Risk theory and modeling of risk situations - Shapkin A.S. Risk modeling Activity of service enterprises under risk conditions

Federal Agency for Education

T O M S POL I T E H N I C H E S K I Y U N I V E R S I T E T

I APPROVED

Dean of AVTF

Gaivoronsky S.A.

" _____ " _______________ 2009

CALCULATION OF OPERATIONAL RISKS

guidelines for the course

CALCULATION OF OPERATIONAL RISKS

Guidelines for the course Guidelines for the course

“Risk theory and modeling of risk situations”

for students of specialty 080116 “Mathematical methods in economics”

Tomsk: Publishing house. TPU, 2009. - 26 p.

Compiled by: Kochegurov A.I.

Reviewer: Babushkin Yu.V.

Methodological instructions were discussed at a 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 and the changed business conditions have required a reorientation of the operating principles of enterprises to the analysis and assessment of various external and internal factors affecting the efficiency of their activities. In foreign countries, even in relatively stable economic conditions, considerable attention is paid to the problem of risk research. The leading principle in the work of an organization (manufacturing enterprise, commercial bank, trading company) is the desire to make a profit. This desire is limited by the possibility of incurring losses. This is where the concept of risk appears and is formed.

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 and beginning of the 20th centuries.

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 was consistent with an orientation towards the predominantly extensive development of the country's national economy and the dominance of administrative methods of management. All this led to the fact that justification of the efficiency of economic activity in a planned economy and, accordingly, all feasibility studies of any projects were done without risk analysis.

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

At the moment, there is still no clear understanding of the essence 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 divergent and sometimes opposing foundations and prerequisites, which makes it possible to have 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 – potential, numerically measurable possibility of loss;

risk – uncertainty associated with the possibility of adverse situations and consequences arising 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 as a result of which the company's financial results may be lower than expected.

From these definitions, the close connection between risk, probability and uncertainty is clearly visible. Consequently, 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.

Let's consider the concept of probability. This term is fundamental to the theory of probability and allows you to quantitatively compare events according to the degree of their possibility. The probability of an event is a certain number, which is greater the more possible 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 associated with the experienced, practical concept of the frequency of an event.

The accuracy of the probability measurement depends on the volume of statistical data and the possibility of their use for future events, i.e. from preserving the conditions in which past events took place. But at the same time, in many cases when making decisions, statistical data is very small in volume or absent altogether, so another way of measuring the probabilities of a situation is used, based on the subjective views of the decision maker.

In this regard, the probabilities measured in this way are called subjective probabilities of the situation. When determining subjective probabilities, the subject’s opinion comes first, reflecting the state of his information fund. In other words, subjective probability is determined on the basis of an assumption based on judgment or personal experience evaluator (expert), and not at the frequency with which a similar result was obtained under similar conditions. Hence the wide variation in subjective probabilities, which is explained by the range 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 addition of uncertainty to the probabilistic situation. Thus, the concept of probability alone is not enough to characterize risk.

Uncertainty presupposes the presence of factors in which the results of actions are not deterministic, and the degree of possible influence of these factors on the results is unknown, for example, incomplete or inaccurate information.

The conditions of uncertainty that occur in any type of business 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 business entities in the process of their functioning experience dependence on a number of factors that can be divided into external (legislation, market reaction to manufactured products, actions of competitors) and internal (competence of company personnel, errors determining project characteristics, etc.).

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

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

Further, it should be taken into account that risk accompanies all processes occurring in an 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 exposed to investment and market risks; and if the enterprise does not take any action, it again bears risks - the risk of lost profits, market risk.

This situation is already inherent in the very definition of the concept “enterprise”, because when carrying out its activities, an enterprise sets certain goals - to receive income, make expenses, etc. Consequently, it plans its activities. But by choosing one or another development strategy, an enterprise may lose its funds or receive an amount less than planned. This is due to the uncertainty of the situation in which it finds itself. In conditions of uncertainty, the management of an enterprise has to make decisions, the likelihood of successful implementation of which (and therefore receiving full income) depends on many factors affecting the enterprise from within and without. In this situation, the concept of risk manifests itself, which means that risk can be characterized as the probability of not receiving planned income in conditions of uncertainty accompanying 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 may affect the achievement of set objectives.

This approach considers the results of an event without separation from the causes. In addition, it draws a line between controllable causes of risk and uncontrollable ones, which would be considered “events” or “circumstances.” Risk factors, which in combination with risk events can cause damage, are organizational gaps, and should be examined for the place they occupy in the business process diagram.

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

As a rule, the main goals that companies pursue when creating a risk management system are the following:

the most efficient use of capital and maximum income;

increasing the sustainability of the company's development, operational 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 risk or effectively manage it, the value of an approach that considers all three aspects of risk (event, impact and the organization's operational 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 risk event, an event without detection leads to missing the event itself, and missing an event without protection leads to damage.

So, 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 a business entity, as a result, there is a variety of risks that arise in the company’s work, and in order to competently manage risks, the company must know what risks its activities are associated with. The classification of these risks is a rather complex problem that economists have been dealing with for quite some time. Moreover, there are more than 40 different risk criteria and more than 220 types of risks, so there is no uniform 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, highlighting three main types of risks [J. M. Keynes. General theory of employment, interest and money. Ch.11]:

business risk – the uncertainty of obtaining the expected income from an investment;

“lender” risk - the risk of non-repayment of a loan, which includes legal risk (evasion of loan repayment) and credit risk (insufficient collateral);

risk of changes in the value of a 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 - thus, the borrower, participating in a risky project, strives to obtain the largest possible difference between the interest on the loan and the rate of return; the lender, taking into account the high risk, also seeks to maximize the difference between the net interest rate and its interest rate. As a result, risks “overlap” each other, which investors do not always notice.

Currently, most often, especially foreign authors, adhere to a classification that necessarily includes the following types of risks:

operational risk;

market risk;

credit risk.

A similar approach is followed by leading Western banks, specialists from the Basel Committee, and developers of risk analysis, measurement and management systems.

To these basic risks are added several more options, occurring in one order or another:

business risk;

liquidity risk;

legal risk;

risk associated with regulatory authorities (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, therefore it is more common in areas related to banking activities. Some authors include liquidity risk in the concept of market risks.

In this work we will rely on the classification that corresponds to the considered area of ​​activity of the consulting company. This, firstly, will allow, at the initial stage of analysis, to limit ourselves to those risks that have a direct impact on the company’s operation. Secondly, taking into account the specifics of the organization’s activities will allow us to set a priority for 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”. In accordance with 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 fulfill its credit obligations. These risks exist both for banks (the classic risk of loan non-repayment), and for enterprises with receivables and organizations operating in the market valuable papers.

Operational risks are the likelihood of direct or indirect losses as a result of uncontrollable events, deficiencies in business organization, inadequate control, wrong decisions, system errors that relate 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 mistakes of the company’s management, its employees, and system problems internal control, poorly developed work rules, etc., i.e. operational risk is the risk associated with the internal organization of the company, as well as the risk of damage environment (environmental risk); risk of accidents, fires, breakdowns; the risk of disruption to the functioning of the facility due to errors in design and installation, a number of construction risks; equipment malfunctions, etc.

Liquidity risk is the risk that a company will not be able to pay off its obligations with available capital at a particular moment. probability of loss due to shortage Money within the required time frame and, as a result, the company’s inability to fulfill its obligations. The occurrence of such a risk event may entail fines, penalties, and damage

business reputation the company, even to the point of declaring it bankrupt. For example, a company must pay 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 creditors will apply penalties to the enterprise. As a rule, liquidity risk arises 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 price fluctuations commodity markets

and currency exchange rates, stock market rates, etc. Market risks The company's volatile assets (commodities, cash, securities, etc.) are most exposed, since their value largely depends on prevailing market prices.

Legal risks – the risk that, in accordance with the current legislation

this moment

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

Information risks mean the likelihood of damage as a result of the loss of information that is significant for the company.

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

Risks are often divided into three categories based on their consequences:

acceptable risk– this is the risk of a decision, as a result of non-implementation of which the enterprise faces loss of profit; within this zone, business activity retains its economic viability, i.e. losses occur, but they do not exceed the expected profit;

critical risk– this is a risk in which the company faces 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 of insolvency of the enterprise;

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’s activities. Thus, risks are divided into two types: clean

risk – the possibility of a loss or zero result; speculative

risk – the probability of obtaining both positive and negative results.

It is obvious that the above classifications are interrelated.

2. Modeling risk situations and managing operational risks

Let us once again note the fact that operational risks are primarily associated with people: direct and indirect business losses arise due to personnel errors, management, theft and abuse, and even in cases where they are caused by failures in telecommunications, computer technology and information technology. systems, in most cases they are based on human errors.

Before we talk about modeling operational risks, let's consider their unique characteristics:

Operational risks are endogenous in nature, which means they are different for each company.

They depend on the company's technology, processes, organization, people and culture, so managing operational risks requires collecting 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, technologies used, competitive environment, etc., as a result of which 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 to business processes, technology, organization and people, i.e. a modeling approach that can measure the impact on operational decisions is needed. For example, how would operational risks change if a company began selling and servicing products online, or if a number of key functions

Will outsourcing be used?

The most common operational risks: errors in computer programs ( failure software

and information technology or systems, equipment and communications failure); personnel errors (n

insufficient qualifications of employees performing this operation; unfair execution of established provisions and regulations; staff overload; random one-time errors);

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

Historically, the highest operational risks and the greatest losses on them occur under 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 lasting more than a few months indicates a lax control environment, negligent management, and lack of recognition of the severity of the problem.

RISK THEORY AND MODELING OF RISK SITUATIONS

LECTURE 1

1. Concept of risk. Risk classification criteria.
2. Mathematical apparatus for modeling and studying risk situations.
3. Basic concepts of game theory. Classification of games.

1. The concept of risk. Risk classification criteria.

CONCEPT OF RISK

Any area human activity, especially economics or business, is associated with decision-making under conditions of incomplete information.

Sources of uncertainty can be very diverse: instability of the economic and 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 of demand for goods, not absolute reliability of production processes, inaccuracy of information, etc.). Economic solutions taking into account the above and many other uncertain factors are taken 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 the possible outcomes or consequences of various actions faced by the decision maker (DM), decision theory considers three types of models:

choice of decisions under conditions of certainty, if for each action it is known that it invariably leads to some specific outcome;

choosing a decision at risk if each action leads to one of many possible particular outcomes, and each outcome has a calculated or expertly assessed probability of occurrence. It is assumed that the decision maker knows these probabilities or can be determined through expert assessments;

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 meaningless.

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 uncontrollable variables. In the noted sense, these terms are used in the mathematical theory of operations research, where they distinguish between decision-making problems under 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 probable and can be determined.

That is, in a risk situation, it is objectively possible to assess the likelihood of events arising as a result of joint activities of production partners, counter-actions of competitors or opponents, the influence of the natural environment on economic development, the introduction of scientific achievements, the transition to a new level of technology, etc.

For risk The situation is characterized by:

-presence of uncertainty(the random nature of the event, which determines which of the possible outcomes is realized in practice);

-availability of alternative solutions;

-the probabilities of outcomes and expected results are known or can be determined;

-probability of loss;

-probability of receiving additional profit.

In conditions market economy Risk is the key to 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, “to take a risk” means “to take a chance, 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". “Risk-taking” means “courage, boldness, determination, enterprise, acting at chance, at random.”

In the Russian language dictionary S.I. Ozhegova defines “risk” as “danger, the possibility of danger” or as “an action of chance in the hope of a happy outcome.”

Let us note an interesting paradox. Expressions like: “He who does not take risks, does not win”, “Risk is a noble cause”, “Without risk there is no business”, etc. have long been known. The opinion has become common that “there are no serious undertakings without risk” and “great risk - great benefit”, etc. At the same time, the expressions “risky step”, “risky event” contain a clear shade of disapproval. Recommendations and instructions to “avoid risk” and “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 of chance, requiring courage, determination, enterprise, in the hope of a happy outcome.”

An entrepreneur who knows how to take risks at the right 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 a management system adaptive to it. That is, special risk management is also necessary, which is based on knowledge economic essence risk, development and implementation of a strategy for dealing with it in business. In conditions of market relations, the problem of accounting and risk assessment acquires independent and applied significance as an important component management theories and practices. Majority management decisions accepted under risk conditions.

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.

Quantitative assessment of the degree of risk, as well as the possibility of constructing confidence intervals based on a known probability, make it possible to influence the risk under consideration with greater reliability. economic process in order to increase profits and reduce risk.

To understand the nature of entrepreneurial risk, the relationship between risk and profit is fundamental. An entrepreneur shows a willingness to take risks in conditions of uncertainty, since along with the risk of losses there is the possibility additional income. While it is clear that an entrepreneur is not guaranteed to make a profit, the reward for his time, effort and ability may result in 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.

By taking risks, an entrepreneur gets a chance to make excess profits and at the same time gets the opportunity to be at a loss. The desire to “earn money” contradicts the goal of “security”. Incomes above the usual, average norm are achieved, as a rule, as a result of risky actions. IN economic theory and practice has proven that a certain amount of risk is a necessary condition receiving income.

Along with this, there is an inverse relationship between the level of risk and liquidity.

The higher the level of liquidity (firm assets, etc.), the lower the level of risk.

High return on assets can be achieved by minimizing inventories, which is fraught with disruption of operational processes and means the risk of loss of liquidity. And excessive thriftiness inevitably threatens asset turnover and profitability.

CRITERIA FOR RISK CLASSIFICATIONS

The risk qualification system includes groups, categories, types, subtypes and varieties of risks.

According to the nature of the consequences, that is, depending on the possible result (risk O event) risks can be divided into two large groups: pure risks and speculative risks.

Ø Pure risksmean 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 cause losses for business activities. Their causes may be natural disasters, accidents, illness of company managers, etc.

Ø Speculative risks are expressed in the possibility of obtaining both positive and negative results. The peculiarity 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 enterprise’s failure to fulfill its plans and obligations for the production of products, goods and services, and other types of production activities, as a result of exposure to external environment, and internal factors.

Commercial risk - this is the risk of losses in the process of financial and economic activities. The reasons for commercial risk may be a decrease in sales volumes, an unexpected decrease in purchase volumes, an increase in the purchase price of goods, an increase in distribution costs, loss of goods during the circulation process, etc.

Financial risk- this is a risk associated with the inability of a company to fulfill its financial obligations. The reasons for financial risk may be changes in the purchasing power of money, failure to make payments, changes in exchange rates, etc.

Depending on the main cause of risks, they are divided into the following categories:natural risks, environmental risks, political risks, transport risks, commercial risks.

To natural risks include risks associated with the manifestation of natural forces: earthquake, flood, hurricane, tsunami, fire, epidemic, etc.

Environmental risks are risks associated with environmental pollution.

Environmental pollution is classified as follows: natural environmental pollution is caused by natural phenomena, usually disasters (floods, volcanic eruptions, mudflows); anthropogenic pollution occurs as a result of human activities.

Environmental risk may arise during the construction and operation of the facility and be integral part industrial risk.

Political risks - these are risks associated with the political situation in the country and the activities of the state. Political risks arise when conditions of the production and trade process are violated that are not directly dependent on the business entity.

Political risks include:

uthe impossibility of carrying out economic activities due to military operations, 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.;

uintroduction of a deferment (moratorium) on external payments for a certain period due to the occurrence of emergency circumstances (strike, war, etc.);

uunfavorable changes in tax laws;

uprohibition or restriction of conversion of national currency into payment currency.

Transport risks - these are the risks associated with the transportation of goods by transport: road, sea, river, rail, air, etc.

Commercial risks mean the uncertainty of the results of a given commercial transaction.

According to structural characteristics commercial risks are divided into property, production, trade and financial.

è Property risks - these are risks associated with the likelihood of loss of the entrepreneur’s property due to theft, negligence, overvoltage of technical and technological systems, etc.

Property risk is the probability of an enterprise losing part of its property, its damage and loss of income in the process of carrying out production and financial activities.

The group of property risks can be divided into the following subtypes:

The risk of loss of property as a result of natural disasters (fires, floods, earthquakes, hurricanes, etc.);

Risk of loss of property due to the actions of criminals (theft, sabotage);

Risk of loss of property as a result of industrial accidents;

Risk of loss or damage to property during transportation;

Risk of alienation of property due to action local authorities authorities or other owners.

In addition, for a specific manufacturing company, there is likely a risk of losing any particular type of property, for example computer technology 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 materially responsible persons at the enterprise, ensuring the organization of security 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 risks associated with losses from production interruption due to exposure various factors, and above all with the loss or damage of fixed and working capital (equipment, raw materials, transport, etc.), as well as risks associated with the introduction of new equipment and technology into production.

è Trading risks- risks associated with loss due to delay in payments, refusal to pay during the transportation of goods, non-delivery of goods, etc.

è Financial risks associated with the likelihood 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).

Risks associated with the purchasing power of money include the following: types of risks: inflation and deflation risks, currency risks, liquidity risks.

Inflation risk - this is the risk that, as inflation rises, cash income received depreciates in terms of real purchasing power faster than it grows. In such conditions, the entrepreneur suffers real losses.

Deflationary risk - this is the risk that with the growth of deflation, a fall in the price level, a deterioration in the economic conditions of entrepreneurship and a decrease in income occur.

Currency risksrepresent the danger of foreign exchange losses associated with changes in the exchange rate of one foreign currency in relation to another, when conducting foreign economic, credit and other foreign exchange transactions.

Liquidity risks - these are risks associated with the possibility of losses when selling securities or other goods due to changes in the assessment of their quality and use value.

Currency risk includes three types of risks: economic risk, translation risk, transaction risk.

è Economic risk for a business firm is that the value of its assets and liabilities may change up or down (in national currency) due to future changes in the exchange rate. This also applies to investors whose foreign investments - shares or debt - generate income in foreign currency.

è Translation riskhas an accounting nature and is associated with differences in the accounting of a firm's assets and liabilities in foreign currency. If the exchange rate falls

è foreign currency in which the firm's assets are denominated, the value of these assets decreases. It should be kept in mind that translation risk is an accounting effect but has little or no reflection on the economic risk of the transaction.

è More important from an economic point of view is transaction risk, which considers the impact of changes in exchange rates on the future flow of payments, and therefore 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 local currency value of a foreign exchange transaction in the future. This type risk exists both when concluding trade contracts and when receiving or providing loans. It consists in the possibility of changing the amount of receipts or payments when converted into national currency.

In addition, it is necessary to distinguish between the exchange rate risk for the importer and the risk for the exporter.

Transaction risk for the exporter - this is a drop in the exchange rate of a foreign currency from the moment of receipt or confirmation of the order until the receipt of payment and during negotiations.

Transaction risk for the importer - this is an increase in the exchange rate in the period of time between the date of order confirmation 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: risk of lost profits, risk of reduced profitability, risk of direct financial losses.

Risk of lost profits - this is the risk of indirect (collateral) financial damage (lost profit) as a result of failure to implement any activity (for example, insurance, hedging, investing, etc.).

Risk of decreased profitability may arise as a result of a decrease in the amount of interest and dividends on portfolio investments, deposits and loans. The risk of decreased profitability includes the following types: interest rate risks and credit risks.

Risks of direct financial losses include the following varieties: stock exchange risk, selective risk, bankruptcy risk, and credit risk.

uExchange risk- this 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.

uRisk of bankruptcy represents a danger as a result of the wrong choice of capital investment, complete loss by the entrepreneur equity and his inability to pay off his obligations.

From the point of view of time duration, business risks can be divided into short-term and permanent.

Short-term ones include risks that threaten an entrepreneur over a certain 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).

Towards constant risks include those that continually threaten business activity in a given geographical area or in a particular sector of the economy (for example, the risk of non-payment in a country with imperfect legal system or the risk of destruction of buildings in an area with increased seismic hazard).

Since the main task of an entrepreneur is to take prudent risks without crossing the line beyond which bankruptcy of the company is possible, it is necessary to highlight acceptable, critical and catastrophic risks.

Acceptable risk- this is the threat of a complete loss of profit from the implementation of a particular project or from business activity in general. In this case, losses are possible, but their size is less than the expected entrepreneurial

arrived. Thus, this type of business activity or a specific transaction, despite the likelihood of risk, retains its economic feasibility.

The next level of risk, more dangerous than acceptable, is critical risk. Critical risk is associated with the danger of losses in the amount of costs incurred to carry out this type of business activity or a separate transaction.

Wherein critical risk of the first degree associated with the threat of receiving zero income, but with reimbursement of 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 carrying out this business activity, that is, losses of intended revenue are likely and the entrepreneur has to reimburse the costs at his own expense.

Catastrophic means risk which is characterized by danger, the threat of loss in an amount equal to or exceeding the entire property status

entrepreneur. As a rule, such a risk leads to 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 a business firm received external loans against expected profits. If this risk arises, the entrepreneur has to repay the loans from personal funds.

2. Mathematical apparatus for modeling and studying risk situations.

The role of quantitative assessment of economic risk increases significantly when it is possible to select an optimal solution from a set of alternative solutions. The optimal solution provides the highest probability of the best result at the lowest costs and losses in accordance with the objectives of risk minimization and programming.

The use of economic and mathematical methods allows us to conduct a qualitative and quantitative analysis of economic phenomena, quantify the value of risk and market uncertainty, and select the most effective (optimal) solution.

Mathematical methods and models make it possible to simulate various economic situations and evaluate the consequences when choosing decisions, without expensive 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, statistical decision theory, and mathematical programming.

Many financial transactions (venture investment, purchase of shares, selling transactions, credit transactions, etc.) are associated with a fairly significant risk. They require assessing the degree of risk and determining its magnitude.

Entrepreneur's risk quantitatively characterized by a subjective assessment of the probable (i.e. expected) value of the maximum and minimum income(loss) from this capital investment. Moreover, the larger the range between the minimum and maximum income (loss) with an equal probability of receiving them, the higher the degree of risk.

The degree of risk is the probability of a loss event 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 enterprise manager. Managers of the conservative type are not inclined to innovation; they usually try

avoid any risk. Agile managers tend to take more risky decisions if the risk is voluntary. In a difficult situation, such managers are oriented towards more risky decisions if they are confident in the professionalism of the performers.

A manager's willingness to take risks is usually influenced by the results of past similar decisions made under conditions of uncertainty.

Losses incurred dictate the choice of a cautious policy, and 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 assessing alternative decision options, 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 decision option.

Risky decisions include those decisions that involve obtaining some result with some degree of probability. This occurs in conditions of uncertainty, when the factors requiring analysis and consideration are very complex, and there is no reliable or sufficient information about them. It is then impossible to be confident that certain results will be achieved. Uncertainty also characterizes many decisions made in rapidly changing circumstances. This situation is very familiar Russian entrepreneurs. When making a choice, the manager considers new project

in conjunction with other options and with already established activities of firms. In order to reduce risk, it is advisable to choose the production of such goods (services), the demand for which changes in opposite directions, that is, when the demand for one product increases, the demand for another decreases, and vice versa.

Unfortunately, not every risk can be reduced through diversification. The fact is that entrepreneurship is influenced by various macroeconomic factors, such as the expectation of a boom or crisis, movement of the bank interest rate, etc. The risk caused by these processes cannot be reduced by the manager through diversification of production. Making management decisions at the enterprise

involves a close link between all types of risk. However, the manager’s best forecasts may not come true due to unexpected and unforeseen circumstances beyond the control of the company itself (economic conflicts, sudden changes in customer tastes, actions of competitors, strikes, unexpected government decisions).

Therefore, in the event of the occurrence of unfavorable events, various possibilities are provided for reducing negative consequences through reserve funds, production capacity, raw materials, finished products; financially supported plans for the reorientation of activities are being developed.

It is possible to significantly reduce risk through skilled work on forecasting and in-house planning, self-insurance and insurance, transferring part of the risk to other persons or organizations through hedging, futures transactions, and option repurchase.

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. When applied to economic problems, the methods of probability theory come down to determining the values ​​of the probabilities of the occurrence of events and to selecting 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 according to the principle of “lucky or unlucky.” An entrepreneur is forced to take risks due to the uncertainty of the economic situation. The greater the uncertainty of the business 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 forces the entrepreneur to look for an opportunity to acquire the missing Additional information, and in the absence of such an opportunity, begin to act at random, relying on your experience and intuition.

The uncertainty of the economic situation is largely determined by the factor of chance. Accident- this is something that happens differently under similar conditions, and therefore it cannot be foreseen and predicted in advance. The mathematical apparatus for studying random variables is provided by probability theory. Probability allows us to predict random events. It gives them quantitative and qualitative characteristics. 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 counteracting factor. Towards counteractions relate disasters, fires and others natural phenomena, wars, revolutions, strikes, various conflicts in labor collectives, competition, changes in demand, accidents, theft, etc. An entrepreneur, in the process of his actions, must choose a strategy that will allow him to reduce the degree of opposition, and therefore reduce the degree of risk. The mathematical apparatus for choosing a strategy in conflict situations is provided by game theory.

The degree of risk is measured by two criteria:

Average expected value,

Fluctuation (variability) of the expected result.

MEASURE OF RISK

The most common point of view is that measure of risk some commercial (financial) decision or operation should be considered the standard deviation (positive square root of the variance) of the value of the efficiency indicator of this decision or operation.

Indeed, since the risk is due to the non-determinism of the outcome of the decision (operation), the smaller the spread (dispersion) of the decision result, the more predictable it is, i.e. less risk.

If the variation (dispersion) of the result is zero, there is no risk at all. For example, in a stable economy, transactions with government securities are considered risk-free.

Most often, the indicator of the effectiveness of a financial decision (operation) is profit.

As an illustration, consider the choice by some person of one of two options

investments under risk conditions.

Let there be two projects A And IN , in which the specified person can invest funds.

Project A at some point in the future provides a random amount of profit.

Let's assume that its average expected value, the mathematical expectation, is equal to t A With

dispersion . For the project IN these numerical characteristics of profit as random

values ​​are assumed to be equal respectivelym BAnd . Mean square

the deviations are equal respectivelyS A And S B.

The following cases are possible:

1) T A = m B, S A < S B, you should select a project A ;

2) T A > m B, S A < S B, you should select a project A ;

3) T A > m B, S A = S B, you should select a project A;

4) TA > m B , S A > S B ;

5) TA < m B , S A< S B .

In the last two cases, the decision to select a project A or IN depends on the decision maker’s attitude to risk.

In particular, in case 4) the project A provides higher average profit,

however, it is also riskier. The choice in this case is determined by what additional

The value of the average profit compensates for the given increase in risk for the decision maker.

In case 5) for the project A the risk is lower, but the expected profit is also lower.

Subjective attitude to risk is taken into account in the Neumann-Morgenstern theory.

Let's look at an example of choosing an investment option.

Example.Let there be two investment projects. The first, with a probability of 0.6, provides a profit of 15 million rubles, but with a probability of 0.4, you can lose 5.5 million rubles. For the second project, with a probability of 0.8, you can make a profit of 10 million rubles. and with a probability of 0.2 to lose 6 million rubles. Which project to choose?

Solution.

Both projects have the same average profitability, equal to 6.8 million rubles:

0,6*15 + +0,4(-5,5) = 0,8*10 + 0,2(-6) = 6,8.

However, the standard deviation of profit for the first project is 10.04 million rubles:

1/2 = 10,04;

and for the second – 6.4 million rubles:

1/2 = 6,4.

Therefore, the second project is more preferable.

Although the standard deviation of solution efficiency is often used

As a measure of risk, it does not accurately reflect reality. There may be 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 by risk we mean the risk of ruin, then the amount of risk should depend on the amount of initial capital of the decision-maker or the company he represents. The Neumann-Morgenstern theory takes this circumstance into account.

3. BASIC CONCEPTS OF GAME THEORY. CLASSIFICATION OF GAMES.

Game theory is the theory of mathematical models of acceptance optimal solutions in conditions of uncertainty, opposing interests of different parties, conflict.

Mathematical game theory is an integral part of operations research.

Operations research problems can be classified according to the level of information about the situation that the decision maker has.

The simplest levels of information about a 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 task comes down to finding the extremum of the function (or its mathematical expectation) under given restrictions. Methods for solving such problems are studied in courses on mathematical programming or optimization methods.

Finally, the third level is uncertain, 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 principles of optimal behavior themselves may not be clear.

Game theory is the 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, in one of which he actually finds himself, about the set of decisions (“strategies”) that he can accept, and about the quantitative measure of the “gain” that he could receive by choosing this strategy in a given situation.

Establishing the principles of optimal behavior under conditions of uncertainty, proving the existence of solutions that satisfy these principles, indicating algorithms for finding solutions constitute the content of game theory.

The uncertainty we encounter in game theory can have different origins. However, as a rule, it is a consequence of the conscious activity of another person (persons) defending their interests. In this regard, game theory is often understood as the theory mathematical models making optimal decisions in conflict conditions.

Mathematical “game theory” is the theory of mathematical models for making optimal decisions in conditions of conflict.

Thus, game theory models can, in principle, meaningfully describe very diverse phenomena: economic, legal and class conflicts, human interaction with nature, biological struggle for existence, etc.

In game theory, all such models are usually called games.

Conflict situation - a situation in which two (or more) parties pursue different goals, and the results of any action of each party depend on the actions of the partners.

A game– mathematical model of a conflict situation.

Winning(payment) – the outcome of the conflict.

Zero sum game – a pairs game in which the gain of one player is equal to the loss of the other.

On the movein game theory is the choice of one of the options provided for by the rules of the game.

Personallyis called the conscious choice by one of the players of one of the possible moves in a given situation and its implementation.

Random moveis called a choice from a number of possibilities, carried out not by the player’s decision, but by some kind of random selection mechanism.

Player strategy – a set of rules that determine the choice of his actions at each personal move, depending on the current situation.

Purpose of Game Theory– determining the optimal strategy for each player.

The mathematical description of the game comes down to listing all the players active in it, indicating for each player all his strategies, as well as the numerical winnings that he will receive after the players choose their strategies. As a result, the game becomes a formal object that can be analyzed mathematically.

Games can be classified according to various criteria.

Firstly , non-cooperative games, in which each coalition (a set of players acting together) consists of only one player. The so-called cooperative theory of non-cooperative games allows players to temporarily unite in coalitions during the game with the subsequent division of the resulting winnings or making joint decisions.

Secondly, coalition games, in which decision-making players, according to the rules of the game, are united into fixed coalitions. Members of the same coalition can freely exchange information and make fully agreed upon decisions.

The winnings of the game can be divided into antagonistic and games with non-zero sum.

By the nature of obtaining information - for games in normal shape(players receive all the information intended for them before the game starts) and dynamic games (information is provided to players during the development of the game).

By the number of strategies - by final And endless games.

LITERATURE

Balabanov I.T. Risk management. - M.: Finance and Statistics, 1996. - 192 p.: ill.

[ 2 ] . Dubrov A.M., Lagosha B.A., Khrustalev E.Yu. Modeling risk situations in economics and business. Tutorial. - M.: Finance and Statistics, 2000. - 176 p.: ill.

Petrosyan L.A., Zenkevich N.A., Shevkoplyas E.V. Game theory. Textbook. – St. Petersburg: BVH-Petersburg, 2012. -432 p.: ill.

Tapman L.N. Risks in the economy. Textbook for universities. - M.: UNITY-DANA, 2002. - 380 p.

Shapkin A.S., Shapkin V.A. Risk theory and modeling of risk situations. Textbook. M.: Publishing and trading 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 textbook discusses approaches to taking into account factors of uncertainty and risk in economic practice, as well as mathematical models used for these purposes. Situations that arise under conditions of uncertainty and lack of information when making management decisions are analyzed. The content is illustrated with 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 conflict conditions was carried out. A consistent presentation of the 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 reinforce the material, each chapter contains tasks and exercises of varying degrees of difficulty.

The textbook is intended for undergraduates, graduate students and teachers of economic universities and departments, students of business schools, managers of enterprises and organizations.

The textbook outlines the essence of uncertainty and risk, classification and factors affecting them; Methods for qualitative and quantitative assessment of economic and financial situations under conditions of uncertainty and risk are provided.

CONTROL 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 risk 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 risk and profit in 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 business situation?

10. What is a risk measure? How is it measured? Give examples.

11. Formulate the basic concepts of game theory.

12. Name the characteristics of the classification of games. Give examples of games.

When managing risks, 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, since it requires a basis for studying and measuring something that did not happen. Currently, there is no other way to describe such hypothetical situations other than using mathematical models called models of risk situations. This represents the basis for quantitative risk management. Its essence lies in the use of economic and mathematical models to predict situations characterized by risk and uncertainty, and to justify 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 figure out which properties are considered important and which are not. Correct description 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, that is, it should clarify for the decision maker how the process can develop, what outcomes will occur, and suggest various actions (for example, to prevent damage).

The most important class of models used in risk management are mathematical models. They allow you to describe the essential aspects of the process or phenomenon being studied in the form of mathematical relationships, and then analyze them using the appropriate mathematical apparatus. The use of mathematical models to predict alternatives for future development is especially important. This is what allows the manager to numerically assess the future consequences of decisions made.

The mathematical models used in risk management are very diverse and have different capabilities. 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 constructing it, one should start from the properties of the modeling object itself. However, similar situations allow us to use similar (if not identical) tools: there are some general approaches to modeling (for example, the use of stochastic differential equations or other mathematical apparatus). If you can use a more or less standard approach, then the modeling process will be simpler (approaches to building a model and obtaining a solution are known).

In the field of quantitative risk management, the most common are probabilistic and statistical models.

For some types of risks, the 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.

The textbook outlines the essence of uncertainty and risk, classification and factors affecting them; Methods for qualitative and quantitative assessment of economic and financial situations under conditions of uncertainty and risk are provided.

A classification of service technologies is given, examples of the activities of service organizations in risk situations are considered.

The methodology for managing investment projects under risk conditions is outlined, recommendations are given for managing an investment portfolio, and an assessment is carried out financial condition and prospects for the development of the investment object, a model for taking risks into account in investment projects is proposed.

Considerable attention is paid to methods and models of management under risk conditions and the psychology of behavior and assessment of the decision maker.

For undergraduate and graduate students of economic universities and faculties, students of business schools, risk managers, innovation and investment managers, as well as specialists from banking and financial institutions, employees of pension, insurance and investment funds.

Chapter 1 PLACE AND ROLE OF ECONOMIC RISKS IN THE ACTIVITIES OF ORGANIZATIONS

1.2. PLACE AND ROLE OF RISKS IN ECONOMIC ACTIVITY

1.3. RISK MANAGEMENT SYSTEM

Chapter 2 RISKS OF SERVICE COMPANIES

Chapter 3 INFLUENCE OF MAIN FACTORS OF MARKET EQUILIBRIUM ON RISK MANAGEMENT

3.2. INFLUENCE OF MARKET EQUILIBRIUM FACTORS ON CHANGES IN RISK

Chapter 4 FINANCIAL RISK MANAGEMENT

4.1. FINANCIAL RISKS

4.2. INTEREST RISKS

4.4. RISK INVESTMENT PROCESSES

4.5 CREDIT RISKS

4.7. INFLATION RISK

4.8. CURRENCY RISKS

4.9. RISKS OF ASSETS

Chapter 5 QUANTITATIVE ESTIMATES OF ECONOMIC RISK UNDER UNCERTAINTY

5.2. MATRIX GAMES

5.5. MULTICRITERIAL PROBLEMS OF SELECTION OF EFFECTIVE SOLUTIONS

5.7. DETERMINING THE OPTIMAL VOLUME OF PRODUCTION OF A GARMENTING ENTERPRISE UNDER CONDITIONS OF UNCERTAINTY

Chapter 6 OPTIMAL DECISION MAKING IN CONDITIONS OF ECONOMIC RISK

6.5. SELECTION OF THE OPTIMAL PLAN USING THE METHOD OF CONSTRUCTION OF EVENT TREES

6.6. COMPARATIVE ASSESSMENT OF SOLUTION OPTIONS

6.8. ACTIVITY OF SERVICE COMPANIES UNDER CONDITIONS OF RISK

Chapter 7 MANAGEMENT OF INVESTMENT PROJECTS UNDER CONDITIONS OF RISK

7.1. INVESTMENT PROJECTS IN CONDITIONS OF UNCERTAINTY RISK

7.3. INVESTMENT IN SECURITIES PORTFOLIO

7.4. ANALYSIS OF THE ECONOMIC EFFICIENCY OF AN INVESTMENT PROJECT

7.5. ACCOUNTING RISK IN INVESTMENT PROJECTS

Chapter 8 RISK MANAGEMENT OF TOURISM

8.2. PSYCHOLOGY OF THE IMPACT OF TOURISM ON PARTICIPANTS AND AROUND

8.3. RISKS ASSOCIATED WITH TOURISM ACTIVITIES

Chapter 9 RISK MANAGEMENT OF HOTELS AND RESTAURANTS

9.4. RISKS INHERENT IN THE HOSPITALITY INDUSTRY AND THEIR MANAGEMENT

Qualitative risk analysis methods

After all have been identified possible risks for a specific project, it is necessary to determine the feasibility of investments, development and work on this project. To do this, an analysis of the risks of the investment project is carried out.

All possible risk analysis methods proposed in theory can be divided into qualitative and quantitative approaches. A qualitative approach, in addition to identifying risks, involves identifying the sources and causes of their occurrence, as well as a cost assessment of the consequences. The main features of the qualitative approach are: identifying simple risks for the project, identifying dependent and independent risks both from each other and from external factors, and determining whether 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 likelihood and time of their occurrence. For the worst-case scenario for the development of the project, the maximum amount of losses for the company is calculated.

In the qualitative approach, the following risk analysis methods are distinguished: method expert assessments; cost feasibility method; method of analogies.

Method of expert assessments.

The expert assessment method includes three main components. Firstly, an intuitive-logical analysis of a 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, issuing expert assessment decisions; this stage is the final part of the expert’s work. Experts formulate a decision on the advisability of working with the project they are researching, and offer an assessment of the expected results, according to different scenarios project development. The third stage, the final one for the expert assessment method, is the processing of all decision results. 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 particular project must be identified.

Experts are asked to fill out a questionnaire with a detailed list of risks related to the project being analyzed, in which they need to determine the likelihood of the risks they have identified on a certain scale. The most common methods of expert risk assessments include the Delphi method, scoring method, ranking, pairwise comparison, and others.

The Delphi method is one of the methods of expert assessments that provides a quick search for solutions, among which the following is selected best solution. The use of this method allows you to avoid contradictions among experts and obtain independent individual decisions, eliminating communication between experts during the survey. The experts are given a questionnaire, to the questions of which they must give independent, as objective as possible assessments, and reasonable assessments. Based on the completed questionnaires, the decision of each expert is analyzed, the prevailing opinion, extreme judgments are identified, decisions are as clearly, accessible and well-reasoned as possible, etc. Subsequently, experts may change their opinion. The entire 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.

Method score risk assessment is made on the basis of a general indicator determined by a number of private expert-assessed indicators of the degree of risk. It consists of the following steps:

• 1) Determination of factors that influence the occurrence of risk;
• 2) Selection of a general indicator and a set of specific criteria characterizing the degree of risk for each factor;
• 3) Drawing up a system of weighting coefficients and rating scales for each indicator (factor);
• 4) Integral assessment generalized criterion for the degree of project risks;
• 5) Development of recommendations for risk management.

The ranking method involves arranging objects in ascending or descending order of some inherent property. Ranking allows you to select the most significant factor from the set of factors being studied. 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 assigned to the i-th object by the j-th expert. The values ​​of 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 jth expert is the sequence of ranks x 1j , x 2j , …, x nj .

This method simple in its implementation, but in evaluating large quantity parameters, experts are faced with the difficulty of constructing a ranked series, due to the fact that it is necessary to simultaneously take into account many complex correlations.

The pairwise comparison method is the establishment of the most preferred 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 pair or establish their equality.

Again, in comparison with the ranking method, pairwise comparison can be carried out with large quantities parameters, as well as in cases of slight 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- 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 is the largest can be considered the most important (significant).

Summation can also be done by columns (), then the most significant factor will be the one with the fewest points.

Expert analysis consists of determining the degree of risk influence based on expert assessments of specialists. The main advantage of this method is the simplicity of calculations. There is no need to collect accurate source data and use expensive and software. However, the level of risks depends on the knowledge of experts. Another disadvantage is the difficulty in attracting independent experts and the subjectivity of their assessments. For clarity and objectivity of the results, this method can be used in conjunction with other quantitative methods (more objective).

Method of relevance and expediency of costs, method of analogies.

A cost-benefit analysis is based on assumptions 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;
• · changes in design boundaries due to unforeseen circumstances;
• · differences in the performance of machines and mechanisms from those envisaged by the project;
• · increase in the cost of the project compared to the original, due to inflation or changes in tax legislation.

To carry out the analysis, first of all, all the above factors are detailed, then a tentative list of possible increases in project costs is compiled for each option for its development. The entire process of project implementation is divided into stages, based on this, the process of financing for the development and implementation of the project is also divided into stages. However, the funding stages are set conditionally, as some changes may be made as the project develops and develops. Phased investment of funds allows the investor to more carefully monitor the work on the project, and if risks increase, either terminate or suspend financing, or begin to take certain measures to reduce costs.

Among qualitative methods risk analysis, the method of analogies is also common. The main idea of ​​this method is to analyze other projects similar to the one being developed. Based on the same risky projects, possible risks, the reasons for their occurrence, the consequences of the risks are analyzed, and the consequences of the impact on the project of unfavorable external or internal factors. The information obtained is then projected onto the new project, which allows us to identify 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 difficulty of this method of analysis is the difficulty of obtaining the most accurate analogue, due to the fact that there are no formal criteria that precisely establish the degree of similarity of situations. But, as a rule, even if the analogue is selected correctly, it becomes difficult to formulate the correct prerequisites for analysis, a complete and close to reality set of scenarios for project failure. The reason is that there are very few completely identical projects or none 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 suitable rather definitions and descriptions of possible risk situations for a particular project than to obtain even a relatively accurate assessment of the risks of an investment project.

Quantitative risk analysis method

To assess the risks of investment projects, the most common quantitative methods of analysis are:

• sensitivity analysis
• · script 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). Sensitivity analysis is divided into several successive stages:

• · the basic values ​​of the resulting indicators are established, the connection 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 original parameters under study are recalculated one by one within the obtained range, new values ​​of the resulting parameters are obtained
• · Initial 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 an investment project to the corresponding risk and the sensitivity of the project to each factor is determined by calculating the elasticity indicator, which is the ratio of the percentage change in the resulting indicator to a change in the value of the parameter by one percent.

Where: E - elasticity index

NPV 1 - the value of the basic resulting indicator

NPV 2 - the value of the resulting indicator when changing the parameter

X 1 - basic value of the variable parameter

X 2 - changed value of the variable parameter

The higher the elasticity index, the more sensitive the project is to changes in this factor, and the more susceptible the project is to the corresponding risk.

Also, sensitivity analysis can be carried out graphically, by plotting the dependence of the resulting indicator on changes in the factor under study. The sensitivity of the NPV value to a change in the factor changes the level of the slope of the relationship; 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 x-axis, the value of the parameter is determined in percentage terms at which the project will become ineffective.

After this, based on the calculations carried out, all the obtained parameters are ranked by degree of significance (high, medium, low), and a “sensitivity matrix” is constructed, with the help of which the factors that are the most and least risky for the investment project are identified.

Regardless of the inherent advantages of the method - objectivity and clarity of the results obtained, there are also significant disadvantages - changes in one factor are considered in isolation, whereas in practice all economic factors are correlated to one degree or another.

Scripting method

The script method provides a description of all possible conditions 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 constructed: pessimistic, optimistic, realistic (or most likely or average)
• · initial information about uncertainty factors is converted into information about the likelihood of individual implementation conditions and certain performance indicators

Based on the data obtained, the indicator is determined economic efficiency project. If the probabilities of the occurrence of a particular event reflected in the scenario are known exactly, then the expected integral effect of the project is calculated using the mathematical expectation formula:

Where: NPVi - integral effect when implementing the i-th scenario

pi is the probability of this scenario

In this case, the risk of project ineffectiveness (Re) is assessed as the total probability of those scenarios (k) in which the expected effectiveness of the project (NPV) becomes negative:

The average damage from the implementation of the project in case of its ineffectiveness (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)

Experts highlight the PERT analysis method (Program Evaluation and Review Technique) as one of the methods of scenario analysis. The main idea of ​​this method is that when developing a project, three project parameters are set - optimistic, pessimistic, most probable. Next, the expected values ​​are calculated using the following formula:

Expected value = [Optimistic value 4xMost likely value + Pessimistic value]/6

Coefficients 4 and 6 were obtained empirically based on statistical data from a large number of projects. Based on the calculation results, the rest of the project analysis is carried out. The effectiveness of PERT analysis is maximum only if the values ​​of all three estimates can be justified.

Decision tree

The decision tree method represents network diagrams, in which each branch, then various alternative options for the development of the project. By following each constructed branch of the project, you can trace all possible stages of the project’s development, and, accordingly, choose the most optimal one, and with the least risks. This analysis method is divided into the following stages:

• · Peaks are determined for each problematic and ambiguous moment in the development of the project, and branches are built ( possible ways developments)
• · For each arc, the probability and possible losses at this stage are determined by an expert method.
• · Based on all the obtained values ​​of the vertices, 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 possible disadvantage of the method is the mandatory presence of a reasonable number of project development options. The main difference is the ability to take full and detailed account of all factors and risks affecting the project. The method is especially used in situations where decisions on project implementation are made gradually and depend on previously decisions made, thus each decision in turn determines the scenario further development project.

Simulation modeling (Monte Carlo method)

Risk analysis of investment projects using the Monte Carlo method combines two previously studied methods: sensitivity analysis method and scenario analysis. In simulation modeling, instead of generating best- and worst-case scenarios, a computer generates hundreds of possible combinations of design parameters based on their probability distribution. Each resulting combination produces its own NPV value. Such a calculation is only possible using special computer programs. The phased scheme of simulation modeling is constructed as follows:

• · factors influencing cash flows project;
• · a probability distribution is constructed for each factor (parameter), and 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 (mathematical expectation and variance);
• · the computer randomly selects the value of each risk factor based on its probability distribution;

Fig.1.3

Fig.1.4

The disadvantages of this risk modeling method include:

• · the existence of correlated parameters greatly complicates the model
• · the type of probability distribution for the parameter under study may be difficult to determine
• · when developing real models, it may be necessary to attract outside specialists or scientific consultants;
• · research of the model is possible only with the availability of computer technology and special application software packages;
• · relative inaccuracy of the obtained results compared to other methods of numerical analysis.

Discount rate adjustment method

Due to the simplicity of the calculations, the Risk Adjustment 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 marginal cost of capital for a company). The adjustment is carried out as follows: the amount of the required risk premium is added, then the criteria for the effectiveness of the investment project are calculated (NPV, IRR, PI). The decision on the effectiveness of the project is made according to the rule of the selected criterion. The higher the risk, the higher the premium.

Risk adjustments are set separately for each individual project, since they completely depend on the specifics of the project under study.