I am in an intellectually playful frame of mind, and I decide to play with Keynes and probability. It makes like 4 weeks that I mess around with the theory of probability, and yesterday my students told me they have a problem with Keynes. I mean, not with Sir John Maynard Keynes as a person, but more sort of with what he wrote. I decided to connect those two dots. Before John Maynard Keynes wrote his ‘General Theory of Employment, Interest, and Money’, in 1935, he wrote a few other books, and among them was ‘A Treatise on Probability’ (1921).
I am deeply convinced that mathematics expresses our cognitive take on that otherwise little known, chaotic stuff we call reality, fault of a better label. I am going to compare John Maynard Keynes’s approaches to, respectively, probability and economics, so as to find connections. I start with the beginning of Chapter I, entitled ‘The Meaning of Probability’, in Keynes’s Treatise on Probability,
‘Part of our knowledge we obtain direct; and part by argument. The Theory of Probability is concerned with that part which we obtain by argument, and it treats of the different degrees in which the results so obtained are conclusive or inconclusive. In most branches of academic logic, such as the theory of the syllogism or the geometry of ideal space, all the arguments aim at demonstrative certainty. They claim to be conclusive. But many other arguments are rational and claim some weight without pretending to be certain. In Metaphysics, in Science, and in Conduct, most of the arguments, upon which we habitually base our rational beliefs, are admitted to be inconclusive in a greater or less degree. Thus for a philosophical treatment of these branches of knowledge, the study of probability is required. […] The Theory of Probability is logical, therefore, because it is concerned with the degree of belief which it is rational to entertain in given conditions, and not merely with the actual beliefs of particular individuals, which may or may not be rational. Given the body of direct knowledge which constitutes our ultimate premises, this theory tells us what further rational beliefs, certain or probable, can be derived by valid argument from our direct knowledge. This involves purely logical relations between the propositions which embody our direct knowledge and the propositions about which we seek indirect knowledge. […] Writers on Probability have generally dealt with what they term the “happening” of “events.” In the problems which they first studied this did not involve much departure from common usage. But these expressions are now used in a way which is vague and ambiguous; and it will be more than a verbal improvement to discuss the truth and the probability of propositions instead of the occurrence and the probability of events’.
See? Something interesting. I think most of us connect the concept of probability to that experiment which we used to perform at high school: toss a coin 100 times, see how many times you have tails, and how many occurrences of heads you had etc. Tossing a coin is empirical: we make very little assumptions and we just observe. How is it possible, then, for anybody to even hypothesise that probability is a science of propositions rather than hard facts?
Now, here is the thing with John Maynard Keynes (and I address this passage to all those of my students who struggle with understanding what the hell did John Maynard mean): John Maynard Keynes had a unique ability to sell his ideas, and his ideas came from his experience. Whatever general principles you can read in Keynes’s writings, and however irrefutable he suggests these principles are, John Maynard tells us the same kind of story that everybody tells: the story of his own existence. He just tells it in so elegantly sleek a way that most people just feel disarmed and conquered. Yet, convincing is not the same as true. Even the most persuasive theorists – and John Maynard Keynes could persuade the s**t out of most common mortals – can be wrong. How can they be wrong? Well, when I fail to own my own story, i.e. when I am just too afraid of looking the chaos of life straight in the eyes (which is elegantly called ‘cognitive bias’), then I tell just the nice little story which I would like to hear, in order to calm down my own fear.
Let’s try to understand John Maynard Keynes’s story of existence, which leads to seeing probabilities as a type of logic rather than data. I browse through his ‘Treatise on Probability’. I’m patient. I know he will give himself away sooner or later. Everybody does. Well, let’s say that according to my experience of conversations with dead people via their writings, each of them ends up by telling me, through his very writing, what kind of existential story made him tell the elegantly packaged theoretical story in the title of the book. Gotcha’, Sir Keynes! Part I – Fundamental Ideas – Chapter III, ‘The Measurement of Probabilities’, page 22 in the PDF I am linking to: ‘If we pass from the opinions of theorists to the experience of practical men, it might perhaps be held that a presumption in favour of the numerical valuation of all probabilities can be based on the practice of underwriters and the willingness of Lloyd’s to insure against practically any risk. Underwriters are actually willing, it might be urged, to name a numerical measure in every case, and to back their opinion with money. But this practice shows no more than that many probabilities are greater or less than some numerical measure, not that they themselves are numerically definite. It is sufficient for the underwriter if the premium he names exceeds the probable risk. But, apart from this, I doubt whether in extreme cases the process of thought, through which he goes before naming a premium, is wholly rational and determinate; or that two equally intelligent brokers acting on the same evidence would always arrive at the same result. In the case, for instance, of insurances effected before a Budget, the figures quoted must be partly arbitrary. There is in them an element of caprice, and the broker’s state of mind, when he quotes a figure, is like a bookmaker’s when he names odds. Whilst he may be able to make sure of a profit, on the principles of the bookmaker, yet the individual figures that make up the book are, within certain limits, arbitrary. He may be almost certain, that is to say, that there will not be new taxes on more than one of the articles tea, sugar, and whisky; there may be an opinion abroad, reasonable or unreasonable, that the likelihood is in the order—whisky, tea, sugar; and he may, therefore be able to effect insurances for equal amounts in each at 30 per cent, 40 per cent, and 45 per cent. He has thus made sure of a profit of 15 per cent, however absurd and arbitrary his quotations may be’.
See? Told you he’s got a REAL story to tell, Sir Keynes. You just need to follow him home and see whom he’s hanging with. He is actually hanging with financial brokers and insurers. He observes them and concludes there is no way of predicting the exact probability of complex occurrences they essentially bet money on. There is some deeply intuitive mental process taking place in their minds, which makes them guess correctly if insuring a ship full of cotton, for reimbursable damages worth X amount of money, in exchange of an insurance premium worth Y money.
The story that John Maynard Keynes tells is through his ‘Treatise on Probability’ is the story of the wild, exuberant capitalism of the early 1920ies, right after World War I, and after the epidemic of Spanish flu. It was a frame of mind that pushed people to run towards a mirage of wealth, and they would run towards it so frantically, because they wanted to run away from memories of horrible things. Sometimes we assume that what’s can possibly catch us from behind is so frightening that whatever we can run towards is worth running forward. In such a world, probability is a hasty evaluation of odds, with no time left for elaborate calculations. There are so many opportunities to catch, and so much fear to run away from that I don’t waste my time to think what an event actually is. It is just the ‘have I placed my bets right?’ thing. I think I understand it, as I recently experienced very much the same (see A day of trade. Learning short positions).
The very same existential story, just more seasoned and marinated in the oils of older age, can be seen in John Maynard Keynes’s ‘General Theory of Employment, Interest, and Money’. I read the ‘Preface’, dated December 13th, 1935, where the last paragraph says: ‘The composition of this book has been for the author a long struggle of escape, and so must the reading of it be for most readers if the author’s assault upon them is to be successful,—a struggle of escape from habitual modes of thought and expression. The ideas which are here expressed so laboriously are extremely simple and should be obvious. The difficulty lies, not in the new ideas, but in escaping from the old ones, which ramify, for those brought up as most of us have been, into every corner of our minds’. The same line of logic is present in country-specific prefaces that follow, i.e. to national translations of ‘General Theory’ published in Germany, France, and Japan.
In 1935, John Maynard Keynes had lived the exuberance of the 1920ies and the sobering cruelty of the 1930ies. He felt like telling a completely new story, yet the established theory, that of classical economics, would resist. How can you overcome resistance of such type? One of the strategies we can use is to take the old concepts and just present them in a new way, and I think this is very largely what John Maynard Keynes did. He took the well-known ideas, such as aggregate output, average wage etc., and made a desperate effort to reframe them. In the preface to the French edition of ‘General Theory’, there is a passage which, I believe, sums up some 50%, if not more, of all the general theorizing to be found in this book. It goes: ‘I believe that economics everywhere up to recent times has been dominated, much more than has been understood, by the doctrines associated with the name of J.-B. Say. It is true that his ‘law of markets’ has been long abandoned by most economists; but they have not extricated themselves from his basic assumptions and particularly from his fallacy that demand is created by supply. Say was implicitly assuming that the economic system was always operating up to its full capacity, so that a new activity was always in substitution for, and never in addition to, some other activity. Nearly all subsequent economic theory has depended on, in the sense that it has required, this same assumption. Yet a theory so based is clearly incompetent to tackle the problems of unemployment and of the trade cycle. Perhaps I can best express to French readers what I claim for this book by saying that in the theory of production it is a final break-away from the doctrines of J.- B. Say and that in the theory of interest it is a return to the doctrines of Montesquieu’.
Good. Sir Keynes assumes that it is a delicate thing to keep the economic system in balance. Why? Well, Sir Keynes knows it because he had lived it. That preface to the French edition of ‘General Theory’ is dated February 20th, 1939. We are all the way through the Great Depression, Hitler has already overtaken Austria and Czechoslovakia, and the United States are in the New Deal. Things don’t balance themselves by themselves, it is true. Yet, against this general assumption of equilibrium-is-something-precarious, the development which follows, in ‘General Theory’ goes exactly in the opposite direction. John Maynard Keynes builds a perfect world of equations, where Savings equal Investment, Investment equals Amortization, and generally things are equal to many other things. Having claimed the precarity of economic equilibrium, Sir Keynes paints one in bright pink.
I think that Keynes tried to express radically new ideas with old concepts, whence the confusion. He wanted to communicate the clearly underrated power of change vs that of homeostasis, yet he kept thinking in terms of, precisely, homeostasis between absolute aggregates, e.g. the sum of all proceedings anyone can have from a given amount of business is equal to the value conveyed by the same amount of business (this is my own, completely unauthorized summary of the principle, which Keynes called ‘effective demand’).
The ‘General Theory of Employment, Interest, and Money’ was somehow competing for the interest of readers with another theory, phrased out practically at the same moment, namely the theory of business cycles by Joseph Alois Schumpeter. I perceive the difference between the respective takes by Keynes and Schumpeter, on the general turbulence of existence, in the acknowledgment of chaos and complexity. Keynes says: ‘Look, folks. This, I mean that whole stuff around, is bloody uncertain and volatile. Still, the good news is that I can wrap it up, just for you, in an elegant theory with nice equations, and then you will have a very ordered picture of chaos’. Joseph Alois Schumpeter retorts: ‘Not quite. What we perceive as chaos is simply complex change, too complex for being grasped once and for all. There is a cycle of change, and we are part of the cycle. We are in the cycle, not the other way around (i.e. cycle is not in us). What we can understand, and even exploit, is the change in itself’.
Where do I stand in all that? I am definitely more Schumpeterian than Keynesian. I prefer dishevelled reality to any nicely ordered and essentially false picture thereof. Yes, existence is change, and any impression of permanence is temporary. My recent intellectual wrestling with stochastic processes (see We really don’t see small change) showed me that even when I use quite elaborate analytical tools, such as mean-reversion, I keep stumbling upon my purely subjective partition of perceivable reality into the normal order, and the alarming chaos (see The kind of puzzle that Karl Friedrich was after).
A vision of game comes to my mind. This is me vs universe. Looks familiar? Right you are. That’s exactly the kind of game each of us plays throughout time. I make a move, and I wait for the universe to make its own. I have a problem: I don’t really know what kind of phenomenon I can account as move made by the universe. I need to guess: has the universe already made its move, in that game with me, or not yet? If I answer ‘yes’, I react. I assume that what has just happened is informative about the way my existence works. If, on the other hand, I guess that the universe has not figured yet any plausible way to put me at check, I wait and observe. Which is better, day after day: assuming that the universe made its move or sitting and waiting? I can very strongly feel this dilemma in my learning of investment in the stock market. Something happened. Prices have changed. Should I react immediately, or should I wait?
I provisionally claim that it depends. The universe moves at an uneven speed. By ‘provisionally’ I mean I claim it until I die, and then someone else will take on claiming the same, just as provisionally. Yet, all that existential instability acknowledged, there are rhythms I can follow. As regards my investment, I discovered that the most sensible rhythm to follow beats on the passive side of my investment portfolio. Every month, I collect the rent from an apartment, downtown, and I invest that rent in the stock market. I discovered that when I orchestrate my own thinking into that monthly rhythm of inflow in equity, it sort of works nicely. I collect the rent around the 5th day of each month, and for like one week beforehand, I do my homework about the market. When the rent comes, I have a scenario in mind, usually with a few question marks, i.e. with uncertainty to deal with. I play my investment game for 1 – 3 days, with occasional adjustments, and this is my move. Then I let the universe (the stock market in this case) make its own move over the next 3 – 4 weeks, and I repeat the same cycle over and over again.
I make a short move, and I let the universe making a long move. Is it a sensible strategy? From my point of view, there are two reasons for answering ‘yes’ to that question. First of all, it works in purely financial terms. I have learnt to wait patiently for an abnormally good opportunity to make profits. When I go too fast, like every day is a decision day, I usually get entangled in a game of my own illusions, and I lose money on transactions which I don’t quite understand. When I take my time, pace myself, and define a precise window for going hunting, usually something appears in that window, and I can make good money. Second of all, it is something I have sort of learnt generally and existentially: chaos is there, and I am there, and a good way to be alongside the chaos is to find a rhythm. When I follow my beat, chaos becomes a flow I can ride, rather than a storm I should fear.