# Deterministic investments under extreme uncertainty

What is “uncertainty”? The earliest definition of “uncertainty” came from Frank Knight. In 1921, Knight pointed out in Risk, Uncertainty, and Profit that measurable uncertainty is distinct from unmeasurable uncertainty. Unmeasured uncertainty is not uncertainty at all. In this regard, John Maynard Keynes pointed out in “The General Theory of Employment, Interest and Money” that what he called “uncertainty” refers to the outbreak of war in Europe, copper prices and interest rates 20 years later, new inventions becoming obsolete or 1970 The kind of uncertainty about private wealth owners and social status. These things have no scientific basis for calculating probabilities, and we have no way of knowing them. This becomes unmeasurable uncertainty. Unmeasurable uncertainty is what is called risk, measurable uncertainty is not.
Knight and Keynes distinguish between “risk” and “uncertainty”. Economist John Kay replaces that distinction with “solvable” and “extreme” uncertainty in his book Extreme Uncertainty. A “solvable” uncertainty is one that can be eliminated by borrowing, or one that can be represented by a probability distribution of known outcomes. “Extreme” uncertainty is uncertainty that has no comparable method to resolve, i.e. we simply don’t know.
Extreme uncertainty cannot be described in terms of probability, not just because we simply don’t know what will happen, often we don’t even know what might happen. Extreme uncertainty does not refer to the “long tail” in statistics. The long tail is an conceivable and well-defined event with a low probability of occurrence, but at least it can be estimated, such as losing several times in a row at roulette. Nor is extreme uncertainty limited to what Nassim Taleb calls “black swans,” although black swans are examples of extreme uncertainty. John Kay’s emphasis is on a wide range of possibilities, between two worlds: a world full of unlikely events, but those events can be described by means of probability assignments; a world full of unexpected event. The possible outcomes of extreme uncertainty extend well beyond financial markets to encompass individual and collective decisions, as well as economic and political decisions.
Economists are good at unraveling the puzzle of complex “economic models.” Therefore, the Nobel Prize in Economics is awarded to those who solve the most difficult puzzles. However, decisions in business, finance, politics, personal development, and the outcomes of those decisions are mostly too complex and poorly defined to be dealt with in a quantifiable probabilistic manner. They are limited by extreme uncertainty.
Real life mostly falls between the opposite extremes of randomness and black swans. Sometimes the true state of the world is a present or past fact, but not everyone knows it. When the problem is known but the range of answers is infinite, the mathematics of applying probability is dubious and the results are ambiguous. We cannot reasonably estimate probabilities for states when the problem is known, but the nature of the problem suggests that the answer is ambiguous. Economic processes that can create growth or volatility are not long-term stable enough to allow us to effectively estimate the probabilities of economic variables. For most interesting general economic problems, we cannot easily estimate the probabilities of the various possible outcomes, and even the possible outcomes are only vaguely defined. So the sensible answer to the question “Is another global financial crisis possible in the next 10 years?” is “I don’t know”.
Applicability of Bayes’ Theorem

Bayes’ theorem calculates conditional probabilities, i.e. what is the probability that A will occur if B has already occurred? This means that when we deal with an uncertain event, we assign it a prior probability. The Monty Hall problem is a famous example of Bayes’ theorem and relies on the so-called “indifference principle”: if we have no reason to think that one thing is more likely to happen than another, we give everything the same probability. Such questions are actually puzzles: there are fully stated questions, and there are known rules and clear answers. In a world of extreme uncertainty, however, problems are rarely fully articulated. The exact answer to the Monty Hall problem can be clearly solved once the implicit and explicit rules of the game are clarified. Clearly, Bayes’ theorem can handle small-world problems with definite solutions.
Prior probability refers to the probability obtained based on past experience and analysis, which is actually a subjective probability. Knight and Keynes emphasized the importance of uncertainty. They argue that probability cannot be applied outside the domain of known or knowable frequency distributions (e.g. roulette, mortality observation, weather). They take extreme uncertainty very seriously, but object to the use of subjective probabilities. The use of subjective probability, and the associated mathematics, seems to turn a mystery of extreme uncertainty into a puzzle with computable answers. And the most enthusiastic celebration of subjective probability over extreme uncertainty is at the University of Chicago, best known by none other than Milton Friedman.
Buffett once expressed his investment strategy vividly: “I think stock investing is the best business in the world…because you never have to be forced to swing a bat. You just wait all day for the ball you like, and then When a fielder takes a nap, he swings the bat and hits it out.” If probabilities form the basis of economic decision-making, then you do “have to swing,” and the world will indeed be willing to bet on every possible bet. But it would be wrong to expect the world to do this kind of trade often, and prudent people would never want to do that. A few professionals like Edward Thorpe have been so successful because they saw anomalies or studied the flow of apparent games of chance with particular care.
Economic and social systems, like weather systems, are non-linear. So, the evolution of the economy is as unpredictable as the weather. And economic forecasting is bound to be more difficult than weather forecasting, because the fundamental physical properties of the weather system have a side of stability, while the basic structure of the economic system lacks stability. Economic development is not governed by fixed physical laws of motion. Although the quality of economic forecasting remains poor, planning for the future economy is still necessary. Because companies have to make investment decisions, the central bank has to adjust to interest rates.
In 1944, von Neumann tried to establish in Game Theory and Economic Behavior that probabilistic reasoning could provide a coherent and rigorous framework for rational decision-making in an uncertain world. Ten years later, statistician Jimmy Savage sought a basis for the existence of subjective probability in Fundamentals of Statistics. Savage stressed that this foundation only applies to the “small world.” The difference between big and small worlds is very important. In the “small world”, people can solve problems by maximizing expected utility; in the “big world”, people actually live in it. Savage is careful to avoid claiming that his analysis can be applied outside the narrow confines of what he calls a “small world.” Problems like Monty Hall have to do with “small worlds” – repeatable games of chance. Economists, however, did not share Savage’s warnings about the scope of his analysis. They adopted Savage’s hypothesis, but claimed that the model thus derived could be directly applied to “big world” policy.
As a result, bank executives rely on the judgment of risk professionals, who in turn rely on Bayes’ theorem, with disappointing results. It is certain that Steve Jobs did not use Bayes’ theorem, he knew that he had limited and incomplete information, and that he was just waiting for “the next big flashpoint”. That’s how good decision-making works in a world of uncertainty, where decision makers struggle to think “what happened?” So John Kay questioned the applicability of Bayes’ theorem.

The Value of the “Small World” Model

In 1950, Princeton University professor Albert Tucker concocted a “prisoner’s dilemma” story. The subsequent theorizing of this story has made the Prisoner’s Dilemma one of the most insightful and fruitful economic models. The purpose of building a model is to turn a mystery into a puzzle, that is, to find a simpler problem that has a definite solution and is still similar enough to the actual problem to generate insight, Inspire the best action strategies. Such models can be called “small-world” models, and practical economic theory usually falls into this category. Adam Smith described the concept of division of labor in terms of the operation of the pin factory; David Ricardo proposed a model of international trade based on comparative advantage.
The models proposed by Tucker, Smith, and Ricardo are all built on easy-to-understand descriptions whose stories illustrate basic economic concepts. Their models can be presented as calculations, numerical examples, or interesting stories, and are particularly fruitful in economics. While these models cannot provide comprehensive or quantitative answers to economic questions, they can illustrate similar examples from the “small world” that help us construct arguments and better understand the nature of mysteries.
The efficient market hypothesis is one of the most controversial models in economics. The basic insight of this hypothesis is that publicly available information is already incorporated into security prices. Public information may be largely integrated into security prices, but public information is not always or completely integrated into prices, so it is still possible for investors to devise successful investment strategies. Both proponents and critics of the efficient market hypothesis seem to have made the mistake of believing that the model is describing “what the world really looks like.” The efficient market hypothesis is a prototype of a model that is instructive, but not “real”.
The “Small World” model is a fictional narrative, and its truth lies in small words, not specifics. In the economic model, “representative actors”, “consumers” and “companies” are not real people or businesses, but a contrived conception, and every detail is the ingenuity of the author, just like Sherlock Holmes The same story – invented by Conan Doyle, not a description of the real world. Economics starts with simple models, which are expressed in the form of narratives, sometimes containing some hypothetical numbers. The economic historian John Clappan once criticized the author of The Wealth of Nations: “It is a pity that Adam Smith did not travel from Kirkcaldy to the Caron factory a few miles away to see them making cannons, but to speak of his A boring pin factory, that pin factory is nothing more than a factory in the old sense.”
Portfolio theory, capital asset pricing models, and the efficient market hypothesis are useful models, even indispensable, but they fail to describe “the world true appearance”. Treating these financial models as reality, populating them with fictitious numbers, and using them as a basis for important decisions can lead to major mistakes, as they did during the global financial crisis and many other occasions The same role ultimately led to the demise of LTCM. Most of the extremes in financial crises stem from events outside the model.
We’re glad we know these “small world” models, and we’re better investors because we know them, but let’s not take them too seriously, let alone believe they describe “what the world really looks like.” appearance”. Even Harry Markowitz, the founder of Portfolio Theory, knew that his theory only worked for small worlds, but his warnings were mostly ignored.
The value of the “small world” model lies in framing a question that provides insight into the “big world” issues facing policymaking, rather than pretending to be able to provide precise measurement guidelines. We cannot derive probabilities, forecasts and policy recommendations from models. Only in the context of the model do probabilities make sense, predictions are accurate, and policy recommendations are well-documented. Interestingly, other disciplines pay more attention to such issues. Bridge builders and aeronautical engineers deal with a solid body of knowledge, and it is quite sensible that metrological answers that do not match prior experience will arouse their suspicion. In economics, however, whenever a surprising result emerges, the most common explanation is that someone made a mistake. In the fields of finance, economics, and business, models have never been describing “the real world”. Understanding and interpreting the output of a model, as well as applying the model to any “big world” situation, always requires informed judgment.
Warren Buffett, George Soros and James Simmons represent three distinct investing styles. They all ignore or even disdain financial theory based on portfolio theory, capital asset pricing models, and efficient market assumptions. In fact, that theory means they couldn’t be as successful as they are now. These financial models highlight key points that all investors should know: the benefits of diversification, the extent to which different assets provide opportunities for true diversification, and the extent to which information is incorporated into security prices. But experience tells us that there is not only one way to make money in financial markets, there is not only one way to explain “what happened”, and there is not only one narrative for “what the financial world really looks like”. There are many effective methods, and the appropriate tool depends on the context and the skill and judgment of the investor. We can indeed benefit from Markowitz’s insights, but the insights we gain from his “small world” model have limitations.
Different attitudes towards uncertainty

The discovery of evolutionary theory was a seminal moment for human thought. Evolution has taught humans to deal with the many extremes of uncertainty encountered in the “big world.” Different attitudes to uncertainty affect the survival chances of individuals and groups. In some environments, such as in business and sports, acting cautiously and looking ahead is to pass up the chance for success. And overestimating your chances of success may even be an advantage. In other settings, risk avoidance may be reasonable. One reason humans survived is that our ancestors were not eaten by predators. Evolution, as Taleb said, favors those who survive. They are not necessarily the ones with the highest expectations.
If we live in a simple, static “small world,” techniques for optimizing and solving “small world” puzzles are the keys to evolutionary success. But for the most part, we don’t live in a “small world.” In the real world, extreme events go hand in hand with survival. For individuals, choosing the strategy most likely to succeed can maximize the odds of winning, but groups of individuals who seek to optimize will eventually be wiped out by rare disasters. Political scientist James Scott once described the reality of this truth: Planting the best trees leads to monocultures that, sooner or later, will be wiped out by unprecedented parasites.
Humans do well because we are all different and different, and because reason has no single way. Optimism is good for survival, and if it is controlled and guided, the effect will be better. Overconfidence is often a disaster at the gambling table, but it’s very important for motivating teammates, business partners, or leaders in the military.
Virgin Group founder Richard Branson is a successful adventurer. Branson isn’t interested in the specifics of cash flow budgeting, but he claims he has a seemingly unfounded system of success. In the “small world,” rational behavior can be reduced to mathematical operations, and those operations are performed in the context of a well-defined problem and a well-understood environment. Branson’s achievement reminds us of an insight Knight made a century ago but long forgotten: the relationship between extreme uncertainty and risk-taking. As Keynes said, the adventurous spirit disappears when we rely only on mathematical expectations. Risk-taking seems to be at odds with axiomatic rationality, but it is the core driving force of capitalist society and a key part of the mystery of success.
Extreme uncertainty is closely related to non-stationarity. There is no stable world framework in which we can learn from past experience and infer future behavior from it. John Kay’s critique is not limited to Bayes’ theorem and economic models, but extends to behavioral economics and reference narratives. Whatever the critique is, it does not mean abandoning modeling or abandoning mathematics, but rather that their applicability must be made clear. The important contribution of economics to the world is that it is practical knowledge, not scientific theory. Thus, the role of the pragmatic economist would be that of a problem solver, like a firefighter, a doctor, and an engineer. Knight knew that extreme uncertainty brought profit opportunities, and the staggering wealth accumulated by the likes of Buffett, Soros, and Simmons proved Knight right.