conveniently complements them. A simulation model is a program that implements some algorithm, to optimize the control of which an optimization problem is first solved.
So, neither a computer, nor a mathematical model, nor an algorithm for studying it separately can solve a rather complicated problem. But together they represent the force that allows you to know the world around you, manage it in the interests of man.
Considering the complex of tasks facing banking analysts, this system should provide:
1. calculation of indicators of the current and future financial conditions of the bank;
2. forecast of the state of individual financial transactions and the balance sheet of the bank as a whole;
3. assessment of the attractiveness of individual financial transactions;
4. synthesis (formation) of management decisions;
5. evaluation of the effectiveness of the adopted management decision;
6. assessment of the completeness and non-redundancy of the sets of indicators of the financial condition of the bank.
The performance of any of these functions requires modeling the financial activities of the bank.
1.3 Banking model
The set of methods used for the analysis and modeling of banking activities is extensive and varied. During the evolution of the mathematical theory of banks, the methods of mathematical statistics, the theory of optimal control, the theory of random processes, the theory of games, the theory of operations research, etc. have been used. It should be remembered that the bank is a complex object that requires an integrated approach. It will be extremely difficult to create an integrated bank model that simultaneously covers liquidity management, asset portfolio formation, credit and deposit policy formation, etc., so we will describe the bank's functioning in a rather aggregated way.
Consider the operation of the bank on a sufficiently large time interval.
Let the bank receive income in the form of payment for its services for the settlement of guarantee operations, brokerage services (or other income independent of the portfolio of assets) - and income from securities acquired with free funds that make up the portfolio of bank assets in the aggregate.
Income from purchased securities consists of interest on securities - and payments of invested funds upon redemption or sale of securities -
(in case of share
where is the interest rate on purchased securities
the average time to maturity of securities purchased by the bank. Kolemaev V.A. Mathematical economics. - M.: UNITI, 1998. P.68.
The bank also receives borrowed funds from the placement of its securities at a rate of - W. We will assume that the securities issued by the bank are initially placed and redeemed at par, and the interest income on them is determined based on the situation in the financial market at the time of issue .
The bank primarily uses the income received to pay for the costs of raising funds, which consist of interest payments on placed securities - and payments of principal amounts of borrowed funds -
where - interest rate on placed securities
Average time to maturity of securities issued by the bank.
In addition, the bank bears expenses independent of the volume of its liabilities - , where:
Consumer price index,
To pay for the rent of premises, to pay for telecommunications costs, as well as other expenses that do not depend on the amount of funds (liabilities) involved.
The bank then pays the necessary taxes. The bank uses the remaining funds to invest in its own infrastructure (internal investment) - and for dividend payments -.
The fact that the bank is obliged to pay some expenses from its net profit can be taken into account by increasing the amount of expenses by dividing by (1-tax rate). There are also taxes that are levied on the amount of income regardless of the costs incurred in generating this income, such as the tax on road users. Such taxes can be taken into account by multiplying the amount of income in advance by (1-tax rate). Similar methods can take into account other features determined by tax deductions, so we will not consider below the problems associated with taxation and tax incentives for certain securities, such as government securities. Note that the costs are paid by the bank in a certain order. First of all, the bank is obliged to redeem previously issued securities and pay interest on them, then it pays expenses that do not depend on the volume of liabilities, taxes, and only after that can pay dividends.
If the bank has free cash, then it directs them to purchase securities (foreign investments) at a rate of -. In case of a lack of funds, the securities in the bank's portfolio can be sold, then it has a negative sign. Artyukhov SV, Bazyukina O.A., Korolev V.Yu., Kudryavtsev A.A. An optimal pricing model based on risk processes with random premiums. // Systems and means of informatics. Special issue. - M.: IPIRAN, 2005. P.102
The amount of money, securities purchased by the bank and securities placed by the bank change over time as follows:
where is the expenditure of money on the purchase of securities (the receipt of money from their sale), and is a rather small time constant characterizing the quality of the bank's assets, in the sense of liquidity. If a bank places all its assets in any one segment of the financial market, then for it there is a value that characterizes the degree of development of this segment. In the general case, it is obtained as a weighted average by the volume of assets from the values characterizing the degree of development of each of the "segments of the financial market in which the assets are located. Since we do not consider the problem of asset formation in this work, A is assumed to be a given value.
The maximum amount of funds that a bank can raise by placing its own securities is limited and depends mainly on the amount of the bank's equity capital, the structure of its balance sheet, the quality of the bank's investment portfolio and other less important performance indicators. We will assume that
where is the bank's reliability coefficient,
The amount of own funds of the bank.
The placement by the bank of its own securities, to raise borrowed funds, also takes place at a certain limited speed, therefore
where is a time constant characterizing the degree of development of the market for other securities issued by the bank. It depends on how developed the bank's infrastructure is, how large the number of market participants with whom the bank cooperates.
Let's introduce a variable - the value of the portfolio of purchased securities. Then equations (1.4) - (1.6) take the form
Let us introduce dimensionless controls: through which the rate of spending money on the purchase of securities and the rate of receipt of money from the placement of bank securities are expressed as follows:
The value corresponds to the buying/selling of securities of third-party issuers as quickly as the efficiency of the securities market allows. The value corresponds to the fastest attraction of borrowed funds by the bank, and - a complete refusal to attract funds.
The main feature of money - which makes them significantly different from securities purchased by a bank, even government ones - is the ability to use them to pay running costs jar. The flow of payments cannot be made if there is not a sufficient supply of money, therefore, the speed of making payments is limited and depends on the amount of money:
where is the characteristic time of receipt of funds in the bank (making payments). Restrictions of this type are called liquidity restrictions.
Payments made by the bank must be divided into two groups:
Obligatory payments. These include payments for the redemption of securities issued by the bank -, the payment of interest on securities - expenses that do not depend on the volume of liabilities - In practice, the bank may delay mandatory payments, but this will lead to serious financial losses, and in case of a long delay, to recognition of it insolvent and eventually liquidated. We will assume that the delay in mandatory payments is completely excluded, that is, the bank is required to constantly maintain liquidity.
Optional payments. Making these payments depends on the management and owners of the bank. These include domestic investment - and dividends - pC 2 .
In order for a bank to maintain liquidity, it is necessary that:
for everyone (1.11)
Thus, we obtain the first phase constraint for our problem, condition (1.11).
Note that from this inequality, under the condition of non-negativity, in particular, it follows that for all
Making optional payments is also limited in speed:
According to this inequality, we can introduce a dimensionless control so that:
Since the bank's share in the financial services market depends on the volume of domestic investment, it is possible to classify expenses, in a sense, as mandatory, at least in most of the planning area. (After reaching the planning horizon T, the bank can be liquidated by its owners). Since the dividend payout cannot be negative, we get one more phase constraint:
for everyone (1.13)
Thus, we have come to the conclusion that domestic investment is indeed mandatory in the sense of the constraint (1.13).
We will assume that in the planning area the bank does not receive "surplus returns", that is, profits that are large compared to equity capital and do not depend on the volume of assets. Therefore, the maximum amount of money that he can attract and receive in the form of profit is limited by a certain constant i.e. for all and this is the third phase constraint (1.14).
The estimate can be obtained based on the maximum amount of borrowings, the ratio of interest rates for attracting and placing funds, the amount of income that does not depend on the amount of assets - .
Note that in most of the planning area it should be close to zero, since it is not profitable for the bank to keep cash that does not generate income, because there are always absolutely reliable government securities in the financial market that bring a fixed positive income.
The absence of “surplus returns” also means that the relative growth rate of the securities rate is limited in the planning area:
We will describe the interests of the bank (its owners) by the desire to maximize the discounted utility of future dividend payments over a sufficiently long time interval. We will assume that the utility received from an immediate payment is times greater than the utility of paying the same amount of funds, taking into account inflation, but after a while . The coefficient is called the discount factor for the utility of dividend payments. Then the functional to be maximized can be written in the following form:
where is the utility function of dividend payments.
When consumption utility plays a role, it is usually required that it be continuous, monotonic, concave and bounded from above, and also imposed on the condition The last condition guarantees that the current consumption is positive at each point in time. Since dividends may not be paid, we will not require the condition, assuming that the utility function has a low aversion to zero consumption.
If a utility function has Arrow-Pratt's constant relative risk aversion: then it can be shown that it can be written as:
To get rid of the high aversion to zero consumption, consider a slightly modified utility function
In this case, the relative risk aversion will depend on the volume of consumption: . Based on (1.9) and (1.11), we obtain
Instead of the function (1.13), consider a straight line passing through the points
Since the function (1.17) will be negative for any volume of dividends, i.e., bounded from above by zero, and also continuous and monotonic for any. Such a utility function has zero Arrow-Pratt relative risk aversion, and by varying the parameter, only the nominal value of dividend payments can be changed. This fact highlights the differences in risk attitudes between the private consumer and the commercial organization. On the one hand, the latter does not have an aversion to risk, since it can exist indefinitely, compared to the duration of a person's life, and is not subject to dangers, like living beings. On the other hand, private consumer who spent the amount of 2*M rubles gets satisfaction from the first spent M rubles more than from the subsequent ones, which determines the concavity of the utility function of consumption for individuals. We will assume that a doubling of dividend payments leads to a doubling of their utility for recipients, which are quite numerous and include both individuals and legal entities. This determines the linearity of the dividend payout utility function. In what follows, we will use the utility function (1.17).
Thus, we obtain the optimal control problem in continuous time
In addition, there is a boundary condition under which it means that the bank is obliged to repay its debt by the end of the planning period.
Here, are phase variables and are controls. Here - the predicted values of the corresponding variables - are considered to be given non-negative functions of time, - constants having the dimension of time.
Note that if at some point it vanishes, then according to equation (1.21), i.e. the solution does not decrease at this point. Accordingly, if at some point it reaches a value, then, i.e., the solution does not increase. Thus, under controls, from equation (1.21), the condition and continuity, we obtain that on the entire segment the volume at face value of the placed securities of the bank is non-negative, i.e., and does not exceed the allowable maximum - , for all (generally speaking, on ).
Then, from the condition and conditions of non-negativity of the given functions, as well as non-negativity, we obtain that for all. Assuming continuity, one can show, using equation (1.20), that for all. In what follows, we will assume that and are continuous and are piecewise continuous on.
Since and from equation (1.20) it follows that. Using this inequality, it is easy to show the existence of such that, for all.
We will not, as suggested earlier, consider how exactly the portfolio of securities purchased by the bank is formed depending on the reliability, profitability and liquidity of the latter, as well as on the preferences of the bank's management. All assets of the bank will be presented in an aggregated form - one variable.
It can be seen from the above that the credit and deposit policy of the bank, determined in the model by the departments and, is inextricably linked with the policy for making dividend payments, set by the department, so we will further study them together.
For the convenience of further study of the work, we write out the notation separately:
The volume of free funds of the bank - cash banknotes in the cash desk of the bank, or money held on corr. bank accounts in the settlement centers of the Central Bank of the Russian Federation, as well as on corr. accounts in other banks
Volume of acquired securities at face value
Volume of placed securities at face value
Income independent of the volume of assets (commissions for settlement and cash services, guarantee transactions, brokerage services, etc.)
planning horizon
Bank equity (capital)
Bank reliability ratio
The rate of spending by the bank of funds for the maintenance of the administrative apparatus, payment for the lease of premises, etc. or expenses that do not depend on the volume of the bank's liabilities in prices at the initial moment of time
The rate of reinvestment in the infrastructure of the bank (internal investment) in prices at the initial moment of time
The rate of dividend payments in prices at the initial moment of time
Current market rate of securities purchased by the bank
Market value of the bank's securities portfolio
Time constant characterizing the degree of development of the financial market, taking into account the distribution of the bank's assets by its sectors
Time constant characterizing the degree of development of the securities market issued by the bank
Nominal growth index of the portfolio of securities acquired by the bank. For each purchased security, the nominal rate is reduced to an annual rate, taking into account reinvestment, then the weighted average annual rate for all securities in the bank's portfolio is calculated. The index is defined as ln (1 + "weighted average annual rate")
Effective growth index of the portfolio of securities acquired by the bank
Index of growth of total debt on placed securities. For each placed security, the nominal rate is reduced to an annual rate, taking into account debt refinancing through new placements of securities, then the weighted average annual rate for all placed securities is calculated. The index is defined as ln (1 + + "weighted average annual rate")
Average maturity of securities purchased by a bank - average maturity of securities issued by a bank - consumer price index
inflation index
Typical time for making payments (receipt of funds)
Velocity of circulation of money in the banking system
The rate of spending money on the purchase of securities of third-party issuers, or the receipt of money from their sale
The rate of receipt of money from the placement of bank securities
Dividend utility discount factor
Arrow-Pratt's relative risk aversion, a parameter used in setting the dividend payout utility function
M* - the maximum amount of money that can belong to the bank
Dividend payout utility function, continuous, monotonic
Bank dividend management
Management of the placement of free funds of the bank
Managing the attraction of funds to the bank.
1.4 The concept of risk in banking
Risk is the potential risk of some adverse outcome.
In the conditions of the market, each of its participants accepts certain rules of the game and, to a certain extent, depends on the behavior of partners. One of these rules can be considered the willingness to take on the risk and take into account the possibility of its implementation in their activities.
Risk is commonly understood as the probability, or rather the threat, of the bank losing part of its resources, shortfall in income or the appearance of additional expenses as a result of certain financial transactions. Shelov O. Management of operational risk in a commercial bank. Accounting and banks, 2006 - No. 6. p.112
In a crisis, the problem of professional banking risk management, prompt accounting of risk factors are of paramount importance for financial market participants, and especially for commercial banks.
The leading principle in the work of commercial banks in the transition to market relations is the desire to obtain as much profit as possible. The higher the expected return on the operation, the greater the risk. Risks are formed as a result of deviations of actual data from the assessment of the current state and future development.
The modern banking market is unthinkable without risk. Risk is present in any operation, only it can be of different scales and be "mitigated" and compensated for in different ways. It would be highly naive to look for banking options that would completely eliminate risk and guarantee a certain financial result in advance.
1.4.1 Classification of banking risks
In the course of their activities, banks are faced with a set of various kinds risks that differ from each other in the place and time of occurrence, external and internal factors affecting their level, and, consequently, the methods of their analysis and methods of their description. Lobanov A.A., Chugunov A.V. Encyclopedia of financial risk management. - M., Alpina Business Books, 2005. P.89. All types of risks are interrelated and affect the bank's activities.
Depending on the sphere of influence or the occurrence of banking risk, they are divided into external and internal.
External risks include risks that are not related to the activities of the bank or a particular client, political, economic and others. These are losses resulting from the outbreak of war, revolution, nationalization, the ban on payments abroad, debt consolidation, the imposition of an embargo, the abolition of an import license, the aggravation of the economic crisis in the country, and natural disasters. Internal risks, in turn, are divided into losses for the main and auxiliary activities of the bank. The former represent the most common group of risks: credit, interest rate, currency and market risks. The latter include losses in the formation of deposits, risks in new types of activities, risks of banking abuse.
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When managing risk, it is often necessary to compare real situations with hypothetical ones (what would happen if things went differently). This greatly complicates the analysis of risk situations, as it requires a basis for studying and measuring what was not. At present, there is no other way to describe such hypothetical situations than using mathematical models called models of risk situations. This is the basis for quantitative risk management. Its essence lies in the application of economic and mathematical models to predict situations characterized by risk and uncertainty, and substantiate appropriate management decisions.
A model is a simplified description of a real object or process that focuses on properties that are important to the researcher and ignores those aspects that seem unimportant to the researcher. The main difficulty of modeling is precisely to find out which properties are considered important and which are not. The correct description of important properties ensures the adequacy of the model, and the correct choice of minor, ignored properties helps to sufficiently simplify such a representation. The model should serve as a decision-making tool, i.e. it should make it clear to the decision maker how the process can develop, what outcomes will take place, and suggest various actions (for example, to prevent damage).
The most important class of models used in risk management are mathematical models. They allow one to describe the essential aspects of the process or phenomenon under study in the form of mathematical relationships, and then analyze them using the appropriate mathematical apparatus. It is especially important to use mathematical models to predict alternatives for future development. This is what allows the manager to numerically assess the future consequences of decisions.
Mathematical models used in risk management are very diverse and have different possibilities. There is no such thing as a universal model. The multiplicity of types of risks and the variety of mechanisms of their occurrence makes this impossible. In different situations, we will use specific tools (in this case, models), because each model is unique in its own way, since when building it, one should start from the properties of the modeling object itself. However, similar situations allow us to apply similar (if not the same) tools: there are some general approaches to modeling (for example, using stochastic differential equations or other mathematical tools). If a more or less standard approach can be applied, then the modeling process will be easier (there are known approaches to building a model and obtaining a solution).
In the field of quantitative risk management, the most common are probabilistic and statistical models.
For some risk types, widespread use of mathematical models is standard, for others it is not yet. Nevertheless, there is an intensive development of various modeling techniques that use the features of risk management. Quantitative risk management is becoming a separate "branch" of risk management.
Name: The theory of risk and modeling of risk situations.
The textbook outlines the essence of uncertainty and risk, classification and factors acting on them; methods for qualitative and quantitative assessment of economic and financial situations under conditions of uncertainty and risk are given.
A classification of service technologies is given, examples of the activities of service organizations in risk situations are considered.
The methodology for managing investment projects under risk conditions is outlined, recommendations are given for managing an investment portfolio, an assessment of the financial condition and development prospects of the investment object is carried out, and a model for accounting for risks in investment projects is proposed.
Considerable attention is paid to the methods and models of risk management and the psychology of behavior and assessment of the decision maker.
For students and graduate students of economic universities and faculties, students of business schools, risk managers, innovation and investment managers, as well as specialists in banking and financial institutions, employees of pension, insurance and investment funds.
Content
Foreword
Chapter 1 THE PLACE AND ROLE OF ECONOMIC RISKS IN THE MANAGEMENT OF ORGANIZATIONS
1.1. Organizations, types of enterprises, their characteristics and goals
1.2. Place and role of risks in economic activity
1.2.1. Definition and nature of risks
1.2.2. Management of risks
1.2.3. Risk classification
1.2.4. System of uncertainties
1.3. Risk management system
1.3.1. Management activities
1.3.2. Risk management
1.3.3. Risk management process
1.3.4. Mathematical methods for assessing economic risks
Chapter 2 RISKS OF SERVICE ENTERPRISES
2.1. Service technologies
2.2. Classification of risks of service enterprises
2.3. Dynamic analysis of the situation in the service market
2.4. Risk management model for service organizations
Chapter 3 IMPACT OF THE MAIN FACTORS OF MARKET EQUILIBRIUM ON RISK MANAGEMENT
3.1. Risk limiting factors
3.2. Influence of Market Equilibrium Factors on Risk Change
3.2.1. Relationship between market equilibrium and commercial risk
3.2.2. Influence of Market Equilibrium Factors on Changes in Commercial Risk
3.2.3. Modeling the process of achieving equilibrium
3.2.4. The impact of changes in demand on the level of commercial risk
3.2.5. The impact of a change in supply on the degree of commercial risk
3.2.6. Building supply-demand dependencies
3.3. Influence of the time factor on the degree of risk
3.4. Influence of Supply and Demand Elasticity Factors on the Level of Risk
3.5. Influence of the taxation factor in market equilibrium on the level of risk
Chapter 4 FINANCIAL RISK MANAGEMENT
4.1. Financial risks
4.1.1. Classification of financial risks
4.1.2. Relationship of financial and operational leverage to total risk
4.1.3. Development risks
4.2. Interest risks
4.2.1. Types of interest risks
4.2.2. Operations with interest
4.2.3. Average percentages
4.2.4. Variable interest rate
4.2.5. Interest rate risks
4.2.6. Interest rate risk of bonds
4.3. Risk of losses from changes in the flow of payments
4.3.1. Equivalent flows
4.3.2. Payment flows
4.4. Risk investment processes
4.4.1. Investment risks
4.4.2. Rates of return on risky assets
4.4.3. net present value
4.4.4. Annuity and sinking fund
4.4.5. Investment appraisal
4.4.6. Risk investment payments
4.4.7. Time discounting
4.5. Credit risks
4.5.1. Factors Contributing to Credit Risks
4.5.2. Credit risk analysis
4.5.3. Credit risk mitigation techniques
4.5.4. Loan payments
4.5.5. Accrual and payment of interest on consumer loans
4.5.6. Credit guarantees
4.6. Liquidity risk
4.7. inflation risk
4.7.1. Relationship between interest rate and inflation rate
4.7.2. inflation premium
4.7.3. Influence of inflation on various processes
4.7.4. Measures to reduce inflation
4.8. Currency risks
4.8.1. Currency Conversion and Interest Accrual
4.8.2. Exchange rates over time
4.8.3. Reduction of currency risks
4.9. Asset risks
4.9.1. Exchange risks
4.9.2. Impact of default risk and asset value taxation
4.10. Probabilistic assessment of the degree of financial risk
Chapter 5 QUANTITATIVE ESTIMATES OF ECONOMIC RISK UNDER UNCERTAINTY
5.1. Methods for making effective decisions under conditions of uncertainty
5.2. Matrix games
5.2.1. The concept of playing with nature
5.2.2. The subject of game theory. Basic concepts
5.3. Efficiency Criteria under Complete Uncertainty
5.3.1. Guaranteed result criterion
5.3.2. Criterion of optimism
5.3.3. Criterion of pessimism
5.3.4. Savage's Minimax Risk Criterion
5.3.5. Criterion of generalized maximin (pessimism - optimism) Hurwitz
5.4. Comparative evaluation of solutions depending on performance criteria
5.5. Multicriteria problems of choosing efficient solutions
5.5.1. Multicriteria tasks
5.5.2. Pareto optimality
5.5.3. Choice of decisions in the presence of multicriteria alternatives
5.6. Decision-Making Model Under Partial Uncertainty
5.7. Determination of the optimal volume of clothing production under uncertainty
5.7.1. Upper and lower price of the game
5.7.2. Reduction of a matrix game to a linear programming problem
5.7.3. Selection of the optimal product range
5.8. Risks associated with the work of a sewing enterprise
Chapter 6 MAKING THE OPTIMAL DECISION UNDER THE CONDITIONS OF ECONOMIC RISK
6.1. Probabilistic Statement of Making Preferred Decisions
6.2. Risk assessment under conditions of certainty
6.3. Choice optimal number jobs in a hairdressing salon, taking into account the risk of service
6.4. Statistical methods for making decisions under risk
6.5. Choosing the optimal plan by building event trees
6.5.1. decision tree
6.5.2. Optimizing your go-to-market strategy
6.5.3. Profit maximization from shares
6.5.4. Selection of the optimal project for the reconstruction of a dry-cleaning factory
6.6. Comparative evaluation of solutions
6.6.1. Choosing the optimal solution using statistical estimates
6.6.2. Normal distribution
6.6.3. Risk Curve
6.6.4. Choosing the Optimal Solution Using Confidence Intervals
6.6.5. Production cost forecasting model
6.7. The emergence of risks when setting the mission of the company's goals
6.8. The activity of service enterprises in conditions of risk
6.8.1. Finishing and design company
6.8.3. Beauty saloon
Chapter 7 MANAGEMENT OF INVESTMENT PROJECTS UNDER RISK
7.1. Investment projects under conditions of uncertainty and risk
7.1.1. Basic concepts of investment projects
7.1.2. Analysis and evaluation of investment projects
7.1.3. Risks of investment projects
7.2. The optimal choice of investment volume, providing the maximum increase in output
7.3. Investments in a portfolio of securities
7.3.1. Investment Management Process
7.3.2. Diversified portfolio
7.3.3. Risks associated with investing in a portfolio of securities
7.3.4. Practical recommendations for the formation of an investment portfolio
7.4. Analysis of the economic efficiency of the investment project
7.4.1. Analysis of associated risk factors
7.4.2. Preliminary assessment and selection of enterprises
7.4.3. Assessment of the financial condition of the enterprise as an investment object
7.4.4. Examples of analysis using financial ratios
7.4.5. Assessment of the prospects for the development of the organization
7.4.6. Comparative financial analysis of investment projects
7.4.7. Analysis of organization survey methods in the field
7.5. Accounting for risk in investment projects
7.5.1. Project risk assessment model
7.5.2. Accounting for risk when investing
7.5.3. Practical conclusions on the management of risky investment projects
Chapter 8 RISK MANAGEMENT OF TOURISM
8.1. Factors affecting the dynamics of tourism development
8.1.1. Development of tourism in Russia
8.1.2. Types and forms of tourism
8.1.3. Features of tourism - as factors of development uncertainty
8.2. Psychology of the impact of tourism on participants and others
8.2.1. Travel motivation
8.2.2. Impact of tourism
8.3. Risks associated with tourism activities
8.3.1. Factors affecting tourism and the tourism economy
8.3.2. Classification of tourism risks
8.4. Economic impact of tourism
8.5. Making a management decision
8.6. Analysis of the activities of the organization providing tourism services at risk
Chapter 9 RISK MANAGEMENT OF HOTELS AND RESTAURANTS
9.1. Development of hotel enterprises
9.2. Restaurant business development factors
9.3. Features and specifics of hospitality
9.4. Risks inherent in the hospitality industry and their management
9.4.1. Identification of risks
9.4.2. Risks of investment projects
9.4.3. Risk Reduction in the Hospitality Industry
9.5. Management decisions in the hospitality business
Chapter 10 MAIN METHODS AND WAYS FOR REDUCING ECONOMIC RISKS
10.1. General principles of risk management
10.1.1. Risk Management Process Diagram
10.1.2. Risk Examples
10.1.3. Choice of risk management techniques
10.2. Diversification
10.3. Risk insurance
10.3.1. Essence of insurance
10.3.2. Main characteristics of insurance contracts
10.3.3. Calculation of insurance operations
10.3.4. insurance contract
10.3.5. Advantages and disadvantages of insurance
10.4. Hedging
10.4.1. Risk Management Strategies
10.4.2. Basic concepts
10.4.3. Forward and futures contracts
10.4.4. Exchange rate hedging
10.4.5. Main aspects of risk
10.4.6. Hedging the exchange rate with a swap
10.4.7. Options
10.4.8. Insurance or hedging
10.4.9. Synchronization of cash flows
10.4.10. Hedging model
10.4.11. Measuring hedge effectiveness
10.4.12. Minimizing hedging costs
10.4.13. Correlated hedging
10.5. Limitation
10.6. Reservation of funds (self-insurance)
10.7. Quality risk management
10.8. Purchasing additional information
10.9. Evaluation of the effectiveness of risk management methods
10.9.1. Risk financing
10.9.2. Assessing the effectiveness of risk management
Chapter 11 PSYCHOLOGY OF BEHAVIOR AND ASSESSMENT OF THE DECISION MAKER
11.1. Personal factors influencing the degree of risk in making managerial decisions
11.1.1. Psychological problems of the behavior of an economic personality
11.1.2. Management actions of an entrepreneur in the service sector
11.1.3. Personal attitude to risk
11.1.4. intuition and risk
11.2. Expected utility theory
11.2.1. Plots of utility functions
11.2.2. Expected utility theory
11.2.3. Accounting for the attitude of the decision maker to risk
11.2.4. Group decision making
11.3. Theory of rational behavior
11.3.1. perspective theory
11.3.2. Rational approach to decision making
11.3.3. Decision Asymmetry
11.3.4. Behavior invariance
11.3.5. The role of information in decision making
11.4. Conflict situations
11.5. The role of the leader in making risky decisions
11.5.1. Decision making under risk
11.5.2. Requirements for the decision maker
11.5.3. Principles for evaluating the effectiveness of decisions made by decision makers
Review questions
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Qualitative risk analysis methods
After all have been identified possible risks for a particular project, it is necessary to determine the feasibility of investments, development and work on this project. To do this, an analysis of the risks of the investment project is carried out.
All possible and proposed risk analysis methods in theory can be conditionally divided into qualitative and quantitative approaches. A qualitative approach, in addition to identifying risks, involves determining the sources and causes of their occurrence, as well as a cost estimate of the consequences. The main features of the qualitative approach are: identifying simple risks for the project, determining dependent and independent risks both from each other and from external factors, and determining whether the risks are avoidable or not.
With the help of qualitative analysis, all risk factors are determined that entail, to one degree or another, losses or losses of the enterprise, as well as the probability and time of their occurrence. For the worst scenario of the project development, the maximum amount of the company's losses is calculated.
In the qualitative approach, the following methods of risk analysis are distinguished: the method of expert assessments; cost-benefit method; analogy method.
Method of expert assessments.
The method of expert assessments includes three main components. Firstly, the intuitive-logical analysis of the problem is based only on the intuitive assumptions of certain experts; only their knowledge and experience can serve as a guarantor of the correctness and objectivity of the conclusions. Secondly, the issuance of expert evaluation decisions, this stage is the final part of the expert's work. The experts form a decision on the expediency of working with the project they are studying, and an assessment of the expected results is proposed, according to different scenarios project development. The third stage, the final one for the method of expert assessments, is the processing of all the results of the solution. In order to obtain a final assessment, all received assessments from experts must be processed, and an overall relatively objective assessment and decision regarding a specific project is identified.
Experts are invited to fill out a questionnaire with a detailed list of risks related to the analyzed project, in which they need to determine the probability of occurrence of the risks identified by them on a certain scale. The most common methods of expert risk assessments include the Delphi method, the scoring method, ranking, pairwise comparison, and others.
The Delphi method is one of the expert assessment methods that provides a quick search for solutions, among which the best solution is subsequently selected. The use of this method allows avoiding contradictions among experts and obtaining independent individual decisions, excluding communication between experts during the survey. Experts are given a questionnaire, on the questions of which they need to give independent, maximally objective assessments, and reasonable assessments. Based on the completed questionnaires, the decision of each expert is analyzed, the prevailing opinion, extreme judgments are revealed, as clearly as possible, accessible and reasoned decisions are made, etc. As a result, experts can change their minds. The whole operation is usually carried out in 2-3 rounds, until the opinions of experts begin to coincide, which will be the final result of the study.
The risk scoring method is based on a generalizing indicator determined by a number of private expertly assessed indicators of the degree of risk. It consists of the following steps:
- 1) Identification of factors that influence the occurrence of risk;
- 2) The choice of a generalized indicator and a set of particular criteria that characterize the degree of risk for each of the factors;
- 3) Drawing up a system of weighting coefficients and a rating scale for each indicator (factor);
- 4) Integral assessment of the generalized criterion of the degree of project risks;
- 5) Development of recommendations for risk management.
The ranking method implies the arrangement of objects in ascending or descending order of some property inherent in them. Ranking allows you to choose the most significant of the studied set of factors. The result of the ranking is the ranking.
If available n objects, then as a result of their ranking by the j-th expert, each object receives a score x ij - the rank attributed to the i-th object by the j-th expert. Values x ij are in the range from 1 to n. The rank of important factor is equal to one, the least significant - to the number n. The ranking of the j-th expert is the sequence of ranks x 1j , x 2j , …, x nj .
This method is simple to implement, however, when evaluating a large number of parameters, experts face the difficulty of building a ranked series, due to the fact that it is necessary to take into account many complex correlations at the same time.
The method of pairwise comparison is the establishment of the most preferable objects when comparing all possible pairs. In this case, there is no need, as in the ranking method, to order all objects, it is necessary to identify a more significant object in each of the pairs or establish their equality.
Again, in comparison with the ranking method, pairwise comparison can be carried out with a large number of parameters, as well as in cases of insignificant differences in parameters (when it is practically impossible to rank them, and they are combined into a single one).
When using the method, a matrix of size is most often compiled nxn, where n- the number of compared objects. When comparing objects, the matrix is filled with elements a ij as follows (another filling scheme can be proposed):
The sum (per line) in this case allows you to evaluate the relative importance of objects. The object for which the amount will be the largest can be recognized as the most important (significant).
The summation can also be done by columns (), then the most significant will be the factor that scored the least number of points.
Expert analysis consists in determining the degree of risk impact based on expert assessments of specialists. The main advantage of this method is the simplicity of calculations. There is no need to collect accurate baseline data and use expensive and software tools. However, the level of risks depends on the knowledge of experts. And also a disadvantage is the difficulty in attracting independent experts and the subjectivity of their assessments. For the clarity and objectivity of the results, this method can be used in conjunction with other quantitative methods (more objective).
The method of relevance and expediency of costs, the method of analogies.
Cost-benefit analysis is based on the assumption that certain factors (or one of them) are causing the project to overspend. These factors include:
- · Initial underestimation of the cost of the project as a whole or its individual phases and components;
- change of design boundaries due to unforeseen circumstances;
- difference in the productivity of machines and mechanisms from that provided for by the project;
- · an increase in the cost of the project compared to the original, due to inflation or changes in tax legislation.
To carry out the analysis, first of all, all the above factors are detailed, then a tentative list is compiled possible promotions project costs for each development option. The entire project implementation process is divided into stages, on the basis of this, the process of financing for the development and implementation of the project is also divided into stages. However, the stages of financing are set conditionally, as some changes may be made as the project is developed and developed. A phased investment of funds allows the investor to more closely monitor the work on the project, and in the event of an increase in risks, either stop or suspend financing, or begin to take certain measures to reduce costs.
Among the qualitative methods of risk analysis, the analogy method is also common. The main idea of this method is to analyze other projects similar to the one being developed. On the basis of the same risky projects, possible risks are analyzed, their causes, the consequences of the impact of risks, and the consequences of the impact on the project of adverse external or internal factors. Then the information obtained is projected onto a new project, which allows you to determine all the maximum possible potential risks. The source of information can be the reliability ratings of design, contracting, investment and other companies regularly published by Western insurance companies, analyzes of trends in demand for specific products, prices for raw materials, fuel, land, etc. .
The complexity of this method of analysis is the difficult support of the most accurate analogue, due to the fact that there are no formal criteria that accurately establish the degree of similarity of situations. But, as a rule, even in the case of choosing the right analogue, it becomes difficult to formulate the correct prerequisites for analysis, a complete and close to reality set of project failure scenarios. The reason is that there are very few completely identical projects or not found at all, any project under study has its own individual characteristics and risks, which are interconnected according to the uniqueness of the project, so it is not always possible to absolutely accurately determine the cause of a particular risk.
A brief description of the cost moderation method and the analogy method indicates that they are more suitable for identifying and describing possible risk situations for a particular project than for obtaining even a relatively accurate assessment of the risks of an investment project.
Quantitative risk analysis method
To assess the risks of investment projects, the following quantitative methods of analysis are most common, such as:
- sensitivity analysis
- scripting method
- simulation modeling (Monte Carlo method)
- discount rate adjustment method
- decision tree
Sensitivity analysis
In the sensitivity analysis method, the risk factor is taken as the degree of sensitivity of the resulting indicators of the analyzed project to changes in the external or internal conditions of its functioning. The resulting project indicators are usually performance indicators (NPV, IRR, PI, PP) or annual project indicators (net profit, accumulated profit). The sensitivity analysis is divided into several successive steps:
- the basic values of the resulting indicators are established, the relationship between the initial data and the resulting ones is mathematically established
- the most probable values of the initial indicators are calculated, as well as the range of their changes (usually within 5-10%)
- the most probable values of the resulting indicators are determined (calculated)
- The initial studied parameters are recalculated in turn within the obtained range, new values of the resulting parameters are obtained
- · The input parameters are ranked according to their degree of influence on the resulting parameters. Thus, they are grouped based on the degree of risk.
The degree of exposure of the investment project to the corresponding risk and the sensitivity of the project to each factor is determined by calculating the elasticity index, which is the ratio of the percentage change in the resulting indicator to the change in the parameter value by one percent.
Where: E - elasticity index
NPV 1 - the value of the underlying resulting indicator
NPV 2 - the value of the resulting indicator when changing the parameter
X 1 - base value of the variable parameter
X 2 - changed value of the variable parameter
The higher the value of the elasticity index, the more sensitive the project is to changes in this factor, and the more the project is exposed to the corresponding risk.
Also, sensitivity analysis can be carried out graphically, by plotting the dependence of the resulting indicator on the change in the factor under study. The sensitivity of the NPV value to a change in the factor varies by the level of the slope of the dependence, the larger the angle, the more sensitive the values, and also the greater the risk. At the point of intersection of the direct response with the abscissa axis, the parameter value is determined in percentage terms, at which the project will become ineffective.
After that, based on the calculations, all the obtained parameters are ranked according to the degree of significance (high, medium, low), and a "sensitivity matrix" is built, with the help of which the factors that are the most and least risky for the investment project are identified.
Regardless of the advantages inherent in the method - the objectivity and clarity of the results obtained, there are also significant drawbacks - the change in one factor is considered in isolation, while in practice all economic factors are correlated to one degree or another.
Scenario Method
The scenario method is a description of all possible conditions for the implementation of the project (either in the form of scenarios or in the form of a system of restrictions on the values of the main parameters of the project) as well as a description of possible results and performance indicators. This method, like all others, also consists of certain sequential steps:
- At least three possible scenarios are built: pessimistic, optimistic, realistic (or most likely or average)
- initial information about uncertainty factors is converted into information about the probability of individual implementation conditions and certain performance indicators
Based on the data obtained, the indicator of the economic efficiency of the project is determined. If the probabilities of the occurrence of one or another event reflected in the scenario are known exactly, then the expected integral effect of the project is calculated by the mathematical expectation formula:
Where: NPVi - integral effect in the implementation of the i-th scenario
pi - the probability of this scenario
At the same time, the risk of project inefficiency (Re) is estimated as the total probability of those scenarios (k) in which the expected project effectiveness (NPV) becomes negative:
The average damage from the implementation of the project in case of its inefficiency (Ue) is determined by the formula:
The main disadvantage of the scenario analysis method is the factor of taking into account only a few possible outcomes for an investment project, but in practice the number of possible outcomes is not limited.
PERT analysis method (Program Evaluation and Review Technique)
One of the methods of scenario analysis is the PERT-analysis method (Program Evaluation and Review Technique). The main idea of this method is that when developing a project, three project parameters are set - optimistic, pessimistic, and most probable. The expected values are then calculated using the following formula:
Expected Value = [Optimistic Value 4xMost Likely Value + Pessimistic Value]/6
Coefficients 4 and 6 are obtained empirically based on the statistical data of a large number of projects. Based on the results of the calculation, the rest of the analysis of the project is carried out. The effectiveness of the PERT analysis is maximum only if it is possible to justify the values of all three estimates.
decision tree
The decision tree method represents network diagrams, in which each branch, then various alternative options for the development of the project. Following along each built project branch, you can trace all possible stages of project development, and, accordingly, choose the most optimal of them, and with the least risks. This method of analysis is divided into the following stages:
- Vertices are determined for each problematic and ambiguous moment in the development of the project, and branches are built (possible paths for the development of events)
- · For each arc, the probability and possible losses at this stage are determined by an expert method.
- · Based on all obtained vertex values, the most probable value of NPV (or other indicator significant for the project) is calculated
- Probability distribution analysis is carried out
The only limitation and possibly a disadvantage of the method is the mandatory availability of a reasonable number of options for the development of the project. The main difference is the possibility of full and detailed accounting of all factors and risks affecting the project. The method is especially used in situations where decisions on the implementation of the project are made gradually, and depend on earlier decisions, thus, each decision in turn determines the scenario for the further development of the project.
Simulation modeling (Monte Carlo method)
Risk analysis of investment projects by the Monte Carlo method combines two previously studied methods: the method of sensitivity analysis and scenario analysis. In simulation, instead of generating best and worst scenarios, hundreds of possible combinations of project parameters are generated by the computer, given their probability distribution. Each resulting combination gives its own NPV value. Such a calculation is possible only with the use of special computer programs. The stage-by-stage scheme of simulation modeling is constructed as follows:
- · the factors influencing cash flows of the project are formulated;
- a probability distribution is built for each factor (parameter), while, as a rule, it is assumed that the distribution function is normal, therefore, in order to set it, it is necessary to determine only two points (expectation and variance);
- · the computer randomly selects the value of each risk factor based on its probability distribution;
Fig.1.3
Fig.1.4
Among the disadvantages of this method of risk modeling are the following:
- the existence of correlated parameters greatly complicates the model
- the type of probability distribution for the parameter under study can be difficult to determine
- · when developing real models, it may be necessary to involve specialists or scientific consultants from outside;
- The study of the model is possible only with the availability of computer technology and special software packages;
- · relative inaccuracy of the obtained results in comparison with other methods of numerical analysis.
Discount rate adjustment method
Because of the simplicity of the calculations, the Risk-adjusted discount rate method is the most applicable in practice. This method is an adjustment to a given basic discount rate that is considered risk-free and minimally acceptable (for example, the company's marginal cost of capital). The adjustment is carried out as follows: the amount of the required risk premium is added, then the investment project efficiency criteria (NPV, IRR, PI) are calculated. The project efficiency decision is made according to the chosen criterion rule. The higher the risk, the higher the premium.
Risk adjustments are set separately for each individual project, as they completely depend on the specifics of the project under study.
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