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From risk to opportunity Lecture 2 John Hey and Carmen Pasca

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Some Rules of the Game 1.The purpose of this course is the development of your intuition, not for you to memorise slides and formula. 2.The first seven lectures are more general than the last five, but the contents of all these lectures concern concepts related to risk. 3.The material on the slides is not for you to memorise; you do not need to know in detail the contents of the slides; the examination will not be a test of memory. 4.This course is interactive; we wait for your ideas; during the course you are free to suggest to us things you want to do; we are ready within reason to change the topics. 5.We are very happy to teach this course, but we require your cooperation and respect. 6.We ask you to come to the front of the lecture theatre and not sit at the back talking and eating; the latter shows disrespect for us and the other students. 7.We reserve the right to throw out students who do not show respect and interest.

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Lecture 2: outline (italics extra material) 1.We start with announcing the result of the CAC 40 bet. 2.We will give you an example of (probability) axioms and their implications. 3.We will discuss the historical evolution of ideas on risk from the ancient Greeks to the economists Knight, Keynes, von Neumann, Morgenstern and Savage. 4.We will define and discuss Expected Values. 5.We will analyse your optimal decision in the CAC 40 bet (assuming neutrality) 6.We will pose the famous St Petersburg problem and ask you to think about it. 7.We will continue the historical development with psychologists and sociologists Kahnemann, Tversky, Beck, Giddens, Douglas, Luhmann, Reischer. 8.There is some extra material on IT in the contemporary age that is optional (slides 33-42). 9.We conclude by asking you to complete an online questionnaire telling us about your risk attitudes. 10.We will pay the winners of the CAC 40 bet.

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First the concluding game from Lecture 1 We concluded the first lecture with a simple game – a bet on the French stock index – CAC40.CAC40 You could either bet on it going up by on Friday the 14 th of September (now) relative to its level ( ) at the end of the lecture on Friday the 7 th of September, or it going down. 12 Students bet on it going Up. 17 Students bet on it going Down. It is now ????.?? It went Up/Down. So each of the 12/17 betting Up/Down get 2.42/1.71 at the end of the lecture. We discuss this later after covering Expected Values.

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Lecture 2: an example of axioms and their implications (revision?) In a situation of risk there are various possible outcomes, collections of which are called events. Denote by E an event and by F the set of all possible outcomes. We have the following axioms about probabilities on the various possible events, where P(E) denotes the probability of event E: 1.For all E in F, P(E) 0. 2.P(F) = 1. 3.For all disjoint E 1 and E 2 (that is, they have no outcomes in common) P(E 1 or E 2 ) = P(E 1 ) + P(E 2 ). The implications are: 1.If E 1 is a subset of E 2 then P(E 1 ) P(E 2 ). 2.P( ) = 0 (where is the empty set). 3.0 P(E) 1 for all E. 4.P(E 1 or E 2 ) = P(E 1 ) + P(E 2 ) - P(E 1 and E 2 ) for any E 1 and E 2. 5.The probability that an event will not happen is one minus the probability that it will.

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Lecture 2 Risk, an historical perspective: The etymology of the word We start with the ancient civilizations. Later we cover the Middle-Ages, the Modern period and end in the present day. The term risk may be traced back to classical Greek, meaning root, later used in Latin for cliff. The etymology of the word is unknown: some suspect it to be Arabic in origin. In Europe is to be found in medieval documents. Latin and vulgar Latin: resicum, risicum, riscus: (cliff in English), récif (in French), is the direct formal origin for Italian (risico, risco, rischio), Spanish riesgo and French risque (from the 18 th century).

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Lecture 2 Risk, an historical perspective: Evolution of the word According to Niklas Luhmann, ancient civilizations were preoccupied by uncertainty about the future. They believed in divinatory practices to provide reliable security against misfortune. The term risk first appears in the transitional period between the late Middle Ages and the early Modern era. Middle Ages: the law of maritime trade and maritime insurance (the distribution of roles between the suppliers of capital and the seafarers).

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Lecture 2 Risk, an historical perspective: The Middle Ages Risk finds significant application in the fields of navigation and trade. Particularly in the Middle Ages when people woke up and dared to discover the world. So that from the 16 th century on, the term acquired a positive meaning; for example in middle-high- German Rysigo was in 1507 a technical term for business; had the meaning to dare, to undertake, to make enterprises, hope for economic success. (Luhmann Sociology of Risk).

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Lecture 2 Risk, an historical perspective: The Middle Ages In the Middle-Ages, maritime insurance was an early instance of planned risk control. Insurance contracts contained words like the following: risicum and fortunam, pro securitate and risico, these are words found in contracts regulating who is to bear a loss in the event of its occurrence. Terminology used in the Middle Ages (and after) include: danger, venture, chance, luck, courage, fear, adventure, prudence.

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Lecture 2 Risk, an historical perspective: The Modern Period Lucien Febvre, historian, (right) rather indirectly referred to risk through the phrase the sense of security (in French le sentiment de sécurité). For him the sense of security varied over time, and he showed that under the Old Regime (pre-Revolution) people relied on trust in God. In the late sixteenth and early seventeenth century, risk management was a newly emerging field in global trade, a field with profound epistemological consequences. The seventeenth and eighteenth centuries saw the birth of probability theory with Cardan, Pascal, Fermat, Daniel Bernoulli and his uncle Jacob Daniel. Blaise Pascal (right) introduced probability theory in 1657.

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Lecture 2 Risk, an historical perspective: the 20 th century During this period, there were contributions to the analysis of risk from many different social sciences; examples include: From the economic perspective: Knight, Keynes, von Neumann and Morgenstern, and Savage. From the psychological perspective: Kahnemann and Tversky. From the sociological perspective: Beck, Giddens, Douglas, Luhmann, Reischer.

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Lecture 2 Risk, an historical perspective: Knights definitions The most famous definition of risk is that provided by Frank Knight (1921) who wrote during a period of active research into the foundations of probabilities. Knight made the crucial distinction between risk and uncertainty. Situations with risk were those where the outcomes were unknown but governed by probability distributions known at the outset. He argued that these situations, where decision making rules such as maximising expected utility can be applied, differ in a deep way from "uncertain" ones, where the outcomes were likewise random, but governed by an unknown probability model. Interestingly and crucially, Knight argued that uncertainty gave rise to economic profits that perfect competition could not eliminate. Contemporaneous authors include Keynes (1921), von Mises (1928), Kolmogorov (1933), Rawls, Allais, Neumann and Morgenstern (1944) and Savage (1954). Later we shall discuss more recent developments.

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Lecture 2 Risk, an historical perspective: Subjective v Objective One debate from this period relates to subjective versus objective interpretations of probability. According to objective interpretations, probabilities are real. We may discover them by logic or estimate them through statistical analyses. (How do you measure? – with a thermometer?) According to subjective interpretations, probabilities are human beliefs. Individuals specify them to characterise their own uncertainty. (Fair? coin.)

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Lecture 2 Risk, an historical perspective: where do probabilities come from? Knight (right) distinguished between probabilities obtained in two different ways: A priori probabilities are derived from inherent symmetries, as in the throw of a die or the toss of a coin (a coin is symmetrical – and there is no reason for it to land more often on one side; a die is symmetrical – there is no reason for it to land more often on one side). Statistical probabilities are obtained through analysis of homogenous data (uniformly repeated). He recognised that, in absence of homogenous data or symmetries, people may still somehow quantify their uncertainty (subjective assessment).

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Lecture 2 Risk, an historical perspective: Subjective assessment Knight, the example of balls: in an urn he considered a situation in which we do not know the proportion of red to black balls but we are allowed to look inside the urn and form our own estimate of that proportion. (This is exactly like the Bingo Blower.)Bingo Blower Knight was loath to attach the label probabilities to opinions formed in the absence of symmetry or homogenous data. He suggested that a priori and statistics reflect measurable uncertainty, and opinions represent unmeasurable uncertainty.

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Lecture 2 Risk, an historical perspective: Risk and uncertainty a la Knight To preserve the distinction… between a measurable uncertainty and an unmeasurable one we may use the term risk to designate the former and the term uncertainty for the latter. This statement is Knights famous definition of risk. Risk relates to objective probabilities. Uncertainty relates to subjective or no probabilities. Knight acknowledged that his use of both of terms risk and uncertaintydid not conform to common usage. Nowadays it is more common to use the term ambiguity.

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Lecture 2 Risk, an historical perspective: Keynes Keynes interpretation of probability is objectivist because he stipulates that probability relationships are rationally determined. (Logic determines probabilities.) According to him, if two individuals consider the same evidence for a proposition, they must assign the same probability based on that evidence. Given any two propositions, the relationship between them is a product of logic. Like Knight, Keynes accepted that in some situations of uncertainty, objective probabilities cannot be assigned.

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Lecture 2 Risk, an historical perspective: Keynes and Knight Accordingly, Keynes interpretation of probability is amenable to Knights distinction between risk and uncertainty. For Knight, propositions are categorized as either risk and uncertainty. Risk can be assessed and calculated in terms of its numerical probabilities. Uncertainty cannot be treated in that manner.

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Lecture 2 Risk, an historical perspective: von Neumann and Morgenstern In Theory of Games and Economic Behaviour (1944), these two authors developed an axiomatic theory of choice under risk, called Expected Utility theory based on four obvious axioms: 1.Completeness: for any two gambles L and M, either L M or L M or L M [where means preferred to, less preferred than, indifferent with; later means preferred or indiffent to]. 2.Transitivity: If L M and M N then L N. 3.Continuity: If L M N then there exists a probability p such that pL+(1- p)N M [where pL+(1-p)N indicates a gamble which leads to L with probability p and to N with probability (1-p)]. 4.Independence: If L M then for any gamble N and any probability p pL+(1-p)N pM+(1-p)N. Do you think that these axioms are reasonable? We will discuss them later.

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Lecture 2 Risk, an historical perspective: Savage Savage in his Foundations of Statistics 1954 made a dramatic extension of Expected Utility theory into Subjective Expected Utility theory. He listed a set of reasonable axioms which implied not only that individuals obeying these axioms maximised their expected utility, but also that they implicitly have subjective probabilities which they attach to the various outcomes and are used to calculate the expected utilities. Magic! We will look at this later.

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Lecture 2 Expected Values (revision?) Suppose some variable X takes n values x 1,x 2,…,x n with associated probabilities p 1,p 2,…,p n, then the Expected Value of X, denoted by EX, is given by EX = p 1 x 1 + p 2 x 2 + …+ p n x n Note that this is simply the weighted average of the values where the weights are the probabilities. Example 1: n=2, x 1 = 100, x 2 = 0, p 1 = 0.5, p 2 = 0.5 (the gamble we sold to Ami) then EX = 0.5* *0 = 50. Example 2: n =3, x 1 = 10, x 2 = 5, x 3 = 0, p 1 = 0.25, p 2 = 0.5, p 3 = 0.25 (symmetrical around 5) then EX = 0.25*10+0.5*5+0.25*0 = 5. Example 3: n =3, x 1 = 10, x 2 = 5, x 3 = 0, p 1 = 0.5, p 2 = 0.25, p 3 = 0.25 (not symmetrical) then EX = 0.5* *5+0.25*0 = 6.25.

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What should you have done in the bet in Lecture 1? Suppose you have your own assessment of the probability p of the index going Up. Suppose n students took part and, excluding you, m have bet Up. Then you have the following payoff matrix (excluding the 1 stake): So (if you are risk-neutral) you should bet Up if pn/(m+1) > (1-p)n/(n-m+1) That is, if p > (m+1)/(n+2). If m is n/2 then this condition reduces to p > ½. If you thought ½ the students are betting on Up, you should have bet on the event you thought most likely. But… The out-turnExpected payoff UpDown Your bet/decision Upn/(m+1)0pn/(m+1) Down0n/(n-m+1)(1-p)n/(n-m+1)

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Lecture 2 Something for you to think about Suppose we toss a fair coin until it comes down Heads and let n denote the number of tosses needed up to and including the first head. Suppose we pay you 2 n. Two questions for you: 1.What is the Expected Payment to you (the Expected Value of the game)? 2.How much would you be willing to pay to play this game? We will answer the first question now and leave you all to think about the answer to the second – particularly those who stayed in last weeks auction until the price reached 50 (the expected value of the gamble). The probability of needing n tosses before the first head is ½ n (for all n). So the expected value of this game is 2(½) (½) (½) (½) (½) = = Yes INFINITY! How much would you pay? We will discuss the implications later.

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Lecture 2 Risk, an historical perspective: Theys and Luhmann Theys, the contemporary historian, suggested a pattern of evolution of the concept of risk that governs the search for security: Europe passed from the notion of risk as divine fatality (against which human protection is of little weight) to that of controlled risk that would have as its corollary the right to security. In contrast Luhmann enriched risk society analysis with his theory of systems. To him risk is not an object but a perception. Here risk is a specific form of dealing with the future that has to be decided in the context of probability and improbability.

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Lecture 2 Risk, an historical perspective: Luhmann There is a long gap between when a decision is made and when its consequences are felt, with random factors affecting them. To talk of risks is to see future losses as the consequence of a decision that has been made. For Luhmann this is where risk differs from danger, with danger being attributable to external causes and corresponding to those affected by decisions. Although the distinction is slight because one person's risk is another person's danger, it points to the key issue of acceptance of risk decisions.

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Lecture 2 Risk, an historical perspective: Ulrich Beck Beck's main contribution was to build risk systematically into a theory of modern society and its dilemmas. Risk is seen as a defining feature of society itself, forming the dark side of industrial successes, technical and scientific progress, and economic growth. It has stimulated changes in social relations, family structure, political and cultural organization, and even the self.

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Lecture 2 Risk, an historical perspective: Beck Unlike the threats of early industrialization, the risks of late modernity (nuclear, chemical, genetic, ecological, etc.) are generated by techno-economic decisions and considerations of utility. The novel aspect of contemporary risk society is that people's decisions as a civilization lead to problems and dangers that radically contradict the established language of control and conventional techniques of calculation.

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Lecture 2 Risk, an historical perspective: Beck Current risks, according to Beck are not socially, spatially, or temporally demarcated; there are no clear-cut solutions; and it is difficult to trace responsibility or assess compensation for those who are affected. In addition, human perception fails to notice many of the risks: they become visible only through scientific interpretation (as in the case of stratospheric ozone depletion), which in turn increases dependence on experts.

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Lecture 2 Risk, an historical perspective: Beck Beck focuses above all on environmental and health risks, especially genetic technology. He later extended the concept of risk to global financial crises and transnational terrorist networks (Beck 2002). Bringing together such disparate phenomena enables him to identify relevant trends in modern societies but has the drawback of implying a less fragmented world than that which Beck perceives.

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Lecture 2 Risk, an historical perspective: Rescher Nicholas Rescher proposed the following definition: Risk is the changing of negativity – of some loss or harm (Risk, a philosophical introduction to the theory of risk evaluation and management, United Press of America, 1983, p. 5.).

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Lecture 2 Risk, an historical perspective: Rowe Risk analysis: W. D. Rowe, An Anatomy of Risk (1977). Risk analysis emerged in the decade of the 1970's as a multidisciplinary enquiry that employed engineering and natural science methodologies in the service of measuring, predicting, and managing a large class of events that were presumed to have physical and biological causes as their basis. The natural science basis of these techniques distinguished them from actuarial, economic or financial risk analysis.

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Lecture 2 Risk, an historical perspective: Rowe Rowe who lays out the framework for a natural science enquiry into the probability of unwanted consequences as the main task of risk analysis but does not use the terms "real" or "actual." Rowe's general framework is carried into more recent discussions by Wilson and Crouch, Risk Assessment and Comparison: An Introduction (236 Science ).

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Lecture 2 Risk, an historical perspective: Risk and globalisation Risk in today's society: risk is related with globalization, science, technologies and innovations and with what trade-offs it is possible to make. Risk and globalization: the globalization process generated complexity and new risks. The evolution of society and the evolution of technology became inseparable. Globalization also generated opportunities: opportunities are not without risks such as those arising from volatile capital movements.

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Lecture 2 Risk, an historical perspective: Technology Dealing today with major technological risks supposed three crucial thinks for firms: risk assessment, risk sharing and risk control. Technological progress is ambivalent: on the one hand it enhances economic growth and the quality of life and on the other hand, it exacerbates the consequences of human error; past experience also reveals that new industrial processes and products often hide lethal side effects that show up only in the long run.

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Lecture 2 Risk, an historical perspective: Technology Major technological risks: refer to the probability of occurrence of dreadful outcomes linked to an explosion a fire, a leakage, or any sudden malfunctioning or misuse of technology (as in Chernobyl, Seveso or Bhopal). Catastrophic risks, which are characterised by small probabilities of large, collective and irreversible losses.

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Lecture 2 Risk, an historical perspective: IT Technical risk is exposure to loss arising to activities such as design and engineering, manufacturing, technological processes and test procedures. Today's IT risks are complexly interconnected inside and outside the enterprise. As IT has increased, the consequences of IT risk have increased as well. It is no longer confined to a companys IT department or data centre.

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Lecture 2 Risk, an historical perspective: IT An IT risk incident has the potential to produce substantial business consequences that touch a wide range of owners. Examples: delays and unexpected costs in development projects, temporary or extended loss of service, data loss or theft, etc. Case studies of companies like Tektronix and Comair. Comair, a $780 million subsidiary of Delta Air Lines, experienced a runaway IT risk incident on December 24, 2004, when the companys crew-scheduling system failed.

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Lecture 2 Risk, an historical perspective: IT case study Without its scheduling system, an airline does not fly. In addition to the damage to the companys reputation, the loss from this single incident was nearly as high as the firms entire $25.7 million operating profit for the previous quarter. It is an example of corporate risk. The Comair case is about the risk of availability. The Tektronix case study: is about agility, the ability to change rapidly with controlled cost and risk (electronics manufacturer).

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Lecture 2 Risk, an historical perspective: IT case study Tektronix arrived at this strategic dilemma gradually. For decades the companys IT department had extended existing systems, built new stand-alone systems, and written software to link systems as needed. Every new solution was an unconscious trade-off of long term agility in favour of short-term benefits. By the early 1990s, Tektronix executives knew their IT systems had problems. It was only when Tektronix executives tried to break from the past that they saw the real threat those familiar annoyances posed.

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Lecture 2 Risk, an historical perspective: IT case study IT risk in terms of business consequences In mid-2005, CardSystems Solutions, Inc. reported that unknown persons had gained unauthorized access to computerized credit transactions for 40 million credit card holders. IT has become more and more central to business over the past twenty years, but many enterprises have not adjusted their processes for making key decisions about IT and IT risks.

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Lecture 2 Risk, an historical perspective: IT The causes of IT risks: most IT risk results not from technology itself but from decision-making processes that consciously or unconsciously ignore the full range of potential business consequences of IT risk. IT governance is embedded in formal structures that allocate rights and responsibilities for decisions in certain IT domains (such as applications, architecture and security) to appropriate business and IT executives. IT risk is now business risk, with business consequences, enterprises must change the way they manage it.

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Lecture 2 Risk, an historical perspective: IT Risk and complexity. Uncontrolled Complexity: complexity per se is not necessarily more risky than simplicity. Complexity without solid engineering increases risk in many ways. Inattention to Risk : Missing or inadequate knowledge. Poor infrastructure management Employee ignorance, negligence, or malfeasance

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Lecture 2 Risk, an historical perspective: Conclusion Over the decades the concepts of risk (and associate concepts) have evolved and changed. There is beginning to be a consensus that there are risks that can be quantified and are in some way objective and uncertainties which may be unmeasurable or only partially measurable. The distinction is not always clear; neither is the distinction between objective and subjective risks. We shall see what social sciences make of all this!

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Lecture 2: Before you go - a survey We are interested in your attitude to risks of various kinds. An experimental economics colleague, Jonathan Alevy, at the University of Alaska has an online survey at his university.online survey We would be grateful if you could go to this site and respond to this survey. In the Identification field please put Sciences-Po followed by your matriculation number. Your responses will be treated in confidence. We will discuss the findings in the next lectures.

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Lecture 2 Goodbye! The winners of the CAC 40 bet can come and be paid. By the way, you will find a specimen (blank) Mid Term examination paper on the website.specimen

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