The why of Radical Uncertainty

A recent post offered an overview of a book by John Kay and Mervyn King titled “Radical Uncertainty: Decision-Making for an Unknowable Future”. It is a rich topic and this post covers the underlying drivers that tend to result in radically uncertain outcomes.

Kay and King nominate “reflexivity” as a key driver of radical uncertainty

The sociologist Robert K. Merton identified reflexivity as a distinctive property of social systems–the system itself is influenced by our beliefs about it. The idea of reflexivity was developed by the Austrian émigré philosopher Karl Popper and became central to the thinking of Popper’s student, the highly successful hedge fund manager George Soros. And it would form part of the approach to macroeconomics of the Chicago economist Robert Lucas and his followers … although their perspective on the problem and its solution would be very different.

Reflexivity undermines stationarity. This was the essence of ‘Goodhart’s Law’–any business or government policy which assumed stationarity of social and economic relationships was likely to fail because its implementation would alter the behaviour of those affected and therefore destroy that stationarity.

Kay and King, Chapter 3: Radical Uncertainty is Everywhere”

Radical uncertainty also features in Richard Bookstaber’s book “The End of Theory: Financial Crises, the Failure of Economics, and the Sweep of Human Interaction”. Bookstaber identifies four broad phenomena he argues are endemic to financial crises

Emergent phenomena.
“When systemwide dynamics arise unexpectedly out of the activities of individuals in a way that is not simply an aggregation of that behavior, the result is known as emergence”.

Non-ergodicity.
“An ergodic process … is one that does not vary with time or experience.
Our world is not ergodic—yet economists treat it as though it is.”

Radical uncertainty.
“Emergent phenomena and non-ergodic processes combine to create outcomes that do not fit inside defined probability distributions.”

Computational irreducibility.
“There is no formula that allows us to fast-forward to find out what the result will be. The world cannot be solved; it has to be lived.

Bookstaber, Chapter 2: Being Human

If you want to delve into the detail of why the world can be radically uncertain then Bookstaber arguably offers the more detailed account; albeit one couched in technical language like emergent phenomena, ergodicity and computational irreducibility. In Chapter 10 he lays out the ways in which an agent based modelling approach to the problem of radical uncertainty would need to specify the complexity of the system in a structured way that takes account of the amount of information required to describe the system and the connectedness of its components. Bookstaber also offers examples of emergent phenomena in seemingly simple systems (e.g. Gary Conways’s “Game of Life”) which give rise to surprisingly complex outcomes.

I am not sure if either book makes this point explicitly but I think there is also an underlying theme in which the models that provide the illusion of control over an uncertain future create an incentive to “manage” risk in ways that increases the odds of bad outcomes based on insufficient resilience. That seems to be the clear implication of Kay and King’s discussion of the limits of finance theory (Chapter 17: The World of Finance). They acknowledge the value of the intellectual rigour built on the contributions of Harry Markowitz, William Sharpe and Eugene Fama but highlight the ways in which it has failed to live up to its promiseI .

We note two very different demonstrations of that failure. One is that the models used by regulators and financial institutions, directly derived from academic research in finance, not only failed to prevent the 2007–08 crisis but actively contributed to it. Another is to look at the achievements of the most successful investors of the era – Warren Buffett, George Soros and Jim Simons. Each has built fortunes of tens of billions of dollars. They are representative of three very different styles of investing.

Kay and King, Chapter 17 The World of Finance

I plan to do one more post exploring the ways in which we navigate a world of radical uncertainty.

Tony (From the Outside)

Who gets the money?

Matt Levine’s “Money Stuff” column (23 April 2020) has some interesting observations commenting on which bank customers received the money the U.S. government made available under its Paycheck Protection Program. The column’s headline focus is developments in the oil market, which is worth reading in its own right, but the bank commentary is further down under the subheading “PPP”.

You can find the column here but there are a couple of extracts below that give you the basic thrust of his comments …

The U.S. government is distributing free money to small businesses so that they can stay afloat, and keep paying workers, during the coronavirus shutdown. It is doing this through the Paycheck Protection Program, in which banks lend the money to small businesses, and then the government (the U.S. Small Business Administration) pays back the loans if the businesses use the money for payroll. This is, broadly speaking, sensible. I once wrote about it:

It is a public-private partnership that plays to each side’s strengths. Banks are, precisely, in the business of vetting applications from local restaurants, examining their financial records and deciding how much money they need. The government, meanwhile, is best equipped to generate magical quantities of money. The banks do something recognizably bank-like—market and underwrite small-business loans—and the government transforms them into magical free money.

Matt Levine, Bloomberg “Money Stuff” column, 23 April 2020

Matt goes on to offer his perspective on the strengths of the program, some of the practical issues of execution but also its potential unintended outcomes

That’s the idea. But if you are enlisting banks to run your program, you are going to get … banks. Like, the banks are going to behave in recognizably bank-like ways while they are doing the bank-like job of handing out the loans. Some of that will be good: You want the banks to check that the small businesses exist and aren’t stealing the money and so forth. Some of it will be good-ish, or debatable: You want the banks to check that the documents are all in order and that the loans match the businesses’ actual financial needs, but you don’t want them to spend so much time checking that the businesses never get their money.

And some of it will be … not exactly bad, necessarily, but at least unrelated to the goals of the program.

I don’t have any insight on whether these big American banks are guilty as charged, or indeed guilty at all. Matt is I think open minded and simply presenting the facts but it is something worth watching as the COVID 19 crisis plays out. As a general observation, I feel like the Australian banks have for the most part made extra (if not extraordinary) efforts to do the right thing by both their customers and the community at large. I am of course a (now semi retired) banker so that colours my observation but, as an ongoing bank shareholder, I expect to be feeling some of the impact of the forbearance in upcoming dividend payments and see that as part of the price of investing in banks.

Tony (From the Outside)

Worth Reading “The Money Formula” by Paul Wilmott and David Orrell.

The full title of this book, co-written by Paul Wilmott and David Orrell, is “The Money Formula: Dodgy Finance, Pseudo Science, and How Mathematicians Took over the Markets“. There are plenty of critiques of modelling and quantitative finance by outsiders throwing rocks but Wilmott is a quant and brings an insider’s technical knowledge to the question of what these tools can do, can’t do and perhaps most importantly should not be used to do. Consequently, the book offers a more nuanced perspective on the strengths and limitations of quantitative finance as opposed to the let’s scrap the whole thing school of thought. I have made some more detailed notes which follow the structure of the book but this post focuses on a couple of ideas I found especially interesting or useful.

I am not a quant so my comments should be read with that in mind but the core idea I took away is that, much as quants would want it otherwise, markets are not determined by fundamental laws, deterministic or probabilistic that allow risk to be measured with precision. These ideas work reasonably well within their “zone of validity” but a more complete answer (or model) has to recognise where the zones stop and uncertainty rules.  Wilmott and Orrell argue market outcomes are better thought of as the “emergent result of complex transactions”. The role of money in these emergent results is especially important, as is the capacity of models themselves to materially reshape the risk of the markets they are attempting to measure.

The Role of Money

Some quotes I have drawn from Chapter 8, will let the authors speak for themselves on the role of money …

Consider …. the nature of money. Standard economic definitions of money concentrate on its roles as a “medium of exchange,” a “store of value,” and a “unit of account.” Economists such as Paul Samuelson have focused in particular on the first, defining money as “anything that serves as a commonly accepted medium of exchange.” … ” Money is therefore not something important in itself; it is only a kind of token. The overall picture is of the economy as a giant barter system, with money acting as an inert facilitator.” (emphasis added)

“However … money is far more interesting than that, and actually harbors its own kind of lively, dualistic properties. In particular, it merges two things, number and value, which have very different properties:number lives in the abstract, virtual world of mathematics, while valued objects live in the real world. But money seems to be an active part of the system. So ignoring it misses important relationships. The tension between these contradictory aspects is what gives money its powerful and paradoxical qualities.” (Emphasis added)

The real and the virtual become blurred, in physics or in finance. And just as Newtonian theories break down in physics, so our Newtonian approach to money breaks down in economics. In particular, one consequence is that we have tended to take debt less seriously than we should. (emphasis added)

Instead of facing up to the intrinsically uncertain nature of money and the economy, relaxing some of those tidy assumptions, accepting that markets have emergent properties that resist reduction to simple laws, and building a new and more realistic theory of economics, quants instead glommed on to the idea that, when a system is unpredictable, you can just switch to making probabilistic predictions.” (emphasis added)

“The efficient market hypothesis, for example, was based on the mechanical analogy that markets are stable and perturbed randomly by the actions of atomistic individuals. This led to probabilistic risk-analysis tools such as VaR. However, in reality, the “atoms” are not independent, but are closely linked … The result is the non-equilibrium behaviour … observed in real markets. Markets are unpredictable not because they are efficient, but because of a financial version of the uncertainty principle.” (emphasis added)

 The Role of Models

Wilmott & Orrell devote a lot of attention to the ways in which models no longer just describe, but start to influence, the markets being modelled mostly by encouraging people to take on more risk based in part on a false sense of security …

“Because of the bankers’ insistence on treating complex finance as a university end-of-term exam in probability theory, many of the risks in the system are hidden. And when risks are hidden, one is led into a false sense of security. More risk is taken so that when the inevitable happens, it is worse than it could have been. Eventually the probabilities break down, disastrous events become correlated, the cascade of dominoes is triggered, and we have systemic risk …. None of this would matter if the numbers were small … but the numbers are huge” (Chapter 10 – emphasis added)

They see High Frequency Trading as the area likely to give rise to a future systemic crisis but also make a broader point about the tension between efficiency and resilience..

“With complex systems, there is usually a trade-off between efficiency and robustness …. Introducing friction into the system – for example by putting regulatory brakes on HFT – will slow the markets, but also make them more transparent and reliable. If we want a more robust and resilient system then we probably need to agree to forego some efficiency” (Chapter 10 – emphasis added)

The Laws of Finance

Wilmott and Orrell note the extent to which finance has attempted to identify laws which are analogous to the laws of physics and the ways in which these “laws” have proved to be more of a rough guide.

 “… the “law of supply and demand” …states that the market for a particular product has a certain supply, which tends to increase as the price goes up (more suppliers enter the market). There is also a certain demand for the product, which increases as the price goes down.”

“… while the supply and demand picture might capture a general fuzzy principle, it is far from being a law. For one thing, there is no such thing as a stable “demand” that we can measure independently –there are only transactions.”

“Also, the desire for a product is not independent of supply, or other factors, so it isn’t possible to think of supply and demand as two separate lines. Part of the attraction of luxury goods –or for that matter more basic things, such as housing –is exactly that their supply is limited. And when their price goes up, they are often perceived as more desirable, not less.” (emphasis added)

This example is relevant for banking systems (such as Australia) where residential mortgage lending dominates the balance sheets of the banks. Even more so given that public debate of the risk associated with housing seems often to be predicated on the economics 101 version of the laws of supply and demand.

The Power (and Danger) of Ideas

A recurring theme throughout the book is the ways in which economists and quants have borrowed ideas from physics without recognising the limitations of the analogies and assumptions they have relied on to do so. Wilmott and Orrell credit Sir Issac Newton as one of the inspirations behind Adam Smith’s idea of the “Invisible Hand” co-ordinating  the self interested actions of individuals for the good of society. When the quantum revolution saw physics embrace a probabilistic approach, economists followed.

I don’t think Wilmott and Orrell make this point directly but a recurring thought reading the book was the power of ideas to not just interpret the underlying reality but also to shape the way the economy and society develops not always for the better.

  • Economic laws that drive markets towards equilibrium as their natural state
  • The “invisible hand” operating in markets to reconcile individual self interest with optimal outcomes for society as a whole
  • The Efficient Market Hypothesis as an explanation for why markets are unpredictable

These ideas have widely influenced quantitative finance in a variety of domains and they all contribute useful insights; the key is to not lose sight of their zone of validity.

…. Finance … took exactly the wrong lesson from the quantum revolution. It held on to its Newtonian, mechanistic, symmetric picture of an intrinsically stable economy guided to equilibrium by Adam Smith’s invisible hand. But it adopted the probabilistic mathematics of stochastic calculus.” (emphasis added) Chapter 8

Where to from here?

It should be obvious by now that the authors are arguing that risk and reward cannot be reduced to hard numbers in the ways that physics has used similar principles and tools to generate practical insights into how the world works. Applying a bit of simple math in finance seems to open up the door to getting some control over an unpredictable world and, even better, to pursue optimisation strategies that allow the cognoscenti to optimise the balance between risk and reward. There is room for more complex math as well for those so inclined but the book sides with the increasingly widely held views that simple math is enough to get you into trouble and further complexity is best avoided if possible.

Wilmott and Orrell highlight mathematical biology in general and a book by Jim Murray on the topic as a source for better ways to approach many of the more difficult modelling challenges in finance and economics. They start by listing a series of phenomena in biological models that seem to be useful analogues for what happens in financial markets. They concede that a number of models used in mathematical biology that are almost all “toy” models. None of these models offer precise or determined outcomes but all can be used to explain what is happening in nature and offer insights into solutions for problems like disease control, epidemics, conservation etc.

The approach they advocate seems have a lot in common with the Agent Based Modelling approach that Andrew Haldane references (see his paper on “Tails of the Unexpected“) and that is the focus of Bookstabber’s book (“The End of Theory”).

In their words …

“Embrace the fact that the models are toy, and learn to work within any limitations.”

Focus more attention on measuring and managing resulting model risk, and less time on complicated new products.”

“… only by remaining both skeptical and agile can we learn. Keep your models simple, but remember they are just things you made up, and be ready to update them as new information comes in.”

I fear I have not done the book justice but I got a lot out of it and can recommend it highly.