Mathematician thinks mathematicians are very important

Ian Stewart, writing in the Guardian, says that the Black-Scholes equation

opened up a new world of ever more complex investments, blossoming into a gigantic global industry. But when the sub-prime mortgage market turned sour, the darling of the financial markets became the Black Hole equation, sucking money out of the universe in an unending stream.

This is just wrong.  The Black-Scholes formula is used by major players in the derivatives market only as a calibration tool, to obtain "implied volatilities" which give one a measure of how far market option prices diverge from an equation all the players know to be a simplification.  And the pricing models used for the mortgage-backed securities that caused the financial crisis have got very little in common with the Black-Scholes equation.

Stewart is wrong too in what he says about Nassim Taleb's notion of "black swans".  In Taleb's conception a black swan is not just an extreme event, it's an event that couldn't possibly have been built into a model because the modeller couldn't reasonably have even considered the possibility of its happening.

Stewart opens his concluding paragraph by asserting that "Despite its supposed expertise, the financial sector performs no better than random guesswork."  He doesn't explain this remark, but it's not a fault of the financial sector if the Efficient Market Hypothesis is nearly true.

Having established to his own satisfaction that financial mathematics caused the financial crisis, Stewart concludes that what's needed is more, better, financial mathematics.  This isn't exactly wrong - who would be against doing things better?  But I am sceptical that we need mathematical advances before we can design a sufficiently stable financial system.

I have the advantage over Stewart of having done this stuff for a living.  And I say that:
- nothing can make financial markets follow any particular model, unless a tradeable arbitrage exists when the market deviates from the model.  (The Black-Scholes model is based on an arbitrage strategy of sorts, but one that operates only in an idealized world: the arbitrage is not tradeable in the sense I mean).  Therefore financial models are tools for understanding financial risk, not for eliminating it.
- financial mathematicians (quants) don't make ill-advised trades: traders do.  It's the duty of the quant and trader both to make sure that traders understand the limitations of the models.
- from a mathematical viewpoint, the financial crisis occurred because traders grossly underestimated the probability of correlated mortgage defaults.  That's got little to do with black swans - it was foreseeable and foreseen that the US housing market wouldn't go up forever.  And not very much to do with models - even the simplest models for mortgage-backed securities had a correlation input.  It's got a lot to do with the hubris of traders who chose to bet the house on their guesses of an unobservable and unhedgeable parameter, and the failures of understanding of the bankers and insurers who let them do it.

Greek budget numbers

In a comment on my previous post about Greece, Frances Coppola helpfully directs my attention to this spreadsheet put together by Yiannis Mouzakis, using data from monthly reports by the Greek finance ministry.  (The reports give year-to-date data, so the spreadsheet backs out each month's figures by subtraction: it's possible that some months' results are affected by restatements of previous months.)  I've created a similar spreadsheet myself: the primary* balance for January-June is a deficit of €5.7bn, for July-December a surplus of €360mn.  The corresponding numbers in Stephanie Flanders' article  are €5.1bn and €1.4bn.

It's possible that Flanders' numbers include two receipts not part of the main budget figures, listed as "Revenue from financial transactions".  The amounts are €952mn in July and €380mn in December.  I suppose this is income from the sale of assets, such as the sale in June of a 10% stake in OTE Telecom.  Adding these sums in gives a July-December primary surplus of €1.7bn.

This looks like good news for Greece.  However, also not included in the figures are some significant outgoings, including €1.38bn in December for "Acquisition of credit institution's preferred shares"  and a further €306mn in the same month for "participation in the share capital increase of various enterprises".  The total of additional outgoings over the six months is €2.6bn. The purchase of preferred shares is the final stage of a bank bailout scheme set up in 2008, and compensates Greek banks for their write-downs on government debts.

So the summary is that the Greek government did run a primary surplus for the last six months of 2011, if you count all its income and only some of its expenditure.

Does this put Greece in a position where default becomes a relatively attractive option?  No, in that it would create a run on the Greek banks at the same time as inflicting further write-downs on them.  Yes, in that the cuts being demanded of it now seem to be aiming for a substantial primary surplus.  It's hard to see why any Greek politician wanting to be re-elected in April would back the Eurozone's demands - even if they think it the right thing to do they'll be waiting hopefully for someone else to say so.

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*"primary" in this context means "not including debt interest payments".  If you have a primary surplus you can consider defaulting, since you don't need new borrowing to keep going.

People who disagree with me are stupid

Or perhaps not. They might not have chosen to consider my argument properly, if at all.  Or I might not have expressed myself clearly enough.  Or they might have a different view of the desirability of trade-offs involved.  Or I might be wrong.

However, there is a line of research purporting to show that right-wing ideology (which disagrees with me) is associated with being a bit thick.  A recent paper added to this corpus has been seized upon by George Monbiot in the Guardian  "conservatism thrives on low intelligence and poor information".  I think that's a fair description of Republican politics in the USA currently - the candidates for the Republican presidential nomination have recently been conducting a series of debates of quite extraordinary stupidity.  But in the UK, the Conservative Party, whose policies are well to the left of the intelligent and thoughtful Barack Obama, strikes me as no less intelligent than the Labour Party.  Its problem is a lack of concern for the problems of the economically unfortunate, not any inferiority in policy analysis, nor a reluctance to argue its case coherently. (Tim Worstall makes the case that in the UK 'conservative' and 'Conservative' may not be the same thing.)

The paper itself finds "that lower general intelligence (g) in childhood predicts greater racism in adulthood, and this effect was largely mediated via conservative ideology".  What the authors did is analyse some existing data from two studies in the UK, each of which tested a group of children then years later asked them questions as adults.  From these data they distilled measures of general intelligence g, social conservativism, racism, socio-economic status, and education level.  They then used a factor analysis to show that social conservatism is quite strongly negatively correlated to g, even taking into account socio-economic status and education level.  Another factor analysis including social conservatism as a factor showed that g is not a predictor of racism once you take social conservatism into account.

There are a lot of criticisms that can be made of the statistical methods: William Briggs outlines them here (but his comments about the tiny correlation along what the paper calls path c' are rather unfair: the authors are clear about it).  But the fundamental problem is that this paper is not setting out to test competing hypotheses, it's just looking for confirmation of one idea, by means of a crude measure of social conservatism.  The paper gives examples of the questions used in this statistic: “Give law breakers stiffer sentences”, “Schools should teach children to obey authority”, and “Family life suffers if mum is working fulltime”.  Similarly, the example questions it gives for the racism statistic are "I wouldn't mind working with people from other races” and "I wouldn’t mind if a family of a different race moved next door”.  What the results tell us is that the same people who answer yes to the 'conservatism' questions tend to answer no to the 'racism' questions, and those people tend to have lower g scores.  But those answers are not just conservative (by one definition) and racist, they are also unnuanced.  Perhaps the same people would have agreed also with some other questions on the questionnaire, such as "Ordinary working people do not get their fair share of the nation’s wealth" or "Private schools should be abolished".  If so, a differently motivated analysis might have found that g is negatively correlated with left-wing views, and left-wing views predict racism.

Perhaps a social scientist would care to conduct a statistical analysis to determine whether social scientists tend to seek confirmation of their own prejudices in the way they choose to analyse data.  Or perhaps it would be safer to get someone else to do it.

Mid-Table Obscurity

There's a strange story in the Guardian, with the headline "UK trails Poland and Bulgaria on adults educated to A-level standard" and the subhead "Lecturers' union says European data shows Britain risks languishing in 'mid-table obscurity' due to rising cost of learning".  You don't have to read on to guess that the story is not going to make sense - there are no fees for A-level education at state schools in the UK.

The statistics behind the story are from Eurostat.  The data are described thus:

The indicator shows the percentage of the adult population (25-64 years old) that has completed upper secondary education. The indicator aims to measure the share of the population that is likely to have the minimum necessary qualifications to actively participate in social and economic life. It should be noted that completion of upper secondary education can be achieved in European countries after varying lengths of study, according to different national educational systems.

So it means no more than having attended school or college for two or more years of what in the UK is called the sixth form.

The lecturer's union - the UCU - has its statement in full on its own site.  It is concerned about "the very real possibility that we will slide further down the table as people find it harder to access education following price hikes and restrictions on places."  I can reassure it that university tuition fees will not make it harder for students to complete sixth form studies.

I'd like to read an intelligent discussion about what proportion of the student population could benefit from sixth form studies, how that should be divided between traditional A-levels and vocational qualifications, and what the rest of the 16-18 year-old population should be doing.  We might even learn from a comparison with the rest of Europe.  The Guardian?  Anyone?

The mystery of the primary surplus

Eleven days ago, Stephanie Flanders, economics editor of the BBC, announced that "the Greek government has slashed its way to a primary budget surplus: as of now it is only borrowing money to pay off the debt...look at the Greek government's budget outturns for the second half of 2011, published earlier this month. As Graham Turner of GFC Economics has noted, these show a real step-change in the effort to cut spending and actually collect more Greek taxes...In the second half of 2011...the Greeks seem to have managed a 1.8bn euro primary surplus."

Sundry bloggers picked up on this remarkable turnaround in Greece's budgetary fortunes, noting that it may make a default more likely, in that if you're running a primary deficit you can't afford to default.  And I made a note to look into how Greece had managed it against all expectations.

So I went looking for the data published in January.  And I couldn't find it.  All the mentions of the story I can find online refer to Flanders' article.  It's not mentioned on the GFC Economics site, nor on the associated blog.  So I had a look at the IMF fiscal monitor update, dated two days before Flanders' article.  "headline deficits were larger than expected in Greece owing in part to a weaker economic outturn..." and at its latest (December) country report on Greece " Through end-September, the primary general government balance fell short of the program target by €280 million, or 0.1 percent of GDP". The plan in that document is for a primary surplus starting in Q2 of 2012, revising a previous plan for a primary surplus from Q4 2011.  And here's the IMF country head in Athens last week, insisting that Greece has achieved a lot, but not taking the opportunity to mention a primary surplus.

I see two possibilities.  One is that Greece, having achieved this breakthrough, has chosen to conceal it from the IMF and whisper it only to Graham Turner, who has exploited his scoop not by publishing it but by passing it on to Stephanie Flanders.  And the other is that there has been a misunderstanding somewhere.  I'm keeping an open mind...

Abiraterone

There's an important newish prostate cancer drug called abiraterone which doctors are keen to prescribe to suitable patients.  The drug was approved by the FDA in the USA in April 2011, and in Europe by the EMA in July.  The UK body responsible for approval drugs for use by the NHS, NICE, started its review process in May 2011, intending to conclude its glacially slow deliberations in May 2012. Today it's issued a draft decision that the drug should not be funded by the NHS.

This is not to say that abiraterone is entirely unavailable on the NHS.  The Cancer Drugs Fund was established last year to pay for unapproved drugs, subject to agreement for each patient by the Strategic Health Authority in their region: your chances are better in some regions than others (which is ironic, since the government said the Fund would end the "postcode lottery": I've no idea why they thought they could do that with a regional decision-making process).

There's no question at all that abiraterone is an important advance.  A phase III trial was stopped at the interim stage in September 2010 because the results were too good for it to be ethical to continue with the control group.  The drug works by blocking the body's production of testosterone in a novel way (prostate cancer, until it becomes hormone refractory, needs testosterone to grow), and was found to increase median survival time by 3.9 months in patients with metastatic castration-resistant prostate cancer.

So has NICE got it wrong?  Cancer Research UK, which helped discover the drug (now owned by Johnson & Johnson), has put out a press release saying so.  But really there's no way to tell.  NICE is supposed to consider not just effectiveness but also price in deciding whether to approve a drug: its starting point is the cost per Quality-Adjusted Life Year (QALY), which should not much exceed £30,000 (I haven't found an official statement of the current number), though other considerations can affect this.  We know how good abiraterone is, but we don't know what price Johnson & Johnson have offered it at, so we can't do the calculation.

Which brings us to NICE's real role in all this: it's implementing a pricing mechanism.  The manufacturing cost of producing a drug like abiraterone is trivial compared with the research and development costs, which are usually estimated at something in the region of a billion dollars.  There is therefore a huge gap between the average price the manufacturer needs to charge globally to make a profit, and the price at which the manufacturer is better off striking a deal in any particular market than walking away.  The NHS needs to keep prices down, the manufacture wants to charge the most it can, there's only one buyer and one seller, but there has to be some basis for price setting.  So the semi-public but not clearly defined QALY mechanism allows the manufacturer to calculate a price at which they think the drug will be approved.  The uncertainty has a reason to exist in that it prevents them from pricing the drug right on the limit.  And to reinforce this, there's no negotiation: the manufacturer offers a price and NICE either accepts it or rejects it.

But the mechanism works only if NICE does actually decline to approve some drugs, otherwise prices for new drugs would drift up.  So it has to apply its methods rigorously.  Meanwhile, the Cancer Drugs Fund has reduced the pressure on manufacturers to quote a price that will be accepted, because they know that they will get some sales even at a higher price.  Hence the failure of the market to clear in this case.

So why has NICE announced a preliminary decision to withhold approval?  It must be to give Johnson & Johnson the chance to make its offer more attractive.  Probably not by anything as crude as cutting the price, but by some mechanism such as providing the drug free to any patient remaining on it beyond a specified length of time.  In part this is because some other countries are willing to pay the official NHS price but no more, so Johnson & Johnson will want to keep the headline price high.

At this point I stop on reflect on the absurdity of the whole thing: humanity has created a system for funding drug development that prevents us giving drugs that are cheap to produce to patients who need them, even in one of the world's wealthier countries which is willing and able to pay something like its share of development costs.

The government has radical plans to change this price-setting process.  When I've read the details I'll comment on how they might work.

Take away that fool's bauble

In 2004, Fred Goodwin, then Group Chief Executive of RBS, was awarded a knighthood for "Services to Banking".  On Tuesday it was announced by the Cabinet Office that Goodwin's knighthood is to be "cancelled and annulled", following a recommendation by the Honours Forfeiture Committee.

I would have thought this would be no great loss to him: he should find it easier to enjoy his considerable wealth as the relatively obscure Mr Goodwin.  But his friends and sympathizers are outraged: Alistair Darling, who was a better Chancellor than Gordon Brown, wrote in the Times that "There is something tawdry about the government directing its fire at Fred Goodwin alone..."  Jackie Stewart says that "No single person or even any single bank created the biggest financial recession in modern times...To have this stripped I think is poor for the constitution and very dangerous for the future."  Simon Walker for the Institute of Directors says "To do it because... you don't approve of someone, you think they have done things that are wrong but actually there is no criminality... is inappropriate and politicises the whole honours system".  Digby Jones doesn't disagree with the decision, but remarks it's surrounded by "a faint whiff of the lynch mob on the village green".

What a load of tosh.  Goodwin was given the knighthood for services to banking, presumably because a grateful nation appreciated the contribution therefrom to the economy in general.  We now know that his banking efforts have cost us many billions of pounds - the price of the bailout depends on what the government gets when it eventually sells its shares in RBS, but currently we're looking at a loss of over £20bn.  Against that you can set the tax revenues it's received over the years as a result of RBS's activities, but the end result is not going to be any great gratitude.  Goodwin's services to banking were less than worthless, it was a horrible mistake to give him the knighthood, and now we've put that right.

Goodwin's not the only one whose knighthood was an obvious error?  Then let's unknight the others too.  No single person created the recession?  Quite true: no single person created the profits at RBS either, but only Goodwin got the knighthood.  The annulment politicises the system?  Very funny: it's awards that are decided by politicians, not annulments.  The whiff of the lynch mob?  That's an odd description of the Head of the Home Civil Service and his colleagues.

The underlying argument seems to be that the annulment of a knighthood is a punishment for wrongdoing, to be decided only after due judicial process.  That's wrong.  No one has the right to a knighthood; it's a privilege awarded to about one millionth of the population each year.  Goodwin doesn't deserve this special privilege, and now he hasn't got it, just like millions of others far less undeserving.
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I've not attached titles to anyone's name in this piece, apart from Mr Goodwin's.  The things are so ephemeral nowadays.