Plight of the Fortune Tellers: Why We Need to Manage Financial Risk Differently

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Other editions. Enlarge cover. Error rating book. Refresh and try again. Open Preview See a Problem? Details if other :. Thanks for telling us about the problem. Return to Book Page. Today's top financial-risk professionals have come to rely on ever-more sophisticated mathematics in their attempts to come to grips with financial risk.

But this excessive reliance on quantitative precision is misleading--and it puts us all at risk. This is the case that Riccardo Rebonato makes in Plight of the Fortune Tellers --and coming from someone who is both an exper Today's top financial-risk professionals have come to rely on ever-more sophisticated mathematics in their attempts to come to grips with financial risk.

This is the case that Riccardo Rebonato makes in Plight of the Fortune Tellers --and coming from someone who is both an experienced market professional and an academic, this heresy is worth listening to. Rebonato forcefully argues that we must restore genuine decision making to our financial planning, and he shows us how to do it using probability, experimental psychology, and decision theory. This is the only way to effectively manage financial risk in a manner congruent with how human beings actually react to chance. Rebonato challenges us to rethink the standard wisdom about probability in financial-risk management.

Risk managers have become obsessed with measuring risk and believe that these quantitative results by themselves can guide sound financial choices--but they can't. In this book, Rebonato offers a radical yet surprisingly commonsense solution, one that seeks to remind us that managing risk comes down to real people making decisions under uncertainty. Plight of the Fortune Tellers is not only a book for the decision makers of Wall Street, it's a must-read for anyone concerned about how today's financial markets are run.

The stakes have never been higher--can you risk it? Get A Copy. Hardcover , pages. More Details Original Title. Other Editions 7. Friend Reviews. To see what your friends thought of this book, please sign up. To ask other readers questions about Plight of the Fortune Tellers , please sign up. Be the first to ask a question about Plight of the Fortune Tellers. Lists with This Book. Community Reviews.

Showing Rating details. He is a visiting lecturer in mathematical finance at the University of Oxford and adjunct professor at the Tanaka Business School, Imperial College London. He has written many books and articles on finance. Reviews Review Policy. Published on. Flowing text, Original pages. Best For. Web, Tablet, Phone, eReader. Content Protection. Read Aloud. Learn More. Flag as inappropriate. It syncs automatically with your account and allows you to read online or offline wherever you are. Please follow the detailed Help center instructions to transfer the files to supported eReaders.

More related to business. See more. Markus Venzin. A new era of global banking and insurance is emerging, with leading banks eager to serve international markets. This book explores the issues that arise for banks in their strategic choices as they move into these new international markets. Building an International Financial Services Firm challenges conventional assumptions from the international management literature on topics such as the limits of globalization, the importance of cultural and institutional distance, the nature of economies of scale and scope, the existence of first mover advantages, the logic behind the global value chain configuration, the speed and timing of market entry, as well as organizational architecture.

It focuses on fundamental strategic decisions such as when, where, and how to enter foreign markets and how to design the organizational architecture of the multinational financial services firm. Using simple theoretical frameworks illustrated by case examples, this book provides a thorough guide to the challenges of the international market for financial services firms, both for those working in the financial services industry, and researchers studying the area.

Trade, Investment and Competition in International Banking. This book outlines the influences on the evolution of international banking and analyses trade and investment in the international banking industry, covering cross-border trade in banking services, foreign direct investment by banks, international financial centres, capital movements, and competition between banks. Focusing on competitive advantage, it compares the leading banks' international business.

This book is of interest to academics and students as well as to bankers.

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It provides a transversal and truly comprehensive overview of the international banking industry, focusing on the organization of the industry and the influences on it, rather than on the functions of banks themselves. Nomi Prins. Central banks and international institutions like the IMF have overstepped their traditional mandates by directing the flow of epic sums of fabricated money without any checks or balances. Meanwhile, the open door between private and central banking has ensured endless opportunities for market manipulation and asset bubbles--with government support.

Through on-the-ground reporting, Prins reveals how five regions and their central banks reshaped economics and geopolitics. The questions that are being asked are not hard ones. I will claim that they are ill-posed ones. We are doing a lot of risk-management engineering as if the pillars of risk-management science were so well-established as not to require much questioning. An aircraft engineer does not question the correctness of the physical laws underpinning the technical prescriptions on how to build safe planes every time he has to redesign the profile of a wing.

He just gets on and does it. Unfortunately, I think that we risk managers have not thought deeply enough about the foundations of our discipline. We are not even clear about the appropriate meaning, in the riskmanagement context, of the most central concept of all: that of probability.

If I am correct, and given that what is at stake is the good functioning of the world economy, both practitioners and regulators should pause for thought. How is this possible? How can the scores of hard-science PhDs employed by banks as risk managers be guilty, of all things, of an unreflective approach to their discipline? If even they are unable to think deeply enough about these problems, who possibly can? Paradoxically, just there, in their finely honed quantitative skills, lies the heart of the problem.

Most of the PhDs employed by banks, some for derivatives pricing, some for risk management, obtained their doctorates at the top U. Why this choice of subjects? As for these young physicists and mathematicians, many, for a variety of reasons, decide that physics, or mathematics, would not suffer unduly if they were to part ways with it and knock at the door of a bank.

So, very hard, but well-defined, technical problems are relatively easy for these quants: finding an efficient technique to solve a very-high-dimensional integral, combining Fourier transforms with Monte Carlo simulations, employing wavelets for signal decomposition, carrying out complicated contour integrals in the complex plane, etc.

Lest I offend anyone, I can safely say that as I write this I am thinking of myself some fifteen to twenty years ago. As for the quants, they love nothing more than xxii P R E FA C E having to tackle technically difficult problems—the more difficult, the better. So, it is not so surprising after all that the quant suggesting that a simpler, less quantitative approach should be used to solve a problem is only slightly less rare than a turkey voting for Christmas.

In the last decade or so the international regulators have been inspired, in writing their rule books, by what they have perceived to be the current cuttingedge industry practice. This approach to regulation has been innovative, refreshing, and laudable. In observing that thousands of quants had been employed around the world to crack tough risk-management problems, the regulators were perfectly justified in concluding that this was indeed the way senior bank managers thought about and managed their risk. If, in the case of market risk, estimating the 99th loss percentile seemed to be the way many bank risk managers looked at and managed risk, why should it be so unreasonable to ask for the What are a couple of nines between friends, after all?

Were these not the smartest kids on the block, after all? The quantitative management of risk has long ceased to be pure or applied science—it is now big business. The less-than-perfect result of this combination was transparent in the terse comments made at the Geneva ICBI riskmanagement conference by a very senior official of one of the international regulatory bodies.

For once, I will leave the comment unattributed. Alas, in my opinion, I believe that in quantitative financial risk management some of the answers have at times been precisely meaningless. With this book I intend to explain not only to the quants but also to the nonquantitative bosses of their bosses and, hopefully, to the regulators and policy makers why I believe this is the case. I also think that a more meaningful, yet still strongly quantitative, way of looking at risk management is possible.

Hard quantitative skills, and the logical forma mentis that comes with them, are therefore not useless—if anything, the technical challenges for a more meaningful approach to risk management that takes at its root Bayesian analysis and subjective probabilities are even greater than for the current, more traditional, probabilistic approach. However, these techniques should be used in a different way than they have been so far and we should reason about financial risk management in a different way than we often appear to now.

So, the quantitative approach probably remains the high road to financial risk management. This way of looking at risk-management problems should have two advantages: it is congruent and resonant with the way human beings actually do think and feel about risk; and, if my suggestions are found useful and convincing, they can be extended without intellectual break into a precise quantitative treatment.

Most importantly, the risk managers quantitative or not who find my way of looking at these problems convincing should be able to ask themselves whether or not they are asking a meaningful question. This is no small feat, and, I believe, is not too difficult. It just requires fewer formulae less plumbing and more thinking. As a consequence, this will be my first book without formulae.

Since I will try to show that a particular quantitative approach to risk management is flawed, and yet I want to reach a general, i. I have tried to tackle it by employing a qualitative and discursive style, while still keeping the reasoning as clear and honest as possible. This is difficult, but should be possible. I therefore resolved not to have any equations at all. These can be skipped by the impatient or nonquantitative reader without loss of continuity. Finally, a word about the choice of the picture that graces the cover of this book.

It is a detail of a painting by Caravaggio called, in English, The Cardsharps. There are some obvious parallels between what is happening in the painting and the contents of this book. There is of course a reference to financial risk. A bit more subtly, however, both the painting and the book try to alert us to the dire consequences in miscalculating the odds of a risky activity. The parallels should not be pushed too far, though.

First, I have failed to distinguish clearly in this book among probability as degree of belief, Bayesian probability, and subjective probability. This is in general not correct. It is correct enough, however, in the context of this book. Second, I am aware that the concept of probability as degree of belief which I implicitly use in this book is not uncontroversial. I cannot go into the objections and possible defenses. For an impassioned and in my opinion convincing defense of probability as degree of belief see E.

For a critique, see, for example, K. Third, I do not discuss in this book the Laplacian definition of probability based on symmetry. It can be very powerful, but its domain of applicability is somewhat restricted and is of little relevance to risk management. It is also not without its logical problems. I am grateful to the publisher for agreeing to reproduce it. I also thank the friends and colleagues who were kind enough to read this manuscript at various stages of its writing and to offer their comments. I am grateful to the delegates at various conferences in Geneva, Boston, and New York with whom I have discussed some of the topics covered in the text.

Their encouragement and comments have been invaluable. Two referees one of whom was Professor Alex McNeil helped me greatly with their suggestions and constructive criticism. It has been a pleasure to work with Princeton University Press, and with Richard Baggaley in particular. Thanks to their efforts this book is much the better.

Needless to say, all remaining errors are mine. I have indeed observed the same disposition among the mathematicians I have known in Europe, although I could never observe the least analogy between the two sciences, unless those people suppose that because the smallest circle hath as many degrees as the largest, therefore the regulation and management of the world require no more abilities than the handling and turning of a globe. It is about the strengths and limitations of this approach.

Since we forget the past at our own peril, we could do worse than remind ourselves that the application of statistics to economic, political, and social matters is hardly a new idea. The closeness of this link, between compilations of numbers, tables of data, and actuarial information on the one hand and the organization and running of a state on the other 2 CHAPTER 1 may today strike us as strange. But even when mathematicians did lend a helping hand in bringing it to life, from the very beginning there was always something much more practical and hard-nosed about statistics.

To see how this happened, let us start at least close to the beginning, and go back to the days of the French Revolution. In the first pages of Italian Journey , Goethe writes: I found that in Germany they were engaged in a species of political enquiry to which they had given the name of Statistics. By statistical is meant in Germany an inquiry for the purpose of ascertaining the political strength of a country, or questions concerning matters of state. It is in fact in that we find another German, Leibniz, trying to forward the cause of Prince Frederick of Prussia who wanted to become king of the united Brandenburg and Prussia.

The interesting point for our discussion is that Leibniz offers his help by deploying a novel tool for his argument: statistics. Prince Frederick of Prussia was at a disadvantage with respect to his political rivals, because the population of Prussia was thought to be far too small compared with that of Brandenburg to command a comparable seat at the high table of power.

If at the time the true measure of the power of a country was the size of its population, the ruler could not be a Prussian. What Leibniz set out to prove was that, despite its smaller geographical size, Prussia was nonetheless more populous than was thought, indeed almost as populous as Brandenburg—and hence, by right and might, virtually as important. How did he set out to do so in those pre-census days? What is of great current interest is the logical chain employed by Leibniz, i. If anyone were ever to doubt that there is real, tangible power in data and in data collection, this first example of the application of the statistical line of argument to influence practical action should never be forgotten.

The modern bank that painstakingly collects information about failures in the clearing of cheques, about minute fraud, about the delinquency of credit card holders and mortgagors perhaps sorted by age, postcode, income bracket, etc. To the children of the Internet age it may all seem very obvious. The first statisticians were not political philosophers or imaginative myth-makers: they were civil servants. What does a third of a child look like? In short, the discipline of probability, to which these French minds contributed so much, appeared to offer the first glimpses of an intriguing promise: a quantitative approach to decision making.

The French way of looking at statistics and of using empirical data has clearly won the day, and rightly so. Perhaps, however, the pendulum has swung too far in the French direction. Perhaps we have come to believe, or assume, that the power of the French recipe marrying empirical data with a sophisticated theory of probability is, at least in principle, boundless. This overconfident extrapolation from early, impressive successes of a new method is a recurrent feature of modern thought.

The more elegant the theory, the greater the confidence in this extrapolation. Few inventions of the human mind have been more impressive than Newtonian mechanics. The practical success of its predictions and the beauty of the theory took a hold on Western thought that seemed at times almost impossible to shake off. Yet two cornerstones of the Newtonian edifice, the absolute nature of time and the intrinsically deterministic nature of the universe, were ultimately to be refuted by relativity and quantum mechanics, respectively.

Abandoning the Newtonian view of the world was made more difficult, not easier, by its beauty and its successes. It sounds almost irreverent to shift in one paragraph from Newtonian physics and the absolute nature of time to the management of financial risk.

Yet I think that one can recognize a similar case of overconfident extrapolation in the current approach to statistics applied to finance. In particular, I believe that in the field of financial risk management we have become too emboldened by some remarkable successes and have been trying to apply similar techniques to areas of inquiry that are only superficially similar. We have come to take for granted that while some of the questions may be hard, they are always well-posed.

And if the policies and practices in question are of great importance to our well-being as is, for instance, the stability and prudent control of the financial system , we are all in great danger. Through financial innovations, a marvelously intricate system has developed to match the needs of those who want to borrow money for investment or immediate consumption and of those who are willing to lend it. But the modern financial system is far more than a glorified brokerage of funds between borrowers and lenders. The magic of modern financial engineering truly becomes apparent in the way risk, not just money, is parceled, repackaged, and distributed to different players in the economy.

Rather than presenting tables of numbers and statistics, a simple, homely example can best illustrate the resourcefulness, the reach, and the intricacies of modern applied finance. Let us look at a young couple who have just taken out their first mortgage on a small house with a local bank on Long Island. Every month, they will pay the interest on the loan plus a small part of the money borrowed. Unbeknownst to them, their monthly mortgage payments will undergo transformations that they are unlikely even to imagine. Despite the fact that the couple will continue to make their monthly mortgage payments to their local bank, it is very likely that their mortgage i.

Once acquired by this institution, it will be pooled with thousands of other mortgages that have been originated by other small banks around the country to advance money to similar home buyers. These assets then receive the blessing of the federal agency who bought them in the form of a promise to continue to pay the interest even if the couple of newlyweds or any of their thousands of fellow co-mortgagors find themselves unable to do so.

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Having given its seal of approval and financial guarantee , the federal institution may create, out of the thousands of small mortgages, new standardized securities that pay interest the rechanneled mortgage payments and will ultimately repay the principal the amount borrowed by the Long Island couple. These new securities, which have now been made appealing to investors through their standardization and the financial guarantee, can be sold to banks, individuals, mutual funds, etc. Some of these standardized securities may also be chopped into smaller pieces, one piece paying only the interest, the other only the principal when and if it arrives, thereby satisfying the needs and the risk appetite of different classes of investors.

So large is this flow of money that every rivulet has the potential to create a specialized market in itself. Few tasks may appear more mundane than making sure that the interest payments on the mortgages are indeed made on time, keeping track of who has repaid their mortgage early, channeling all the payments where they are due just when they are due, etc. A tiny fraction of the total value of the underlying mortgages is paid in fees for this humble servicing task. Yet so enormous is the river of mortgage payments, that this small fraction of a percent of what it carries along, its flotsam and jetsam, as it were, still constitutes a very large pool of money.

And so, even the fees earned for the administration of the various cash flows become tradeable instruments in 8 CHAPTER 1 themselves, for whose ownership investment banks, hedge funds, and investors in general will engage in brisk, and sometimes furious, trading. The trading of all these mortgage-based securities, ultimately still created from the payments made by the couple on Long Island and their peers, need not even be confined to the country where the mortgage originated.

The same securities, ultimately backed by the tens of thousands of individual private mortgage borrowers, may be purchased, say, by the Central Bank of China. This body may choose to do so in order to invest some of the cash originating from the Chinese trade surplus with the United States. But this choice has an effect back in the country where the mortgages were originated. By choosing to invest in these securities, the Central Bank of China contributes to making their price higher. But the interest paid by a security is inversely linked to its price.

The international demand for these repackaged mortgages therefore keeps or, actually, pushes down U. As the borrowing cost to buy a house goes down, more prospective buyers are willing to take out mortgages, new houses are built to meet demand, the house-building sector prospers and employment remains high.

The next-door neighbor of the couple on Long Island just happens to be the owner of one small enterprise in the building sector as it happens, he specializes in roof tiling. The strong order book of his roof tiling business and his optimistic overall job outlook make him feel confident about his prospects. Confident enough, indeed, to take out a mortgage for a larger property. So he walks into the local branch of his Long Island bank. Au refrain. There is nothing special about mortgages: a similarly intricate and multilayered story could be told about insurance products, the funding of small or large businesses, credit cards, investment funds, etc.

What all these activities have in common is the redirection, protection from, concentration, or diversification of some form of risk. But there is more. All these pieces of financial wizardry must perform their magic while ensuring that the resulting pieces of paper that are exchanged between borrowers and lenders enjoy an elusive but all-important property: the ability to flow smoothly and without interruptions among the various players in the economy. All the fancy pieces of paper are useful only if they can freely flow, i.

As the mortgage example suggests, if an occlusion occurs anywhere in the financial flows that link the payments made to the local Long Island bank to the foreign exchange management reserve office of the Bank of China, the repercussions of this clogging of the financial arteries will be felt a long way from where it happens be it on Long Island or in Beijing. Luckily, the smooth functioning of this complex system does not have to rely on the shocks not happening in the first place: [T]he interesting question is not whether or not risk will crystallize, as in one form or another risks crystallize every day.

Rather the important question is whether … our capital markets can absorb them. But if the shock is too big or if, for any reason, some of the adjusting mechanisms are prevented from acting promptly and efficiently, the normal repair mechanisms may not be sufficient to restore the smooth functioning of the financial flows. In some pathological situations, they may even become counterproductive. Tell me, for example, who is in charge of the supply of bread to the population of London. Nobody is in charge and yet, most of the time, all of these transactions, and many more, flow without any problems.

The financial system is robust, by virtue of literally hundreds of self-organizing corrective mechanisms, but it is not infinitely robust. How does this happen?

Hedge Funds and Risks - Financial Markets by Yale University #15

This is all well and good unless all of the depositors simultaneously want their money back. As long as all the users make their decisions close-to-independently, only a relatively small safety margin of spare electricity, spare phone line capacity, petrol in filling stations, food on supermarket shelves, etc. Banks, are, however, different, and not in a way that makes a bank regulator sleep any more peacefully. We do so spontaneously, not because some regulation tells us to behave this way, and it is rational for us to do so.

But if a rumor spreads that a bank is not solvent, the individually rational thing to do is to rush to the head of the queue, not to come back tomorrow when the queue, which currently circles two blocks, will be shorter: by tomorrow the queue may well be shorter, but only because there may be no money left in the vault. This is how runs on banks occur: given the asymmetry of information between insiders and depositors, the same response run for the till!

In most industrialized societies, governments have stepped in by creating deposit insurance. In the case of a healthy bank, this arrangement can prevent the run from occurring in the first place. A possible explanation of how these collective behaviors may become ordered can be found in D. It therefore imposes another stipulation to this otherwise too-good-to-be-true arrangement: the government, the covenant goes, will indeed step in to guarantee the deposits of the public even if the bank were to fail; but, in exchange for these arrangements, which are extremely useful for the public and for the banks, it will acquire a supervisory role over banking operations.

Of course it is well within the remit of the government to care about systemic financial risk even in the absence of deposit insurance, but this commitment certainly focuses its mind. The management of financial risk therefore acutely matters, not only to the financial institutions in the long chain from the small Long Island bank to the Bank of China, but to the public at large and, as the agent of the public and the underwriter of deposit insurance, to the government.

So, the long chain of financial institutions that sell, buy, and repackage risk care intensely about controlling financial risk—if for no other reason, then simply as an exercise in self-preservation. Shocks and disturbances of small-to-medium magnitude can be efficiently handled by the inbuilt feedback mechanisms of the financial markets. Given this state of affairs, it is not surprising that the regulatory bodies that are mandated to control the stability and proper functioning of the international financial system are basing more and more of their regulatory demands on the estimation of the probability W H Y T H I S B O O K M AT T E R S 15 of occurrence of extremely rare events.

This is just the definition of Value-at-Risk VaR , which we will discuss in detail in the following chapters. At this stage, we can take this expression to mean that financial institutions are required to estimate the magnitude of an adverse market event so severe that an even worse one should only be expected to occur once every thousand years.

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How would you try to estimate such a quantity? What data would you want to have? How many data records would you need? And where would you find them? As we saw, it is not just the regulators who have a strong interest in keeping the financial cogs turning smoothly. Banks and other financial institutions to a large extent share the same concerns—if for no other reason than because surviving today is a pretty strong precondition for being profitable tomorrow.

There is far more to the risk management of a financial institution than avoiding perfect storms, though. Modern i. In this light, possibly the most common and important questions faced almost every day at different levels of a bank are therefore of the following type: What compensation should we, the bank, require for taking on board a certain amount of extra risk?

Should we lend money to this fledgling company, which promises to pay a high interest but which may go bankrupt soon? Should we begin underwriting, distributing, and making a market in bonds 16 CHAPTER 1 or equities, thereby earning the associated fees and trading revenues but accepting the possibility of trading losses? Should we retain a pool of risky loans, or are we better off repackaging them, adding to them some form of insurance, and selling them on? Of course, how a financial institution should choose among different risky projects has been the staple diet of corporate finance textbooks for decades.

Down in the financial trenches, it is a pressing question for all the decision makers in a bank, from the most junior relationship manager to its CEO and finance director. But it is only after the often rather vague risk appetite policy has been articulated that the real questions begin: How should these lofty risk principles be applied to everyday decisions and, most importantly, to strategic choices?

Compare how much, after this discounting, each new project is worth today. Choose the one with the greatest present value today. Next problem please. Diversification or concentration of risk i. More about this later. In chapter 8 I will therefore try to explain what it promises a lot , and what it can deliver alas, I fear somewhat less. I will frame that discussion in the wider context of the use and misuse of traditional statistical tools for financial risk management.

For the moment, what is of relevance in this introductory chapter is that the make-or-break condition for the economic-capital project to succeed, and for a lot of current quantitative risk management to make sense, is that it should be possible to estimate the probability of extremely remote events—or, in statistical jargon, that it should be possible to estimate extremely high percentiles. Of course, more data and more powerful techniques will help, but only up to a point. Asking what the In fact, your theory is not even wrong. Your theory makes no predictions at all.

These statements do contain predictions. Unfortunately, they are untestable. This claim is in itself an important one, since so much effort appears to be devoted to the estimation of these exceedingly low probabilities. Apart from the feasibility issue, I believe that there is a 18 CHAPTER 1 much deeper and more fundamental flaw in much of the current quantitative approach to risk management. So, for instance, we observe the historical default frequency of AA-rated firms, and equate this quantity to the probability that a AAfirm may default in the future. The philosophy that underpins the identification of frequencies with probabilities is defensible.

In some scientific areas it is both sensible and appropriate. It is not, however, the only possible way of understanding probability. In the risk-management domain I believe that the view of probability-as-frequency often underpins a singularly unproductive way of thinking. At the risk of spoiling a point by overstressing it, I am tempted to make the following provocative claim. According to the prevailing view in risk management: We estimate the probabilities, and from these we determine the actions. For most of the types of problems that financial risk management deals with, I am tempted to say that the opposite should apply: We observe the actions, and from these we impute the probabilities.

This statement may strike the reader as a puzzling one. What kind of probabilities am I talking about? Surely, if I want to advertise my betting odds on a coin-tossing event, first I should determine the probability of getting heads and then I should advertise my odds. The estimation of probability comes first, and action follows. What could be wrong with this approach? The real problem is that very few problems in risk management truly resemble the coin-flipping one. It may come as a surprise to the reader, but there are actually many types of probabilities.

Yet the current thinking of risk managers appears to be anchored, without due reflection, to the oldest and most traditional view. Unfortunately, I will show in the next chapter that none of these requirements really applies to most of the financial-risk-management situations that are encountered in real life. Fortunately, there are views of probability that are better suited to the needs of risk management. If the conditions of applicability for the frequentist limiting case apply, a Bayesian is likely to be delighted—if for no other reason, because there are thousands of books that teach us very well how to compute probabilities when we flip identical coins, draw blue and red balls from indistinguishable urns, etc.

But the abundance of books on this topic should not make us believe that the problems they beautifully solve are quite as numerous. This cannot be good, and it is often dangerous. This, in great part, is what this book is about, and why what it says matters. There is another aspect that current risk-management thinking does not seem to handle in a very satisfactory way: how to go from probabilistic assessments to decisions.

Managing risk in general, and managing financial risk in particular, is clearly a case of decision making under uncertainty. Well-developed theories to deal with this problem do exist, but, rightly or wrongly, they are virtually ignored in professional financial risk management. Most of the effort in current risk management appears to be put into arriving at the probabilities of events sometimes very remote ones , with the implicit assumption that, once these probabilities are in front of our eyes, the decision will present itself in all its selfevidence. So, these days it is deemed obvious that a quantitative risk manager should be well-versed in, say, extreme value theory or copula theory two sophisticated mathematical tools to estimate the probabilities of rare or joint events, respectively.

However, judging by the contents pages of risk-management books, by the fliers of risk-management conferences, or by the questions asked at interviews for risk-management jobs, no knowledge, however superficial, is required or even deemed to be desirable about, say, decision theory, game theory, or utility theory. What can we do instead? To answer this question, I will try to explain what the theoretically accepted tools currently at the disposal of the decision maker have to offer. I will also try to suggest why they have met with so little acceptance and to explain the nature of the well-posed criticisms that have been leveled against them.

I would like to suggest that some of the reasons for the poor acceptance of these decision tools are intrinsic to these theories and do reflect some important weaknesses in their setup. Therefore, understanding one set of issues what type of probability matters in risk management will help with solving the other how we should use these probabilities once we have estimated them.

This link will also provide a tool, via subjective probabilities and how they are arrived at, for reaching acceptable risk-management decisions. In essence, I intend to show that subjective probabilities are ultimately revealed by real choices made when something that matters is at stake. In this view probabilities and choices i.

Decisional consistency, rather than decisional prescription, is what a theory of decisions in risk management should strive for: given that I appear comfortable with taking the risk and rewards linked to activity A, should I accept the risk—reward profile offered by activity B? In this vein, I will offer some guidance in the last part of this book as to how decisions about risk management in lowprobability cases can be reached. I will simply try to offer some practical suggestions, and to show how the line of action they recommend can be analyzed and understood in light of the theoretical tools that we do have at our disposal.

I intend to show that we can be both surprisingly good and spectacularly bad at dealing with uncertain events. Risk blunders are not the prerogative of the man in the street. Experts and extremely intelligent people have fared just as badly, and at times even worse, when thinking about risk. If this rule were reasonable, you should be happy to wager all your wealth your house, your savings, everything for a fifty—fifty chance of doubling it.

Please pause for a second and ask yourself whether you would.

It was Bernoulli who first highlighted how unsatisfactory this answer was. More constructively, he also proposed a better solution. He did so with the story of Sempronius, a late-Renaissance merchant. A sketch of his argument is very instructive. The seas are perilous and pirate infested. Experience has taught Sempronius that, on average, only one ship in two makes the journey home safely. The other is lost forever. Sempronius has an idea.

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  4. See a Problem?.
  5. His goods are gold, spices, silk, and precious stones, all very light and easy to transport. He can easily ask his merchant friends to load them in a corner of their large ships and they will not charge him for the service. Yet, something suggests to us that the expectation of his wealth is not the only thing that matters, and that he will be better off with four ships than one.

    Many eggs and a single basket spring to mind. Laplace and Fermat refused to be convinced by this argument, and kept on arguing that, in evaluating an uncertain prospect, one should only look at the expectation of the outcome. No advantage whatsoever would be reaped, they claimed, by entrusting the precious wares to four different ships. What do you think?

    Plight of the Fortune Tellers: Why We Need to Manage Financial Risk Differently

    This is but one striking example of bizarre thinking about risk and of the fact that being very clever may, at least in this field, not always help. On the other hand, there are areas related to risk and probability where even the uninitiated fare reasonably well. Take Shakespeare, famous for many things but not, to my knowledge, for his mathematical insight. My wind, cooling my broth, Would blow me to an ague, when I thought What harm a wind too great might do at sea. Believe me, no: I thank my fortune for it, My ventures are not in one bottom trusted, Nor to one place; nor is my whole estate Upon the fortune of this present year: Therefore, my merchandise makes me not sad.

    The Merchant of Venice 1. His model is obviously not without flaws, as many modern critics are all too eager to point out, but, if judged by the ratio of how much it explains to how many input parameters it requires, it stills sets a standard of parsimony and explanatory power. First of all, he is neither a mathematician, nor a philosopher, nor an exceptionally wise man, but a good, solid, commonsensical merchant.

    So, Bernoulli does not want to introduce a character of exceptional wisdom and intelligence and ask how this extraordinarily gifted individual would crack a difficult problem of choice under uncertainty. He was asking himself what Tom, Dick, and Harry would do.

    The solid and commonsensically appealing answer to a risk-diversification problem offered by Sempronius is a good example of what I mentioned in the opening lines of this chapter: sometimes experts can be spectacularly bad at thinking about risk Fermat and Pascal were ; but at other times even laymen seem to be able to find unexpectedly good risk solutions.

    And, as this story suggests, over-intellectualizing a risk problem can be a very efficient route to producing risk nonsense. Witness, again, Fermat and Pascal. But we do not have to go back a few centuries to find bewildering statements about risk and stubborn refusals to use common sense. As late as , the then-standard reference work on financial investments by Williams implicitly recommended that investors should place all their wealth in the investment with the maximum expected return.

    His book on investing was published by no less august an institution than Harvard University Press.