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**From risk to opportunity Lecture 3**

John Hey and Carmen Pasca

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**Lecture 3 Different approaches to risk: Overview**

Today we put in the lecture various ‘extra’ slides. I am not an expert in economics; Professor Hey is. There are some slides that are his, you should read them, but I will not talk to them. Professor Hey will expect you to have read them when he gives his lectures. But first a refresher on what we asked you to do (some of this material John will talk about later).

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**Have you done what we asked you to do in Lecture 2?**

How many of you proved the implications of the axioms of probability theory? How many of you think the EU axioms are reasonable? John Hey will talk about these in Lecture 10. We have now corrected the payoff matrix for the CAC 40 gamble. How many of you did it? How much would you pay for the St Petersburg gamble. Between €0 and €5? Between €5 and €10? Between €10 and €15? Between €15 and €20? More than €20? An infinite amount? John Hey will talk about this too in Lecture 10. How many of you have responded to the Jonathan Alevy online survey? How many of you have understood that the easy question on the specimen Mid Term examination is easy?

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**Lecture 3 Different approaches to risk: Overview**

This lecture sets the scene for subsequent lectures by discussing the various different approaches to risk in the social and human sciences: philosophical, epistemological, political, sociological, ethical, psychological and economic; it also explores the relationships and connections between these different approaches. In particular, this lecture focuses on how the issue of risk gave rise to important new problems for several disciplines.

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**Lecture 3 Different approaches to risk: The birth**

In 1494, Luca Pacioli (right) wrote the first printed work on probability: Summa de arithmetica, geometria, proportioni e proportionalita. In 1550, Geronimo Cardano (right) inspired by the Summa wrote a book about games of chance called Liber de Ludo Aleae, which means A Book on Games of Chance. The real birth of probability theory was in the seventeenth and eighteenth centuries with Pascal, Fermat, Daniel Bernoulli (right) and his uncle Jacob Daniel.

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**Lecture 3 Different approaches to risk: Pascal**

Blaise Pascal (right) argued that uncertainty is about people, their beliefs and their courage, while calculated risk is based on information, knowledge and credible scenarios. Pascal used the calculation of probability (and in particular the notion of mathematical expectancy) to bet that God exists.

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**Lecture 3 Different approaches to risk: from 15th to 17th centuries**

During the fifteenth century several probability works emerged. Calculations of probabilities became more noticeable during this time period even though mathematicians in Italy and France remained unfamiliar with these calculation methods. With his colleague, Pierre de Fermat (right), Pascal came to the conclusion that people are naturally risk averse - the more risk is involved with a particular asset, the greater the return that investors will require as compensation.

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**Lecture 3 Different approaches to risk: A bet**

In the mid-seventeenth century, a simple question directed to Blaise Pascal by a nobleman sparked the birth of probability theory, as we know it today. Chevalier de Méré (right) (a gambler who is said to have had unusual ability “even for the mathematics”) gambled frequently to increase his wealth. He bet on a roll of a die that at least one 6 would appear during a total of four rolls. What do you think the probability is? (See the next slide.) From past experience, he knew that he was more successful than not with this game of chance.

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**Lecture 3 Different approaches to risk: A new bet**

Tired of his approach, he decided to change the bet. He bet that he would get a total of 12, or a double 6, on twenty-four rolls of two dice. Soon he realized that his old approach to the game resulted in more money. He asked his friend Blaise Pascal why his new approach was not as profitable. Pascal worked through the problem and found that the probability of winning using the new approach was only 49.1 percent compared to 51.8 percent using the old approach. (You try to check this!)

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**Lecture 3 Different approaches to risk: Pascal and Fermat**

This problem proposed by Chevalier de Méré is said be the start of famous correspondence between Pascal and Pierre de Fermat. They continued to exchange their thoughts on mathematical principles and problems through a series of letters. Historians think that the first letters written were associated with the above problem and other problems dealing with probability theory.

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**Lecture 3 Different approaches to risk: Bernoulli**

In the 17th and 18th centuries, James Bernoulli (right) ( ) wrote Ars Conjectandi. In this he presented combinations and permutations which encompass most of the results still used today, included a series of problems on games of chance with explanations, and finally, and most importantly, he revealed the famous Bernoulli theorem, later called the law of large numbers. Daniel Bernoulli (right) in On the Measurement of Risk (1731) wrote about risky propositions.

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**Lecture 3 Different approaches to risk: The paradox**

‘Paradox’ in the theory of probability published by Daniel Bernoulli in 1730 in the Commentarii of the St Petersburg Academy. Bernoulli’s theory of choice was based on moral expectation (as he called it, now called expected utility). The theory had a solution for the Petersburg Paradox, which had exposed the difference between the mathematical expectation of a prospect and its value to ‘me’: “its expectation is infinite but its value to me is not”. The paradox: Someone offers you the following opportunity: he will toss a fair coin... ... if it comes up heads on the first toss he will pay you one dollar; if heads does not appear until the second throw, two dollars, and so on, doubling your winnings each time heads fails to appear on another toss.

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**Lecture 3 Different approaches to risk: The paradox**

The game continues until heads is first thrown, when it stops. What is a fair amount to pay for this opportunity? Well, the expected value of this game is ... ... infinite (as we showed in Lecture 2) But people will not pay an infinite amount. This lead to the idea that people are interested in the expected utility to them of the gamble. And implies the utility function is concave. We shall explain more later.

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**Lecture 3 Different approaches to risk: Laplace**

Pierre Simon Laplace (right) ( ) wrote Théorie Analytique des probabilités, published in 1812. This book outlined the evolution of probability theory, providing extensive explanations of the results obtained. In this book Laplace presented the definition of probability, which we still use today, and the fundamental theorems of addition and multiplication of probabilities along with several problems applying the Bernoulli process.

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**Lecture 3: Different approaches to risk**

Hypothesis proposed by the mathematician Daniel Bernoulli that expands on the nature of investment risk and the return earned on an investment. Bernoulli stated that an investor's acceptance of risk should incorporate not only the possible losses that can occur, but also the utility, or intrinsic value, of the investment itself. Bernoulli's hypothesis essentially states that one should not accept a highly risky investment choice if the potential returns will provide little utility, or value.

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**Lecture 3 Different approaches to risk: Expected Utility theory**

After the publication of von Neumann and Morgenstern’s Theory of Games and Economic Behaviour in 1945, and Savage’s Foundations of Statistics 1954, the consensus was that (Subjective) Expected Utility theory was the answer. We shall study this later but let us state it here. Suppose some variable X takes n values x1,x2,…,xn with associated probabilities p1,p2,…,pn, The Expected Value of X, EX, is given by EX = p1x1 + p2x2 + …+ pnxn Expected Utility theory says people choose between gambles on the basis of their expected utilities, denoted by EU(X), and obviously given by EU(X) = p1u(x1) + p2u(x2) + …+ pnu(xn) where u(.) is the individual’s utility function (defined over the outcomes). This theory is wonderfully elegant (which is why it might appeal to economists). We shall study it in depth later.

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**Lecture 3 Different approaches to risk: methodology**

If the real world does not show behaviour that a model predicts, then it is the model that needs to be revised. This was the case with Expected Value or Expected Utility theory, which predict that people would accurately assess probabilities and payoffs to make a rational choice in the face of risk. Expected Value theory implies that a person should be indifferent between a 50 percent chance of winning 1,000 and a guaranteed payment of 500. Also Expected Utility theory has predictions which do not appear to be realistic (see the Allais ‘paradox’) and this led to pressure against Expected Utility theory.

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**Lecture 3 Different approaches to risk: Allais**

Maurice Allais (a very famous French economist) in 1952 organized a symposium on risk. Allais asked the conference participants (famous economists) various questions on risky choice. Allais found that the participants (including Savage, who changed his mind next morning!) did not always choose the lotteries that Expected Utility theory predicted, and his findings became known as the Allais Paradox. See the next slide for an example. Allais formulated his own theory (which is now largely discredited).

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**Lecture 3 Different approaches to risk: Allais Paradox**

There are many examples. Here is just one. Consider two pairs of gambles: A gives you €300 with certainty. B gives you €400 with probability 0.8 and €0 with probability 0.2. Which would you choose A or B? C gives you €300 with probability 0.25. D gives you €400 with probability 0.2 and €0 with probability 0.8. Which would you choose C or D? If you chose A and D you violate Expected Utility theory. Why? Put u(€400)= 1, u(€300)= u and u(€0 )=0. Then EU(A) = u, EU(B) = 0.8, EU(C) = 0.25u and EU(D) = 0.2 (check for yourselves). So A preferred to B means that u > 0.8, while D preferred to C means that 0.2 > 0.25u, or 0.8 > u. You cannot have u > 0.8 and 0.8 > u at the same time! Later we shall explain why this behaviour violates the axioms of EU (as shown in lecture 2).

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**Lecture 3 Different approaches to risk: the approach of psychologists**

Starting with Kahneman and Tversky, psychologists attempted to explain the Allais and other Paradoxes by examining human decision-making processes. Notice the difference with economics methodology – although both are concerned with the individual (unlike sociology as we will see later) – economics starts with axioms. Psychologists prefer to describe the process with which individuals take decisions. They focus on editing and evaluation. The first main contender to Expected Utility theory was Kahnemann and Tversky’s Prospect Theory, published in Econometrica in 1979.

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**Lecture 3 Different approaches to risk: Prospect Theory**

Prospect Theory has three key differences from Expected Utility theory (though the first is not really important): A value function v(.) assigns a value to a payoff. The negative portion of the value function is steeper than the positive portion, so the absolute value of a loss is greater than the absolute value of an equivalent win. (A special form of a utility function.) A weighting function w(.) on the probabilities, so that true probabilities are not used. A reference point r which moves depending upon the decision problem (implicitly fixed in EU). The functional is thus PT(X) = w(p1)v(x1-r) + w(p2)v(x2-r) + …+ w(pn)u(xn-r)

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**We shall discuss some of these later in the course. **

Lecture 3 Different approaches to risk: other economists and psychologists Since the launch of Prospect Theory, both economists and psychologists have been busy developing new theories to take into account empirical (largely experimental) evidence. A list of risk theories in 1995 included Allais' 1952 theory (Allais 1952) Anticipated Utility theory (Quiggin 1982); Cumulative Prospect theory (Tversky and Kahneman 1992); Disappointment theory (Loomes and Sugden 1986 and Bell 1985); Disappointment Aversion theory (Gul 1991); Implicit Expected (or linear) Utility theory (Dekel 1986); Implicit Rank Linear Utility theory (Chew and Epstein 1987); Implicit Weighed Utility theory (Chew and Epstein 1987); Lottery Dependent EU theory (Becker and Sarin 1987); Machina's Generalised EU theory (Machina 1982); Perspective theory (Ford 1987); Prospect theory (Kahneman and Tversky 1979); Prospective Reference theory (Viscusi 1989); Quadratic Utility theory (Chew, Epstein and Segal 1991); Rank Dependent Expected (or Linear) Utility theory (Chew, Karni and Safra 1987); Regret theory (Loomes and Sugden 1982 and 1987); SSB theory (Fishburn 1984) ; Weighted EU theory (Chew 1983 and Dekel 1986); Yaari's Dual theory (Yaari 1987). There is nowadays a consensus that Cumulative Prospect Theory (of which EU is a special case) is the best and many of the others are dead. At the present time an intense debate about theories of behaviour under ambiguity is underway and the outcome is not yet clear. We shall discuss some of these later in the course. We note that economists continue to base theories on axioms, though nowadays the axioms are motivated by processes of decision-making. Economists and psychologists are converging.

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**Lecture 3 Different approaches to risk: Sociology**

We now move on to sociological theories. Note the change of focus and methodology. The two central theories of sociological risk research which started to dominate the field in the early 1990s were the Risk and Culture approach of Douglas and Wildavsky (1982) and the Risk Society approach of Ulrich Beck (1986, 1992). Also Giddens approach of the “Third way” was significant: Giddens follows through the implications of a critical citizenry and a decline in the capacity of nation states to manage the political economy for the political order.

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**Lecture 3 Different approaches to risk: Sociology**

A number of studies (Ewald 1986) show that risk emerged as a social category and as a concern for government in relation to social insurance at least as early as the nineteenth century. Recent work in sociology deals with the perception of risk by taking the classic diachronic scheme on the evolution of the perception of risk from a theological interpretation to a secular rational interpretation.

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**Lecture 3 Different approaches to risk: Sociology approach 1**

In the sociological literature on risk there are three main approaches the idea of Risk Society (Beck, 1986, 1992): risk and modernization (the concept of uncertainty in a societal perspective, Risk Society on environmental hazards). The risks are the expression of reflexive modernity. Global risks: according to Beck, it is necessary to think of all social changes in the global perspective. Implicitly risks are global.

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**Lecture 3 Different approaches to risk: Sociology approach 2**

Risk culture (Lash) or socio-cultural approach (Tulloch/Lupton). Issues of identity and those concerning emotion, affect, and the positive idea of risk tend to be raised mainly in the context of this research stream. The central assumption is that there is a relation between modes of social organization and the responses to risk and that culture are adequately represented by the dimensions of the grid/group scheme.

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**Lecture 3 Different approaches to risk: Sociology approach 3**

The attempt of standardised studies on risk culture is to examine how people’s risk-perception is culturally biased. It shows that only a minor part of variance of perceived risk can be explained by culture. A third approach, Governmentality, refers to Foucault (1991) and the question of how institutions and organisations organize power and govern populations. In the discourses on risk in different disciplines, trust is always an important issue.

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**Lecture 3 Different approaches to risk: Beck**

Beck’s thesis claims modernization undermines its own foundations. He identifies two central developments. First, qualitatively new risks (or better: dangers, threats, and harms) produced as unforeseen and unintended side effects of industrialized modernity are emerging. A risk logic increasingly replaces the traditional logic of social class.

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**Lecture 3 Different approaches to risk: New risks**

New risks, for example, BSE, smog, radiation, climate change, genetically modified food, and ozone depletion, mainly follow logics of allocation other than those of social class. Whilst these risks appear as unexpected side effects of industrialized modernity, they also cannot be solved easily on the basis of available knowledge. Uncertainty becomes a fundamental experience of modernity where it was once successfully overcome by science and technique.

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**Lecture 3 Different approaches to risk: Beck**

The risk society approach claims that risks are real and also socially constructed. That risks or hazards also affect the social ( increased the social inequalities). Beck focused in ethical aspect of risk decisions. Beck problematised the individual in relation to the social in a way that is an advance in complexity. For Beck ethical choices are the basis of social responsibility.

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**Lecture 3 Different approaches to risk: Ethics**

Most discussions of risk are developed in broadly consequentialist terms, focusing on the outcomes of risks as such. Risk from a virtue ethical perspective to decision to take the risk. Making ethical decisions about risk is not fundamentally about the actual chain of events that the decision sets in process, but about the reasonableness of the decision to take the risk in the first place.

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**Lecture 3 Different approaches to risk: Ethics**

Ethical aspect of risk, it is by nature to be associated with the notion of the individual as ethical being. The ethical dimensions of risk: the distinction between monetary or numerical value and ethical value of risk. The ethical, and not the monetary, value is the central aspect in ethical risk assessment.

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**Lecture 3 Different approaches to risk: Ethical Risk Assesment**

Lots of pressure from both inside and outside the organization towards increasing ethical risk assessment in organizations: Internally, frauds are costly. Relationship management is costly. Externally, there is movement by governments here and abroad concerning tightened ethical risk assessment.

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**Lecture 3 Different approaches to risk: Ethical Risk Assesment**

New Sources of Ethics Standards Sarbanes Oxley Internal controls, code of ethics for execs NYSE standards Expanded audit committee standards, annual CEO certification of corporate governance Sentencing guidelines Culture that includes ethical conduct, periodic ethics risk analysis DOJ principles of prosecution Adequacy of compliance program, history of similar wrongdoing

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**Lecture 3 Different approaches to risk: Ethical Risk Assesment**

Three sources of ethical risk: The industry The company The individual

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**Lecture 3 Different approaches to risk: Ethical Risk Assesment**

The industry How intense is the competition? (More=Higher Risk) Where is the competition most severe? Sales, Design, etc. How valuable is information about the competitor? (More=Higher Risk) What type of information? To what unit of the company? How differentiated is the product? (Less=Higher Risk) How important are a few large customers? (More=Higher Risk) How important are trade associations? How much contact is there between companies? (More=Higher Risk) Is there overcapacity in the industry? (More=Higher Risk) Does the industry have multiple relationships with its customers or business partners? (If Yes=Higher Risk) How closely regulated is the industry? (More=Higher Risk) How involved is organized crime in the industry? (More=Higher Risk)

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**Lecture 3 Different approaches to risk: Ethical Risk Assesment**

The company structure strategy How hierarchical is the company? (More=Higher Risk) How independent are the company divisions? (More=Higher Risk) How different are company policies in divisions? (More=Higher Risk) How closely do divisional financial and accounting staff work with headquarter’s staff? (Less=Higher Risk) To what extent does the company have “multiple” relationships with other companies? (More=Higher Risk) How much business does the company do in “problematic” countries? (More=Higher Risk) How much business does the company do with “problematic” industries? (More=Higher Risk) How much business does the company do with “problematic” suppliers and business partners? (More=Higher Risk) How flexible is the company in adjusting goals and objectives when industry conditions change? (If Not=Higher Risk)

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**Lecture 3 Different approaches to risk: Ethical Risk Assesment**

The company – Ethics System Does the company have a code of conduct? (Yes=Less Risk) Does the company have a values statement? (Yes=Less Risk) Are the CEO and other leaders known for their ethics? (Yes=Less Risk) Does the company communicate frequently regarding the ethics code and values statement? (Yes=Less Risk) Does the company conduct meaningful ethics training? (Yes=Less Risk) Does the company incorporate ethical and value-oriented behavior formally into the performance evaluation system? (Yes=Less Risk) Does the company reward ethical behavior in practice? (Yes=Less Risk) Does the company have an effective system for reporting ethical violations and concerns? (Yes=Less Risk) Does the company have an effective mechanism for employees to raise questions on difficult ethical choices? (Yes=Less Risk) Does the company renew its ethical code and values on a periodic basis? Does the company ever punish senior executives for unethical conduct? (Yes=Less Risk)

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**Lecture 3 Different approaches to risk: Ethical Risk Assesment**

The individual Does the company’s ethics program credibly emphasize that ethics is every employee’s business? (Yes=Less Risk) Does the company’s ethics program seek to develop employee skills in identifying and reasoning about ethical issues? (Yes=Less Risk) Does the company seek to rein in arrogance and hubris, and encourage humility and openness in its leaders? (Yes=Less Risk) Does the company do a thorough background check on every new hire, including verifying degrees and employment history? (Yes=Less Risk) Does the company screen out employees with problematic ethical incidents in their background? (Yes=Less Risk) How decisive is the company dealing with ethical violations which arise? (More=Less Risk) How effective is the employee assistance program in helping employees with personal or financial problems? (More=Less Risk)

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**Lecture 3 Different approaches to risk: Conclusion**

Different disciplines have different approaches to modelling and assessing risk. Economists focus on individuals and like to have axioms of rationality. Psychologists also focus on individuals but are more concerned about processes. Sociologists are concerned more with cultural aspects of society and the interaction between individuals. Their analysis is at a more aggregative level – that of society rather than the individual.

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Lecture 3 Goodbye!

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