WHY THIS BOOK - PDF document

CHAPTER 1 WHY THIS BOOK MATTERS But what I … thought altogether unaccountable was the str ong disposition I observed in [the mathematicians of Laputa] towar d news and politics, perpetually enquiring into public af fairs, giv­ ing their judgement on matters of state, and passionately dis­ puting every inch of a party opinion. I have indeed observed the same disposition among the mathematicians I have known in Eur ope, although I could never observe the least analogy between the two sciences, unless those people suppose that because the smallest cir cle hath as many degr ees as the lar gest, ther efor e the r egulation and management of the world r equir e no mor e abilities than the handling and turning of a globe. Jonathan Swift, writing about the mathematicians of Laputa ST ATISTICS AND THE ST ATE T his book is about the quantitative use of statistical data to man­ age nancial risk. It is about the str engths and limitations of this appr oach. Since we for get the past at our own peril, we could do worse than r emind ourselves that the application of statistics to economic, political, and social matters is har dly a new idea. The very wor d “statistics” shar es its r oot with the wor d “state,” a con­ cept that, under one guise or another , has been with us for at least a few centuries. The closeness of this link, between compilations of numbers, tables of data, and actuarial information on the one hand and the or ganization and r unning of a state on the other 2 CHAPTER 1 may today strike us as strange. But it was just when the power of this link became evident that statistics as we know it today was “invented.” So, in its early days pr obability theory may well have been the domain of mathematicians, gamblers, and philosophers. But even when mathematicians did lend a helping hand in bring­ ing it to life, fr om the very beginning ther e was always something much mor e practical and har d-nosed about statistics. T o see how this happened, let us start at least close to the beginning, and go back to the days of the Fr ench Revolution. In the rst pages of Italian Journey (1798), Goethe writes: I found that in Germany they wer e engaged in a species of polit­ ical enquiry to which they had given the name of Statistics .B y statistical is meant in Germany an inquiry for the purpose of ascertaining the political str ength of a country , or questions con­ cerning matters of state. By the end of the eighteenth century , when Goethe explained his understanding of the wor d “statistics,” the concept had been ar ound in its “gr ubby” and practical form for at least a century . It is in fact in 1700 that we nd another German, Leibniz, trying to forwar d the cause of Prince Fr ederick of Pr ussia who wanted to become king of the united Brandenbur g and Pr ussia. The inter ­ esting point for our discussion is that Leibniz of fers his help by deploying a novel tool for his ar gument: statistics. Prince Fr ed­ erick of Pr ussia was at a disadvantage with r espect to his polit­ ical rivals, because the population of Pr ussia was thought to be far too small compar ed with that of Brandenbur g to command a comparable seat at the high table of power . If at the time the tr ue measur e of the power of a country was the size of its popu­ lation, the r uler could not be a Pr ussian. What Leibniz set out to pr ove was that, despite its smaller geographical size, Pr ussia was nonetheless mor e populous than was thought, indeed almost as populous as Brandenbur g—and hence, by right and might, virtu­ ally as important. How did he set out to do so in those pr e-census days? By an ingenious extrapolation based solely on the Prussian WHY THIS BOOK MA TTERS 3 r egister of births , which had been started seventeen years earlier and car efully updated since.   The details of how the estimate was r eached need not con­ cern us her e—pr obably so much the better for Leibniz, because the jump fr om the birth data collected over seventeen years to the total size of the population was, by modern statistical stan­ dar ds, awed. What is of gr eat curr ent inter est is the logical chain employed by Leibniz, i.e., the link between some limited infor ­ mation that we do have but that, per se, we may consider of little importance—What do we car e about births in Pr ussia?—to infor ­ mation that we would desperately like to have but is curr ently beyond our r each: for Leibniz and Prince Fr ederick, ultimately , what is the might of the Pr ussian army? If anyone wer e ever to doubt that ther e is r eal, tangible power in data and in data collec­ tion, this rst example of the application of the statistical line of ar gument to inuence practical action should never be for gotten. The modern bank that painstakingly collects information about failur es in the clearing of cheques, about minute fraud, about the delinquency of cr edit car d holders and mortgagors (per haps sorted by age, postcode, income bracket, etc.) employs exactly the same logic today: data give power to actions and decisions . T o the childr en of the Internet age it may all seem very obvious. But, at the beginning of the eighteenth century , it was not at all self- evident that, in or der to gain contr ol over the r unning of the state, looking at har d, empirical, and “boring” data might be mor e use­ ful than cr eating engaging ctions about “natural man,” “noble savages,” social contracts between the king and the citizens, etc. The rst statisticians wer e not political philosophers or imagina­ tive myth-makers: they wer e civil servants. The parallels between these early beginnings and today’s debates about statistics r un deeper . As soon as the power of bas­ ing decisions on actual data became appar ent, two schools of thought quickly developed, one in France (and Britain, Scotland
Hacking, The T aming of Chance . 4 CHAPTER 1 in particular) and one in Pr ussia. Generalizing gr eatly ,   the Fr ench school advocated an interpr etation of the data on the basis of the “r egularities of human natur e”: deaths, births, illness, etc., wer e, accor ding to the Fr ench and British schools of thought, no less r egular , and ther efor e no less amenable to rigor ous quanti­ tative analysis, than, say , oods or other “natural” phenomena. Ir onically , the Pr ussian school, that had founded the statistics bur eau, failed to r eap the full advantage of its head start because it r emained suspicious of the Fr ench theor etical notions of “statis­ tical law” when applied to human phenomena—and, pr edictably , derided the Fr ench statisticians: “What is the meaning of the state­ ment that the average family has 2.33 childr en? What does a thir d of a child look like?” Per haps it is not surprising that the country of the fathers of pr obability theory (Descartes, Pascal, Bernoulli, Fermat, etc.) should have been on the quantitative side of the debate. Indeed, 100 years befor e statistics wer e born, Bernoulli was alr eady asking questions such as, “How can a mer chant divide his car go between ten ships that ar e to brave the pirate-infested seas so as to mini­ mize his risk?” In so doing, he was not only inventing and making use of the eponymous pr obability distribution, he was also dis­ covering risk aversion, and laying the foundations of nancial risk management. Pr obability and statistics ther efor e seemed to be a match made in heaven: pr obability theory would be the ves­ sel into which the “har d” statistical data could be pour ed to r each good decisions on how to r un the state. In short, the discipline of pr obability , to which these Fr ench minds contributed so much, appear ed to of fer the rst glimpses of an intriguing pr omise: a quantitative appr oach to decision making. The Pr ussian–Fr ench debate was not much mor e constr uc­ tive than many of the pr esent-day debates in nance and risk management (say , between classical nance theorists and behav­ ioral nanciers), with both parties mainly excelling in caricatur ­ ing their opponent’s position. Looking behind the squabbling, the
For a mor e nuanced discussion of the two schools, again see Hacking, The T aming of Chance . WHY THIS BOOK MA TTERS 5 ar guments about the applicability and usefulness of quantitative techniques to policy decisions have clearly evolved, but r everber ­ ations of the 200-year -old Franco-Pr ussian debate ar e still r ele­ vant today . The Fr ench way of looking at statistics (and of using empirical data) has clearly won the day , and rightly so. Per haps, however , the pendulum has swung too far in the Fr ench dir ection. Per haps we have come to believe, or assume, that the power of the Fr ench r ecipe (marrying empirical data with a sophisticated theory of pr obability) is, at least in principle, boundless. This over condent extrapolation fr om early , impr essive suc­ cesses of a new method is a r ecurr ent featur e of modern thought. The mor e elegant the theory , the gr eater the condence in this extrapolation. Few inventions of the human mind have been mor e impr essive than Newtonian mechanics. The practical success of its pr edictions and the beauty of the theory took a hold on W estern thought that seemed at times almost impossible to shake of f. Y et two cornerstones of the Newtonian edice, the absolute natur e of time and the intrinsically deterministic natur e of the universe, wer e ultimately to be r efuted by r elativity and quantum mechan­ ics, r espectively . Abandoning the Newtonian view of the world was made mor e dif cult, not easier , by its beauty and its successes. It sounds almost irr ever ent to shift in one paragraph fr om Newtonian physics and the absolute natur e of time to the man­ agement of nancial risk. Y et I think that one can r ecognize a sim­ ilar case of over condent extrapolation in the curr ent appr oach to statistics applied to nance. In particular , I believe that in the eld of nancial risk management we have become too emboldened by some r emarkable successes and have been trying to apply similar techniques to ar eas of inquiry that ar e only supercially similar . W e have come to conclude that we simply have to do “mor e of the same” (collect mor e data, scr ub our time series mor e car e­ fully , discover mor e powerful statistical theor ems, etc.) in or der to answer any statistical question of inter est. W e have come to take for granted that while some of the questions may be har d, they ar e always well-posed. 6 CHAPTER 1 However , if this is not the case but the practice and the policy to contr ol nancial risk r emain inspir ed by the nonsensical answers to ill-posed questions, then we ar e all in danger . And if the policies and practices in question ar e of gr eat importance to our well-being (as is, for instance, the stability and pr udent contr ol of the nancial system), we ar e all in gr eat danger . WHAT IS AT STAKE? Thr ough nancial innovations, a marvelously intricate system has developed to match the needs of those who want to borr ow money (for investment or immediate consumption) and of those who ar e willing to lend it. But the modern nancial system is far mor e than a gloried br okerage of funds between borr owers and lenders. The magic of modern nancial engineering tr uly becomes appar ­ ent in the way risk , not just money , is par celed, r epackaged, and distributed to dif fer ent players in the economy . Rather than pr e­ senting tables of numbers and statistics, a simple, homely example can best illustrate the r esour cefulness, the r each, and the intrica­ cies of modern applied nance. Let us look at a young couple who have just taken out their rst mortgage on a small house with a local bank on Long Island. Every month, they will pay the inter est on the loan plus a (small) part of the money borr owed. Unbeknownst to them, their monthly mortgage payments will under go transformations that they ar e 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.e., the rights to all their payments) will be pur chased by one of the lar ge federal mortgage institutions (a so-called “government-sponsor ed agency”) cr eated to oil the wheels of the mortgage market and make housing mor e af for dable to a lar ge portion of the population. Once acquir ed by this institution, it will be pooled with thousands of other mort­ gages that have been originated by other small banks ar ound the country to advance money to similar home buyers. All these WHY THIS BOOK MA TTERS 7 mortgages together cr eate a single, diversied pool of inter est- paying assets (loans). These assets then r eceive the blessing of the federal agency who bought them in the form of a pr omise to con­ tinue to pay the inter est even if the couple of newlyweds (or any of their thousands of fellow co-mortgagors) nd themselves unable to do so. Having given its seal of appr oval (and nancial guar ­ antee), the federal institution may cr eate, out of the thousands of small mortgages, new standar dized securities that pay inter est (the r echanneled mortgage payments) and will ultimately r epay the principal (the amount borr owed by the Long Island couple). These new securities, which have now been made appealing to investors thr ough their standar dization and the nancial guar ­ antee, can be sold to banks, individuals, mutual funds, etc. Some of these standar dized securities may also be chopped into smaller pieces, one piece paying only the inter est, the other only the prin­ cipal when (and if) it arrives, ther eby satisfying the needs and the risk appetite of dif fer ent classes of investors. At every stage of the pr ocess, new nancial gadgets, new nancial instr uments, and new market transactions ar e cr eated: some mortgages ar e set aside to pr ovide investors with an extra cushion against interr up­ tions in the mortgage payments; additional securities designed to act as “bodyguar ds” against pr epayment risk ar e generated; modied instr uments with mor e pr edictable cash ow str eams ar e devised; and so on. So lar ge is this ow of money that every rivulet has the poten­ tial to cr eate a specialized market in itself. Few tasks may appear mor e mundane than making sur e that the inter est payments on the mortgages ar e indeed made on time, keeping track of who has r epaid their mortgage early , channeling all the payments wher e they ar e due just when they ar e due, etc. A tiny fraction of the total value of the underlying mortgages is paid in fees for this humble servicing task. Y et so enormous is the river of mortgage payments, that this small fraction of a per cent of what it carries along, its otsam and jetsam, as it wer e, still constitutes a very lar ge pool of money . And so, even the fees earned for the adminis­ tration of the various cash ows become tradeable instr uments in 8 CHAPTER 1 themselves, for whose ownership investment banks, hedge funds, and investors in general will engage in brisk, and sometimes furi­ ous, trading. The trading of all these mortgage-based securities, ultimately still cr eated fr om the payments made by the couple on Long Island and their peers, need not even be conned to the country wher e the mortgage originated. The same securities, ultimately backed by the tens of thousands of individual private mortgage borr ow­ ers, may be pur chased, say , by the Central Bank of China. This body may choose to do so in or der to invest some of the cash orig­ inating fr om the Chinese trade surplus with the United States. But this choice has an ef fect back in the country wher e the mortgages wer e originated. By choosing to invest in these securities, the Cen­ tral Bank of China contributes to making their price higher . But the inter est paid by a security is inversely linked to its price. The international demand for these r epackaged mortgages ther efor e keeps (or , actually , pushes) down U.S. inter est rates and borr ow­ ing costs. As the borr owing cost to buy a house goes down, mor e pr ospective buyers ar e willing to take out mortgages, new houses ar e built to meet demand, the house-building sector pr ospers and employment r emains high. The next-door neighbor of the couple on Long Island just happens to be the owner of one small enter ­ prise in the building sector (as it happens, he specializes in r oof tiling). The str ong or der book of his r oof tiling business and his optimistic overall job outlook make him feel condent about his pr ospects. Condent enough, indeed, to take out a mortgage for a lar ger pr operty . So he walks into the local branch of his Long Island bank. Au r efrain . Ther e is nothing special about mortgages: a similarly intricate and multilayer ed story could be told about insurance pr oducts, the funding of small or lar ge businesses, cr edit car ds, investment funds, etc. What all these activities have in common is the r edi­ r ection, pr otection fr om, concentration, or diversication of some form of risk. All the gadgets of modern nancial engineering ar e simply a bag of tricks to r eshape the one and only tr ue underlying WHY THIS BOOK MA TTERS 9 “entity” that is ultimately being exchanged in modern nancial markets: risk. But ther e is mor e. All these pieces of nancial wizar dry must perform their magic while ensuring that the r esulting pieces of paper that ar e exchanged between borr owers and lenders enjoy an elusive but all-important pr operty: the ability to ow smoothly and without interr uptions among the various players in the econ­ omy . All the fancy pieces of paper ar e useful only if they can fr eely ow , i.e., if they can be r eadily exchanged into one another (ther eby allowing individuals to change their risk pr ole at will), or , ultimately , into cash. V ery aptly , this all-important quality is called “liquidity .” By itself, sheer ingenuity in inventing new nancial gadgets is ther efor e not enough: the pieces of paper that ar e cr eated must not only r edir ect risk in an ingenious way , they must also continually ow , and ow without hindrance. As the mortgage example suggests, if an occlusion occurs anywher e in the nancial ows that link the payments made to the local Long Island bank to the for eign exchange management r eserve of ce of the Bank of China, the r eper cussions of this clog­ ging of the nancial arteries will be felt a long way fr om wher e it happens (be it on Long Island or in Beijing). It is because of this inter connectedness of modern nancial instr uments that nancial risk has the potential to take on a so-called “systemic” dimension. Fortunately , like most complex interacting systems, the nan­ cial system has evolved in such a way that compensating contr ols and “r epair mechanisms” become active automatically (i.e., with­ out r egulatory or government intervention) when some pertur ­ bation occurs in the or derly functioning of the network. Luckily , the smooth functioning of this complex system does not have to r ely on the shocks not happening in the rst place: [T]he inter esting question is not whether or not risk will crystal­ lize, as in one form or another risks crystallize every day . Rather the important question is whether … our capital markets can absorb them.

P . T ucker , Executive Dir ector for Markets and member of the Monetary Pol­ icy Committee, Bank of England, Financial Stability Review December 2005:73. 1 0 CHAPTER 1 And indeed, most of the time, surprises ar e r eadily and “auto­ matically” absorbed by the system. But if the shock is too big or if, for any r eason, some of the adjusting mechanisms ar e pr e­ vented fr om acting pr omptly and ef ciently , the normal r epair mechanisms may not be suf cient to r estor e the smooth func­ tioning of the nancial ows. In some pathological situations, they may even become counterpr oductive. If this happens, the ef fects can quickly be felt well beyond the world of the whirling pieces of paper and can begin to af fect the “r eal economy .” It is exactly because, in a modern economy , the boundaries between the nancial plumbing and the r eal economy have become so blurr ed and por ous that the management of nancial risk is today vitally important—and vitally important to everyone, fr om W all Str eet nanciers down to the young couple on Long Island. One of the salient characteristics of the modern economy is that an amazingly complex web of interactions can develop among agents who bar ely , if at all, know each other , to pr oduce r esults that give the impr ession of a str ong and conscious coor ­ dination (an “intelligent design”). This is, of course, in essence nothing but Adam Smith’s invisible hand in action, but the com­ plexity of modern-day nancial arrangements would have been unthinkable when The W ealth of Nations was written. Accepting that “no one is in char ge” but that an intricate network of trans­ actions will, most of the time, work very well r emains to this day dif cult to accept fr om an intuitive point of view . “Please understand that we ar e keen to move towar d a market economy ,” a senior Soviet of cial whose r esponsibility had been to pr ovide br ead to the population of Saint Petersbur g in its communist days told economist Paul Seabright,   “but we need to understand the fundamental details of how such a system works. T ell me, for example, who is in char ge of the supply of br ead to the popula­ tion of London.” In the industrialized W estern world we may have for gotten how astonishing the r eply is (“nobody is in char ge”), but
P . Seabright (2004), The Company of Strangers (Princeton University Pr ess). WHY THIS BOOK MA TTERS 1 1 this does not make it any less so. In a similar vein, looking at a small portion of butter of fer ed as part of an in-ight meal, Thomas Schelling (r hetorically) asks: How do all the cows know how much milk is needed to make the butter and the cheese and the ice cr eam that people will buy at a price that covers the cost of maintaining and milking the cow and getting each little piece of butter wrapped in aluminum foil with the airlines’s insignia printed on it?
Of all these complex, r esilient, self-or ganizing systems, the ­ nancial industry is pr obably one of the most astonishing. Nobody was “in char ge” to ensur e that when the couple fr om Long Island walked into their local bank branch they would get a competitive quote for their mortgage in hours; nobody was in char ge to make sur e that the depositor who pr ovided the funds needed by the couple to pur chase their house would be forthcoming just at the right moment; nobody was in char ge when the same depositor changed his mind a week later and withdr ew the money he had deposited; nobody was in char ge to ensur e that a buyer would be willing to part with his money within hours, or minutes, of the security fr om the pool of mortgages being cr eated and of fer ed on the market; and when, thousands of miles away , a Bank of China of cial decided to invest some of the Chinese trade sur ­ plus in the pur chase of the same security , nobody had commu­ nicated his intentions and nobody had arranged for a market maker to buy the security itself fr om the primary investor and hold it in his inventory . Nobody is in char ge and yet, most of the time , all of these transactions, and many mor e, ow without any pr oblems. Ther e, however , in that innocent “most of the time,” is the r ub. The nancial system is r obust, by virtue of literally hun­ dr eds of self-or ganizing corr ective mechanisms, but it is not innitely r obust. This is not surprising because the cornerstone institution of the nancial system, the bank itself, is pr ecariously
T . Schelling (1978), Micr omotives and Macr obehavior (New Y ork and London: Norton). 1 2 CHAPTER 1 per ched on the bor der of stability: just because nobody is in char ge, every day a bank owes its existence to the law of lar ge numbers. How does this happen? The most fundamental activ­ ity of a bank is the so-called “maturity transformation”: accept­ ing money fr om depositors who may want it back tomorr ow , and lending the “same money” to borr owers who may want to hold on to it for thirty years. This is all well and good unless all of the depositors simultaneously want their money back. In normal conditions, of course, it is virtually impossible for this to happen, and the statistical balance between random with­ drawals fr om depositors and equally random r epayments fr om borr owers r equir es a surprisingly small safety buf fer of “liquid cash.” And, by the way , many other arrangements in our nobody- is-in-char ge industrialized world r ely on a similar (appar ently fragile and pr ecarious) statistical balance: fr om the pr ovision of food to the distribution of electricity , the use of r oads, telephone lines, petr ol stations, etc. As long as all the users make their decisions close-to-independently , only a r elatively small safety mar gin (of spar e electricity , spar e phone line capacity , petr ol in lling stations, food on supermarket shelves, etc.) has to be kept. Conditions, however , ar e not always “normal.” For a variety of r easons, unpr edictable coor dination of actions can occur that br eak the independence in the decisions and disr upt the appar ­ ently most r obust systems: in the 1980s, for instance, the simul­ taneous switching on of millions of kettles during the commer ­ cial br eak of a TV pr ogram br oadcasting a British r oyal wedding caused chaos acr oss the electricity grid.   Similarly , fears about the r obustness of supply can, in next to no time, empty supermar ­ ket shelves and cr eate queues at petr ol stations. The r umors at the r oot of these unusual coor dinated behaviors need not be tr ue for the ef fect to be highly disr uptive and, in some cir cumstances, potentially devastating: in a state of imperfect information a set of rationally calculating agents looking after their self-inter est will
Seabright, The Company of Strangers . WHY THIS BOOK MA TTERS 1 3 all r each the same conclusions, and close-to-simultaneously head for the supermarket or the petr ol station.   The amazing ef ciency and r esilience of the supply chain in the industrialized world ther efor e contains a potentially fragile cor e for many goods and services. Banks, ar e, however , dif fer ent, and not in a way that makes a bank r egulator sleep any mor e peacefully . If, a few minutes after midnight on New Y ear ’s eve, we nd it dif cult to make a telephone call to wish a happy new year to our loved ones, we desist fr om calling for ten minutes and, by doing so, avoid clogging the line even mor e. W e do so spontaneously , not because some r egulation tells us to behave this way , and it is rational for us to do so. But if a r umor spr eads that a bank is not solvent, the individually rational thing to do is to r ush to the head of the queue, not to come back tomorr ow when the queue, which curr ently cir cles two blocks, will be shorter: by tomorr ow the queue may well be shorter , but only because ther e may be no money left in the vault. This is how r uns on banks occur: given the asymmetry of information between insiders and depositors, the same r esponse (r un for the till!) applies in the case of the perfectly healthy bank as in the case of the one that r eally has got itself into nancial dif culties. How can these panics be pr evented when the rational behav­ ior is to do what everyone else is trying to do—and when this “rational” behavior exacerbates, rather than alleviates, the pr ob­ lem? In most industrialized societies, governments have stepped in by cr eating deposit insurance. The soothing pr omise of the gov­ ernment to depositors that it stands behind the bank’s commit­ ment to r epay (with the implication that their monies ar e safe no matter what) can pr event, or stem, the ood of withdrawals. In the case of a healthy bank, this arrangement can pr event the r un fr om occurring in the rst place.
For an inter esting discussion about the consequences of spontaneously or ga­ nized collective behaviors, see, for example, C. P . Chamley (2004), Rational Herds (Cambridge University Pr ess). A possible explanation of how these collective behaviors may become or der ed can be found in D. W atts (1999), Small W orlds— The Dynamics of Networks between Order and Randomness (Princeton University Pr ess). 1 4 CHAPTER 1 It is important to understand that this underwriting of risk by the government is benecial for the public but it is also extr emely benecial for the banks. For this r eason this insurance is not of fer ed “for fr ee.” V ia the deposit guarantee the government develops a keen, rst-hand nancial inter est in the good work­ ing of banks, but only shar es in the downside, not in the pr ot the bank may make. It ther efor e imposes another stipulation to this otherwise too-good-to-be-tr ue arrangement: the government, the covenant goes, will indeed step in to guarantee the deposits of the public even if the bank wer e to fail; but, in exchange for these arrangements, which ar e extr emely useful for the public and for the banks , it will acquir e a supervisory r ole over banking opera­ tions. (Of course it is well within the r emit of the government to car e about systemic nancial risk even in the absence of deposit insurance, but this commitment certainly focuses its mind.) The management of nancial risk ther efor e acutely matters, not only to the nancial institutions in the long chain fr om the small Long Island bank to the Bank of China, but to the public at lar ge and, as the agent of the public and the underwriter of deposit insurance, to the government. So, the long chain of nan­ cial institutions that sell, buy , and r epackage risk car e intensely about contr olling nancial risk—if for no other r eason, then sim­ ply as an exer cise in self-pr eservation. But the national and inter ­ national r egulators who have been appointed to take a br oader , system-wide, view of nancial risk also str ongly car e and justi­ ably see themselves as the ultimate safeguar d of the soundness of the r eal economy (“ultimate,” in that they come into play if all other self-corr ecting mechanisms fail). Shocks and disturbances of small-to-medium magnitude can be ef ciently handled by the inbuilt feedback mechanisms of the nancial markets. It is the “perfect storms” that have the poten­ tial to cr eate havoc and destr oy wealth on a massive scale. Given this state of af fairs, it is not surprising that the r egulatory bodies that ar e mandated to contr ol the stability and pr oper functioning of the international nancial system ar e basing mor e and mor e of their r egulatory demands on the estimation of the pr obability WHY THIS BOOK MA TTERS 1 5 of occurr ence of extr emely rar e events. In statistical terms, these r equir ements ar e expr essed in terms of what ar e called, in techni­ cal parlance, “extr emely high per centiles.” For instance, the r eg­ ulators ar e r equesting mor e and mor e fr equently , and in wider and wider contexts, that a 99.9th, one-year per centile of some loss distribution be calculated for r egulatory capital purposes. This is just the denition of V alue-at-Risk (V aR), which we will discuss in detail in the following chapters. At this stage, we can take this expr ession to mean that nancial institutions ar e r equir ed to esti­ mate the magnitude of an adverse market event so sever e that an even worse one should only be expected to occur once every thousand years. Let us pause and “feel the magnitude” of this statement. A mor e familiar (although not strictly identical) question is the fol­ lowing: “How bad must a ood/snow fall/dr ought be for you to be condent that we have experienced a worse one only once since the battle of Hastings in 1066?” Again, let us pause and feel the magnitude of the statement. How would you try to estimate such a quantity? What data would you want to have? How many data r ecor ds would you need? And wher e would you nd them? As we saw , it is not just the r egulators who have a str ong inter est in keeping the nancial cogs turning smoothly . Banks and other nancial institutions to a lar ge extent shar e the same concerns—if for no other r eason than because surviving today is a pr etty str ong pr econdition for being pr otable tomorr ow . Ther e is far mor e to the risk management of a nancial institution than avoiding perfect storms, though. Modern (i.e., post-Markowitz) portfolio theory sees the trade-of f between expected r eturn and risk (variance of r eturns) as the cornerstone of modern nance. In this light, possibly the most common and important questions faced almost every day at dif fer ent levels of a bank ar e ther e­ for e of the following type: What compensation should we, the bank, r equir e for taking on boar d a certain amount of extra risk? Should we lend money to this edgling company , which pr omises to pay a high inter est but which may go bankr upt soon? Should we begin underwriting, distributing, and making a market in bonds 1 6 CHAPTER 1 or equities, ther eby earning the associated fees and trading r ev­ enues but accepting the possibility of trading losses? Should we r etain a pool of risky loans, or ar e we better of f r epackaging them, adding to them some form of insurance, and selling them on? Of course, how a nancial institution should choose among dif fer ent risky pr ojects has been the staple diet of corporate nance textbooks for decades. Down in the nancial tr enches, it is a pr ess­ ing question for all the decision makers in a bank, fr om the most junior r elationship manager to its CEO and nance dir ector . The risk policy of the bank (what is these days called its “risk appetite”) is typically set at a very senior level in rather br oad and generic terms. But it is only after the (often rather vague) risk appetite pol­ icy has been articulated that the r eal questions begin: How should these lofty risk principles be applied to everyday decisions and, most importantly , to strategic choices? The standar d textbook answer to these questions used to be disarmingly simple: “Just discount the expected cash ows fr om the new pr ospective pr ojects at the ‘appr opriate’ risky rate. Com­ par e how much, after this discounting, each new pr oject is worth today . Choose the one with the gr eatest pr esent value today . Next pr oblem please.” Even glossing over the dif culty in assessing the “appr opri­ ate” rate of discount, this way of looking at the budgeting and cap­ ital allocation pr ocess appears to suf fer fr om at least one impor ­ tant shortcoming: unless the bank alr eady has an “optimal” mix of risk, 1 the appr oach appears to neglect the interaction between the new pr ojects and the existing business activities. Diversication or concentration of risk (i.e., the undesirability of putting all of one’s eggs in one basket, no matter how str ong the basket looks) is not r eadily handled by the discounted-cash ow method.   T o over come this shortcoming, a new appr oach, termed the “economic-capital pr oject,” has r ecently been suggested. Unfor ­ tunately , ther e is no consensus about the pr ecise meaning and applicability of the term, as it is often used in dif fer ent, and even
A brief caveat in passing: it may not be optimal for the banks to diversify , but for investors to do so. Mor e about this later . WHY THIS BOOK MA TTERS 1 7 contradictory , ways. In chapter 8 I will ther efor e try to explain what it pr omises (a lot), and what it can deliver (alas, I fear some­ what less). I will frame that discussion in the wider context of the use and misuse of traditional statistical tools for nancial risk management. For the moment, what is of r elevance in this intr oductory chapter is that the make-or -br eak condition for the economic-capital pr oject to succeed, and for a lot of curr ent quan­ titative risk management to make sense, is that it should be possi­ ble to estimate the pr obability of extr emely r emote events—or , in statistical jar gon, that it should be possible to estimate extr emely high per centiles. “NOT EVEN WRONG”: SENSE AND NONSENSE INFINANCIAL RISK MANAGEMENT One of the points that I make in this book is that the very high per centiles of loss distributions (i.e., r oughly speaking, the pr oba­ bility of extr emely unlikely losses) cannot be estimated in a r eliable and r obust way . I will ar gue that the dif culty is not simply a tech­ nical one, which could “simply” be over come by collecting mor e data or by using mor e sophisticated statistical techniques, but is of a fundamental natur e. Of course, mor e data and mor e power ­ ful techniques will help, but only up to a point. Asking what the 99.975th per centile of a one-year loss distribution is is not a tough question, it is a close-to-meaningless one. Famously , W olfgang Pauli, one of the founders of quantum mechanics, dispatched the theory of a student of his with the ultimate putdown: “Y our theory is not corr ect. In fact, your theory is not even wr ong. Y our theory makes no pr edictions at all.” This is not quite the case with some utterances fr om har dcor e quantitative risk managers. These state­ ments do contain pr edictions. Unfortunately , they ar e untestable. This claim is in itself an important one, since so much ef fort appears to be devoted to the estimation of these exceedingly low pr obabilities. This, however , is not the main “message” of my book. Apart fr om the feasibility issue, I believe that ther e is a 1 8 CHAPTER 1 much deeper and mor e fundamental aw in much of the curr ent quantitative appr oach to risk management. Ther e is a “sleight of hand” r outinely performed in the risk-management domain that allows one to move fr om observed fr equencies of a certain event to the pr obabilities of the same event occurring in the futur e. So, for instance, we observe the historical default fr equency of AA-rated rms, and equate this quantity to the pr obability that a AA rm may default in the futur e. This association (fr equency = pr obability) implies a view and an application of the concept of pr obability that, at the very least, should not be taken for granted. I believe that this “sleight of hand” is indicative of the way we look at pr obabil­ ities in the whole of the risk-management ar ena. The philosophy that underpins the identication of fr equencies with pr obabili­ ties is defensible. In some scientic ar eas it is both sensible and appr opriate. It is not, however , the only possible way of under ­ standing pr obability . In the risk-management domain I believe that the view of pr obability-as-fr equency often underpins a sin­ gularly unpr oductive way of thinking. At the risk of spoiling a point by overstr essing it, I am tempted to make the following pr ovocative claim. Accor ding to the pr evailing view in risk man­ agement: We estimate the pr obabilities, and fr om these we determine the actions. For most of the types of pr oblems that nancial risk manage­ ment deals with, I am tempted to say that the opposite should apply: We observe the actions, and fr om these we impute the pr obabili­ ties. This statement may strike the r eader as a puzzling one. What kind of pr obabilities am I talking about? Sur ely , if I want to advertise my betting odds on a coin-tossing event, rst I should determine the pr obability of getting heads and then I should advertise my odds. The estimation of pr obability comes rst, and action follows. What could be wr ong with this appr oach? WHY THIS BOOK MA TTERS 1 9 In the coin-ipping case, pr obably nothing (although in the next chapter I will raise some r easonable doubts as to whether , even in this stylized case, the appr oach r eally always works as well as we may think). The r eal pr oblem is that very few pr oblems in risk management tr uly r esemble the coin-ipping one. It may come as a surprise to the r eader , but ther e ar e actually many types of pr obabilities. Y et the curr ent thinking of risk managers appears to be anchor ed, without due r eection, to the oldest and most traditional view . It is a view of pr obability (called the “fr equen­ tist view”) that applies when we enter a statistical “experiment” with random outcomes with absolutely no prior beliefs about the likelihood of its possible outcomes; when our subsequent beliefs (and actions) ar e fully and only determined by the outcome of the experiment; and when the experiments can be r epeated over and over again under identical conditions. Unfortunately , I will show in the next chapter that none of these r equir ements r eally applies to most of the nancial-risk-management situations that ar e encounter ed in r eal life. Fortunately , ther e ar e views of pr obability that ar e better suited to the needs of risk management. They ar e collectively subsumed under the term “Bayesian pr obability .” Bayesian pr obability is often seen as a measur e of degr ee of belief, susceptible of being changed by new evidence.   The fr equentist pr obability is not dis­ missed, but simply becomes a limiting, and unfortunately rather rar e, case. If the conditions of applicability for the fr equentist lim­ iting case apply , a Bayesian is likely to be delighted—if for no other r eason, because ther e ar e thousands of books that teach us very well how to compute pr obabilities when we ip identical coins, draw blue and r ed balls fr om indistinguishable urns, etc. But the abundance of books on this topic should not make us believe that the pr oblems they (beautifully) solve ar e quite as numer ous. Unfortunately , the “Bayesian r evolution” has almost com­ pletely bypassed the world of risk management. Sadly , quanti­ tative risk managers, just when they claim to be embracing the
See chapter 3 for a fuller description. ��WHY THIS BOOK MATTERS 21 I will argue that some of the lore around the economic-capital project is no exception. 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 reect some important weaknesses in their setup. However, some of the reasons are intimately linked to the “type of probability” relevant in risk management. 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 ulti­revealed by real choices made when something that matters is at stake. In this view probabilities and choices (i.e., decisions) are not two distinct ingredients in the decisional process, but become two sides of the same coin. 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 prole 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 low-probability cases can be reached. Clearly, I will not even pretend to have “solved” the problem of decision making under uncer­tainty. 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 ��20 CHAPTER 1 more sophisticated and cutting-edge statistical techniques, actu­ally appear to be oblivious to the fundamental developments in the understanding of the nature of probability that have taken place in the last half century. This cannot be good, and it is often dangerous. This, in great part, is what this book is about, and why WHATThere 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 nancial 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 nancial 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 self-evidence. 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 iers of risk-management conferences, or by the questions asked at interviews for risk-management jobs, no knowledge, however supercial, is required (or even deemed to be desir­able) about, say, decision theory, game theory, or utility theory. A potpourri of recommendations, rules of thumb, and “self-evident truths” do exist, and sometimes these are cloaked under the rather grand term of “industry best practice.” Yet, it only takes a little scrutiny to reveal that the justications for these decisional rules of thumb are shaky at best, sometimes even contradictory. Alas, For general queries, contact webmaster@press.princeton.edu © Copyright, Princeton University Press. No part of this book may be distributed, posted, or reproduced in any form by digital or mechanical means without prior written permission of the publisher. For general queries, contact webmaster@press.princeton.edu © Copyright, Princeton University Press. No part of this book may be distributed, posted, or reproduced in any form by digital or mechanical means without prior written permission of the publisher. For general queries, contact webmaster@press.princeton.edu © Copyright, Princeton University Press. No part of this book may be distributed, posted, or reproduced in any form by digital or mechanical means without prior written permission of the publisher. For general queries, contact webmaster@press.princeton.edu © Copyright, Princeton University Press. No part of this book may be distributed, posted, or reproduced in any form by digital or mechanical means without prior written permission of the publisher. For general queries, contact webmaster@press.princeton.edu © Copyright, Princeton University Press. No part of this book may be distributed, posted, or reproduced in any form by digital or mechanical means without prior written permission of the publisher. For general queries, contact webmaster@press.princeton.edu © Copyright, Princeton University Press. No part of this book may be distributed, posted, or reproduced in any form by digital or mechanical means without prior written permission of the publisher. For general queries, contact webmaster@press.princeton.edu © Copyright, Princeton University Press. No part of this book may be distributed, posted, or reproduced in any form by digital or mechanical means without prior written permission of the publisher. For general queries, contact webmaster@press.princeton.edu © Copyright, Princeton University Press. No part of this book may be distributed, posted, or reproduced in any form by digital or mechanical means without prior written permission of the publisher. For general queries, contact webmaster@press.princeton.edu © Copyright, Princeton University Press. No part of this book may be distributed, posted, or reproduced in any form by digital or mechanical means without prior written permission of the publisher. For general queries, contact webmaster@press.princeton.edu © Copyright, Princeton University Press. No part of this book may be distributed, posted, or reproduced in any form by digital or mechanical means without prior written permission of the publisher. For general queries, contact webmaster@press.princeton.edu © Copyright, Princeton University Press. No part of this book may be distributed, posted, or reproduced in any form by digital or mechanical means without prior written permission of the publisher. For general queries, contact webmaster@press.princeton.edu © Copyright, Princeton University Press. No part of this book may be distributed, posted, or reproduced in any form by digital or mechanical means without prior written permission of the publisher. For general queries, contact webmaster@press.princeton.edu © Copyright, Princeton University Press. No part of this book may be distributed, posted, or reproduced in any form by digital or mechanical means without prior written permission of the publisher. For general queries, contact webmaster@press.princeton.edu © Copyright, Princeton University Press. No part of this book may be distributed, posted, or reproduced in any form by digital or mechanical means without prior written permission of the publisher. For general queries, contact webmaster@press.princeton.edu © Copyright, Princeton University Press. No part of this book may be distributed, posted, or reproduced in any form by digital or mechanical means without prior written permission of the publisher. For general queries, contact webmaster@press.princeton.edu © Copyright, Princeton University Press. No part of this book may be distributed, posted, or reproduced in any form by digital or mechanical means without prior written permission of the publisher. For general queries, contact webmaster@press.princeton.edu © Copyright, Princeton University Press. No part of this book may be distributed, posted, or reproduced in any form by digital or mechanical means without prior written permission of the publisher. For general queries, contact webmaster@press.princeton.edu © Copyright, Princeton University Press. No part of this book may be distributed, posted, or reproduced in any form by digital or mechanical means without prior written permission of the publisher. For general queries, contact webmaster@press.princeton.edu © Copyright, Princeton University Press. No part of this book may be distributed, posted, or reproduced in any form by digital or mechanical means without prior written permission of the publisher. For general queries, contact webmaster@press.princeton.edu © Copyright, Princeton University Press. No part of this book may be distributed, posted, or reproduced in any form by digital or mechanical means without prior written permission of the publisher. For general queries, contact webmaster@press.princeton.edu © Copyright, Princeton University Press. No part of this book may be distributed, posted, or reproduced in any form by digital or mechanical means without prior written permission of the publisher.