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.

 

 

Recently read – “The Moral Economy: Why Good Incentives Are No Substitute For Good Citizens” by Samuel Bowles

The potential for incentives to create bad behaviour has been much discussed in the wake of the GFC while the Financial Services Royal Commission in Australia has provided a fresh set of examples of bankers behaving badly. It is tempting of course to conclude that bankers are just morally corrupt but, for anyone who wants to dig deeper, this book offers an interesting perspective on the role of incentives in the economy.

What I found especially interesting is Bowles account of the history of how the idea that good institutions and a free market based economy could “harness self interest to the public good” has come to dominate so much of current economic and public policy. Building on this foundation, the book examines the ways in which incentives designed around the premise that people are solely motivated by self interest can often be counter-productive; either by crowding out desirable behaviour or by prompting people to behave in ways that are the direct opposite of what was intended.

Many parts of this story are familiar but it was interesting to see how Bowles charted the development of the idea over many centuries and individual contributors. People will no doubt be familiar with Adam Smith’s “Invisible Hand”  but Bowles also introduces other thinkers who contributed to this conceptual framework, Machiavelli and David Hume in particular. The idea is neatly captured in this quote from Hume’s Essays: Moral, Political and Literary (1742) in which he recommended the following maxim

“In contriving any system of government … every man ought to be supposed to be a knave and to have no other end … than private interest. By this interest we must govern him, and, by means of it, make him notwithstanding his insatiable avarice and ambition, cooperate to public good” .

Bowles makes clear that this did not mean that people are in fact solely motivated by self-interest (i.e “knaves”), simply that civic virtue (i.e. creating good people) by itself was not a robust platform for achieving good outcomes. The pursuit of self interest, in contrast, came to be seen as a benign activity that could be harnessed for a higher purpose.

The idea of embracing self-interest is of course anathema to many people but its intellectual appeal is I think obvious.  Australian readers at this point might be reminded of Jack Lang’s maxim “In the race of life, always back self-interest; at least you know it’s trying“. Gordon Gekko’s embrace of the principle that “Greed is good” is the modern expression of this intellectual tradition.

Harnessing self-interest for the common good

Political philosophers had for centuries focused on the question of how to promote civic virtue but their attention turned to finding laws and other public policies that would allow people to pursue their personal objectives, while also inducing them to take account of the effects of their actions on others. The conceptual foundations laid down by David Hume and Adam Smith were progressively built on with competition and well defined property rights coming to be seen as important parts of the solution.

“Good institutions displaced good citizens as the sine qua non of good government. In the economy, prices would do the work of morals”

“Markets thus achieved a kind of moral extraterritoriality … and so avarice, repackaged as self-interest, was tamed, transformed from a moral failing to just another kind of motive”

Free market determined prices were at the heart of the system that allowed the Invisible Hand to work its magic but economists recognised that competition alone was not sufficient for market prices to capture everything that mattered. For the market to arrive at the right (or most complete) price, it was also necessary that economic interactions be governed by “complete contracts” (i.e. contracts that specify the rights and duties of the buyer and seller in all future states of the world).

This is obviously an unrealistic assumption. Apart from the difficulty of imagining all future states of the world, not everything of value can be priced. But all was not lost. Bowles introduces Alfred Marshall and Arthur Pigou who identified, in principle, how a system of taxes and subsidies could be devised that compensated economic actors for benefits their actions conferred on others and made them liable for costs they imposed on others.

These taxes and subsidies are of course not always successful and Bowles offers a taxonomy of reasons why this is so. Incentives can work but not, according to Bowles, if they simplistically assume that the target of the incentive cares only about his or her material gain. To be effective, incentives must account for the fact that people are much more complex, social and moral than is strictly rational from an economic perspective. Bowles devotes a lot of the book to the problem with incentives (both positive and negative, including taxes, fines, subsidies, bonuses etc) which he categorises under three headings:

  1. “Bad News“; incentives send a signal and the tendency is for people to read things into incentives which may not have been intended but prompt them to respond negatively (e.g. does this incentive signal that the other party believes I am not trustworthy or lazy)
  2. Moral Disengagement”; the incentive may create a context in which the subject can distance themselves from the moral consequences of how they respond
  3. “Control Aversion”; an incentive that compromises a subject’s sense of autonomy or pride in the task may reduce their intrinsic motivation to perform the task well

Having noted the ways that incentives can have adverse impacts on behaviour, Bowles notes that civic minded values continue to be an important feature of market based economies and examines why this might be.

“If incentives sometimes crowd out ethical reasoning, the desire to help others, and intrinsic motivations, and if leading thinkers celebrate markets as a morality-free zone, it seems just a short step to Karl Marx’s broadside condemnation of capitalist culture”

One answer is that trading in markets encourages people to trust strangers and that the benefits of trading over time teach people that trust is a valuable commodity (the so called “doux commerce” theory).

While admitting his answer is speculative, Bowles rejects “doux commerce” as the whole answer. He argues that the institutions (property rights, rule of law, etc) developed by liberal societies to protect citizens from worst-case outcomes such as personal injury, loss of property, and other calamities make the consequences of mistakenly trusting a defector much less dire. As a result, the rule of law lowers the bar for how much you would have to know about your partner before trusting him or her, thereby promoting the spread of trusting expectations and hence of trusting behavior in a population.

The “institutional structure” theory is interesting but there is still much in the book worth considering even if you don’t buy his explanation. I have some more detailed notes on the book here.