Risk, Uncertainty, and Black Swans

In 2009, in the midst of the financial and economic crises, Robert Skidelsky, the acclaimed three volume biographer of Keynes, added a fourth, Keynes: The Return of the Master. It is a radical and provocative assessment of economic theory since Keynes, insisting that at its core Keynes’ s Keynesianism was about uncertainty, about the irreducible uncertainty that cannot be cast in probabalistic terms, about Donald Rumsfeld’s famous “unknown unknowns” in contrast to the “known unknowns” that pass as risk. It is this uncertainty that lies behind booms and panics and accounts for the inherent instability of markets and thus of capitalism itself. For Keynes, says Skidelsky, “the unmanaged capitalist economy is inherently unstable.” The notion that financial markets could be self-regulating, that was so prevalent amongst the poweful and within our profession only yesterday, was anathema to Keynes.

Paul Krugman, the Nobel prize winning economist who writes a widely read column in the New York Times, while recognizing the validity of Skidelsky’s  reading of Keynes – I have already drawn on Krugman’s lucid explanation – insists on a different and more customary reading, that Keynes is about the slaying of Say’s Law that supply creates its own demand, that because money can be hoarded and credit withheld, there can be an equilibrium  with unemployment, hence recessions and depressions, and a deflationary gap that needs to be closed. This was the body blow that Keynes dealt to neo-classical economics.

Skidelsky does not so much disagree with Krugman as see him as part of the problem. There has emerged in recent times, Skidelsky reminds us, the New Classical Economics of Chicago’s Robert Lucas and the rational expectations school, and the New Keynesian Economics of Princeton’s Paul Krugman and Columbia’s Joseph Stiglitz  (all three being Nobelists) – also known in some circles as freshwater and saltwater schools. They see each other as mortal enemies, the first insisting on the perfection of markets and the second on their imperfection.  This is most evident in their different understanding of market information, including unavoidably their perceptions about the future.

And, it must be instited upon, they are very different in terms of their political propensities, the New Keynesians being on the side of the good and the New Classicists not. Nevertheless, insists Skidelsky, at their core they are the same. They both believe that the unknown is knowable, that is, both buy into the theory of rational expectations. The New Classical Economics believes that  is simply so. The New Keynesian Economics believe it can be made so as by correcting for asymmetries of information – where one side in a market transactions knows much more than the other. In effect, the New Keynesians accept the logic of the New Classicists and, as Skidelsky succintly puts in, “in economics logic is everything.”

If this seems like a harsh way to treat Krugman and Stiglitz, Skidelsky just  happens to believe that until economics gets it right, the real world, which is dependent on we economists for theories and models - in short, for ideas – can’t hope to get it right; take it as a compliment. As it is, in the World’s Biggest Casino, we, the economists, do the heavy lifting, while they, the hedgers and the speculators, spin the wheel and take in the chips.

Stiglitz in his new book, Freefall: America, Free Markets, and the Sinking of the World Economy, writes “Among the long list of those to blame for the crisis, I would include the economics profession, for it provided the special interests with arguments about efficient and self-regulating markets – even though advances in economics during the preceding two decades had shown the limited conditions under which that theory held true.” He seems to be saying that if the New Keynesians had been listened to there wouldn’t have been a crisis. “The New Keynesian solution is to say that people are rational but have information problems,” writes Skidelsky who insists that there is simply an “inescapable information deficit.”

In the 1960s, when I was alive and well, the Keynesians came to believe that they could fine-tune the economy. It turned out they couldn’t and that failure opened the door to monetarisms and its elaborations. Today the New Keynesians may believe that they can correct the imperfections of financial markets – today’s version of fine-tuning  – but if this can’t be done there will simply be more crises.

Skidelsky reminds us that there is yet a further and very real and relevant problem, that of the Black Swan as admumbrated by Nassim Taleb. Black Swans are rare and extreme events. In principle a probability attaches to them but in fact they are so improbable that they are ignored by models based on the bell curve. Though known unknowns, they are, being unpredictable  as to time and place, really unknown unknowns. But they happen; indeed, the Great Depression was surely a Black Swan. Skidelsky argues that the financial crisis which still haunts us is likewise one. If so, count this a further failing of orthodoxy, both New Classical and New Keynesian – though Stiglitz says that he and other likeminded economists foresaw the crisis, though not its precise date, by noting the number of financial crises that preceded it in other countries, like Mexico, Argentina, Thailand, etc.

Nor does Skidelsky see behavioural economics as any real advance. Indeed, he is dismissive of it: “The adoption of ‘irrationality’….as a general explanation smacks of theoretical panic.”

But how does this matter for what truly matters, namely, economic policy for the public good?  Insofar as financial markets abound in innovations of fiancial instruments which ultimately rest on the assumption that probabilities are knowable which are not, the case for regulation, for deep regulation, is compelling. Better to stop the mess from happening than focusing on trying to clean up afterwards. In Skidelsky’s words: “Macroeconomic policy boils down to reducing the amount of uncertainty in the economic system as a whole.” Put most bluntly: “The future is not out there waiting to be learned; we create it ourselves.”

And insofar as the costs of mismanaged risk is borne disproportionately by the innocent as collateral damage, namely, by ordinary folk, irreducible uncertainty strengthens the case for safety nets to keep the losers from falling too far. In the words of the German sociologist Ulrich Beck, “Wealth rises to the top while risk sinks to the bottom.”

Post  Keynesians, those who remained close to the spirit of Keynes, like Hyman Minsky and Paul Davidson, have paid the price of being marginalized within the economics profession. So, if economics itself is the problem, reform will not come easily. But, like Keynes, Skidelsky thinks that ultimately it is ideas that rule the world and that economists therefore have an obligation to change the economics that we teach and practice. Without an economics to do the math and legitimize their behaviour, financial actors will be less able to do damage. Professional hubris must cease feeding capitalist greed.

In this grossly materialist world, power speaks the language of greed and certainty knowns as orthodox economics. It is no accident that economics is the dominant discourse of business schools, that without it they would be without clothes to hide their intellectual nakedness. Deny power the language and power is humbled.

For his part Skidelsky writes: “I have come to see economics as a fundamentally regressive discipline, its regressive nature disguised by increasingly sophisticated mathematics and statistics.” “[I]t was the wrong ideas of economists which legitized the deregulation of finance, and it was the deregulation of finance which led to the credit explosion which collapsed into the credit crunch.” A little fine-tuning of the discipline will not suffice.

At the graduate level, Skidelsky thinks microeconomics, with its basis in rational behaviour narrowly conceived and in certainty of outcomes, should be sent to the business schools where it can be supplemented by wider case studies. (I personally love this one.)

Macroeconomics should be taught as one half of a double major with philosophy or history or sociology or politics, etc. etc. but not mathermatics. “A broadly based postgraduate course in macroeconomics would study not just the implications of particular policies for economic stability, growth and development, but also their social and moral implications.”

Skidelsky is not optimistic this will happen. But he cites Thomas Kuhn’s position that paradigms will crumble when the burden of anomalies becomes excessive and, with the present crisis, more anomalies have been exposed with slight evidence that the conventional wisdom, being more of the same, will lead to their correction. “The time is ripe for a new ‘paradigm shift’, which needs to build on Keynes’ original insight into the nature of behaviour under conditions of uncertainty.”

There is at least the possibility – we cannot pretend to the probability – of a more vibrant progressive economics. We who call ourselves progressive would be wise to stay our course.

(I am indebted to John Hutcheson for insisting I read Skidelsky and to Duncan Cameron for first  telling me about Taleb and Black Swans, but I am alone responsible for the views expressed here.)


  • Nice post,

    As I see it the problem with the black swan is that it gets modelled as possible but not probable: lying somewhere at the extreme end of the two tails. So it can be managed: the non-probable future can be hedged.

    If the black swan were to be recast as uncertainty it would change our perspective. Uncertainty can be related to the fact that the future is unknowable in a fundamental sense such that a probability distributions of previously encountered outcomes (history) won’t cut it. It seems to me that engineers get the idea of uncertainty. In crucial applications like an aircraft there is a built in redundancy on crucial systems. If we took this approach to financial regulation then both the liberal economist and the neoliberal populist would bemoan useless duplication, regulatory red tape and inefficiency.

    So the plane gets flown with one hydraulic system because the probability of failure is said to rest on the extreme end of the distribution. Then when the plane crashes we are told: don’t panic planes crash all the time and that is the price of the freedom to fly.

    Again nice post.

  • This is a great article, I have been waiting for this per sey, when we try a diffrent understanding of what Kynes wrote.

    I tried to hint at this before about economic certainties, through the dismal savings rate. When “the only way on masse for people to save responsibility our in times of economic uncertainties”

    A stance of my understanding of regulation “However if your the type who thinks separating consumer banking from capital market activities is detrimental or forcing compolsury savings then you must elminate the government involvement because otherwise allowing parties to take on risk with government guarantees through insured deposits is equaly damaging or if not worse because it enables greed to have no fear in the marketplace with money not their own which creates imbalances & distorts future investment” Which in my opinion was a huge form economic certainty.

    Another one was “The underlying fact remains No one will Save with economic certainties and artificially low rates. When people thought that housing wouldn’t stop appreciating were was the saving then.”

    We will find ourselves taking about the Bancor, mainly because of US dollar weakness, which wont revitalize their exports, and when higher taxes fail to bring in more revenue. It will however price them immedietly out of imports which will impact Canada.

    Black Swans are not unpredictable, their timing is. For Instance a Black swan for economists, that you would fret. A inflationary depression in the US states would ruin the hopes and ambitions of using Fiscal measures for decades to come.

    Especially considering how communication is interconnected that if the US tries to pay its debtors with money of less value then today will have huge phyological implications when the so called great country is left smoldering from a failed fiscal measures which will be obvious because of failed conventional wisdom on deflation.

  • I think my stance more or less on regulation is like Travis. Yet Im a conservative, you dont see me bemoaning regulation because of my bemoaning of insured deposits. You dont see me bemoaning about higher taxes because my bemoaning of public spending.

    In another way, being a conservative I cannot vote for lower taxes if spending is left untouched. If its polotically impossible to not spend, then its irresponsible to have lower taxes. At least I try to learn the misconceptions we share about one another.

  • I do think find these swirling around in my brain a lot these days doing a creative dance-

    “I have come to see economics as a fundamentally regressive discipline, its regressive nature disguised by increasingly sophisticated mathematics and statistics”

    (I wish somehow we had better information but we don’t right now, and if we did I do wonder if it would matter. We have done fine enough without it- at least if you are from the popular schools with all those shiny naked models.)

    – “with its basis in rational behaviour narrowly conceived and in certainty of outcomes, should be sent to the business schools where it can be supplemented by wider case studies”

    ( in contradiction to my last statement, I think at the micro level we can and do get the information and to me this is where economics from the progressive level has lost its way. I believe very strongly that in the age of information and data, we can and must make progress in taming the beast at the micro level. Shifting it off to the business schools leaves us with nothing to connect to the reality of our macro planning models.

    Alternatives can and must be developed at this level- the future is the micro- from tech change, innovation, greening of the economy, this all has got have a progressive solution. I just don;t understand why you would want to push this off. Planning at this level is a must, and more than a profit motive must somehow be the magic that develops through an information/ needs/ equality based space. (it is not some soviet quantity school I am talking here, something a whole lot more responsive, innovative and economically and environmentally friendly))

    I have been modeling this idea in terms of information, and I know it will be the future and progressives will not be naked ones at the micro level, we sure at this point.

  • Particular thanks to Travis for his very helpful comments on Black Swans. The analogy to the possibility of a plane crashing is indeed useful.

  • Hi Mel,

    At first I was quite struck by Nassim’s idea of Black Swans (indeed I threw a blog post up about it some good while back) but then when I started thinking about what he was saying it seem to me to amount to the fact that risk was not adequately priced in because the models being used on the street had effectively cut the last 5% of the left hand side of the distribution out from their models. His critique is reasonable enough. I think his story about about fat Vinny the old wise man who has been around long enough to smell a bubble but whose warnings are ignored because the young bucks models only go back ten years and thus not only are rare events viewed as extremely rare they simply are not in the model is compelling. But I think the problem is deeper, much deeper.

    Some critics have argued that liberal economists merely make the assumption of rational expectations because it makes the model tractable. That is, in absence of needing to solve the model liberal economists would not insist on rational expectations: it is just the necessity of precision.

    I do not buy this argument and not because I think that the precision they have purchased is worthless with respect to reality (it bugs me but it is not a deal breaker). The problem I have is that at the ontological level (and let me coin a new term here) scientific liberalism, of which liberal economists are surely the van guard, are busy trying to prove that an economy in which property owners (not cars or houses but means by which society must reproduce itself) are free to do as they please with their property is not only a necessary condition of liberty but will on the whole lead to an ever increasing betterment of society in general.

    Viewed from this angle, rational expectations is not merely a simplifying assumption necessary to make the model tractable it is necessary in the ideological sense of furthering the ideological project of liberalism. When a liberal economists demands: why do you not include me in the progressive camp? He (most probably) or she is not being disingenuous. In their mind they are the van guard of progress because they are busy via scientific liberalism of demonstrating the path to human betterment which is of course always defined as growth. Distribution of that growth or catastrophic failures of the system are just the price of the freedom dance.

    Of course the high modernist cousin to scientific liberalism is scientific socialism: “just one more five year plan and we will get it right” said the commissar. There was a legitimacy to that position when the system was new, when there was no history; just a series of experiments where time would tell if they got it right. scientific liberalism cheats at this game: they both want to prove the maximisation of happiness; and then when the gig is up they want to default to satisficing (http://en.wikipedia.org/wiki/Satisficing).

    So having removed the secondary and tertiary hydraulic back-up systems they proclaim the predetermined crash as a natural event when the original claim was that eliminating those systems would not jeopardize safety. It is fundamentally dishonest and sad commentary on scientific liberalism that it can so effortlessly move from the best of all possible worlds to a necessary evil in the same breath. But like its cousin scientific socialism it has yet to meet its Waterloo.

  • Should hare read: *unlike* its cousin

  • yes Travis, you are very much, unlike my American Cousin, who is a right wing, lost his house because of healthcare bills he had to pay for a major operation to his mother, but went into the streets wildly protesting against the somewhat small progressive changes to healthcare reform.

    I feel a little out of my league critiquing Mel, but I have been involved for some time at the micro level from a government policy standpoint but ultimately a progressive labour oriented standpoint- which over the past 3-4 years has over taken my government policy perspective. And yes I don;t have all the details worked out yet- I am working on it.

    I guess I will have to write an update/expansion to Braverman to prove my point. Okay, I will report back in a few years on this subject- its gonna take me awhile.

  • and Travis, I meant to say, that was a fine post- one of your better ones and of course Mel, I do find a whole lot of comfort in your macro world- quite a sane voice you have and a nice post- sorry for getting caught up in my micro cave- I know if I rub these sticks together I might get a fire.

    Travis you are reminding me a bit of Bruno Latour. Their was/ is such a huge fight within the philosophy of science. the scientists are still quite upset- economics has always had a similar struggle- but given the past couple years of economic crisis, I would say we are now in a legitimacy crisis- that is if you can get the otherside to actually acknowledge the last couple of years. It was too big to just sweep under the carpet but they will and have been trying that.

    In many ways I think it is time to declare war within the field- ( i know we have been having our own little private war, but it is time we went public like never before) As Mel writes above, it is time to get this crisis within the field of economics to the next level. We have got to use this time as a means to further show the public that the gatekeepers of rationality are naked. They see these fully clothed lavish economic gods, it is time. I know it has always been time, but really and truly it is time- not now but right now! A call to arms. (Okay so its late)

    Maybe we should fly in Bruno Latour to the conference!

  • Oh shit Paul just threw me in with the constructionists. That is really mean. What is next? Jim accusing me of having a corn theory of value:).

  • I tried but ultimately you would not fit in, thus I stated, “reminding me a bit”. I did like some of the work of the Latour crowd, whether it actually resulted in much output terms of reality is another thing. The important thing to realize is, we have a whole lot of fantasy going on within our own field and somehow as referenced by Mel above,

    “he cites Thomas Kuhn’s position that paradigms will crumble when the burden of anomalies becomes excessive and, with the present crisis, more anomalies have been exposed with slight evidence that the conventional wisdom, being more of the same, will lead to their correction.”

    Am I wrong to interpret this in a similar manner to Polanyi’s double movement?

  • Paul Yes, I suppose it is like Polanyi’s double movement in some ways. If so, it argues for dissenters to help make it happen

  • Kuhn is a weird kind of dude. As Latour would readily admit there simply is no acid test for what constitutes an essential anomaly. Let us take the min wage argument as a good example. There is an economist of notorious stature that getto cruzes here often. His position on the min wage is not that it will kill jobs but that it is not an efficient mechanism for ameliorating poverty because the majority of families in poverty have little connection to the min wage. Now let us just leave that where it is and accept it, the problem of course is that min wage fight is not simply about poverty alleviation it is also about neoclassical price theory. When are good worthwhile lurker changes the acid test from neoclassical price theory to poverty alleviation he thinks he has been clever but the problem is he has tacitly turned his back on neoclassical price theory and thereby sold the farm to buy a tractor. That he does not bother to update the general neoclassical theory of price formation in light of his tacit admission that it is not a general theory but a very circumscribed theory is nothing more than telling. A true bayesian would update which in the case of the min wage and its ambiguous effects on employment would demand that he revise his general faith in neoclassical price theory. To do that, however, would call the whole general theory into question. And this is not the first nor the last time the hard core has been challenged at a devastating level yet they soldier on with the sense that they can loose almost all the battles yet the war is still theirs.

    When it comes to the social sciences theories do not stand or fall merely on their explanatory capacity they partly stand on their relationship to power this is what both kuhn and Latour miss. So yes I am a constructionist in the sense that I believe the world can only be, inadequately, interpreted by our appropriation of the external world in thought. But I do not believe that our dependence on inadequate (as in there is not a 1:1 correspondence between THE word and objects) concepts means that social reality is conceptually determined. That is why I made the corn joke. Corn cannot be the social numeraire. Nor gold for that matter (the vise of Austrians) only relations between human beings can be the foundation for a true social science. If you want true micro foundations you have to start there. Everything else is ideology in the bad sense of the word.

  • Like I said before Travis, civilization is something that lurker you mention (or ghettos cruzes (never heard of that one, but I kind of like it)), does not comprehend.

    What was I listening to last night- umm, the period after WW I and the great depression the formation of the Frankfurt school to counter liberalism’s failings, and the formation of the fascists and the communists. In some respects, we are potentially in this period again- a few variations, many academics, intellectuals, and artists back then had to actually pick a side and be on that Side, and if it meant moving countries you did it.

    We are not there in terms of that extreme, that I am aware of, but when I make my remarks that we need a call to much wider and more intense public debate within the field, it happened to a much greater degree in history when the system came off the rails the way it did.

    So for example the Frankfurt school up and left Germany and relocated to the USA. Its project, as you probably know was an update to Marx by infusing Freud and the many notions of the cultural conveyors over social construction re-invigorating or potentially contaminating some of Marx’s determinism and the power and rule of economics. (depends on your view) These were big swings in beliefs and theories back then, and much has changed since that period. And yes each and everyone of those systems that were brought about by movements and beliefs were constructed by power, culture, double movements and what have you but all melted into air. We have some leftovers spilled on the table, and many ideas wanting to push modernity in new directions.

    I do believe we are at this inflection point of dramatic change, and despite the fact that we may see a recovery, our globalized economic system is unique in the entire history of the universe and it has become a hard core junky. Its drug right now is speculative bubbles, the fix gets us to the next boom, but like a junky, the boom is shorter and shorter and the bust becomes deeper and more dangerous.

    And despite all these changes, despite all the possibilities, despite all the destruction of boom and busts, and despite all that we know, the best we can get for a progressive movement in place is what we have here on this side of the ocean is pathetically brutal for those that who have to sit and take a reduced pension, roll back in wages, increased poverty, more precarious work, and listen to the mantra of the bankers, the financiers, the popular press, the institutionalized neo-con economists serving as the gods to the economy (who by the way have been institutionalized since they were like 5 years old, never once leaving the institution or the tit of the power and resources of the wealthy!)

    So you do realize, we are at this point within the economics field for progressives, where it is time to take the gloves off. It is time to get into the debates, it is time to think about a stronger more unified labour movement, it is time to propose new policy options, it is time to engage the friendly politicians, it is time encourage collaborative efforts, a time to breath in the new tech and exploit the communication and a time to deeply reflect on this opportunity. We have some positive happenings south of the border in terms of power ( a bit watered down of late but still some potential).

    We need to have a refocusing of who we are and how we identify and put more imagination to a world that could and should be than the polarized, regressive, risk society that the other side keeps bringing down the pipe. 30 years is a long time, and I for one ain’t going back to the same old same old without a good fight.

    Okay I should get myself a 1-800 number, or better yet a 1-900 number. Or maybe I should just shut up and go away.

    We need to find the keys to the double movement and sorry if I feel the need to search, but I know if I rub these sticks together in my cave- a fire just might start and I can warm up a bit.


  • Paul maybe it is just a good old fashioned problem of organization. I would be one of the first to argue that progressives need a new animating vision of the welfare state but even if we had one we lack the organizational capacity to sell the vision and mobilize citizens. Real organizing requires a much more sustained effort than organizing election campaigns every now and again. Long term organizing must be sustained by highly motivated organizers between elections and it must be the type of movement that empowers those it seeks to mobilize. I fear parties like the NDP have lost their capacity to cold call and cold sell door by door. In fact the only party that can do this, ironically, is the reform elements of the conservative party.

  • your right Travis, I guess I am just learning about depth and width of the challenges and sometimes I get a bit carried away in my quest for solutions.

    I wish I could believe in the simplistic notions of markets and profits, it would make economics so much easier to comprehend. However when you get deep inside such notions one begins to understand there are so many more threads of complexity. Just think of market the construct seems so robust, but chase it down in such a manner as Marx did, and it is the interconnections with the social fabric that is ultimately important, and not the actual market itself. And the mechanisms in place we use to commodify such ideas, say as labour, actually destroy and transform the very essence right to the core of the human being. Yet, those that make the rules and the formulations of equations, do not seem to grasp such simple notions.

    It truly is an amazing historical spectacle in the slow moving transformation through time and space. Layer upon layer of definition, generation upon generation, submitting so uni-dimensionally and easily into the mold. The whole is definitely made up of more than the sum of these parts that we call human. Some as Marx said, less than animal, and I will say researching such workplace practices, whether it be in an office or a factory or a farm yard, the process defines and molds us into these tools.

    Damn even playing my guitar I get callouses, but alas if my hardened thumb produces a more efficient strum, it is fine, the I in me chose to join physically with the air waves and harmonics.

    I guess the notion of selling to regenerate and potentially not like it- was totally subsumed by the commodification of culture. A key point that seems to be spinning through the air waves. Maybe as culture rots into a global declining profits festering reality show, the cameras will finally just turn inside out and point straight back at ourselves- will we be entertained enough by watching ourselves? or will the shiny flashy lose its luster and maybe the culture bursts releasing us all so that we actually become amused once again with things as local politics.

    Maybe organizing can jump this barrier of the bewildering and suspicious stares of the TV eyes looking back at me when canvassing door to door.

  • On economists relocating to places sympathetic to their projects–I know one Marxist economist (Michael Lebowitz, used to teach at SFU in Vancouver) who a few years ago moved to Venezuela to get in on the Bolivarian Socialism-for-the-21st-century thing. So I suppose perhaps it is happening again at least to some extent.

    On the Black Swans, I think there is perhaps some confusion as to just what they are. Very unlikely events which have a large impact on the economy, creating risk that can’t be predicted–I think such things do exist. But people have been referring to the Great Depression and the current economic problems as such events, and I think that’s highly misleading. A Black Swan would be something like a major incident off the Iranian coast leading to bombing of Iran and the closing of the Strait of Hormuz to oil tankers. A Black Swan would be a major technological breakthrough which made large industries suddenly obsolete and many investments worthless. Such things are independent variables, as it were–things coming from outside the economic sphere but having an impact on it.
    The Great Depression and the mortgage/financial meltdown, on the other hand, were not Black Swans at all. They were events which were not predicted by mainstream economists because mainstream economists were using lousy models for prediction (and indeed apparently doing their best to ignore some of what even those models should have been telling them), but in fact they were quite predictable, and far from being unlikely, were basically inevitable. The current economic crisis was not just predictable but predicted by quite a few people; that they were ignored does not mean the events were not predictable. When people talk about these events as Black Swans it is a way of avoiding the fundamental flaws in their models by pointing to superficial ones.

    Finally, none of this talk of risk, even when such things as Black Swans are included, deals with the problem of intelligence. The economics of investment is competitive and near-zero-sum for many purposes. That is, for one person to gain, another generally has to lose. For me to buy low and sell high, someone has to have sold low, and someone has to have bought high.
    So this is a contest of tactics and strategy, not a random statistical fluctuation. In such contests there can be no optimum strategy that holds for all time; what will beat the opposition depends on what the opposition is doing.
    Let me give an example from medieval warfare. Lance cavalry, the armoured knight, is superior to sword-and-shield infantry, and indeed to most infantry with normal sized weapons. Knights rode down infantry in battle after battle throughout the middle ages. But it was eventually discovered that infantry with extremely long weapons–the pike–could defeat cavalry. Indeed, they had a major and decisive advantage; the pike phalanx was massively superior to the mounted knight. Surely this meant that the answer was simple–the best strategy called for the deployment of pike phalanxes, the ultimate battlefield weapon! Well, no. Turns out sword and shield infantry will defeat pike phalanxes; the pikes are too unwieldy and the sword and shield men will block and close, getting in past the pike heads. So it’s a circular problem. Add in ranged weaponry, terrain considerations and on and on, and there just isn’t a general solution saying “A rational tactician will choose X forces”. Similarly, there isn’t a general solution saying “A rational tactician will choose X investment strategy”. The game changes based on the tactics of the opposing players, and the question of whether big investors have decided to try to break Greece is at least as cogent as the question of whether some unexpected exterior risk will change the situation. Doing math is not adequate to the issue not so much because of random unknown risks as because of all the people trying to fiddle the system. There is no reason to assume their actions all end up approximating random noise.

  • Mike was my mentor at SFU.

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