Thursday, 26 July 2012

Teaching kids to gamble

I do a workshop of couple of hours each summer with kids who have finished their Standard Grades (GCSEs in England, i.e they are 16) and are moving on to their Highers (A-level) labelled "Deal or no Deal".  My aim is to encourage students to think a bit differently about maths, in particular to appreciate the relevance tof maths to areas other than the physical / natural sciences.

The workshop is popular, I had thought it was because the TV show was popular but it turns out only a couple of kids watch the show regularly.  The students had been told
The world is uncertain and mathematics is exact, so how can maths help in making decisions about the future?

The workshop will look at a number of simple games that involve making decision when you don't know what will happen, and investigate how maths can help you make the winning choice.  The workshop will show how maths is as important in understanding economics, biology and psychology as in understanding physics or engineering.
I started the workshop by talking about the role of gambling in mythology/religion, referring to Hellenic, Hindu, Chinese and Biblical examples.  I then suggested that gambling (or casting lots) is something common to all cultures, like language, mathematics, music and art are, but physics and agriculture are not.  To explore this point further I split the group into groups of five and ask them to gamble for smarties.  One of the 5 is given more smarties than the rest and the idea is that by playing fair games this imbalance is corrected.  There is a simple java simulation (don't play it too long as one player usually wipes out the others) and I go on to talk about how anthropologists think that gambling prevents the establishment of hierarchies in neolithic societies (eg Mitchell or Altman).

The group was of 25 and so I got them to order themselves by date of birth - there were two pairs sharing the same birthday.  The purpose of this was to enable the group to split into pairs who did not know each other (well).  I then got the pairs to participate in the Ultimatum Game and then talk about how "fairness" is a learnt human concept (Murnighan and Saxon, Henrich et al., Jensen et al.).

I then talk about how Cardano undertook the first mathematical analysis of gambling in response to trying to address the issue of the ethics of gambling.  I give one of the key quotes and then explain how the idea of mathematical expectation comes out of this.  When the group were happy that this was all OK, I present the Petersburg game and ask for offers to play it.  The best offer is 2 I then calculate the game's expectation.

Some of the students identify the risk as the key issue, and after a brief discussion I offer some more games based on dice and ask which one each participant prefers.  Un-remarkably almost half prefer B, the lowest variance game, and I explain that variance is a measure of uncertainty and is associated with risk.

I then ask whether taking a risky decision is always a bad idea.  I present the case of a bird in winter who needs to find food to survive the night and outline this as a game.  The students work out there is a risky and safe strategy (based on variance) and I ask them to try and work out if there is a good strategy, playing safe or taking risks.  After the students play about and we discuss their suggestions I run through a java simulation. The simulation (after a few runs) enables me to demonstrate that the re are two regions in the time-berry state space were taking risks is better than playing safe.

I then discuss the Deal or No Deal game, and, with the results of 22 games, I discuss how a mathematician might analyse the game.  I finish off with Cardano's 350 year old advice, maths is of little practical value but does help in understanding, and the only way to be ethical in gambling is through science.

Monday, 16 July 2012

Is "Risk Intelligence" a dangerous concept?

At a time when there is an emphasis on inter disciplinary research, it is not that useful to divide science into separate categories.  However one distinction that, as a mathematician, I find useful is  between Romantic and Enlightenment science.  Enlightenment science is concerned with the universal, and is developed by collaborative analysis, and, to facilitate both the collaboration and analysis, mathematics plays an important role.  Romanticism emerged in the second half of the eighteenth century and dominated British and German culture in the following half-century.  Romantic science emerges out of senses trying to understand the whole, rather than the parts, sentiment over reason, and is often the result of an individual genius's struggle, frequently against dark forces.  

The archetypical romantic scientists are Alexander Humboldt, Lewis and Clark and Darwin, who developed science through exploration.  The archetypal romantic mathematician is Galois, whose career was hindered by his reliance on intuition rather than the clear proof favoured by the French Academy and a myth has grown up around him that he did his most significant work the night before he was killed in a duel over a love affair.

I have been thinking a lot about the transformation from Enlightenment to Romanticism, because there seems to have been a massive change in the relationship between science and finance in the first half of the nineteenth century, at the time that Romanticism dominated culture.  

I thought about this distinction after listening to Dylan Evans promoting his book Risk Intelligence on the radio. Evans defines Risk Intelligence as the "ability to estimate probabilities accurately" (0.24 on audio), such as the chance a horse wins a race (0.52).  Evans goes on to make the point that our educational system does not train people in making decisions under uncertainty (1.29), what he calls a "twilight zone" (1.40).  Further on he explains that because finance (2:57) became to rely on mathematical models and the "intuitive gambler types were edged out and as a result Wall Street haemorrhaged risk intelligence" (3:35), and this transformation was partly responsible for the failures of finance.

One point I would agree with Dr Evans on, that there needs to be an effort to get concepts around uncertainty onto school curricula.  In fact, at the "Credit Crisis Five Years On" meeting recently I asked Andy Haldane if he felt the Bank of England had a role to play in helping shape curricula in this way.  I think there are significant issues with Evans' view that the chance of a horse winning a race can be estimated accurately, Knightian uncertainty / Keynes' irreducible uncertainty' spring to mind.  However, my main concern is in the claim that it was the use of mathematics that was partially responsible for the failures of finance.

It struck me that in the interview,  Evans seems to be endorsing Romantic Science, there is an emphasis on "intuition" over mathematics in what he says and reference to "twilight", the darkness that is a feature of Romanticism.  But just because Risk Intelligence might be a Romantic idea, doesn't mean to say it is dangerous. The danger with a concept like Risk Intelligence is the emphasis on there are some people who are "good" at risk, there is a link to that other idea that emerged out of Romanticism, the idea of genius, and that mathematics is a hindrance, not a help, in finance.

Why is mathematics important in finance?  It goes back to why Fibonacci's Liber Abaci was a publishing phenomena at a time when books were hand copied - the mathematics it described enabled merchants to write down, disseminate, discuss and improve their financial models.  This is the point of mathematics, whether in physics or finance, and why mathematics is such an important part of Enlightenment science but missing from the Romantic: Enlightenment science is collaborative and needs a common language, and its arguments are written in that language, mathematics.

The problem with modern finance is not in the mathematical models, but in that the models were an end in themselves and not a means for developing a consensus, understanding, knowledge about finance. Banks employed geniuses to develop these models in house that they kept secret, or, they bought black boxes that had been created by geniuses elsewhere.  When mathematicians, such as Phillipe Artzner and Freddy Delbaen  or Michael Gordy, shone a light on the some of the leading industry models, their illumination was blocked by the towering geniuses, the "masters of the universe", working in banking.

When you read the book, rather than listen to the interview, the issue of mathematics in finance is not as significant.  In fact, the whole book rests on a mathematical model of RQ (compare with IQ or Samuelson's "Portfolio IQ", "PQ"), which is implemented on-line for you to test your own RQ.  

Evans claims the motivation behind RQ is a 1986 paper Ceci and Liker where RQ is identified as a type of intelligence uncorrelated with IQ.  Unfortunately, Ceci and Liker's science was not up to much, and within two years this key result was overturned by better analysis.  In fact "RQ" seems to be highly correlated to "IQ".  Evans argues that Banking regulation should involve measuring the RQ of bankers.  The problem is anyone can "game" RQ (when I did the test I got a very high score of 80 because I realised immediately what was going on). 

Having laid the basis of RQ Evans attempts to describe how you can improve your RQ, which boils down to understanding the limitations of what you know.  This does not strike me as particularly novel, and might be labelled as "science", which has been described as "organised scepticism".  

In fact, Evans' criticism of maths in finance turns out to be  more a criticism of calculation in finance, and this has been addressed more tangentially, but more eloquently, by the philosopher Richard Sennett in The Craftsman.  Sennett makes the point that we can all be craftsmen in the modern age, if we learn a craft.  Developing RQ seems no different from becoming skilled in understanding risk.  What is important in becoming a craftsman is hard work in a social context (crafts were traditionally regulated by a guild) and this is why I feel RQ is not simply a banal idea but a dangerous one.

The Romantic Evans seems to believe in an intuitive genius that can be developed outside  of the workshop, I think this is dangerous because I believe the solution to banking
's problems lies in open discussion and debate about the risks and rewards of finance (i.e. science), and that good bankers are skilled craftsmen who have learnt their trade by spending hours developing their skill in the work place.  If something has happened in finance over the last 25 years it is that banks have not been recruiting schoolboy apprentices (I knew three people who left school to go into finance, one to a Bank of England apprenticeship) who they train up over five years, but have been recruiting staff "off the shelf" out of universities and assuming that these academically trained men and women have the right skills for banking.  Or they have recruited ready-made business experts such as Andy Hornby and Fred Goodwin.

Dylan Evans's central argument, that people who are gifted in making risky decisions can be identified and hired to run finance, relegating the need for good ethics, is dangerous.

Thursday, 5 July 2012

A banker, a pharmacist and physicist walk into a pub .... and pay $3 billion

One of my favourite jokes:  "I make all the big decisions at home - what our policy on Iran, Chinese exchange rates and the Eurozone crisis should be.  I leave the mundane issues - like where we live, how we raise our children, where we go on holiday - to my wife".  Given the news coverage yesterday, dominated by Barclays, the Higgs-Boson and GSK there could be a version "Physical scientists investigate all the important questions - the origin of the universe, the existence of the Higgs Boson and why the dinosaurs became extinct.  We leave the mundane issues - like why banks fail or how to respond to the diabetes epidemic - to the Social Scientists".

A Higgs Boson like(?) particle has been found, modulo a "5-sigma" event - recall Goldman's heralded the Credit Crisis in August 2007 by going public with a much (much, much, much) more rare 25-sigma event.    Call me churlish, but having spent $3 billion plus (and the plus is augmented by much of the fitting, commissioning and operation of the machines is done by PhD students working at levels that would probably breach the European Working Time Directive and UK minimum wage legislation, luckily its in Switzerland) it was inevitable that they would find the Boson.  A bit like it was inevitable that Wayne Rooney, the "white Pele", apparently, would play a central role in England's Euro 2012 performance, because he costs Manchester United so much.

My point is, if the UK's contribution to the $3 billion LHC had been diverted into serious scientific study of markets, involving many disciples and not just the Platonic forms of neo-classical economics, things might (modulo a 5?-sigma event) be different in the sense that people might (modulo a 5?-sigma event) be better off.  The trouble is, the "scientific establishment" rarely take the social sciences that seriously, possibly because it is about "us" and not "things", and so rarely give it priority in funding.

In this respect, mathematics is a social science.  In 2010 the outgoing "President of the Board of Trade" for the UK, Lord Mandelson, who was responsible for signing off the science funding budget, allocated some £40 million to enhancing Blackpool Tower, about the same as he allocated to maths research that year.  Enhancing the imitation of the French Eiffel Tower rather than enhancing the imitation of French achievement in mathematics.  Mathematics enables experiment when there is no apparatus - the Higgs Boson was (is) a mathematical object that exists as a physical(?) object because $3 billion has been spent to build the lab for the physical experiments.  This is why mathematics is fundamental to understanding markets, because we cannot undertake experiments in markets, not because asset prices are Levy processes.

Bio-tech, is firmly in the camp of legitimate science since Tony Blair bet the UK's research pot on in 1997.  However,  bio-tech has not grown in the past 15 years in the same way that finance has grown, Blair's investment has not paid dividends.  Just as the ethics of big banking are in crisis, so are the ethics of big pharma.    GSK were fined, that magic number of, $3 billion, about 6 times the fine on Barclays.  Was GSK's crime 6 times worse than Barclays?  If so why haven't there been calls for judicial or parliamentary investigations into the behaviour of the UK's pharmaceutical industry? If Barclays' sin was equivalent to GSK's, why the small sanction?

Could it be that the government  spending money on bio-tech research puts the industry under public scrutiny, this puts pressure on the regulator to ratchet up the sanctions.  Bankers pour money into the coffers, rather than take money out, on condition that the government leaves the industry to its own, hidden, devices.

All these calls for a judicial enquiry into the behaviour of the UK banks are a bit lame, in my opinion.  There has recently been an excellent judicial review of practices in financial services, Lord Penrose's Review of the collapse of Equitable Life.  The Equitable was the world's oldest public (i.e. open to all) life insurers that collapsed around the time that LTCM collapsed, essentially the firm had been giving away long term swaptions (Guaranteed Annuity Rates), rather than providing them at a cost.  The "hole" that the Equitable left was estimated at the time as about the same size as the LTCM hole (around $3 billion), though as the Equitable was a life company the current loss suffered by policy holders is in the region of £4 -£5 billion (note the change in currency).  The government at the time asked the Scottish Judge, George Penrose, to conduct a review of the collapse in 2001 and he reported in 2004.  Some quotes:
One of the regulators involved with Equitable referred to the boundary between prudential and conduct of business regulation as more an awkwardness than a lacuna. While that may be a fair comment on how the two branches were intended to operate, in practice the lack of co-ordination of prudential and conduct of business regulation in relation to the Society was unacceptable. (ch 20, 64)
 Many readers of this report will be frustrated that it has not provided answers to two questions: who is at fault for the problems encountered by the Society, and who deserves redress as a consequence? It has been no part of this inquiry to attempt to answer either question. The first inevitably involves issues of the scope of duty and of breach of duty that I was not asked to consider and that I would have been unwilling to consider as part of an inquisitorial process. The current proceedings at the instance of the Society speak eloquently of the complexity of the questions that arise from allegations of breach of duty relating to a relatively short period compared to the period covered by the inquiry, and a selection of issues from the wider range that I have discussed. An open adversarial process such as would have been necessary to replicate the litigation process over the longer period and the wider range of issues would have been beyond contemplation. (ch 20, 77, my italics)
 Almost 10 years on, it seems, not much has changed, apart from in 2010 the government agreed to compensate the policyholders for the lax regulation.  A few weeks ago I received a cheque for £159, some 15 years after the firm collapsed.

It is interesting that in 1998, LTCM collapsing owing $3 billion spawns congressional hearings,  books and TV programmes, by 2012 $3 billion is a corporate fine.