Unit 2: THE RISK MANAGEMENT PROCESS

Contents
2.0 Aims and Objectives
2.1 Introduction
2.2 Risk Management Defined
2.3 Objectives of Risk Management
2.4 Possible Contributions of Risk Management
2.5 The Risk Management Process
2.5.1 Risk Identification
2.5.1.1 Sources of Risk
2.5.1.2 Identification of Exposures
2.5.1.3 The Range of Risk Identification Techniques
2.5.1.4 Common Features of Risk Identification
2.5.2 Risk Management
2.5.2.1 Poisson Distribution
2.5.2.2 Binomial Probability Distribution
2.5.2.3 Normal Distribution
2.6 Tools of Risk Management
2.6.1 Risk Control Tools
2.6.2 Risk Financing Tools
2.7 Selection of Risk Management Tools: Quantitative Approaches
2.7.1 Expected Utility Model
2.7.2 The Worry Factor Model
2.8 Summary
2.9 Answer to Check Your Progress Exercise

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2.0 AIMS AND OBJECTIVES

After studying this unit, you should be able to:

 define risk management and briefly explain its purpose.
 describe briefly the basic components of risk management.
management.

2.1 INTRODUCTION

We have looked at the nature of risk and the various classifications into which it can be put.
The concept, which develops, is one of risk as an all-pervasive force in the world; a negative
feature in life bringing unfortunate, or unlooked for, outcomes. The various classifications
that we have used all tend to support the view that risk is to be avoided at all costs. It would
be valuable
valuable to stop here for a moment and take stock of what this means. Are we to conclude
that risk has no beneficial side to it? Is it solely a negative concept, implying loss and not
gain? Has the world gained nothing from the existence of risk?

2.2 RISK MANAGEMENT DEFINED

Dear student, the following definitions of risk management have been forwarded for your
study. Thoroughly study the definitions and compare their essence.

Definition 1
Risk Management refers to the identification; measurement and treatment of exposure to
potential accidental losses almost always in situations where the only possible out comes are
losses or no change in the status.

Definition 2
Risk Management is a general management function that seeks to assess and address the
causes and effects of uncertainty and risk on an organization. The purpose of risk management
is to enable an organization to progress towards its goals and objectives in the most direct,
efficient, and effective path. It is concerned with all risks.

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 Definition 3
Risk Management is the executive function of dealing with specified risks facing the business
enterprise. In general, the risk manager deals with pure, not speculative risk.

What are the specific duties of a risk manager? Could you get any hint from the above
definitions? Please write down your response in the space provided below.

The risk manager has certain specific duties. These include:

1. To recognize exposures to loss; the risk manager must, first of all, be aware of the
possibility of each type of loss. This is a fundamental duty that must precede all other
functions.
2. To estimate the frequency and size of loss; to estimate the probability of loss from
various sources.
3. To decide the best and most economical method of handling the risk of loss, whether
it be by assumption, avoidance, self-insurance, reduction of hazards, transfer,
commercial insurance, or some combination of these methods.
4. To administer the programs of risk management, including the tracks of constant
revaluation of the programs, record keeping and the like.

2.3 OBJECTIVES OF RISK MANAGEMENT

Risk management has several important objectives that can be classified into two categories:
pre-loss objectives and post-loss objectives.

Pre-loss objectives. A firm or organization has several risk management objectives prior to
the occurrence of a loss. The most important include economy, the reduction of anxiety, and
meeting externally imposed obligations.

The first goal means that the firm should prepare for potential losses in the most economical
way possible.
possible. This involves an analysis of safety program expenses, insurance premiums, and
the costs associated with the different techniques for handling losses.

The second objective, the reduction of anxiety,

anxiety, is more complicated. Certain loss exposures
can cause greater worry and fear for the risk manager, key executives, and stockholders than

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other exposures. For example, the threat of a catastrophic lawsuit from a defective product
can cause greater anxiety and concern than a possible small loss from a minor fire. However,
the risk manager wants to minimize the anxiety and fear associated with all loss exposures.

The third objective is to meet any externally imposed obligations.

obligations. This means the firm must
meet certain obligations imposed on it by outsiders. For example, government regulations
may require a firm to install safety devices to protect workers from harm. Similarly, a firm’s
creditors may require that property pledged as collateral for a loan must be insured. The risk
manager must see that these externally imposed obligations are met.

Post-loss objectives. The first and most important post-loss objective is survival of the firm.
firm.
Survival means that after a loss occurs, the firm can at least resume partial operation within
some reasonable time period if it chooses to do so.

The second post-loss objective is to continue operating.

operating. For some firms, the ability to operate
after a severe loss is an extremely important objective. This is particularly true of certain
firms, such as public utility firm, which must continue to provide service. The ability to
operate is also important for firms that may loss customers to competitors if they cannot
operate after a loss occurs. This would include banks, bakeries, dairy farms, and other
competitive firms.

Stability of earnings is the third post-loss objective. The firm wants to maintain its earnings
per share after a loss occurs. This objective is closely related to the objective of continued
operations. Earning per share can be maintained if the firm continues to operate. However,
here may be substantial costs involved in achieving this goal ( such as operating at another
location), and perfect stability of earnings may not be attained.

The fourth post-loss objective is continued growth of the firm.

firm. A firm may grow by
developing new products and markets or by acquisitions and mergers. The risk manager must
consider the impact that a loss will have on the firm’s ability to grow.

Finally, the goal of social responsibility is to minimize the impact that a loss has on other
persons and on society.
society. A sever loss can adversely affect employees, customers, suppliers,
creditors, taxpayers, and the community in general. For example, a severe loss that requires

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shutting down a plant in a small community for an extended period can lead to depressed
business conditions and substantial unemployment in the community.

2.4 POSSIBLE CONTRIBUTIONS OF RISK MANAGEMENT

Because risk management, as defined in this reading material, is concerned with pure risks, it
may be regarded by some as the true “dismal science.” Pure risks can only hurt a firm or
family, and the purpose of risk management is to minimize the hurt at minimum cost. Upon
closer investigation, however, one discovers that the possible contributions of risk
management to businesses, families, and society are highly significant.

To a Business
The possible contributions of risk management to a business can be divided into five major
categories. The contributions that the risk manager will make in a particular case depend upon
the objectives set for this function (see objectives of risk management) and the extent to
which these objectives are achieved.

First, risk management may make the difference between survival and failure. Some losses,
such as large liability suits or the destruction of a firm's manufacturing facilities, may so
cripple a firm that without proper advance preparation for such event the firm must close its
doors. Even if risk management did not contribute to the economic health of businesses in any
other way, this one benefit would make it a critical function of business management.

Second, because profits can be improved by reducing expenses as well as increasing income,
risk management can contribute directly to business profits (or, in the case of nonprofit
organizations or public agencies, to operating efficiency). For example, risk management may
lower expenses through preventing or reducing accidental losses as the result of certain low-
cost measures, through transferring potential serious losses to others at the lowest transfer fee
possible, through electing to take a chance on small losses unless the transfer fee is a bargain,
and through preparing the firm to meet most economically those losses that it has decided to
retain.

Third, risk management can contribute indirectly to business profits in at least six ways.

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i. If a business has successfully managed its pure risks, the peace of mind and confidence
this creates permits its managers to investigate and assume attractive speculative risks
that they might otherwise seek to avoid. For example, if a firm had to worry about
windstorm damage to its plants and industrial injuries to its employees, it might elect to
limit itself to its present markets. Freed of this worry, it might expand to new markets.

ii. By alerting general managers to the pure-risk aspects of speculative ventures, risk
management 'improves the quality of the decisions regarding such ventures. For
example, a firm that was deciding whether to lease or purchase a building might reach
the wrong decision if it ignored the differing economic impacts of accidental physical
damage to the building.

iii. Once a decision is made to assume a speculative venture, proper handling of the pure-
risk aspects permits the business to handle the speculative risk more wisely and more
efficiently. For example, a business may develop its product lines more aggressively if
it knows that it is adequately protected against suits by persons who may be harmed
accidentally by defective products.

iv. Risk management can reduce the fluctuations in annual profits and cash flows. Keeping
these fluctuations within bounds aids planning and is a desirable goal in itself. Investors
regard more favorably a stable earnings record than an unstable one.

v. Through advance preparations, risk management can in many cases make it possible to
continue operations following a loss, thus retaining customers or suppliers who might
otherwise turn to competitors.

vi. Creditors, customers, and suppliers, all of whom contribute to company profits, prefer
to do business with a firm that has sound protection against pure risks. Employees also
prefer to work for such firms.

Fourth, the peace of mind made possible by sound management of pure risks may itself be a
valuable noneconomic asset because it improves the physical and mental health of the
management and owners.

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Fifth, because the risk management plan may also help others, such as employees, who would
be affected by losses to the firm, risk management can also help satisfy the firm’s sense of
social responsibility or desire for a good public image.

To a family
Risk management can provide families with the same five major classes of benefits. For
example, by protecting the family against catastrophic losses, risk management may enable a
family to continue a lifestyle that might otherwise be severely threatened or disrupted. Indeed
the continued existence of the family unit might be at stake. Second, sound risk management
may enable the family to reduce its expenditures for insurance without reducing its protection.
Because a family cannot deduct insurance premiums from its taxable income, a dollar
reduction in insurance premiums may be worth more than an additional dollar of income.
Third, if a family has adequate protection against the death or poor health of the breadwinner,
damage to or disappearance of their property, or a liability suit, they may be willing to assume
greater risks in equity investments or career commitments. They may also find it easier to
secure a mortgage or personal loan. Fourth, family members are relieved of some physical
and mental strain. Fifth, families may also gain some satisfaction from a risk management
program that helps others as well as themselves or that improves their image.

To the Society
To the extent that individual businesses and families benefit from risk management, so does
the society of which they are members. Society also benefits from the more efficient use risk
management permits of business and family resources and from the reduction in social costs
associated with business and family financial reverses.

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2.5 THE RISK MANAGEMENT PROCESS

Dear student, as you may have noted it in the definitions forwarded to describe risk
management, risk management is the identification, measurement and treatment of property,
liability, and personnel pure-risk exposures. What does the process specifically involve? What
are the sequence of activities to be performed in the risk management process? Do you have
any idea?

The process involves five steps. These are:

i. Identifying loss exposures. The loss exposures of the business or family must be
identified. Risk identification is the first and perhaps the most difficult function that
the risk manager or administrator must perform. Failure to identify all the exposures of
the firm or family means that the risk manager will have no opportunity to deal with
these unknown exposures intelligently.

ii. Measuring the losses. After risk identification, the next important step is the proper
measurement of the losses associated with these exposures. This measurement
includes a determination of (a) the probability or chance that the losses will occur, (b)
the impact the losses would have upon the financial affairs of the firm or family,
should they occur, and (c) the ability to predict the losses that will actually occur
during the budget period. The measurement process is important because it indicates
the exposures that are most serious and consequently most in need of urgent attention.
It also yields information needed in step 3.

iii. Selection of the risk management tools. Once the exposure has been identified and
measured, the various tools of risk management should be considered and a decision
made with respect to the best combination of tools to be used in attacking the problem.
These tools include primarily (a) avoiding the risk, (b) reducing the chance that the
loss will occur or reducing its magnitude if it does occur, (c) transferring the risk to
some other party, and (d) retaining or bearing the risk internally. The third alternative
includes, but is not limited to, the purchase of insurance. Selecting the proper tool or
combination of tools requires considering the present financial position of the firm or

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 family, its overall policy with reference to risk management, and its specific
objectives.

iv. Implementing the decision made. After deciding among the alternative tools of risk
treatment, the risk manager must implement the decision made. If insurance is to be
purchased, for example, establishing proper coverage, obtaining reasonable rates, and
selecting the insurer are part of the implementation process.

v. Evaluating the result. The results of the decisions made and implemented in the first
four steps must be monitored to evaluate the wisdom of those decisions and to
determine whether changing conditions suggest different solutions.

Dear student, this process will be discussed in greater detail in this and the subsequent units.

As is true of management in general, risk management may be described as both an art and a
science. Risk managers must still rely heavily upon nonquantitative techniques that depend
upon deduction and intuitive judgments. Yet certain broad principles of risk management
have been developed. Furthermore, during the recent past, quantitative techniques have
become more commonplace and more sophisticated. These principles and some of the current
developments in scientific risk management will be presented at various points in this reading
material. In time these guides to risk management will be improved and new ones will be
created, but sound judgment will continue to play an important role.

2.5.1 Risk Identification

Dear student, what idea do you have about risk identification? Please write down your
response in your own words in the space provided below.
___________________________________________________________________________
___________________________________________________________________________

Risk identification is the process by which an organization is able to learn areas in which it is
exposed to risk. Identification techniques are designed to develop information on sources of
risk, hazards, risk factors, perils, and exposures to loss. It seems quite logical to inquire in to
the sources of organizational risks at this particular moment. A discussion of the sources is
presented below.

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2.5.1.1 Sources of Risk
Sources of risk are the sources of factors or hazards that may contribute to positive or
negative outcomes. Sources of risk can be classified in several ways. For instance, the
following sources of risk represent one listing:

i. Physical Environment. Clearly, the physical environment is a fundamental source

of risk. Earthquakes, drought, or excessive rainfall can all lead to loss. The ability
to fully understand our environment and the effects we have on it - as well as those
it has on us - is a central aspect of this source of risk. The physical envi ronment
may be the source of opportunity as well, for example, real estate as an investment,
agribusiness, and weather as a contributing factor to tourism.
ii. Social Environment. Changing traditions and values, human behavior, social
structures,
structures, and institutions are a second source of risk.
iii. Political Environment. Within a single country, the political environment can be
an important source of risk. A new party can move the nation into a policy di-
di-
rection that might have dramatic effects on particular organizations (new stringent
regulations on toxic waste disposal). In the international
international realm, the political
environment is even more complex. Not all nations are democratic in their form of
government, and some have very undemocratic attitudes
attitudes and policies toward
business. Foreign assets might be confiscated by a host government or tax policies
might change dramatically. The political environment also can promote positive
opportunities through fiscal and monetary policy, enforcement
enforcement of laws, and the
education of the population.
iv. Legal Environment. the expected laws and directives may be issued by the
government which may render risky environment to the businesses operating in the
country. In the international domain, complexity increases because
because legal standards
can vary dramatically from country to country. The legal environment also
produces positive outcomes in the sense that rights are protected and that the legal
system provides a stabilizing influence on society.
v. Operational Environment.
Environment. Processes and procedures of an organization generate
risk and uncertainty. A formal procedure for promoting, hiring, or firing

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 employees may generate a legal liability. The manufacturing process may put
employees at risk of physical harm. Activities of an organization may result in
harm to the environment. International businesses may suffer from risk or
uncertainty due to unreliable transportation systems. The operational environment
also provides gains, as it is the ultimate source of the goods and services by which
an organization succeeds or fails.
vi. Economic Environment. Although the economic environment often flows
directly from the political realm, the dramatic expansion of the global marketplace
has created an environment that is greater than any single government. Although a
particular government’s actions may affect international capital markets, control
of capital markets is beyond the reach of a single nation. Inflation, recession, and
depression are now elements of interdependent economic systems. On a local
level, interest rates and credit policies can impose significant risk on an
organization.
vii. Cognitive Environment. A risk manager’s ability to understand, see, measure,
and assess is far from perfect. An important source of risk for organizations is the
difference between the perception of the risk manager and reality. The cognitive
environment is a challenging source of risk to identify and analyze. The analyst
must contemplate such questions as “How do we understand the effect of
uncertainty on the organization? and “How do we know whether a perceived risk
is real?” An evaluation of the cognitive environment partly addresses the
distinction between risk and uncertainty as defined in Chapter 1.

2.5.1.2 Identification of Exposures

A given peril or hazard can originate in any one of several environments. Fire, for example,
could arise from the physical environment (a lightning strike) or the social environment
(arson, civil unrest). Sources of risk are essentially of no concern to an organization unless
that organization is exposed or vulnerable to the perils that arise from those environments.
Therefore, an important aspect of risk identification is exposure identification. Although in
the broadest sense an entire organization is at exposure to risk, it is useful to develop
categories of exposures for analytical purposes. This reading material considers four

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categories of risk exposures: physical asset exposures, financial asset exposures, liability
exposures, and human exposures.

i Physical Asset Exposures. Ownership of property gives rise to possible gains

or losses to physical assets and to intangible assets (goodwill, political support, intel-
intel-
lectual property), that arise from these exposures. Property may be damaged, de-
de-
stroyed, lost, or diminished in value in a number of ways. The inability to use property
for a period of time, the so-called time element loss, is often overlooked by individuals
and organizations. Conversely, property exposures to risk may result in gain or
enhancement.
ii Financial Asset Exposures. Ownership of securities such as common stock
and mortgages creates this type of exposure. This exposure can occur either from own-
own-
ership of the security or when the organization issues a security held by others. A
financial asset conveys rights that are enumerated in financial terms, such as the right
to receive income or the right to purchase an asset at a specified price. Unlike physical
property, loss or gain to a financial asset can occur without any physical change in the
asset itself. Often these gains and losses occur as a consequence of changing market
conditions or changes in the value of the rights conveyed by the security as perceived
by investors.
iii Liability Exposures. Obligations imposed by the legal system create this type
of exposure. Civil and criminal law detail obligations carried by citizens; state and
federal legislatures impose statutory limitations on activities; governmental agencies
agencies
promulgate administrative rules and directives that establish standards of care. Legal
obligations that differ from country to country are an increasingly important aspect of
this area.

Unlike property exposures to risk, liability exposures do not have an upside. That is,
liability exposures generally can be considered pure risks. It is true that the law
establishes rights as well as obligations, and the enforcement of a right can result
result in a
gain.

iv Human Asset Exposures. Part of the wealth of an organization arises from its
investment in humans: the human resources of the organization. Possible injury or

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 death of managers, employees, or other significant stakeholders (customers, Secured
Secured
creditors, stockholders, suppliers) exemplifies this type of exposure. Human asset
exposures also can lead to gains, as exemplified by improvements in productivity.
productivity. One
might, for example, view a highly technical piece of machinery as source of loss
(worker injury) and gain (increased productivity). In such a case, the risk management
strategy is likely to incorporate elements that will reduce the potential for loss while
maximizing the likelihood of gain (employee training, for instance). As a final note,
loss of human assets does not always imply physical harm. Economic insecurity is a
common type of loss, unemployment and retirement
retirement being excellent examples. Both
the physical and economic welfare of human beings are components of this type of
exposure to risk.

2.5.1.3 The Range of Risk Identification Techniques

How is risk to be identified? Where would you begin to start the task of identifying risk in a
major factory complex, a shopping center, an airport, a department store chain, a bank? Do
you expect that you would arrive at the premises, assuming always that the actual premises
existed and that we were not concerned with risks at the planning stage, with a clipboard to
begin the task? The world of industry and commerce is far too complex and sophisticated to
allow for proper risk identification
identification simply by a ‘walk round the premises’.

Specific techniques will have to be employed to aid your identification of risk. However, no
one method for risk identification will be appropriate for all forms of risk, or even for similar
forms of risk in different situations. There is a range of techniques
techniques available and these
techniques can be classified
classified in a number of ways.

 Some are best used on site, while others are ‘desk based’ methods not requiring site
visits.
 Some will be more appropriate to the development
development stages of a project, while others are
best used once the project has been commissioned and is up and running.
 There are qualitative techniques which make little or no use of statistical measurement
and others which are highly quantitative in their approach.
approach.
 Certain techniques are very general in their approach
approach to risk, while others are
extremely detailed,
detailed, even microscopic, in their approach.

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  There are techniques, which are very appropriate
appropriate for post-loss situations, while others
are primarily
primarily for use prior to any loss having taken place.

These divisions highlight the variety of techniques, which are available, but in themselves the
divisions
divisions have no practical value. What they do underline
underline is the fact that there are different
ways in which risk can be identified and that techniques do exist to match particular needs. As
we work our way through the techniques, we will suggest the advantages and disadvantages
of each one and where each one could be used.

Organizational Charts
We start the list of risk identification techniques with organizational charts.
charts. These are
intended to highlight broad areas of risk rather than specific, individual risks such as fire,
security or liability. The organizational chart encourages the risk identifier
identifier to take a birds-eye
view of the organization: to stand back and above the day-to-day operation and take stock of
the risks which exist. This term ‘risk
‘risk identifier’ does need some explanation. In many
organizations there will be a risk or insurance
insurance manager employed whose job, in part, will be
the identification of risk. Where no risk manager
manager exists, it may be that the insurance company
performs the risk identification function. In other cases, an insurance broker or consultant may
take on the role of identifying risk. The term risk identifier
identifier is intended to refer to anyone
who has the task of identifying risk.

Most organizations will have charts of some kind or another. Even if they are only in publicity
material,
material, there will be some starting point for building a suitable organizational chart. It is
wise to involve as many people as possible in the construction of the chart, in order to ensure
that it is not unrealistic
unrealistic or over-simplistic in its make-up.

Physical Inspections
The organizational chart took a very broad view of the risks to which an organization could be
exposed.
exposed. The physical inspection of premises, plant or processes takes a different approach.
Everyone understands what is meant by physical inspection, it is possibly the most common
and best understood
understood of all the techniques available.

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The inspection of plant, processes or premises can be a time-consuming job, and the nature of
so many industrial sites is that they are complex. Prior to the actual visit, it is necessary to do
some preparation work so that time is not wasted during the visit itself. This preparatory work
would include finding out exactly what processes were carried out at the premises, the nature
of the service or product manufactured, the nature of the machinery, the physical layout of
the premises and the details from the last physical inspection if there has been one. All of this
information will help and may cut down the time you have to spend on ascertaining
ascertaining basic
information during the visit. The visit should be kept for the identification of risk, not the
finding of information, which was available before the visit.

Checklists
Checklists deal with the particular problem of the time-consuming nature of physical
inspections. The basic idea of the checklist is that a pro-forrna is sent to the site for
completion by someone there. This dispenses with the need for a physical inspec tion and
hence cuts the time and cost of identification.
identification.

The checklist acts as the source of information about risk. It really takes the place of the
personal visit and so it has to be drawn up very carefully. It is wise, when constructing a
checklist for the first time, to consult as widely as possible in order to ensure that all aspects
of risks are taken into account. In particular, the following points are worth keeping in mind:

 The checklist should be simple to understand

 The checklist should be free from ambiguity.
 The checklist should be short
 The checklist should not be threatening

Having given careful thought to the construction of the form, there is one final decision,
which has to be made, and that relates to the style of the checklist. There are various styles in
operation, but for illustration consider the illustration below;

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 FIRE CHECKLIST
Please read the following list and ensure that all the
items are satisfactory. Sign the form and return it
to……………………………..
 Fire doors
 Fire exists
 fire alarms
 Extinguishers
 Stacking of goods
 Removal of waste

This is an extract from a checklist which simply lists a number of points. It is related to the
fire risk and the items which are to be checked all relate in some way to fire. The respondent
has to make sure that all the items have been looked at and that he is satisfied that they are in
order, before returning the form.

Flow charts
We move now to a far more detailed form of risk identification than either the organizational
chart or the checklist, and one which is more specific in its identification than the physical
inspection.

In many organizations there is some kind of flow. This could take the form of:
 Production flow,
flow, where raw materials come in at one end of a process and a finished
product emerges at the other end. There was an identifiable
identifiable flow through the system.
 Service flow, where there may not be raw materials
materials but the business may depend on
flow of another form. It could be the flow of people, as in the case of a restaurant or hotel.
 Money flow, as in the case of a bank or an insurance company. Money comes in at
one end and various promises are made, the effects of which are seen at some later date.

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In each case there are various stages in the flow, and at each stage there are risks which could
impede or halt the flow. Any interruption to the flow will have consequences for revenue and
profit. A flow chart can be used to identify the key stages, and structure the analysis of the
risks at each stage.

The Financial Statement Method

The financial statement method was proposed
proposed by A.H. Criddle (1962). Although this
approach was intended for private organizations,
organizations, the concepts of the financial statement
approach can be generalized in public sector organizations as well. By analyzing the balance
sheet, operating statements, and supporting documents, Criddle maintains, the risk manager
can identify property, liability, and human asset exposures of the organization. By cou pling
these statements with financial forecasts and budgets, the risk manager can discover future
exposures. Financial statements reveal this information because every organizational
transaction ultimately involves either money or property.

Under this method, each account title is studied to determine what potential risks it creates.
The results of the study are reported under the account titles. Criddle
Criddle argues that this approach
is reliable, objective, based on readily available data, presentable in clear, concise terms, and
able to be applied by either risk managers or professional consultants. Moreover, it translates
risk identification into financial terminology familiar to other managers, accountants, and
bankers. Although Criddle
Criddle does not suggest that the financial statement method could be used
to identify both speculative and pure risks, many account titles would be expected to include
both types.

Interactions with Other Departments

Frequent interactions with other departments provide another source of information on
exposures to risk. These interactions may include oral or written reports from other
departments on their own initiative or in response to a regular reporting system that keeps the
risk manager informed of developments. The importance of such a communications network
should not be underestimated. These departments are constantly creating or becoming aware
of exposures that might otherwise escape the risk manager’s attention. Indeed, the risk
manager’s success in risk identification is heavily dependent on the cooperation of other
departments.

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Unfortunately, risk managers often hear about new exposures long after they are created. In
developing interactions with other managers and departments, the risk manager must
overcome the natural reluctance of others to reveal unfavorable information. Most managers
would not be expected to reveal activities that create the potential for unfavorable
developments. A critical task for a risk manager is to persuade others that revealing possibly
unfavorable information is in their own interest. Incentives for revealing this type of
information can be tied to the organization’s system for allocating the cost of losses. For
example, losses arising from unreported activities could result in a penalty when charged
against a manager’s account. To avoid confusion and possible ill will, the existence of such a
penalty should be clearly communicated to managers at the same time they are asked for
information on risk-creating activities.

Interactions with Outside Suppliers and Professional Organizations

In addition to communicating with other departments, the risk manager normally interacts
with outsiders who provide services to the organization. These outsiders, for example, might
include accountants, lawyers, risk management consultants, actuaries or loss-control
specialists. The objective would be to determine whether the outsiders have identified
exposures that otherwise would be missed. Possibly, the outsiders themselves may create new
exposures.

Involvement with professional organizations and use of published material is another valuable
source of information. For example, the annual meeting of the Risk and Insurance
Management Society normally includes sessions focusing on specific problems faced by areas
of industry. In addition, a number of organizations
organizations that focus on specialized areas of risk
management have been formed in response
response to demands of risk managers in these areas.

Contract Analysis
Many of an organization’s exposures to risk arise from contractual
contractual relationships with other
persons and organizations. An examination of these contracts may reveal areas of exposures
that are not evident from the organization’s
organization’s operations and activities. In some cases, contracts
may shift responsibility to other parties.

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Statistical Records of Losses
Where available, statistical records of losses can be used to identify sources of risk. These
records may be available from risk management
management information systems developed by
consultants or, in some cases, the risk manager. These systems allow losses to be analyzed
according to cause, location, amount, and other issues of interest.

Statistical records allow the risk manager to assess trends in the organization’s loss experience
and to compare the organization’s loss experience with the experience
experience of others. In addition,
these records enable the risk manager to analyze issues such as the cause, time, and location
of the accident, to identify the injured individual
individual and the supervisor, and any hazards or other
special factors affecting the nature of the accident. Common patterns or frequently appearing
sets of circumstances
circumstances point toward issues requiring special attention. For example, if ladders
appear
appear frequently as a cause of accidents, the organization’s risk manager is well advised
advised to
investigate ladders and their use and possibly set up a training program on safe practices.

When a significant amount of data on past losses is available, the risk manager may use this
information to develop forecasts of loss costs. These forecasts may be developed through
trending or loss development. Forecasts obtained using loss development are extremely useful
in budgeting for programs in which an organization directly pays costs using its own funds
(i.e., a self-insurance program). An organization that uses its own funds to pay the cost of
work-related injuries or to provide health benefits to its own employees has a vital interest in
projecting costs of the program.

Incident Reports
A network of information sources can be very useful in identifying
identifying possible losses. Ideally,
the information provided through this network should include not only reports of accidents
and near accidents, but also reports of incidents that could have resulted in injury or damage
but presumably did not. Frequently, good fortune and luck allow a person to escape without
injury from an incident that posed a serious threat. Information on these events is useful in
preventing injury or damage if the circumstances are repeated, but only if the risk manager is
aware of the potential problem.

39
A system for reporting of incidents usually includes a form for recording important
information. In addition to date, time, location and identity of parties involved in the incident,
the form should request information that later could prove helpful in preventing similar
occurrences or mitigating the injury or damage if it occurs. In designing the form, a risk
manager should recognize that a long period of time may elapse between the recording of the
information and its incorporation into an injury-prevention program. As an example, some
areas of regulation require employers to keep records of employee exposure to hazardous
materials for 30 years beyond the period of employment. The records offer evidence on the
degree of care exercised by the employer, but only to the extent that information is complete
and specific.

Comments appearing earlier in the section entitled “Interactions with other Departments” are
especially applicable to incident-reporting systems. Essentially, a risk manager is asking
others to reveal information that reflects unfavorably on their housekeeping practices. For
example, a risk manager of a hospital who is concerned about the organization’s exposure to
medical liability is requesting hospital employees to report mistakes such as incorrect
administration of drugs that might reflect unfavorably on their own careers and reputation.
Earning the trust of employees that the information will be used fairly removes an obstacle to
the manager’s gaining their cooperation in this effort.

2.5.1.4 Common Features of Risk Identification

We have looked at a number of individual techniques
techniques and it is now necessary to say
something of a more general nature about the task of risk identification,
identification, regardless of the
technique selected. We can do this by commenting on a number of common
common features of risk
identification.

 The task of risk identification must be given the proper priority in an organization. It’s
an important
important function, as many of the risks which are to be identified can put their way
into the very core of the existence of the organization itself.
 There is a range of techniques available and no one technique can be used in all
situations. As we have dealt with each technique, we have commented on the relevant
uses to which it can be put. Thought must be given to the na ture of each risk and the
best technique, or combination
combination of techniques, selected.

40
  The task of risk identification is a continuing one: the one-off exercise is of little value
in many practical cases. The nature of industry is such that it is constantly changing
and it is therefore essential that risk identification takes place at regular intervals.
 Efficient record keeping is an important part of identification of risk. A great deal of
valuable information is obtained at the time of risk identification,
identification, and this should be
stored carefully for later use and referral.
 Other people, in addition to the risk identifier, should be involved in the process of
risk identification
identification whenever possible. Organizations are complex and no one person
will have all the knowledge which will be required to enable risks to be identified.
 The cost of risk identification must be remembered.
remembered. There is little point in spending
Br.10 to identify risks which in the worst case can only ever cost Br. 1. Identifying
risk is important, but it costs money and this cannot be overlooked.
overlooked.
 Finally, a measure of common sense and imagination
imagination are valuable attributes to have
when flying
flying to identify risk.

2.5.2 Risk Measurement

Once the risk manager has identified the risks that the firm is facing, his next step would be
the evaluation and measurement of the risks. Risk measurement refers to the measurement of
the potential loss as to its size and the probability of occurrence.

The risk manager, by using available data from past experience, tries to construct a
probability distribution of the number of events and/or the probability distribution of total
monetary losses. This would, indeed, require knowledge of certain statistical techniques and
concepts. The probability distribution of number of events and/or total monetary losses
would enable the risk manager to estimate, among other things, the size of possible monetary
losses and the corresponding probabilities of occurrence.

The following example is considered for illustrative purpose. The data presented below
represents the number of cars operated (similar in type of use) by a firm in each year, the
corresponding number of accidents occurred and the total monetary losses incurred in
connection with the accidents.

41
 Number of
Year Number of cars Amount of loss
Accidents

1 10 1 Birr 2500
2 12 2 4200
3 14 3 4500
4 15 3 6000
5 20 2 6500
6 20 3 6600
7 25 4 6000
8 25 5 8000
9 29 3 7500
10 30 4 10000

SUM 200 30 61800

MEAN 20 3 6180
STA. DEV. 1.15 2115

Probability of Accident = 3/20 = 0.15

Monetary loss per accident over 10 years = 6180/3 = 2060

Suppose in year 11 the number of cars owned by the firm increased to 40. The risk manager
wants to construct a probability distribution of accidents on the basis of the data collected
above.

2.5.2.1 Poisson Distribution

The Poisson probability distribution can be used for the analysis. The only information that is
crucial in constructing a Poisson probability distribution is the expected number of accidents
(the mean). Once the mean is determined the probability of any number of accidents will be
easily calculated using the following formula:

42
 p (r) = M r . e –M
r!
Where e = 2.71828
r = number of occurrences
M = Expected number of Accidents = (pn)
STD = Standard Deviation = SQRT (M)
n = number of Exposed Units = 40
SQRT=Square-root
Accordingly,
M = pn = 0.15 * 40 = 6 accidents
STD = SQRT(M) = 2.45

The Poisson probability distribution allows for unlimited number of accidents occurring to the
object under consideration, (car). This means that a particular car can possibly experience
more than one accident. This is normally the case in real life situation.
Using the Poisson process, the following probability distribution is constructed.

Number of Amount Probability Expected Expected

Accident Loss* number of amount of
accidents loss**
0 0 0.0025 0 0
1 2060 0.0149 0.0149 30.69
2 4120 0.0445 0.0892 183.26
3 6180 0.0892 0.2676 551.26
4 8240 0.1339 0.5356 1103.34
5 10300 0.1606 0.8030 1654.18
6 12360 0.1606 0.9636 1985.02
7 14420 0.1377 0.9639 1985.63
8 16480 0.1033 0.8264 1702.38
9 18540 0.0688 0.6192 1275.55
10 20600 0.0413 0.4130 850.78
11 22660 0.0225 0.2475 509.85
12 24720 0.0113 0.1356 279.34
13 26780 0.0052 0.0675 139.26
14 28840 0.0022. 0.0308 63.45
15 30900 0.0009 0.0135 27.81
16 32960 0.0003 0.0048 9.89
17 35020 0.0001 0.0017 3.50
18 37080 0.0001 0.0018 3.71
SUM 1.0000 5.9997 12359.39

43
 * Number of accidents multiplied by the loss per accident.

** Amount of loss multiplied by the probability.

Once the probability distribution is developed, it would not be difficult, to determine the
probability of any number of accidents that are likely to occur. Let r represent the number of
accidents,

p(r > = 3) = 1 - (.0025+.0149+.0445)

= 0.9381

This is the probability that there would be at least three accidents in the year. Similarly, the
probability that the number of accidents equal or exceed 13 is given by:

p(r > = 13) = .0052+.0022+.0009+.0003+.0001+.0001

= 0.0088

Accordingly,

p(3 < = r < 13) = 0.9381-0.0088

= 0.9293
This indicates that the risk manager's expectation of accidents is heavily concentrated between
3 and 13 accidents.

The expected annual total monetary loss is Birr 12359.39 as determined on the table above.
The expected dollar loss per accident is obtained by dividing the expected annual total
monetary loss by the expected number of accidents.

Expected Monetary Loss per Accident = 12359.39

6

= 2059.90
The calculation of standard deviation of total monetary loss is presented below. The standard
deviation is 5046,40. From earlier analysis the following measures were obtained:

P = 0.15
n = 40

44
Expected Number of Accidents = M = np =0 .15*40 = 6
SD of Accidents = SD = SQRT (M) = SQRT(6) = 2.4495
Expected Annual Total Monetary Loss = 12359.9
Standard Deviation of Annual Monetary Loss = SD of accidents x loss per accident
= 2.45 x 2059.90
= 5046.7

Risk Relative to the Mean (Coefficient of Variation) or RM

RM = SD of Loss/expected loss

= 5046.4/12359.9

= 0 . 408

Or

RM = SD of accidents/expected number of accident

= 2.45/6

= 0.408
RM 0.408 indicates the variability of total annual monetary losses from the expected value,
(the mean). The higher the Coefficient of Variation (RM), the higher the risk, meaning
variability increases. In this example total annual monetary losses could deviate 40.8% from
the mean in either direction. For example the range, for 1 standard deviation is Birr 7314 to
Birr 17406. On the table above, this range is approximated by Birr 6180 to Birr 18540. The
probability that total annual monetary loss falls in this range is 0.8542, which is obtained by
adding all the probabilities in the range. In terms of number of accidents, the risk manager
expected to observe 3 to 9 accidents about 85.42 percent of the time.

Number of Monetary Deviation Deviation DS times

accidents loss Mean from mean squared Probability probability
0 0 12360 -12360 152769600 0.0025 381924
1 2060 12360 -10300 106090000 0.0149 1580741
2 4120 12360 -8240 67897600 0.0446 3028233
3 6180 12360 -6180 38192400 0.0893 3410581
4 8240 12360 -4120 16974400 0.1339 2272872
5 10300 12360 -2060 4243600 0.1603 680249.1

45
 6 12360 12360 0 0 0.1606 0
7 14420 12360 2060 4243600 0.1377 584343.7
8 16480 12360 4120 16974400 0.1033 1753456
9 18540 12360 6180 38192400 0.0688 2627637
10 20600 12360 8240 67897600 0.0413 2804171
11 22660 12360 10300 106090000 0.0225 2387025
12 24720 12360 12360 152769600 0.0113 1726296
13 26780 12360 14420 207936400 0.0052 1081269
14 28840 12360 16480 271590400 0.0022 597498.9
15 30900 12360 18540 343731600 0.0009 309358.4
16 32960 12360 20600 424360000 0.0003 127308
17 35020 12360 22660 513475600 0.0001 51347.56
18 37080 12360 24720 611078400 0.0001 61107.84
SUM 25465419
Standard deviation = SQRT (25465419) = 5046.4
Risk measures:
Risk relative Mean, (R M) = 5046.4/12359.9 = 0.408

The standard deviation of total annual monetary loss can also be determined as follows:
SD of Accidents x expected monetary loss per Accidents
2.44949 x 2060 = 5046

Risk Relative to the number of Exposure Units or Rn

Rn = SD of accidents/number of items exposed to risk

= 2.24495/40 = 0.061
R n indicates the deviation from the expected outcome as a percentage of the total number of
exposure units. Accordingly, given one standard deviation, the actual accidents could vary
from the expected accidents by about 6.1% of the total number of exposure units. The higher
the percentage, the higher the variability(higher variance), and consequently, the higher the
risk.

POSSIBLE DECISIONS
Self-Insurance

1. To keep reserve fund equal to the expected total annual monetary loss

Reserve Fund = Birr 12,360

2. To keep reserve fund equal to the expected value of the loss plus an amount to cover for
one standard deviation of the expected value.

46
 Reserve Fund = 12,360+ 5,046 = Birr 17,406

3. To keep reserve fund equal to the maximum probable loss (ignoring losses with a
probability of occurrence less than 1%)

Reserve Fund -= Birr 24720

RISK AND LOW OF LARGE NUMBERS

Suppose the exposure units are to be increased to 50, (n=50)

Mean Number of Accidents = M = 0 .15*50 = 7.5

SD of Accidents = 3D = SQRT (7.5) = 2.7386

RM = 2.73S6/7.5 = 0.365
Rn = 2.7386/50 = 0.054772
It is possible to simulate this process to see how risk decreases as the number of exposure
units increase. Here is the summary.

n M Sd RM Rn
40 6 2.4495 .408 .06124
50 7.5 2.7386 .365 .05478
100 15 3.8730 .258 .03873

The mean (M) increases proportionately while RM and Rn decrease less than proportionately.

2.5.2.2 Binomial Probability Distribution

The Risk Manager may also use the Binomial probability distribution to measure risk. To use
the Binomial distribution the Risk Manager must be familiar with the basic assumptions of the
distribution to avoid misleading results. The first assumption is that the objects are
independently exposed to loss. The other assumption is that each exposed unit suffers only
one loss in a year. With this assumption in mind, the following illustrative example is
considered. A fleet of 5 delivery trucks are operated by a business. If an accident happens to
a particular track, it becomes a total loss. New trucks are purchased at the beginning of every
year to make up the lost ones so that the firm always starts the new fiscal period with a fleet
of 5 delivery tracks.

47
First it is assumed that monetary loss per accident is constant at Birr 5000.

Number of NUMBER OF Total Monetary

Year Trucks ACCIDENTS Loss

1 5 2 Birr 10000
2 5 2 10000
3 5 3 15000
4 5 2 10000
5 5 1 5000
SUM 25 10 50000
MEAN 5 2 10000
SD .707 3162.27
Monetary loss per accident = 10000/2 = 5000

The probability of an accident can be estimated as:

p = 2/5 = .4
With this information as a point of departure it would be possible to construct a binomial
probability distribution for the following variables of interest:

1. Probability distribution of Number of accidents

2. Probability distribution of Total monetary losses

1. PROBABILITY DISTRIBUTION NUMBER OF ACCIDENTS

Under the binomial probability distribution the probability of observing exactly r occurrences
is given by:

P (r) = n!(Pr . q (n-r) )

[n – r]!

Where: p is the probability of accident

q is 1 –p
n is the number of items exposed to risk

Using this formula the following probability distribution is constructed.

48
 Number of Probability Expected No. of
Accidents Accidents
0 0.07776 0
1 0.25920 0.2592
2 0.34560 0.6912
3 0.23040 0.6912
4 0.07680 0.3072
5 0.01024 0.0512
SUM 1.00000 2.0000
The expected number of accidents is 2. The standard deviation can be determined in the usual
manner, which turns out to be 1.095.

The probability that the firm will face some accident is 0.92224, (1-0.07776). This probability
is so high that the risk manager should take appropriate measures to handle the risk.

FORMULA FOR MEAN AND SD OF A BINOMIAL DISTRIBUTION

The mean and the standard deviation of a binomial probability distribution can also be
determined using the following formula;

Mean = M = np
SD = SD = SQRT(npq)

Accordingly,

M = 5*0.4 =2
SD = SQRT(5*0.4*0 .6) = 1.095

RISK MEASURES

Risk Relative to Mean, (coefficient of variation)

RM = 1.095/2 = .5475

Risk relative to the number of exposure units

Rn = 1.095/5 = 0.219

RISK VS LAW OF LARGE NUMBERS

49
Risk relative to the mean

RM = (np(l-p))1/2
np

R2M = np(l-p)

R2M = np(l-p)

n2 P2

R2M = (1-p)
np

R2M = ((l-p)/np)'/2 RM decreases as n increases

Risk relative to the number of Exposure units

Rn = (np (1-p)1/2
n
R2 = np(l-p) = p(l-p)
n2 n

Rn = (p (l-p)/n)1/2 Rn decreases as n increases

To illustrate the situation suppose the exposure units are to be increased to 20, (n = 20),

M = np = 20*0.4 = 8

SD = SQRT(np(l-p) ) = SQRT(20*0.4*0.6) =2.19

Then,
Rm = SD/M = 2.19/8 = 0.27375
Rn = SD/n = 2.19/20 = 0.1095

50
Increasing the number of exposure units to 100 will give the values for Rm and Rn as shown
on the table below.
n M SD RM Rn
5 2 1.095 0.54750 0.21900
20 8 2.190 0.23735 0.10950
25 10 2.449 0.2449 0.09796
50 20 3.464 0.1732 0.06928
100 40 4.899 0.12247 0.04899

The risk does not decrease in proportion to the increase in the number of exposure units.
Consider also the following example.

P= 0.4
n1= 25
n2 = 50

Rn 1 = (n 1 p (1-p)1/2
n1
Rn 2 = (n 2 p (1-p)1/2
n2
Rn 2/ Rn 1 = (n 2 p (1-p)1/2 / n 2 = (n 2 p (1-p)1/2 n 1
(n 1 p (1-p)1/2/n 1 (n 1 p (1-p)1/2 n 2

R 2 n 2/ R 2 n 1 = n 1/n 2

R 2n 2 = R 2 n 1 (n 1/n 2)

Rn 2 = R n 1 (n 1/n 2) 1/2

Rn 2 = Rn 1

(n 2/n 1) 1/2

OTHER PROPERTIES

n = 5
Mean = np
SD = SQRT(np(1-p))

51
 1. Suppose p = 0
SD = SQRT(5*0*1) = 0

Risk relative to the number of exposure units

Rn = 0/5 = 0

*Risk is zero when p = 0; meaning it is certain that the event will not happen.
2. Suppose p = 0.5
SD = SQRT (5*.5*.5) = 1.118
Rn = 1.118/5 = 0.2236

Relative risk to the number of exposure units reaches its maximum when p = 0.5 (binomial
distribution). Conversely, risk relative to the mean reaches its maximum when p approaches
zero.

2. PROBABILITY DISTRIBUTION OF TOTAL MONETARY LOSSES

The binomial probability distribution of total monetary losses is constructed as follows:

Number of Monetary Probability Expected

Accidents Loss Monetary Loss
0 0 0.07776 0
1 5000 0.25920 1296
2 10000 0.34560 3456
3 15000 0.23040 3456
4 20000 0.07680 1536
5 25000 0.01024 256
SUM 1.000 10000

The expected total annual monetary loss is Birr 10000. The standard deviation of total annual
monetary loss is calculated as follows:

SD of number of Accidents x expected monetary loss per accident

1.095 x 5000 = 5475

Risk relative to the mean monetary loss will then become:

RM = 5475/10000 = 0.5475
Risk relative to the maximum possible loss is:

52
 Rn = 5475/25000 = 0.219

The next example reflects a situation where the amount of loss per accident is not constant.
Here, the loss per accident is assumed to be either Birr 5000 or Birr 10000. As a result there
will now be two probability distribution of monetary loss per accident. The following data is
collected for the analysis.

Year Number of Number of Amount of Loss*

Trucks Accidents
1 5 2 Birr 10000 each
2 5 2 5000 each
3 5 3 5000 each
4 5 2 10000 each
5 5 1 5000 each
SUM 25 10 70000
Mean 5 2 14000
SD 0.707 6519
* Loss per accident is either Birr 5000 or Birr 10000.

The probability of an accident is estimated to be 0.4 (2/5). The probability distribution of

monetary loss per accident is constructed as follows:

Loss per Frequency Relative

Accident Frequency
5000 6 0.6
10000 4 0.4
10 1.0
The probability that an accident will entail a loss of Birr 5000 is 0.6. similarly, the probability
that an accident entails a cost of Br. 10000 is 0.4.

The mean monetary loss per accident is Birr 7000; and the variance of monetary loss per
accident is 6000000, 0.6 (5000 – 7000)2 + 0.4 (10000 – 7000) 2. Accordingly, the standard
deviation of monetary loss per accident will be the square root of 6000000, which is 2449.49.

Constructing the Probability Distribution of Total Monetary Losses

The table presented on the next page shows the summary of the construction process.

53
 Loss Amount Probability Expected Loss
0 0.07776 0
5000 0.15552 777.60
10000 0.22810 2281.00
15000 0.21565 3234.75
20000 0.16478 3295.60
25000 0.09370 2342.50
30000 0.04393 1317.90
35000 0.01534 536.90
40000 0.00433 173.20
45000 0.00079 35.55
50000 0.00010 5.00
1.00000 14000.00

Minimum loss = 0
Expected total monetary loss = 14000.00
Maximum possible total loss = 50000.00
Maximum probable total loss(Assuming that losses with
Probability less than 1% are ignored) = 35000.00

The probability that the fire will face some monetary loss is 0.92224 (1 – 0.07776). the
probability that monetary loss equals or exceeds Birr 10000 is 0.76672 , ( 1 – (0.07776 +
0.15552)).

One measure of risk could be to express the expected annual total monetary loss as a
percentage of the maximum possible loss. This is equal to 28% (14000/50000). It could be
used as a rough measure of loss severity. One way of determining the standard deviation of
total annual monetary losses. The expected monetary loss per accident is Birr 7000,
(14000/2). Earlier the standard deviation of monetary loss per accidents was found to be
2449.49. Consequently, the standard deviation of total annual monetary loss is calculated
using the following formula:

Let:
(ENA) = Expected Number of Accidents in a Year
VA = Variance of the Number of Accidents in a Year.

54
(EMA) = Expected Monetary Loss per Accident
SDM = the Standard Deviation of Monetary Loss per Accident.

SD of Total Annual
Monetary Losses = SQRT ((VA * E (MA) 2 + (SDM) 2 * E (NA))
= SQRT ((1.2) (7000) 2 + (2449.49) 2 (2))
= SQRT (58800000 + 12000000)
= 8414.27

2.5.2.3 Normal Distribution

The risk Manager may assume that the number of accidents or total annual monetary losses
are approximately normally distributed. Under such circumstances, he may use the Normal
distribution in measuring the number of accidents or the total annual monetary losses.

If observations are normally distributed, the Risk Manager will have a good insight of the size
of possible losses at much grater ease. This is because the normal distribution can be well
explained by identifying only two parameters, the mean and the standard deviation.

For illustrative purpose let us consider the example under the binomial distribution with a slight change.
Year Number of Total Monetary
Accidents Loss
1 2 Birr 10000
2 2 10000
3 3 15000
4 2 10000
5 2 10000
SUM 55000
MEAN 11000
SD 2000

The Normal distribution has the following properties:

 68.27
68.27%
% of the observations fall within the range of one standard deviation of the
mean.
 95.45 % of the observations fall within the range of two standard deviation of the
mean.

55
  99.73% of the observations fall within the range of three standard deviations of the
mean.
The implication of this for the Risk Manager, in the case of monetary losses, is that he would,
construct the following interval estimation about the true mean monetary loss.

The true mean monetary loss is expected to fall in the range of Birr 9000 and Birr 13000 with
a probability of 0.6827.

The true mean monetary loss is expected to fall in the ranges of Birr 7000 and Birr 15000
with a probability of 0.9545.

The true mean monetary loss is expected to fall in the range of Birr 5000 and Birr 17000 with
a probability of 0.9973.

DETERMINING THE SIZE OF EXPOSURE UNITS

Consider a Binomial probability distribution with p = 0.4 and n = 10.
Expected Number of Accidents = Mean = .4 * 10 = 4
Standard Deviation = SQRT( 10*.4*.
10*.4*.6)
6) = 1.55

RM = 1.55/4 = 0.3875

Now, suppose the Risk Manager (given p = .4) wants to have RM of 20%; and to achieve this
level of variation he wants, to know the number of exposure units, (n).

Mean = np = .4n

SD = SQRT (npq) = SQRT (n*.4*.6)

(n*.4*.6) = SQRT (.24n)

R M = (.24n)1/2 , 0.20 = ( .24n)1/2

.4n .4n

56
 .24n - .0064n2 = 0

n = 37.5

FORMULA

RM = Z (np(1-p))1/2 , Z = confidence level in number of standard

deviations.
np

RM = Z (np(l-p))1/2

R 2 M n2p2 = Z2 np(l-p)
n = Z2p(l-p)
R 2 M p2

n = Z2 (1-p)
R 2M P

Risk Relative to the Number of Exposure Units:

Rn = 1.55/10 = 0. 155

Suppose the risk manager wants to have Rn of 10% with a probability of 0.6827.
What should be the number of exposure units to satisfy the requirement?

0.10 = (np(1-p) 1/2

n

0.10n = (.24n)1/2

0.01n2 - .24n = 0

n = 24

When n = 24, SD = (0.4* 0. 6*24) 1/2, which is 2.4.

Consequently,

Rn = 2.4/24 = .10

Rn = Z (np(l-p))1/2
n

57
Rnn = Z (np(1-p))1/2
R n 2 n 2= Z (np(1-p)) , (divide both sides by n)
R n2 n = Z p(1-p))
n = Z p(1-p))
R n2

2.6 TOOLS OF RISK MANAGEMENT

After the risk manager has identified and measured the risks facing the firm, he or she must
decide to handle them. There are two basic approaches. First, the risk manger can use risk
control measures to alter the exposures in such a way as (1) to reduce the firm’s expected
property, liability, and personnel losses, or (2) to make the annual loss experience more
predictable. Risk control measures includes avoidance, loss prevention and reduction
measures, separation, combination, & some transfers.

Second, the risk manger can use risk-financing measures to finance the losses that do occur.
Funds may be required to repair or restore damaged property, to settle liability claims, or to
replace the services of disabled or deceased employees or owners. In some, the firm will
decide not to restore the damaged property or replace the disabled or decreased person.
Nevertheless, it may also have suffered a financial loss through a reduction in its assets or its
future earning power. The tools in this second category include those transfers, including the
purchase of insurance, that are not considered under risk control devices and retention, which
includes, “self insurance”.

2.6.1 Risk Control Tools

i. Avoidance
One way to control a particular pure risk is to avoid the property, person, or activity with
which the exposure is associated by (1) refusing to assume it even momentarily or (2) an
exposure assumed earlier, most examples of risk avoidance fall in the risk category. To
illustrate a firm can avoid a flood loss by not building a plant in a flood plain. An existing loss

58
exposure may also be abandoned. For example, a firm that produces a highly toxic product
may stop manufacturing that product. Similarly, an individual can avoid third party liability
by not owning a car. Product liability can be avoided by dropping the product. Leasing avoids
the risk originating from property ownership.

The major advantage of avoidance is that the chance of loss is reduced to zero if the loss
exposure is not acquired. In addition, if an existing loss exposure is abandoned, the possibility
of loss is either eliminated or reduced because the activity or product that could produce a loss
has been abandoned.

Avoidance, however, has two disadvantages. First, it may not be possible to avoid all losses.
For example, a company cannot avoid the premature death of a key executive. Similarly, a
business has to own vehicles, building, machinery, inventory, etc… Without them operations
would become impossible. Under such circumstances avoidance is impossible. In fact there
are circumstances where avoidance is a viable alternative. For example, it may be better to
avoid the construction of a company near river bank, volcano-prone areas, valleys, etc.
because the risk is so great.

The second disadvantage of avoidance is that it may not be practical or feasible to avoid the
exposure. For example, a paint factory can avoid losses arising from the production of paint.
However, without any paint production, the firm will not be in business.

ii. Loss Prevention and Reduction Measures

These measures refer to the safety actions taken by the firm to prevent the occurrence of a loss
or reduce its severity if the loss has already occurred. Prevention measures, in some cases,
eliminate the loss totally although their major effect is to reduce the probability of loss
substantially. Loss reduction measures try to minimize the severity of the loss once the peril
happened. For example, auto accidents can be prevented or reduced by having good roads,
better lights and sound traffic regulation and control, fast first-aid service and control, fast
first-aid service and the like. Loss prevention and Retention measures must be considered
before the Risk manager considers the application of any risk financing measures.

Following are some examples of loss prevention and reduction plans.

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Loss Prevention Measures:

 Research on fire protection equipment and appliances.

 Construction using fire insensitive materials.
 Automatic smoke detectors, fire alarms.

 Burglar alarms in costly business situation, jewelry, diamonds.

 Locational choice, avoiding construction near petrol stations, chemical reservoirs,

waste disposal areas, etc.

 Tight quality control to prevent risk of product liability.

 Educational programs to the public using available media.

 Multiple suppliers, buffer stocks.

 Safety measures, adequate lighting, ventilation, special work clothes to prevent

industrial accidents.

 Regular inspection of machinery to prevent explosions, breakdowns, etc..

 Accounting controls (Internal Control).

 Electronic metal detectors to check passengers for arms and explosives in the airline
business.

 Automatic gates at crossing lines to prevent collisions train and motor vehicles.

 Warning posters (NO SMOKING!! DANGER ZONE!!)

Loss Reduction Measures:

 Installing automatic sprinklers.

 First aid kit

 Evacuation of people, CHERNOBYL

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  Immediate clean-up operations, EXXON – VALDEZ, Alaska oil spill

 Fire extinguishers, guards.

Appropriate measures take to prevent accidents bring benefits not only to the firm, but also to
the society as well. For example, a destruction of inventory of a firm, could be a total loss to
the firm in particular. The society also faces a real economic loss because those goods are no
more available to people. Thus, the importance of Loss Prevention and Reduction measures
should not be underestimated by a firm. To design effective LP and R measures, it may be
helpful to identify the causes of accidents.

Some of the causes of accident and the possible Loss Prevention and Reduction measures are
indicated below.

Causes of accidents Loss prevention measures

- Working on dangerous equipment with less care - Safety seminars, inspection at regular times
- Improper use of equipment - Training, safety seminars
- Violating Safety Procedures and Regulations. - Safety seminars, warning, dismissal
- Human error, Negligence - Training, safety seminars
- Use of inappropriate tools - Provide appropriate tools
- Lack of protective clothing - Provide necessary protective clothing
- Use of defective equipment - Regular inspection and maintenance
- Inadequate Knowledge about the job Training
- Working while physically ill - Sick leave, don’t allow to work until recovery
- Mental Disturbance of employee Day-off to the employee

Date should be kept regarding accidents occurred. The causes of these accidents must be
investigated. Pre-designed forms may be employed to report on accidents and their causes.
This could allow for the design of a much better LP and R measures.

LP and R measures entail costs. These costs include expenditures for the acquisition of safety
equipment and services, operating expenses such as salary payments to guards, inspectors,
safety engineers and other employees engaged in safety work. Other costs are also incurred in
connection with safety training and seminars. The risk manager will have to design the LP
and R measures in the most efficient way in order to minimize such costs without reducing
the desired safety level.

iii. Separation

61
Separation of the firm’s exposures to loss instead of concentrating them at one location where
they might all be involved in the same loss is the third risk control tool. For example, instead
of placing its entire inventory in one warehouse the firm may elect to separate this exposure
by placing equal parts of the inventory in ten widely separated warehouse. To the extent that
this separation of exposures reduces the maximum probable loss to one event, it may be
regarded as a form of loss reduction. Emphasis is placed here, however, on the fact that
through this separation the firm increases the number of independent exposure units under its
control. Other things being equal, because of the law of large number, this increase reduces
the risk, thus improving the firm’s ability to predict what its loss experience will be.

iv. Combination/Diversification
Combination is a basic principle of insurance that follows the low of large numbers.
Combination increases the number of exposure units since it is a pooling process. It reduces
risk by making loses more predictable with a higher degree of accuracy. The difference is that
unlike separation, which spreads a specified number of exposure units, combination increases
the number of exposure units under the control of the firm.

In the case of firms, combination results in the pooling of resources of two or more firms. One
way a firm can combine risks is to expand through internal growth. For example, a taxi-cab
company may increase its fleet of automobiles. Combination also occurs when two firms
merge or one acquires another. The new firm has more buildings, more automobiles, and
more employees than either of the original companies. This leads to financial strength,
thereby minimizing the adverse effect of the potential loss. For example, a merger in the same
or different lines of business increases the available resources to meet the probable loss.

Diversification is another risk handling tool, most speculative risk in business can be dealt
with diversification. Businesses diversify their product lines so that a decline in profit of one
product could be compensated by profits form others. For example farmers diversify their
products by growing different crops on their land. Diversification however, has limited use in
dealing with pure losses.

VI. Non-insurance Transfer

Transfer, the final tools to be discussed, may be accomplished in two ways. These are:

62
  Transfer of the activity or the property. The property or activity responsible for the
risks may be transferred to some other person or group of persons. For example, a firm
that sells one of its buildings transfers the risks associated with ownership of the
building to the new owner. A contractor who is concerned about possible increase in
the cost of labor and materials needed for the electrical work on a job to which he/she
is already committed can transfer the risk by hiring a subcontractor for this portion of
the project.

This type of transfer, which is closely related to avoidance through abandonment, is a

risk control measure because it eliminates a potential loss that may strike the firm. It
differs from avoidance through abandonment in that to transfer a risk the firm must
pass it to someone else.

 Transfer of the probable loss. The risk, but not the property or activity, may be
transferred. For example, under a lease, the tenant may be able to shift to the landlord
any responsibility the tenant may have for damage to the landlord’s premises caused
by the tenant’s negligence. A manufacture may be able to force a retailer to assume
responsibility for any damage to products that occurs after the products leave the
manufacturer’s premises even if the manufacturer would otherwise be responsible. A
business may be able to convince a customer to give up any rights the customers might
have to give the business for bodily injuries and property damage sustained because of
defects in a product or a service.

2.6.2 Risk Financing Tools

i. Retention
Retention means that the firm retains part or all of the losses that result from a given loss
exposure. Retention can be effectively used in a risk management program when certain
conditions exist. First, no other method of treatment is available. Insurers may be unwilling to
write a certain type of coverage, or the coverage may be too expensive. Noninsurance
transfers may not be available. Loss control can reduce the frequency of loss, but not all

63
losses can be eliminated. In these cases, retention is a residual method. If the exposure cannot
be insured or transferred, then it must be retained.

Second, the worst possible loss is not serious. For example, physical damage losses to
automobiles in a large firm's fleet will not bankrupt the firm if the automobiles are separated
by wide distances and are not likely to be simultaneously damaged.

Finally, losses are highly predictable. Retention can be effectively used for workers'
compensation claims, physical damage losses to automobiles, and shoplifting losses. Based on
past experience, the risk manager can estimate a probable range of frequency and severity of
actual losses. If most losses fall within that range, they can be budgeted out of the firm's
income.

ii. Insurance

Commercial insurance can also be used in a risk management program. Insurance can be
advantageously used for the treatment of loss exposures that have a low probability of loss but
the severity of a potential loss is high.

If the risk manager decides to use insurance to treat certain loss exposures, five key areas
must be emphasized.

- Selection of insurance coverage’s

- Selection of an insurer

- Negotiation of terms

- Dissemination of information concerning insurance

coverage

- Periodic review of the insurance programs

2.7 SELECTION OF RISK MANAGEMENT TOOLS: QUANTITATIVE APPROACHES

This section discusses some quantitative approaches that may be used in selecting risk
management tools. Two models are discussed:
discussed: Expected Utility Models and The Worry
Factor Model.

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2.7.1 Expected Utility Model
The expected utility model places emphasis on the risk manager’s attitude towards risk. This
means that the model takes into account differences in risk attitude of risk managers. Risk
managers are likely to assign varying utility points to a given monetary loss. As a result their
decisions as to which of the risk management tools to select for a particular situation is likely
to differ. Under this model, therefore, the risk manager is making a decision on the basis of
expected loss of utility.

To illustrate the model, consider the example under binomial distribution where we have a
constant monetary loss per accident, Birr 5000. The probability distribution was as follows:
Number of Monetary Probability
Accidents Loss
0 0 0.07776
1 5000 0.25920
2 10000 0.34560
3 15000 0.23040
4 20000 0.07680
5 25000 0.01024

DERIVATION OF THE UTILITY FUNCTION

1. a. assign an arbitrary utility index of 1 to the maximum possible loss.
U (L max) = U(25000) = 1.00
b. assign an arbitrary utility index of zero to the minimum loss.
U(L min) = U(0) = 0
2. Ask the person how much he would be willing to pay in order to transfer the risk in which
he faces a 50 –50 chance of losing the maximum loss (Birr 25000) or nothing. The amount
the person is willing to pay to transfer the risk will have the following utility value:
U(T 1) = 0.5(1) + 0.5(0) = 0.5 , T = Transfer cost
Suppose the person is willing to pay Birr 13750. The utility value assigned to this
transfer cost will be 0.5
3. Ask the person how much he would be willing to pay in order to transfer the
risk in which there is 50 percent chance of losing the transfer cost in (2) above, (Birr
13750) or nothing. The amount he offers will have a utility value of:
U (T 2) = 0.5 (utility of T 1) + 0.5 (utility of zero)

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 = 0.5 (0.5) + 0.5 (0)
= 0.25

Suppose that the person is willing to pay transfer cost of Birr 7700. Consequently, the
utility value of Birr 7700 will be 0.25.
4. This procedure is continued until enough information is collected to construct
the utility function. The summary is given below:

Possible Loss Probability Utility Index

25000 0.5 1.00

13750 0.5 0.50
7700 0.5 0.25
4389 0.5 0.125
2400 0.5 0.0625
1300 0.5 0.03125

The next step is to determine the utility index for losses of Birr 5000, 10000, 15000 and
20000 using linear interpolation.

Linear Interpolation

Given two extreme values, X U and X L, with a corresponding utility index of U (X U) and U (X
), the utility index for X M, U (X M), will be found using the following formula:
L

U (X M) = U (X L) + [(X M - X L) ÷ (X U - X L)] [U (X U) - U (X L)]

Example
The utility value of Birr 5000 loss is determined x U(x) as follows:
7700 .25
5000 ?
4389 .125

XM-XL = 5000 – 4389 = 611

XU-XL = 7700 – 4389 = 3311

U (X U) - U (X L) = 0.25 - 0.125 = 0.125

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U (5000) = 0.125 + (611/3311) (0.125) = 0.14807

In the same manner, the utility points for losses of Birr 10000,15000 and 20000 are calculated
below.

U (10000) = .25 + (2300/6050) (.25) = 0.34504

U (l5000) = .50 + (1250/11250) (.50) = 0.55556

U (20000) = .50 - (6250/11250) (.50) = 0. 77770

Now it is possible to determine the Expected Utility Loss as shown below:

Possible Utility Probability (2*3) (1*3)

Loss Index Expected Expected
Utility Monetary
Loss Loss
0 0 0.07776 0 0
5000 0.14807 0.25920 0.03838 1296
10000 0.34504 0.34560 0.11925 3456
15000 0.55556 0.23040 0.12800 3456
20000 0.77778 0.07680 0.05973 1536
25000 1.00000 0.01024 0.01024 256
SUM 1.00000 0.3556 10000

Consequently, if the risk manager does not want to buy an insurance policy (retain the risk),
the expected loss in utility would be 0.3556. He can also find the monetary equivalent for
this expected utility loss. The monetary equivalent is:
X (0.3556) = 7700 + (0.1056/0. 25) (6050) = 10255.52.

This monetary equivalent indicates that if the risk manager is intending to buy insurance, he
will be willing to pay premium up to Birr 10255.52. In this case the risk manager pays more
than the expected monetary loss, which is Birr 10000. He is, therefore, considered as a risk
averse.
averse. The margin to the insurer is only 2.56% of the Expected Monetary loss,
(255.52/10000). This margin, however, is so small that an insurance company may not
provide protection at this premium level.

PARTIAL RETENTION
Suppose the risk manager considers the following options:

67
 1. Retain losses up to Birr 5000, and purchase insurance to transfer losses exceeding the
5000 limit.
2. Retain losses up to Birr 10000, and purchase insurance to transfer losses exceeding the
10000 limit.
1. Retain up to Birr 5000 Loss
If the risk manager wishes to retain losses up to Birr 5000, the next step will be to determine
the expected loss in utility of absorbing those losses exceeding Birr 5000. This is calculated as
follows:

Expected utility Loss = 0.3556 - 0.03838 = 0.31722

Monetary Equivalent: X (0.31722) = 7700 + (0.06722/0.25) (6050)
= Birr 9326.72
Expected Monetary Loss = 10000 - 1296 = Birr 8764

The risk manager is willing to pay up to Birr 9326.72 in premiums to transfer the risk for
which the Expected Monetary is Birr 8704.

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2. Retain up to Birr 10000 Loss
Under this option the expected loss in utility of absorbing those losses exceeding Birr 10000
is calculated below.
Expected Utility Loss = 0.3556 - (0.03838 + 0. 11925)
= 0.19797
Monetary Equivalent:
X(0.19797) = 4389 + (0.07297/0.125) (3311)
= 6321.83
Expected Monetary Loss:
10000 - (1296+3456) = 5248
The risk manager is willing to pay up to Birr 6321.83 in premiums to transfer the risk that has
an expected monetary loss of Birr 5248. Summary of the alternative decisions is given below.

Decisions Expected Monetary Expected Insurer’s

Utility Loss Equivalent of Monetary margin (%
(%)
Utility Loss
No insurance 0.3556 10255.52 10000 2.56
Retain up to 5000 0.31722 9326.72 8704 7.15
Retain up to 10000 0.19737 6321.83 5248 20.46

Other Options
1. Insurance coverage for annual premium payment of Birr 12000.
2. Buy Birr 20000 insurance policy with Birr 5000 deductibles for annual premium payment
of Birr 7000.
3. Buy Birr 15000 insurance policy with Birr 10000 deductibles for annual premium
payment of 2500.
4. Buy no insurance policy, retain the risk.

1. Complete Coverage, Birr 25000

Under this decision, losses of any amount will be borne by the insurance company. The
only loss the firm incurs is insurance payment, Birr 12000.

The utility point for Birr 12000 payment is determined as follows:

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 U (12000) = 0.25 + (4300/6050) (0.25) = 0.42769

Potential Utility Probability Expected Expected

Loss point utility loss monetary
loss
12000 0.42769 1 0.42769 12000

2. Buy Insurance with Birr 5000

Deductibles

A deductible is a specified amount of the potential loss that the insured agrees to bear under
an insurance contract. Thus, in the event of a loss, the insurer will pay to the insured the
amount of loss less the deductible.

For a 20000-insuranoe policy with Birr 5000 deductibles the potential loss is determined as
follows:
Potential Loss = Premium Charge + monetary loss – insurance receipts

Number of Potential loss

Accident
0 7000 + 0– 0 = 7000
1 7000 + 5000 – 0 = 12000
2 7000 + 10000 – 5000 = 12000
3 7000 + 15000 – 10000 = 12000
4 7000 + 20000 – 15000= 12000
5 7000 + 25000 – 20000 = 12000

The expected utility of loss for this decision is determined below.

potential Utility Probability Expected Expected
Loss Point Utility Loss Monetary
Loss
7000 0.2236 0.07776 0.01739 544.32
12000 0.4277 0.92224 0.39444 11066.88
SUM 1.00000 0.41183 11611.20

3. Buy Insurance with Birr 10000

Deductibles

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For Birr 15000 insurance with Birr 10000 deductibles, the potential loss is calculated as
follows:
Number of Potential loss
Accident
0 2500 + 0 – 0 = 2500
1 2500 + 5000 – 0 = 7500
2 2500 + 10000 – 5000 = 12500
3 2500 + 15000 – 10000 = 12500
4 2500 + 20000 – 15000 = 12500
5 2500 + 25000 – 20000 = 12500

The expected utility loss of this decision is summarized below.

Potential Utility Probability Expected Expected

Loss Point Utility Loss Monetary
Loss
2500 0. 0583 0.07776 0.0045 194.4
7500 0.2424 0.25920 0.0628 1944.0
12500 0.4483 0.66304 0.2972 8288
SUM 1.00000 0.3645 10426.4

4. Retention

If the risk manager decides to retain the risk, the Expected Utility Loss is 0.3556, and the
Expected Monetary Loss is Birr 10000.

Summary of the four alternatives is given below:

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 Expected Expected
Decision Utility monetary
Loss Loss
1. Complete Coverage, Birr 25000 0.4277 12000.00
2. 20000 Insurance, 5000 deductibles 0.4118 11188.61
3. 15000 Insurance, 10000 deductibles 0.3645 10426.40
4. Retention 0.3556 10000.00

According to the Expected Utility Model, the risk manager selects that alternative which
brings the lowest expected utility loss. In this example, the model suggests for retention of
the risk.

The model did not recommend insurance for a number of reasons. Among others is the
premium charge which may not be reasonable to the risk averse manager. Now, let us try to
determine the margin to the insurer.

In alternative 1 (complete insurance coverage), the insurer charges premium of Birr 12000.
The Expected Value of Payment the insurer is Birr 10000. His margin is, then, 20% of
expected value of payment. For Alternative 2 and Alternative 3 the calculation is shown
below:

Alternative 2 (20000 Insurance with 5000 Deductibles)

Number of Payment by Probability EV of Payment by

Accidents Insurer Insurer
0 0 0.07776 0
1 0 0.25920 0
2 5000 0.34560 1728
3 10000 0.23040 2304
4 15000 0.07680 1152
5 20000 0.01024 204.8

Total expected value of payment 5388.8

The same procedure is followed to determine the Expected Value of Payment by the insurer
for Alternative 3. The summary is given below.

Alternative EV of Payment by Premium charge Insurer’s

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 Insurer Margin (%)
1 10000 12000 20%
2 5388.8 7000 29.9%
3 2073.6 2500 20.6%

2.7.2 The Worry Factor Model

This model tries to assign a monetary value to the mental stress (worry) that may experience
because of the presence of risk. Consequently the monetary value assigned to this worry is
treated as part of the cost of managing the risk.

To apply the worry model the Risk manager will have to follow certain steps.
1. Determine the premium payment for each decision under consideration.
2. Determine the expected value of uncovered monetary loss.
3. Assign a worry value to the expected value of uncovered loss.
4. Determine the total loss for each decision. The total loss can be calculated by
summing up the premium, the expected value of the uncovered loss and the worry
value.

What will be the decision rule?

The decision rule for this method is to select an alternative that has the lowest total loss. For
illustrative purpose s the four alternatives discussed under the expected utility model are
considered. Those alternatives are listed below.

Alternatives Premium
1. Complete coverage Br 25000 12000
2. Br 20000 insurance policy with Br 5000 deducted 7000
3. Br 15000 policy with Br 10000 deductibles 2500
4. Retention 0

EXPECTED VALUE OF UNCOVERED LOSS

The total loss would be the sum of the premium, the expected value of uncovered loss
(EVUL) and the worry value. That is,

TOTAL LOSS = PREMIUM + EVUL + WORRY VALUE

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Therefore, the decision rule is to select the alternative that has the lowest total loss. Dear
student, please note that both tangible as well as intangible losses are considered in the worry
factor model. let’s see the computations of total loss under each of the above alternatives.

i. Complete coverage Br. 25000

a. Premium = 12,000
b. EVUL = there is a full coverage
c. Worry value = 0  no mental stress
d. Total loss = 12,000 + 0 + 0 = 12,000

ii. Br. 20,000 insurance policy with Br 500 deductibles

a. Premium = 7000
b. EVUL = 4611.20

Number of (a) (b) c = a –b Probability EVUL

accidents Monetary Insurance Uncovered
loss payment loss
0 0 0 0 0.07776 0
1 5000 0 5000 0.25920 1296
2 10000 5000 5000 0.34560 1728
3 15000 10000 5000 0.23040 1152
4 20000 15000 5000 0.07650 384
5 25000 20000 5000 0.01024 51.20

c. Worry value = 30% of EVUL is 30% (4611.20) = 1383

d. Total loss = 7000 + 4611 + 1383 = 12994

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 iii. Br 15000 policy with Br 10000 deductibles

a. Premium = 2500
b. EVUL = 7926

No. Of Monetary loss Insurance Insurance loss Prob. EVUL

accident payment
0 0 0 0 0.07776 -
1 5000 0 5000 0.25920 1296
2 10000 0 10000 0.34560 3456
3 15000 5000 10000 0.23040 2304
4 20000 10000 10000 0.07680 768
5 25000 15000 10000 0.01024 102.4

c. Worry value = 50% of EVUL

= 50% X 7926 = Birr. 3963
d. Total loss = 2500 + 7926 + 3963 = Birr. 14389

iv. Retention
a. Premium = 0
b. EVUL = Expected loss = 10000
c. Worry value = 75% X EVUL
= 75% X 10000 = 7500
d. Total loss = premium + EVUL + worry value
= 0 + 10000 + 7500 = 17500

The summary of all the above work may be presented in the following manner.

Decision Premium EVUL Worry Factor Total loss

option
1 12000 0 0 12000
2 7000 4611 1383 12994
3 2500 7921 3963 14369
4 0 10000 7500 17500

Decision: Select the full insurance coverage because its total loss is the lowest.

The Expected Utility Model led the risk manager to retain the risk. The Model does not take
into consideration the intangible cost associated with worry. The Worry Method, however,

75
assigns an arbitrary value to the mental stress of the manager. Consequently, the total loss is
bound to increase.

If the objectives were to minimize the expected tangible monetary loss, the following costs
would have been compared; and-retention might have been considered.

Decision Total loss (excluding worry)

1. Complete coverage 12000
2. 20000 with 5000 deductible 11611
3. 15000 with 10000 deductibles 10426
4. Retention 10000

One better approach of estimating the worry value for each alternative could be to determine
the minimum worry value for that alternative by comparing the alternative with the
insurance option. For the above example the following minimum values are established.

1. To select alternative 1 (complete insurance cover) over alternative 2, the

minimum worry value of alternative 2 should be Birr 389, (12000-11611),
which is about 8.4% of EVUL.

2. To select alternative 1 over alternative 3, the minimum worry value of

alternative 3 should be Birr 1574, (12000 -10426) which is about 19.9% of
EVUL.

3. To select alternative 1 over alternative 4, the minimum worry value of

alternative 4 should be Birr 2000, (12000-10000), which is 20% of the EVUL.

The risk manager may consider another approach to determine the worry value. For example,
the Expected Monetary Loss under alternative 4 (retention) is Birr 10000. The EVUL for this
alternative is also Birr 10000. Now, suppose the risk manager is willing to purchase complete
insurance cover for a premium payment of Birr 12000. In doing so, the risk manager is getting
rid of the worry associated with the 10000 EVUL under the retention option. Consequently,
the ex—MR payment (Birr 2000) can be considered as the cost of eliminating the worry by
transferring the risk through insurance. Also, it may be assumed that the risk manager
attaches equal degree of worry to each Birr of uncovered loss. This gives a worry value of
0.20 for each Birr of EVUL, (2000/10000). The analysis under Worry Method will then
becomes as follows:

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 Decision Premium EVUL Worry Total
Value loss
1. Complete cover 12000 0 0 120

2. 20000 with 5000 deductibles 7000 4611 922.2 125

3. 15000 with 10000 deductibles 2500 7926 1585.2 120
4. Retention 0 10000 2000 1201

Clearly, insurance is preferred to retention although the total cost of the two alternatives is the
same. Regarding alternative 2 and alternative 3, the risk manager will have to bargain with the
insurer concerning the premium payment. To select alternative 2 over alternative 1
(complete insurance cover) the risk manager will have to demand a reduction in premium of
at least Birr 534 (12534 - 12000). Similarly, to sell alternative 3 over alternative 1, the
reduction in premium should be at least Birr 11.2. (12011.2 - 12000).

Models are abstractions of real world situation. Their usefulness in real life situation
depend, among other things on whether or not their assumptions and the variables they
incorporate reflect the prevailing situation in the practical field. The usefulness of the two
models discussed above in risk management should also be approached along these lines.

Check Your Progress Exercise

1. Define the concept of risk management.
…………………………………………………………………………………………………
…………………………………………………………………………………………………
………………………………………………………………………………………………….

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2. Identify the steps involved in risk management process and
explain them in short.
…………………………………………………………………………………………………
…………………………………………………………………………………………………
………………………………………………………………………………………………….

3. Given the following binomial probability distribution for the next year.

No of Monetary loss Probability

accidents
0 Br. 0 0.40
1 5000 0.25
2 10,000 ?
3 15,000 0.12
4 20,000 0.05
5 30,000 0.03

Based on the above information, determine:

A. The average number of accidents per year
B. The expected monetary loss per year
C. The maximum possible loss
D. The probability that the firm will suffer some loss.

4. Out line and describe briefly the risk control measures.

…………………………………………………………………………………………………
…………………………………………………………………………………………………
…………………………………………………………………………………………………
5. Discuss the risk financing tools.
…………………………………………………………………………………………………
…………………………………………………………………………………………………
…………………………………………………………………………………………………

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2.8 SUMMARY

Risk management is denned as a systematic process for identifying and evaluating pure loss
exposures faced by an organization or individual, and for selecting and administering the most
appropriate techniques for treating such exposures. All pure risks are considered, including
those that are uninsurable.

 There are several important differences between risk management and insurance
management. First, risk management places greater emphasis on the identification and
analysis of pure loss exposures. Second, insurance is only one of several methods for
handling losses; the risk manager uses a wide variety of methods to handle losses. Third,
risk management provides for the periodic evaluation of all methods for meeting losses,
not just insurance. Finally, risk management requires the cooperation of other individuals
and departments throughout the firm.
 Risk management has several important objectives. Preloss objectives include the
goals of economy, reduction of anxiety, and meeting externally imposed obligations.
Postloss objectives include survival of the firm, continued operation, stability of earnings,
continued growth, and social responsibility.
 There are four steps in the risk management process. Potential losses must be
identified. The potential losses must then be evaluated in terms of loss frequency and loss
severity. An appropriate method or combination of methods for treating loss exposures
must be selected. The risk management program must be implemented and properly
administered.
 The major methods for treating loss exposures in a risk management program are
avoidance, retention, noninsurance transfers, loss control, and insurance.
 Retention can be used if no other method of treatment is available, the worst possible
loss is notserious, and losses are highly predictable. If retention is used, some method for
paying losses must be sheeted. Losses can be paid out of the firm’s current net income; an
unfunded or funded serve can be established to pay losses; the necessary funds can be
borrowed; or a captive insurer can be formed.

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 The advantages of retention are that the firm may be able to save money on insurance
premiums there may be a reduction in expenses; loss prevention is encouraged; and cash
flow may be increased. The major disadvantages are the possibility of greater volatility in
losses in the short run, of higher expenses if loss control personnel must be hired, and of
possible higher taxes.
 There are several advantages of noninsurance transfers. The risk manager may be able
to transfer some uninsurable exposures; noninsurance transfers may cost less than
insurance; and the potential loss may be shifted to someone who is in a better position to
exercise loss control. However, there are several disadvantages. The transfer of a potential
loss may fail because the contract language is ambiguous; the firm is still responsible for
the loss if the party to whom the potential loss is transferred is unable to pay the loss; and
an insurer may not give sufficient premium credit for the transfers.
 Loss control is extremely important in a risk management program. Loss-control
activities are designed to reduce both loss frequency and loss severity.
 Commercial insurance can also be used in a risk management program. Use of
insurance involves a selection of insurance coverages, selection of an insurer, negotiation
of contract terms with the insurer, dissemination of information concerning the insurance
coverages, and periodic review of the insurance program.
 A risk management program must be properly implemented and administered. This
involves preparation of a risk management policy statement, close cooperation with other
individuals and departments, and periodic review of the entire risk management program.

2.9 ANSWER TO CHECK YOUR PROGRESS EXERCISE

1. Risk management is the process of identification, measurement; and treatment of pure

risks.
2. i) Risk identification: is the process by which a business systematically and
continuously identities property, liability, and personnel exposures as soon as or before
they emerge.
ii) Risk measurement: is the process of determining the potential loss as to its size and
the probability of occurrence.

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 iii) Tools of risk handling: there are various ways of handling risks. Generally, there are
two basic approaches (risk control tool and risk handling tool). Risk control tool is
designed to change the loss exposure itself, the objective is to reduce the frequency or
severity of the potential losses. On the other hand, risk financing tool is a technique
designed to provide money to deal with those losses that occur. For the detail refer
unit 3 and 4.
i) Implementation: this is the stage when the actual operation is started. Once the
risk-handling tool is selected, the manager should start to undertake the
implementation process.
ii) Controlling (Monitoring): at this stage, the risk manager should evaluate the
undertaken processes to ensure that risk management process is effectively
performed. And if necessary corrective actions should be taken.

3. A. 1.26 Mean
B. 6450 Birr
C. 30,000 Birr
D. 0.6 = 60%
4. Refer to section 2.8.1
5. Refer to section 2.8.2

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