Introduction

Two major difficulties arise in formulating risk assessments: first, a faulty or incomplete information base from which to make the assessment and, second, the limited and varied ability of individuals to process information presented to them. The faulty information base is discussed in Chapter 10 when looking at risk perceptions in situations of physical danger. In this chapter we consider the information-processing problem familiar to readers from situations which require the assembling of complex probabilities from a mass of simple probabilities. For example, in whist or bridge, some players consistently play against the odds, apparently being unaware of them in situations where their form is relatively complex.

Availability of information

The ease with which specific relevant instances can be recalled from memory affects markedly our judgement of relative frequency of events. The frequency of well-publicized events is commonly overestimated (for example, deaths due to cancer, deaths due to fires in offices or factories) while the frequency of less well-publicized events is underestimated (for example, deaths due to car accidents, or to diabetes). Moreover the chance availability of particular key pieces of information can affect the overall judgement. Most people have at some time been at a meeting where a member has thrown in a single isolated scrap of information which has then had a marked effect on the estimate of some uncertain quantity and affected the subsequent decision taken; the other members present at the meeting may well have found it difficult to put the piece of information in proper perspective.

Basic assessment

Discussion of investment risk is frequently clouded by the word investment being used in two different senses. The first sense is the buying and selling of securities, say gilt-edged Government stock or ordinary shares in the XYZ Company. This sense is referred to as financial investment. The second sense is where a company (nationalized or private) or an individual decides to put some money into, say, building a factory and equipping it with machines and raw materials to make and market some new product or service. This is referred to as project investment. The processes involved, and the way risk is assessed and handled, are very distinct. Project investment is considered in the present chapter; financial investment is discussed in Chapters 7 and 8.

The normal limited liability company quoted on the Stock Exchange has a capital structure designed to handle the risks inherent in the development of new ideas or products. Debenture loans are commonly linked to company ownership of land, buildings and machinery and equipment; ordinary shares, or equity, are linked to the development costs of new products. Bank loans and overdrafts cover working capital, stocks, etc. Debentures and bank overdrafts carry defined rates of interest, while ordinary shares (equities) have a variable rate of dividend dependent on profits. The market value of the shares likewise varies with the current, and anticipated, levels of dividend payments.

A company seeking to acquire substantial fresh capital for risk investment purposes will basically do it in two ways, frequently in combination. First, it will retain a proportion of its profits each year, i.e the dividends paid will not be at the maximum possible level.

Introduction

Decisions can be crudely split into two kinds. The first relates to decisions connected with current problems that have an immediacy of application, many of which are colloquially referred to as ‘patch-up jobs’. The payoff from each individual decision of this kind is likely to be fairly low, but the frequency of such decisions in any organization is commonly high. The second kind of decision is the search for new opportunities and the making of decisions that will influence the organization's fortunes over the longer term. Managers are generally concerned with both types of decision, the mix for an individual manager depending very broadly on his seniority and level of management. Most junior and middle managers are primarily concerned with the former type of problem-solving situations; senior managers are primarily concerned with the latter type of strategic decisions. Risk enters both types of decision, although in rather different ways. The balance between what is termed (Chapter 3) ‘risk’ as opposed to ‘uncertainty’ is generally different in the two cases, the latter being rather more prominent in strategic decisions. The definition of objectives, however, is commonly rather precise and specific in short-term decisions. Section B.2 looks at problem-solving situations, Section B.3 at the longer-term strategic decisions.

Problem solving

Once an immediate problem has been recognized, three major kinds of action may be taken:

(a) interim

(b) adaptive

(c) corrective

The first, interim action, is generally taken before the cause of the problem has been found. It is in the nature of a stopgap operation to keep some process going.

The background

Risk is about future happenings and enters everybody's lives at numerous points. A mountaineer going on an expedition can break a leg, or be killed. A business person keeping an appointment in Birmingham may be involved in a serious road accident. A traveller in Africa may contract dysentery. A gambler entering a casino could lose all his capital in a night. The company in which an individual has invested may go into liquidation. An entrepreneur starting a new business venture can lose his capital when an expected market fails to materialize. A government may be thrown off course when a major trading bloc operates a cartel against it.

Economic progress is impossible without taking risks; indeed it is arguable that even the maintenance of an economic status quo involves risk taking. Hence risk has about it an aura of achievement and progress, communities commonly rewarding those who handle difficult risk situations successfully. Effective handling of risks requires first their assessment and, secondly, their subsequent incorporation in the decision-making process. Exploring these themes in a variety of business, economic, political and social settings forms the primary objective of this book.

Introduction

In recent years a great deal of theoretical and empirical work has been published on the movements of equity share prices. This reflects the considerable interest currently being shown in the formation and performance of investment portfolios, particularly with regard to their equity (share) content. Controlling a portfolio is essentially a matter of making buy-and-sell decisions and, since portfolio managers must be interested in future performance, information about future prospects is needed. Newspapers and stockbrokers commonly give only limited help with enigmatic statements such as ‘… the market for electrical shares could be up 25% within the year, or even more if inflation moderates. On the other hand it could…’

An analyst faced with this portfolio management problem would doubtless start by analysing the past variability of shares. Of course, there is no guarantee that the future mirrors the past, but it is reasonable to assume that a portfolio composed of shares with histories of high variability will also have a less predictable future performance than a portfolio of shares whose past performance has been more stable. The basic concept in portfolio management theory is that some shares are consistently more volatile or variable than other shares. The more variable the company's shares, the riskier is that share.

Share variability

The monthly fluctuations in price over four years for a share that is generally regarded by analysts as having high risk (Paterson Zochonis) and one that is similarly regarded as having low risk (British American Tobacco) are shown in Figure 8.1. The values have been adjusted to a common starting price of 100, with all dividends re-invested.

Introduction

In the next three chapters various methods used to determine the probabilities required for decision making are explored and four broad approaches distinguished:

1. (a) the enumeration (or theoretical) approach;

2. (b) the relative frequency or collective principle;

3. (c) the actuarial approach;

4. (d) the subjective (or personal) approach.

Items (a), (b) and (c) are covered in this chapter, item (d) in Chapter 3. Chapter 4 then looks at questions of bias in assessments, and how these can be ameliorated. Whichever approach is employed to determine probabilities, the basic rules for handling probabilities, summarized briefly in Appendix A, remain the same.

The enumeration approach

A coin is tossed to determine whether you or your opponent should have the choice to serve first in a tennis match. The coin has two sides which look evenly balanced. You consider them equally likely and consequently assign them both a probability of 1/2. The same procedure could be followed in a board game using an ordinary six-sided die, each face appearing equally likely and therefore assigned a probability of 1/6. In taking part in a roulette game it is again assumed without great deliberation that the 36 slots (or 37 including the zero) are all equally likely. In the local village fete, 500 tickets are sold in a raffle for an electric mixer. You hold five tickets and assume unconsciously that your chances of winning are 1 in 100.

In these instances the assessment is made on the grounds that, if there are m different outcomes whose relative likelihood of occurrence seem indistinguishable, and only one outcome is a ‘success’, then its probability is 1/m.

Introduction

Public policy is an all-embracing term. In this chapter, three strands are distinguished for discussion. The first relates to social policies, such as the wearing (or non-wearing) of seat belts; the second to commercial-type decisions that come within the public domain (for example, the development of Concorde, the possibility of a Channel Tunnel, or the planned size of British Steel); the third to decisions in the political area concerning matters such as the scale of disaster preparations, or the balance of public expenditure between education and health services. These sub-divisions are not watertight, but provide a framework for discussion.

Two general points tend to colour most decisions in the public policy domain. The first is the view of politicians that their primary task is to be re-elected. This leads to an overriding emphasis on the short-term effects of decisions, with correspondingly lower emphasis on longer-term consequences. This would not matter if the areas in which public policy operated were confined to those of little consequence and easy reversibility but with the increasing involvement of governments – particularly in the UK–with commercial-type operations and large-scale capital development programmes, this shortened time horizon has some very unfortunate side effects. Moreover, such a policy framework conditions those concerned with decisions outside the public domain to think not so much in terms of ‘what can be done best within this Government policy’ but ‘what can be done that will as far as possible be robust under a change of Government policy’.

The second point relates to Government accounting conventions.

Introduction

There are basic rules to which all probabilities must conform. Thus the manner in which probabilities of compound events are derived from those of simple events is quite invariant and independent of the methods by which the probabilities of the simple events have been initially obtained.

All probabilities are non-negative and expressed on a scale from 0 to 1. (Occasionally the scale is expressed in percentage terms from 0 to 100.) The greatest degree of probability which any future event can have is certainty, and the scale assigns this a probability of 1.00 (or 100%). At the other end of the scale, the lowest degree of probability that a future event can have is ‘impossibility’ to which is assigned a probability of zero. The next two sections introduce the basic rules for the addition and multiplication of probabilities when compound events are concerned.

Addition of probabilities

A stationery shop stocks three types of stapling machine. Examination of past records shows that 40% of customers purchase a machine of type A, 35% one of type B, and 25% of type C. Types A and B are made by manufacturer X, type C by manufacturer Y. A customer comes in to buy a stapling machine; what is the probability that he will buy one made by manufacturer X?

Denote by P(A) the probability that a machine of type A is purchased, etc. and by P(A + B) the probability that either type A or type B is purchased. Then Then

P(A) = 0.4, P(B) = 0.35 and P(A + B) = 0.75

Risk and uncertainty

The collective principle for risks outlined in Chapter 2 can be applied to many situations inside and outside commerce. But in some circumstances no immediate relevant collective springs to mind. This chapter looks at such situations where probability estimates cannot be made by the collective approach on a basis that would necessarily command overall agreement. Such situations are sometimes labelled ‘uncertainty’ and differentiated from ‘risk’ situations.

The separation of uncertainty from risk is a frequent practice in industrial circles. Examples cited in this context are political uncertainties such as nationalization, economic uncertainties such as forthcoming rates of inflation, or changes in the rates of interest. Many statisticians argue cogently that there is no real distinction between risk and uncertainty as defined in this way. The distinction really being made, it is argued, is between repeatable and non-repeatable events. Thus games of chance such as roulette are repeatable, just as the actuary of an assurance company regards death as a repeatable event, in the sense that a large population is at risk and alternative events ‘death’ or ‘no death’ are repeated for each person in the population each year. Although one cannot be dogmatic about a single person dying, one can be reasonably specific about the number of persons dying from among a large group in a specified period. But the outcome, ‘the next President of the United States will be a woman’ is not of the same category. To count up the number of eligible voters who are women (W) and men (M) respectively and express the chance as the proportion W/(M+W)

Introduction

This chapter looks at a number of ways in which various aspects of risks to life (or limb) can be assessed and treatment decisions made. The discussion is divided into three parts. Sections 11.2 and 11.3 deal with the concept of total risk. Section 11.4 deals with the assessment of medical risks, illustrated in Section 11.5 by the smoking controversy. Sections 11.6 and 11.7 then deal with the problems facing the doctor in a therapeutic situation, linking assessments of probability with those of utility, and suggesting expectation of life as a useful measure of utility for decision purposes. Chapter 12 returns to the discussion of outcome values, and attempts to link the kinds of risks discussed in this and other chapters to the costs of risk avoidance or minimization measures in the public policy domain.

The total risk concept

The total cost (or loss) to society of many endeavours is not always solely the main items apparently ascribed to the endeavour. Thus the social cost of constructing a large building is not just the direct building costs and the cost of the one fatal accident that occurred on site, but also the costs corresponding to the physical risks involved in producing the various raw materials needed, making the steel and bricks, transporting the products, etc. in terms of deaths, sickness and disabilities. Although many of these deaths and injuries are ‘statistical’ in the sense that they cannot be identified as being directly linked to the project concerned, it seems reasonable to include and not discard such deaths (and accidents) on an average statistical basis.

Risk is all pervasive. An individual faces physical risks from driving a car, career risks from the possible bankruptcy of one's employer, financial risks from investing his or her savings in equities. A company faces the risk of collapse of a traditional market, or of research failure for a new product. A government may face an unexpected strike or a foreign government's rebuff to a diplomatic overture. While in some areas, such as life assurance, risk is well understood and systematically handled in an accepted manner, this is not common in other areas of economic and social activity.

The proceedings of a 1980 Royal Society symposium on risk were published under the title The Assessment and Perception of Risk. Lord Ashby's introduction gave a commercial example concerning the damages involved from a collision between two ships. The fifteen papers in the volume dealt, however, almost exclusively with areas of personal physical risk. I hope this book will help to answer the kind of question posed by Lord Ashby and redress the narrow perspective given to the subject, no doubt accidentally, by the Royal Society symposium.

The three principal messages conveyed are: first, risk arises in some form or other in virtually all fields of endeavour; second, it is important neither to ignore risk nor to be frightened by it; third, systematic methods to assess and handle risks can be developed. After an introduction and four general chapters dealing with risk assessment, the book examines the progress that has been made in handling risk in seven distinct fields. While these fields are not exhaustive, they cover the more common risk areas.