Qualitative risk analysis methods

After all possible risks for a particular project have been identified, it is necessary to determine the feasibility of investing, developing and working 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 offer an assessment of the expected results, according to different scenarios for the development of the project. The third stage, the final one for the method of expert assessments, is the processing of all the results of the decision. 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 the most 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 an estimated list of possible increases in project costs is compiled for each option for its development. 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 influence of risks, and the consequences of the impact on the project of adverse external or internal factors are also studied. 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.

THEORY OF RISK AND MODELING OF RISK SITUATIONS

LECTURE 1

1. The concept of risk. Criteria for risk classifications.
2. Mathematical Apparatus for Modeling and Studying Risk Situations.
3. 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 a market economy, risk is the key moment of entrepreneurship. The problem of risk and profit is one of the key ones in economic activity, in particular in production and financial management.

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 is 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 shows a willingness 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 to 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 to operational processes and means the risk of liquidity loss. 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 losses in the process of financial and 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 of financial resources (that is, cash).

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 in the sale of securities 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 activities in a given geographic area or in a particular industry (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 against 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 AT , 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 with

dispersion . For the project AT 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 AT 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?

Decision.

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 of mathematical models for making optimal decisions in conflict conditions.

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 choice.

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.

First of all , 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 of 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.

Federal Agency for Education

T O M S AND Y POLITE

APPROVE

Dean of AWTF

Gaivoronsky S.A.

"_____" _______________ 2009

CALCULATION OF OPERATIONAL RISKS

course guidelines

CALCULATION OF OPERATIONAL RISKS

Guidelines for the course Guidelines for the course

"Risk Theory and Modeling of Risk Situations"

for students of the specialty 080116 "Mathematical Methods in Economics"

Tomsk: Ed. TPU, 2009. - 26 p.

Compiled by: Kochegurov A.I.

Reviewer: Babushkin Yu.V.

Methodical instructions were discussed at the meeting of the Department of Applied Mathematics on November 16, 2008.

Head Department V.P.Grigoriev

1. The concept of economic risk and risk classification

The processes currently taking place in Russia, the changing business conditions have required a reorientation of the principles of the work of enterprises towards the analysis and evaluation of various external and internal factors affecting the efficiency of their activities. In foreign countries, even in relatively stable business conditions, considerable attention is paid to the problem of risk research. The leading principle in the work of the organization (manufacturing enterprise, commercial bank, trading company) is the desire for profit. This desire is limited by the possibility of incurring losses. This is where the concept of risk comes into play.

I would like to note that this concept has a fairly long history. But they began to study various aspects of risk most actively only at the end of the 19th - beginning of the 20th century.

There was no interest in the problem of economic risks in the USSR, and the reasons for this are obvious: the economic policy of the USSR for a long time corresponded to the orientation towards the predominantly extensive development of the national economy of the country and the dominance of administrative methods of management. All this led to the fact that the rationale for the effectiveness of economic activity in a planned economy and, accordingly, all feasibility studies of any projects did without risk analysis.

The implementation of modern economic reform in Russia aroused interest in the consideration of risk in economic activity, and the risk theory itself in the process of forming market relations not only received its further development, but became practically in demand.

To date, there is still no unambiguous understanding of the nature of risk. Each financial manager has his own idea of ​​risk, methods for assessing it and ways to determine its size. In addition, risk is a complex phenomenon that has many different and sometimes opposite foundations and prerequisites, which makes it possible for there to be several definitions of risk concepts from different points of view, and here are just a few of them:

risk - possible danger; acting at random in the hope of a happy outcome;

risk is a potential, numerically measurable possibility of loss;

risk - uncertainty associated with the possibility of adverse situations and consequences during the implementation of the project;

risk is a concept used to express uncertainty about events and / or their consequences that may materially affect the objectives of the organization;

risk - any event due to which the financial results of the company's activities may be lower than expected.

It should also be noted that the concept of "risk" is interpreted in different ways and depending on the scope of risk management. For mathematicians, risk is a distribution function of a random variable, for insurers it is an insurance object, the amount of possible insurance compensation associated with an insurance object, for investors it is the uncertainty associated with the value of investments at the end of the period, the probability of not reaching the goal, for economists it is an event, associated with a hazardous event that may or may not occur, etc.

From these definitions, the close relationship between risk, probability and uncertainty is clearly visible. Therefore, for the most complete and accurate disclosure of the “risk” category, it is necessary to substantiate such concepts as “probability” and “uncertainty”, since the probabilistic nature of market activity and the uncertainty of the situation during its implementation underlies risks.

Consider the concept of probability. This term is fundamental to the theory of probability and allows quantitative comparison of events in terms of their degree of possibility. The probability of an event is a certain number, which is the greater, the more likely the event is. Probability is the possibility of obtaining a certain result. Obviously, the event that occurs more often is considered more likely. Thus, first of all, the concept of probability is connected with the experimental, practical concept of the frequency of an event.

The accuracy of measuring probabilities depends on the amount of statistical data and the possibility of using them for future events, i.e. from maintaining the conditions under which past events occurred. But at the same time, in many cases, when making decisions, statistical data are very small in volume or not available at all, therefore, another way of measuring the probabilities of the situation is used, based on the subjective views of the decision maker.

In this regard, the probabilities measured in this way are called the subjective probabilities of the situation. When determining subjective probabilities, the opinion of the subject, reflecting the state of his information fund, comes first. In other words, subjective probability is determined on the basis of an assumption based on the judgment or personal experience of the evaluator (expert), and not on the frequency with which a similar result was obtained in similar conditions. Hence the wide variation in subjective probabilities, which is explained by the spectrum of different information or possibilities of operating with the same information.

Dependence on the volume of initial information and on the subject leads to the fact that uncertainty is added to the probabilistic situation. Thus, the concept of probability alone is not enough to characterize risk.

Uncertainty implies the presence of factors under which the results of actions are not deterministic, and the degree of possible influence of these factors on the results is unknown, for example, it is incompleteness or inaccuracy of information.

The conditions of uncertainty that take place in any type of entrepreneurial activity are the subject of research and the object of constant observation by economists of various profiles.

Such an integrated approach to the study of the phenomenon of uncertainty is due to the fact that economic entities in the course of their functioning are dependent on a number of factors that can be divided into external (legislation, market reaction to products, actions of competitors) and internal (competence of the company's personnel, fallibility defining the characteristics of the project, etc.).

Another approach to the classification of uncertainty is used in the design of work and is associated with human uncertainty, with the impossibility of accurately predicting the behavior of people in the process of work. Technical uncertainty is much less than human uncertainty, it is associated with the reliability of equipment, the predictability of production processes, the complexity of technology, the level of automation, etc. Social uncertainty is determined by the desire of people to form social bonds and help each other.

Under these conditions, the development of construction projects and business plans, forecasting and planning of production volumes, sales and cash flows can be approximate calculations. Often, activities can bring losses instead of the expected profit.

Further, it should be taken into account that the risk accompanies all the processes taking place in the enterprise, regardless of whether they are active or passive. In this case, the third side of the risk is revealed - its belonging to any activity. For example, if an enterprise plans to implement a project, it is subject to investment, market risks; and if the enterprise does not carry out any actions, it again bears risks - the risk of lost profits, market risk.

This provision is already embedded in the very definition of the concept of “enterprise”, because in the course of its activities, the enterprise sets certain goals - to receive income, incur costs, etc. Therefore, it plans its activities. But, choosing this or that development strategy, the enterprise may lose its funds or receive an amount that is less than planned. This is due to the uncertainty of the situation in which it is located. In conditions of uncertainty, the management of the enterprise has to make decisions, the probability of successful implementation of which (and, therefore, the receipt of income in full) depends on many factors that affect the enterprise from the inside and outside. In this situation, the concept of risk is manifested, which means that the risk can be characterized as the probability of shortfall in planned income in the face of uncertainty associated with the activities of the enterprise.

Then it is possible to give the most appropriate definition of the concept of "risk". So, risk is the probability of an event occurring or the occurrence of circumstances associated with a given structure of business processes that can affect the achievement of goals.

This approach considers the results of an event without detaching from the causes. In addition, he draws a dividing line between controllable causes of risk and uncontrollable ones, which would be considered "events" or "circumstances". Risk factors that, when combined with risk events, can cause damage are organizational gaps and should be examined for their place in the business process diagram.

Thus, it should be noted that risk is a complex concept that is caused by uncertainty and is closely related to probabilistic processes. The risk is inextricably linked with the activities of the enterprise, regardless of whether this activity is active or passive. However, there are general goals that an effective risk management process should contribute to.

As a rule, the main goals pursued by companies when creating a risk management system are as follows:

the most efficient use of capital and maximum income;

increasing the sustainability of the company's development, work efficiency, overall productivity, reducing the likelihood of losing part or all of the company's value;

image improvement.

But whether the goal is to eliminate risks or manage them effectively, the value of an approach that addresses all three aspects of risk (event, impact, and organization's operating structure) is extremely high. This logical approach occurs three times: before the event (prevention), during the event (detection), and after the event (protection). A threat without prevention leads to a risky event, an event without detection leads to a missed event, and a missed event without protection leads to damage.

So, in order to achieve the above goals, it is necessary to reveal the essence of the main types of risk that the company faces.

Since the concept of risk covers almost all activities of an economic entity, as a result, there is a variety of risks that arise in the work of the company, and in order to correctly manage risks, the company must know what risks its activities are associated with. The classification of these risks is a rather complex problem, which has been dealt with by economists for quite a long time. Moreover, there are more than 40 different risk criteria and more than 220 types of risks, so there is no common understanding in the economic literature on this issue.

Thus, J. M. Keynes was one of the first to classify risks. He approached this issue from the side of the entity carrying out investment activities, identifying three main types of risks [J. M. Keynes. General Theory of Employment, Interest and Money. ch.11]:

entrepreneurial risk - the uncertainty of obtaining the expected income from investing funds;

"Lender" risk - the risk of non-repayment of a loan, including legal risk (avoidance of repayment of a loan) and credit risk (insufficiency of collateral);

risk of change in the value of the monetary unit - the probability of losing funds as a result of changes in the exchange rate of the national currency (market risk).

Keynes noted that these risks are closely intertwined - so the borrower, participating in a risky project, seeks to get the largest possible difference between the interest on the loan and the rate of return; the creditor, given the high risk, also seeks to maximize the difference between the net rate of interest and his interest rate. As a result, the risks are "superimposed" on each other, which is not always noticed by investors.

At present, most often, especially foreign authors, adhere to a classification in which the following types of risks necessarily appear:

operational risk (operational risk);

market risk (market risk);

credit risk.

This approach is followed by leading Western banks, experts of the Basel Committee, developers of systems for analysis, measurement and risk management.

To these basic risks are added several more options that occur in one sequence or another:

business risk (business risk);

liquidity risk;

legal risk (legal risk);

regulatory risk.

The last 4 risks do not appear in all developments. Thus, the risk associated with regulatory authorities is most relevant for banking organizations, so it is more common in areas related to banking. Liquidity risk is included by some authors in the concept of market risks.

In this work, we will rely on the classification that corresponds to the considered direction of the consulting company. This, firstly, will allow at the initial stage of the analysis to limit ourselves to those risks that have a direct impact on the company's work. Secondly, taking into account the specifics of the organization's activities will allow us to prioritize the study of profile risks and consider first of all those that have the greatest impact on the organization's activities.

The most comprehensive classification of risks is the Risk Management Guidelines for Derivatives. According to this document, the organization faces the following types of risks:

Credit risks (including repayment risk) are probable losses associated with the refusal or inability of a counterparty to fully or partially meet its credit obligations. These risks exist both for banks (the classic risk of default on a loan), and for enterprises that have accounts receivable and organizations operating in the securities market.

Operational risks are the probability of direct or indirect losses as a result of uncontrollable events, shortcomings in business organization, inadequate control, wrong decisions, system errors that are related to human resources (unprofessional, illegal actions of company personnel), technologies, property, internal systems, relationships with the internal and external environment, legislative regulation and individual risky projects. This can include risks associated with errors of the company's management, its employees, problems with the internal control system, poorly developed work rules, etc., i.e. operational risk is the risk associated with the internal organization of the company's work, as well as the risk of damage to the environment (environmental risk); the risk of accidents, fires, breakdowns; the risk of disruption in the functioning of the facility due to design and installation errors, a number of construction risks; equipment failures, etc.

Liquidity risk is the risk that a firm will not be able to repay its obligations with available capital at a particular moment. the probability of a loss due to a lack of funds in the required time frame and, as a result, the inability of the company to fulfill its obligations. The occurrence of such a risk event may entail fines, penalties, damage to the business reputation of the company, up to declaring it bankrupt. For example, a company must pay off its accounts payable within two weeks, but due to a delay in payment for shipped products, it does not have cash. It is obvious that the creditors will impose penalties on the enterprise. As a rule, liquidity risk occurs due to unprofessional management of cash flows, receivables and payables.

Market risks are possible losses resulting from changes in market conditions. They are associated with fluctuations in prices on commodity markets and exchange rates, exchange rates on stock markets, etc. Market risks are most susceptible to volatile assets of the company (commodities, cash, securities, etc.), since their value largely depends on prevailing market prices.

Legal risks - the risk that, in accordance with the current legislation, the partner is not obliged to fulfill its obligations under the transaction.

Often, these risks are closely intertwined - a vivid example is the situation with the notorious English bank “Barings” - shortcomings in internal control systems (operational risk) and, as a result, the game on the stock exchange of one of the employees led to the impossibility of closing futures positions on SIMEX (risk of losing liquidity) due to incorrect price forecasting (market risk).

So, after conducting a study of the current situation in the company, we can say that at present the priority for “Success” is to reduce operational risks. Therefore, in this work we will focus on operational risks, their assessment and management.

In addition to the above classification, risks can be classified according to other criteria. For example, strategic and informational risks are often singled out.

Information risks are understood as the probability of damage as a result of the loss of information significant for the company.

Strategic risks are the risk of loss due to uncertainty arising from a company's long-term strategic decisions. In addition, they affect the company as a whole, and the application of the implemented risk analysis system to them at the enterprise can often lead to a change in the course of the company, give a clear assessment of the company's planned actions to create a competitive advantage and conquer the market. A company's strategic risk assessment should take into account both the microeconomic environment (such as its closest competitors, changes in market conditions or resource prices) and the macroeconomic environment (in particular political risks that are difficult to assess).

Often, according to their consequences, risks are divided into three categories:

acceptable risk- this is the risk of a decision, as a result of which the enterprise is threatened with loss of profit; within this zone, entrepreneurial activity retains its economic expediency, i.e. losses take place, but they do not exceed the size of the expected profit;

critical risk- is the risk at which the company is threatened with loss of revenue; in other words, the critical risk zone is characterized by the danger of losses that obviously exceed the expected profit and, in extreme cases, can lead to the loss of all funds invested by the enterprise in the project;

catastrophic risk- the risk at which the insolvency of the enterprise occurs; losses can reach a value equal to the property status of the enterprise. This group also includes any risk associated with a direct danger to human life or the occurrence of environmental disasters.

The basis for the following classification of risks is also the nature of the impact on the results of the enterprise. Thus, risks are divided into two types:

clean risk - the possibility of a loss or a zero result;

speculative risk is the probability of obtaining both a positive and a negative result.

It is obvious that the above classifications are interconnected.

2. Modeling of risk situations and operational risk management

2.1 Features of operational risks

Once again, we note the fact that operational risks are primarily associated with a person: direct and indirect business losses arise due to errors of personnel, management, theft and abuse, and even in cases where they are caused by failures in the operation of telecommunications, computers and information technologies. systems, in most cases they are based on human errors.

Before talking about operational risk modeling, let's look at their unique characteristics:

Operational risks are endogenous in nature, and therefore different for each company. They depend on the technologies, processes, organization, people and culture of the company, therefore, in order to manage operational risks, it is necessary to collect company-specific data. It should be noted that most companies do not have a long history of relevant data. And industry data may not be entirely applicable.

Operational risks are dynamic and constantly changing depending on the strategy, business processes, applied technologies, competitive environment, etc., as a result, it becomes clear that even the historical data of the company itself may not be relevant indicators of current and future risks.

The most effective risk mitigation strategies include changes in business processes, technology, organization and people, i.e. a modeling approach is needed that can measure the impact on operational decisions. For example, how will operational risk change if a company starts selling and servicing products over the Internet, or if some key functions are outsourced?

The most common operational risks:

errors in computer programs failure of software and information technology or systems, failure of equipment and communications);

personnel errors (n insufficient qualification of the employees performing this operation; unfair execution of established provisions and regulations; personnel overload; random one-time errors);

errors in the function distribution system(duplication of functions; exclusion of individual functions);

lack of a work plan or its poor quality leads to delays in making managerial decisions, and the formalization of plans and procedures for action in critical situations not only facilitates the identification of problematic aspects, but also reduces the risk of labor conflicts.

Historically, the highest operational risks and the biggest losses on them occur in the presence of the following circumstances:

concentration occurs in a non-core area of ​​activity, where the company's management is not aware of the real risks associated with these trading operations;

an event duration of more than a few months indicates a careless control environment, careless management, and a lack of awareness of the seriousness of the problem.

Description : The textbook "Risk Theory and Modeling of Risk Situations" was written in accordance with the requirements of the State Educational Standards of the 2nd generation of the Ministry of Education of the Russian Federation. It corresponds to the programs of the disciplines "Risk Theory and Modeling of Risk Situations" and "Mathematical Methods of Financial Analysis" special. 061800 "Mathematical Methods in Economics", the discipline program "Decision Theory and Risk Management in the Financial and Tax Sphere" spec. 351200 "Taxes and taxation", the program of discipline "Management" spec. 061100 "Management", as well as a number of economic specialties containing the discipline "Management", since "Risk Management" is part of this discipline.
The textbook "Risk Theory and Modeling of Risk Situations" contains eleven chapters.
The first chapter "The place and role of economic risks in the management of organizations" defines the organization, considers the types of organizations, their characteristics and goals. The place and role of risks in economic activity is determined, the definitions and essence of risks are given. The classification of uncertainties and risks is given, the risk management system is revealed, the basic concepts of risk management are given. The main mathematical methods for assessing economic risks are considered and their characteristics are given.
The second chapter "Risks of service enterprises" is devoted to service technologies and their differences from industrial technologies. The classification of risks of enterprises in the service sector is given and a dynamic analysis of the situation in the service market is given. A risk management model for service sector organizations is proposed.
The third chapter "The influence of the main factors of market equilibrium on risk management" is devoted to the study of the influence on the change in the degree of economic risk of such factors characterizing the uncertainty of a market economy as: risk limits, uncertainty in supply and demand, time accounting, elasticity, taxation, etc.
In the fourth chapter "Financial risk management" the theoretical foundations of financial risk management are created on the basis of methods of financial and actuarial mathematics. A classification of financial risks is presented, the main parameters inherent in the considered financial risks are identified, and using the proposed mathematical methods, analytical dependencies are given for their assessment. This makes it possible to carry out a comparative quantitative analysis of risks and, on its basis, to choose such risk management methods that are the most effective.
The fifth chapter "Quantitative assessment of economic risk under uncertainty" considers methods for making effective decisions under uncertainty, using various performance criteria. Multicriteria problems of choosing efficient solutions are studied. A garment enterprise is considered, for which the optimal production volume is selected under conditions of uncertainty and the functioning of the enterprise in a risky situation is investigated.
The sixth chapter "Making the optimal decision under risk" is devoted to the presentation of probabilistic and statistical methods for making effective decisions and choosing the optimal solution using confidence intervals. The problem of choosing the optimal number of jobs in a hairdressing salon, taking into account the risk of service, is considered. Using the decision tree method, the problems of optimizing the strategy for entering the market, maximizing profit from shares and choosing the optimal project for the reconstruction of a dry cleaning factory are considered. The material devoted to the emergence of risks in setting the mission and goals of the company is touched upon. The activities of the company for the decoration and design of premises, the enterprise for baking bakery products and their subsequent sale and the beauty salon under risk are investigated.
The seventh chapter "Management of investment projects under risk" gives the basic concepts of investment projects, their analysis and evaluation, investment risks are given. We study investments in a portfolio of securities, the purpose of which is to form an effective portfolio, made up of a combination of risk-free and risky assets. Methods are given for analyzing the economic efficiency of an investment project and for a comparative financial analysis of investment projects. The methodology for accounting for project risks is considered and practical recommendations for their management are given.
The eighth chapter "Risk management of tourism" is devoted to the types and forms, dynamics of tourism development in Russia. The uncertainty factors of tourism development and the risks associated with tourism activities, as well as their classification are considered. The economic impact of tourism and the specifics of making a managerial decision are studied. The analysis of activity of the organization on rendering of tourist services in the conditions of risk is given.
The ninth chapter "Risk management of hotels and restaurants" discusses the development factors, features and specifics of hospitality, the risks inherent in the hospitality industry, and their management. Recommendations are given to reduce and manage risks in the hospitality business.
In the tenth chapter "Basic methods and ways to reduce economic" risks, economic tools for reducing risks are studied on the basis of mathematical modeling: diversification, insurance, hedging using forward and futures contracts, swaps and options, etc., and also summarizes methods for improving risk management aimed at to reduce their level and increase profitability. An assessment of the effectiveness of risk management methods is given.
Chapter eleven "Psychology of behavior and assessment of the decision maker" is devoted to the study and systematization of the influence of psychological factors on the behavior of market participants and the formation of packages of recommendations for risk management and the choice of effective solutions. Conflict situations and the role of the manager in making risky decisions are considered.
At the end of the textbook "Risk Theory and Modeling of Risk Situations", questions for repetition and self-control are given for each chapter.
Textbook content

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

• 1.3.1. Management activities
• 1.3.2. Risk management
• 1.3.3. Risk management process
• 1.3.4. Mathematical methods for assessing economic risks

• 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

• 4.1.1. Classification of financial risks
• 4.1.2. Relationship of financial and operational leverage to total risk
• 4.1.3. Development risks

• 4.2.1. 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

• 4.3.1. Equivalent flows
• 4.3.2. Payment flows

• 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

• 4.5.1. 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

• 4.7.1. Relationship between interest rate and inflation rate
• 4.7.2. inflation premium
• 4.7.3. The impact of inflation on various processes to reduce inflation

• 4.8.1. Currency Conversion and Interest Accrual
• 4.8.2. Exchange rates over time
• 4.8.3. Reduction of currency risks

• 4.9.1. Exchange risks
• 4.9.2. Impact of default risk and taxation
• 4.9.3. Asset value maximization

• 5.2.1. The concept of playing with nature
• 5.2.2. The subject of game theory. Basic concepts

• 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

• 5.5.1. Multicriteria tasks
• 5 5 2. Pareto optimality
• 5.5.3. Choice of decisions in the presence of multicriteria alternatives

• 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

• 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

• 6.6.1. 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

• 6.8.1. Interior decorating and design firm
• 6.8.2. Enterprise for baking bakery products and their subsequent sale
• 6.8.3. Beauty saloon

• 7.1.1. Basic concepts of investment projects
• 7.1.2. Analysis and evaluation of investment projects
• 7.1.3. Risks of investment projects

• 7.3.1. 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

• 7.4.1. 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

• 7.5.1. Project risk assessment model
• 7.5.2. Accounting for risk when investing
• 7.5.3. Practical conclusions on the management of risky investment projects

• 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

• 8.2.1. Travel motivation
• 8.2.2. Impact of tourism

• 8.3.1. Factors affecting tourism and the tourism economy
• 8.3.2. Classification of tourism risks

• 9.4.1. Identification of risks
• 9.4.2. Risks of investment projects
• 9.4.3. Risk Reduction in the Hospitality Industry

• 10.1.1. Risk Management Process Diagram
• 10.1.2. Risk Examples
• 10.1.3. Choice of risk management techniques

• 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

• 10.4.1. 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

• 10.9.1. Risk financing
• 10.9.2. Assessing the effectiveness of risk management

• 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

• 11.2.1. 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

• 11.3.1. 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

• 11.5.1. 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

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.