All New Wilmott Jobs Board                     (b)

You Naughty Spies

I'd like to share statistics that I recently discovered after installing the Ghostery privacy tool, used for finding and blocking trackers on websites.

There's been a lot in the news about Edward Snowden and his information about the data collected by the US agency NSA. Quite rightly so. In the UK this information is being published by The Guardian newspaper. I was on The Guardian website for some reason (believe me, I don't do this often) and Ghostery told me there were 17 trackers monitoring me. This seemed a lot. On wilmott.com we have just two or three. Being an inquisitive sort, I went to the front pages of other UK newspapers, magazines, etc. And guess what?

That's right, The Guardian, who have got all foamy at the mouth about the NSA spying, are doing more spying than any of these other websites.

Here is the data, taken from the front pages only of each website.

Guardian 17
Daily Telegraph 13
Mirror 13
Spectator 12
Daily Mail 11
Times 11
Express 9
Sun 8
Private Eye 3
wilmott.com 2
BBC 0

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Trolls, Troll Hunters and Troll Groupies - the wilmott.com experience

Trolls are in the news with a vengeance. We are hearing about anonymous tweet threats of rape, threats of bombing, and imagined details of a certain academic's lady garden. Many of the commentators are new to being on the receiving end of trolling. Many haven't even had their first proper troll experience, they are Troll Virgins. So I thought the time was right for me to go public with some of our experiences here at wilmott.com, and my own views on the subject. For we have been there, done that, and got the slime-stained T-shirt!

The first time wilmott.com experienced trolling was around 2003/4. I was so naive that I didn't even know such a creature existed. From asking around, it seemed no one else knew either. Perhaps the trolls themselves didn't then know there was a name for them!

Trolls in those days didn't just join an online discussion forum and start abusing people. No, that's a more recent phenomenon made easy by Twitter. In those days that would have led to immediate banning on most forums. So they tended to play a longer game. They would start off by being a helpful member of their chosen community and then gradually start picking fights with people. It had to be done cleverly. The initial arguments would have a small element of justification about them, just enough to suck the innocent bystander into the argument...and it didn't matter on which side. Other trolls would then crawl out from under their stones and join in. Then they would ramp things up. The helpful side was discarded. Full-scale abuse took its place. It left a residue of confusion...why has this member started getting so upset? Have we done something wrong?

I was disturbed, how had a hitherto friendly forum turned nasty and so quickly?

On wilmott.com we value freedom of speech very highly. Certainly more highly than on any other forum in our field. Trolling will not usually get people banned from wilmott.com. (Nor, for the record, will requests for banning from other members!) But then things started to get more serious than verbal nonsense. The website started receiving Denial of Service attacks. The physical address of our webmaster was posted online and threats of violence made against him.

What were we to do? Some people advised going to the police, some said start a civil suit, some suggested a clamp down on discussions and heavy moderation. The best advice I got was to treat this as a personality problem, and not a legal one.

We didn't contact the police. We didn't name and shame. We didn't start heavy moderation.

All we ever did was to ban the worst of the trolls and some of those who were egging them on. And we stopped accepting new members with anonymous email addresses. It harmed business, but we stood by the principle of maintaining freedom of speech.

Years later I discussed our experience with Jimmy Wales. His experience with Wikipedia was exactly the same, starting with the friendly enthusiasm of the site, followed by the influx of the trolls, and then how to deal with them without destroying the site and without limiting freedom of speech. We both came independently to the same conclusions.

Since 2004 the site has been much less aggressive. I believe our policy has worked, and I hope it has been appreciated.

We get emails from people who have experienced trolling on other forums, and my advice is usually to simply ignore it. Our worst trolls are still active elsewhere and I get emails specifically about them. Some of the stories I hear are very disturbing. Do their investors (for some are hedge fund managers) know who they have invested their millions in? I think the trolls are naive. Anything you do on the internet is hard to erase. I know they usually think they can remain hidden, but that very arrogance is going to be their downfall.

Trolling is similar, in my view, to keying cars, to any vandalism. I think that Twitter has shown us the real nature of many people, and just how disgusting that nature is. Without Twitter they would still be sick people, but we would have less information about their nature and their numbers. There are a lot of them.

I do not believe that the correct way to deal with trolls is through the police or through limiting free speech. The police have far more important things to deal with. And god knows I've been on the receiving end of more than my share of free speech! But I take it as a compliment, that my success has stirred up so much envy!

There is a caveat here: The bullying of vulnerable people (children, the recently bereaved, for example) most definitely should be pursued with the full weight of the law.

My recommendation for dealing with trolls is that employment contracts for people in positions of responsibility should automatically ask for all of a person's usernames. Employers (and indirectly customers) have the ability then to fire the worst offenders. Not declaring usernames would be treated as a sackable offence. In our field this means that Due Diligence questionnaires should ask for all usernames of partners, risk managers, almost everyone, as one of the standard questions.

And let's start with the politicians, the MPs. All MPs are to declare all their usernames, just like they declare their financial interests. There are plenty of opportunistic MPs jumping on the faux-outraged bandwagon/trolley(?) so this should be easy to arrange!

Talking of faux outrage, this brings me on to other players in the Game of Trolls. Although I obviously have no time for trolls I also am not keen on the Troll Hunters, those, again I will use the word 'opportunistic,' who make a great fuss of the often Lesser Troll, and go out of their way to interfere and often to name the troll. I think of trolls, like most people do, as sad loners, but I do hope for their redemption and therefore do not want to see lives ruined by their premature exposure.

And then there's the Troll Groupie. I have seen nothing much written about this species. They hang around trolls, encourage them, without doing the dirty work themselves. We have a few on wilmott.com. I do find such sycophants very creepy. But again, freedom of speech and all that.

In summary:

1. Ignoring the trolls should be the default.

2. The law should be reserved for dealing with proper cases of possible physical or mental harm. Protect the vulnerable. But journalists, politicians, etc. should just take it on the chin.

3. Usernames should be declared by politicians, hedge fund managers, teachers, doctors, and anyone in a position of responsibility.

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Fitch Acquires 7city - great news for the CQF!

Fitch and 7city are forming "Fitch 7city Learning," press release below. This is fantastic news for the CQF as it means an already brilliant course is now unstoppable in its goal to improve quant finance and risk education globally!

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PRESS RELEASE:

Jan 24 - Fitch Group today announced it has acquired 7city Learning, a leading provider of learning and development solutions for the financial services industry. Fitch is combining 7city with its Fitch Training unit to form Fitch 7city Learning, a global leader in financial training.

Paul Shaw, previously CEO of 7city, will lead Fitch 7city Learning. The financial terms of the transaction have not been disclosed.

Fitch 7city Learning will benefit from 7city's industry-leading solutions for delivering financial services training combined with Fitch's global presence and platform. Fitch 7city will specialise in global development and delivery of training in four key areas: regulatory and certification exam training (i.e. Chartered Financial Analyst, Certificate in Quantitative Finance); professional skills training; custom e-learning solutions for client organisations; and credit, risk and corporate finance training, which is currently provided through Fitch Training.

"7city is an innovator in promoting understanding of financial concepts and practices - something we view as core to Fitch's role in global markets," said Paul Taylor, President and CEO of Fitch Group. "Fitch has long believed that transparency contributes to efficient markets, but the real market value of transparency is not how much is shared but rather how much is understood. Paul Shaw and the 7city team have successfully paired a strong intellectual and practical foundation in learning with a superior sense of global customer service. We are delighted to have them as part of Fitch Group."

"Fitch Group is an outstanding fit for 7city. Both companies are growth oriented, globally focused and committed to broadening knowledge and perspectives," Mr. Shaw commented. "Fitch 7city has an opportunity to impact global markets in a profoundly positive way through promoting greater understanding among individuals and leading financial institutions."

Formed in 2000 with a vision to build both time and cost-efficient solutions to support its clients' learning and development needs, 7city is recognised by financial professionals and analysts around the world for the quality of its innovative training methods. Based in London with offices in New York, Singapore and Dubai, the company has more than 150 employees serving a broad spectrum of top-tier financial institutions, companies and organisations. 7city previously was majority-owned by Gresham Private Equity.

Fitch Group is a global leader in financial information services with operations in 36 countries. In addition to Fitch 7city Learning, the Group includes: Fitch Ratings, a global leader in credit ratings and research; and Fitch Solutions, a leading provider of credit market data, analytical tools and risk services. Fitch Group is 50% owned by Paris-based Fimalac and 50% owned by New York-based Hearst Corporation.

Have You Had An Illness That Wasn't Your Fault?

Scientific advance that is certainly to be exploited by ambulance-chasing lawyers: DNA sequencing of MRSA used to stop outbreak. This is the beginning of the story that I've been predicting for years. Thanks to the genetic mutation of diseases you can now trace the source of an illness back to the source, i.e. that dastardly person who didn't disinfect their hand before, during and after using a door handle. Hot stock tips: Anything medical; Lawyers; Insurance companies; Producers of disinfectants; etc.

I hate lawyers.

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High Frequency Trading and the UK Government’s Whitewash

The UK Government’s Foresight Project has just announced the results of its two-year investigation into electronic trading and markets. And the good news for hedgies is that they’ve decided that high-frequency trading is mostly safe!

Let the party continue!

And the bad news? None really.

That’s unless you believe government reports should be unbiased, independent, forward thinking, etc. etc.

One group of journalists from The Bureau of Investigative Journalism has observed that the Foresight panel, the “High Level Stakeholder Group” made up of senior individuals from relevant institutions, is not exactly unbiased. Their nice analysis is here.

The story I was told by one of the Bureau’s journalists was that anyone who was anti HFT was discreetly dropped from the investigation. For example…er, me! In the early days of the project, two years ago, I was asked to contribute…and then after hearing my views the Foresight team went strangely quiet on me. And it wasn’t just me, it turns out that lots of other people were also found to be surplus to requirements.

The list of members of the Stakeholder panel is here.

It’s not even subtle is it? The majority of those on the panel directly benefit from HFT.

The report takes the tired, old, shallow viewpoint about HFT adding liquidity, without delving any deeper. Yes, there’s lots of statistics in there. But excuse me for thinking that a panel with the name of ‘Foresight’ ought really to make some effort to look beyond the past into possible future scenarios. It may not be easy to estimate the probability of various scenarios but it’s not hard to figure out their effects. The project made little attempt in that direction.

I’m disappointed in many ways: Partly because I was dropped and so missed an opportunity to serve Queen and country; Partly because the result was not independent, resulting in precisely the outcome that the government wanted; Partly because few have picked up this rather important story. But mostly I’m disappointed because the rigging of the panel was so blatant, so arrogant in its execution, and so narcissistic the belief that they’d get away with it.

This Foresight report is already being quoted as the most important and most detailed analysis of computer trading ever. It is bound to have a major influence on the future of the financial markets. And it’s a complete whitewash.

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My Experience Of The OCC And Their Understanding Of Risk

I can now reveal that is was the OCC...

The nameless regulator I criticized in my blog on calibration, "Bankers Can't Avoid Risk by Hiding It," was the Office of the Comptroller of Currency in Washington.

The OCC has had a lot of negative publicity recently for their less-than-rigorous examination of JPMorgan in the run up to that bank's multi-billion dollar losses.

Just to recap what I said before, the OCC were unintentionally encouraging banks to hide model risk by requiring calibration when the role of the regulator should be to point out the downside of calibration and instead ask about the stability of the calibrated parameters. Certainly the concept of model risk, and the difference between hiding risk and hedging it, seemed beyond them. So it didn't come as a surprise to me that the difference between hedging and speculation also proved too much for their very theoretical brains.

To add a bit of balance here, my experience of the OCC was not dissimilar to my experiences of many quant teams in banks. By this I mean that they love to talk mathematics but struggle to talk markets. When you've had a quant education that's too academic then all you've seen is complete markets and risk neutrality, so it's almost understandable that you don't appreciate model risk. It doesn't exist in complete markets! And of course in the risk-neutral world you pretend as if everything earns the same rate of return and risk has no value!

It's all beginning to make sense!

Part of the solution is more robust education and better critical thinking.

But the cynic in me thinks that if regulators were better educated in the 'practice' of banking then there'd be less trading, smaller bonuses and fewer donations to political parties.

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New Flag For Old

Replace the Scottish Blue with the Welsh Green? It has a certain 'freshness' about it. I don't think it works as well on a tie, but the new flag is actually much better than the old on a waistcoat, for those gentlemen with sufficient chutzpah.

What do you think?

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Europe - What's the point?

I have always believed that the EU and the Euro are simply ego trips for a few Northern European politicians, their desire for a legacy. For Southern and Eastern Europeans the EU and Euro are a quick route, during the good times, to riches. There is absolutely no reason for a club of such different peoples to succeed.

Most arguments in the EU’s favour are complete nonsense. For example:

1. Trade: You don’t need a club for efficient trade. This is clearly seen throughout the world by the size and growth of trade with China and India. What you need is efficiency in production and transport, you need control over wages and taxes.

2. Mobility of skills: Each country needs to create its own skilled people otherwise there is far too great an exposure to a critical component of a country’s wellbeing.

Most of the arguments in favour of the EU are examples of extremely shallow thinking. The desire for 23 (at least) of the EU’s constituent countries to increase their links when it is clear that they are falling apart is a typical knee-jerk bridge burning. But bridge burning is only good if it increases the probability of success. This is not the case here. It increases the damage when the inevitable happens. (I look forward to the day when a TV news item on the tightening of European links is followed immediately by an item on Scotland seeking devolution from the UK. I rather expect that comparisons will not be drawn.)

David Cameron has exercised the UK veto on the vote for closer fiscal ties. These ties would have imposed constraints on constituent countries’ budgets with punishments for violation. So punishment for something that is often going to be impossible without the flexibility of multiple currencies. Come back, King Canute, maybe you can advise here!

Meanwhile Nick Clegg wants the UK to be at the “heart of Europe” so that we can have an impact on international events, our relationship with the US being somewhat on the wane. One can rarely go wrong by asking any politician, “So what?” In this case if we want to have an international impact then we need to prove that we deserve this, not by hanging onto others’ coat-tails, whether they are American or European.

If you want to have international clubs then they need to have certain properties, for example:

1. Complementarity: There is no point in countries banding together unless they can each offer the other something. (Unless a country is so tiny as to benefit from economies of scale.)

2. Values: There must be a commonality of values, otherwise any union will bring animosity. I don’t think that the taxpayers of Northern Europe are exactly keen on bailing out the tax-avoiders of Southern Europe.

All of this leads to the inevitable conclusion that the UK is better off out of the EU, and much better off by building up the influence of the Commonwealth.*

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*Not only do they speak English and play cricket, but they mostly drive on the left-hand side of the road and use the same electric plug!

Taxation To Slow Down High-Frequency Speculation While Not Affecting Hedging Activity

The Tobin (or Robin Hood) Tax was proposed decades ago by the eponymous Nobel Laureate (that’s James Tobin, not Robin Hood) as a means of stabilizing currencies via a small tax on all transactions. Every few decades the idea comes back, although no longer confined just to foreign exchange. There are various reasons why it keeps being dismissed, reasons such as infeasibility, elimination of incentives, requirement for the initiative to be global, etc. One assumes, though, that it’s the political clout of the bankers that is the real reason why this has not been adopted. My sense is that the time might now be right for the adoption of the Tobin Tax, thanks to the valid fear over high-frequency trading and thanks to the widely held low opinion of bankers. Countries are going to have to learn to cooperate thanks to the recent financial crises, and what better place than a tiny little tax? And the technology is in place.

But there’s the question of how tiny is tiny. Tobin himself said “let’s say 0.5%.” It wasn’t meant as a well-thought-out number, and it’s certainly far too high given typical bid-ask spreads. So what is a better number?

Trading happens for a number of reasons. Let’s focus on just two, hedging and speculation. Hedging is generally considered to be a good thing, as it is meant to reduce risk. Speculation can be good or bad. In my opinion it’s bad when it happens at such a high frequency that the relationship between the share price of a company and its value becomes irrelevant to making money. So let’s say we want a tax that’s big enough to hamper the shortest-term speculation, while small enough not to affect hedging.

The mathematics of hedging of derivatives in the presence of transaction costs goes back to Hayne Leland (1985) for simple calls and puts. Later this was extended to incorporate any derivatives by Hoggard, Whalley and yours truly. Out of this work comes a simple non-dimensional parameter related to costs, volatility and hedging frequency that tells you how much your hedging will affect you P&L. It’s all in PWIQF2 if you want the details.

Supposing that you wanted to have less than 1% effect on profitability of a derivative (and that number is open to discussion but is easily well within the margins of model error), and supposing you hedge every day in a market with 20% volatility (again, two numbers that you are free to dispute or change), then the tax could be at most 0.008% of the value of each trade. Around one basis point.

Would this level affect good hedging? No. Would it affect speculation over medium and long term? No. Would it dampen short-term speculation? You bet.

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Bankers Can’t Avoid Risk by Hiding It

(A version of this was first published on Bloomberg.com on May 24, 2011.)

One of the supposed silver linings of our recent economic disaster was the idea that we finally understood how hazardous our exotic financial instruments are and that bankers were finding a better way to "manage" that risk. But if at least one of the common practices in banking is anything to go by, risk-management procedures in many cases continue to hide the very dangers they are trying to measure.

This may result in banks taking bigger positions, and end up taking more real risk than they should. And it gets worse.

The practice in question goes by the name of "calibration," which is best described using a non-financial example.

Springs are the basis for simple weighing machines. Attach a weight to the end of a spring and it will stretch. Measure how much the spring stretches. Repeat using a different weight. You will find that the extension is proportional to the weight. (Up to a certain point. If the weight is too great this relationship breaks down, and the spring may not even return to its rest state.)

This relationship is named Hooke’s Law after the English scientist who described it in the 17th century, Robert Hooke. F=kx, where F is the force or weight, x is the extension of the spring and k is some constant. To use this in practice, just attach a known weight to the spring and measure its extension. You know F, you know x, you can then infer the k. This is calibration. Once you know k, you can weigh anything else, take the extension and multiply by k and hey presto!

Now let’s see how this idea is applied in finance.

Your goal is to value some complex financial structured product. You have a valuation model with lots of lovely mathematics. But the model requires the input of parameters. You may need volatility, probability of default and other numbers, depending on the model and the instrument. A collateralized-debt obligation, for example, would require the input of lots of default parameters. Yet those parameters are for future volatility, future default risk and so on. How can we possibly know what these parameters are?

Typically, people seek guidance from simpler products, such as options and credit-default swaps, that are widely traded in the market. These simpler products also depend on the same unknown parameters, but their value is known since they are traded. With these simpler products, you work backwards, from value in the market, to find the unknown parameters -- in much the same way as you find the k for the spring. Once the parameters have been found, you can then use them in valuing other, non-traded, so-called exotic financial instruments.

So where’s the harm?

The beauty of Hooke’s model is that whatever weights are used to calibrate the spring, you get the same k. The stability of the parameter is a sign of a good model. This doesn’t happen in finance. You calibrate your derivatives one day, and then come back a week later to find your parameters have changed. This indicates the model is wrong. If finance were a proper science, then this simple and blatant failure of the model would result in it being tossed out and require a trip back to the drawing board.

In the context of the CDO, we might get information about the probability of default of the individual companies making up the instrument by looking at the credit-default swaps for those companies. But how much real information can there be in those CDS prices, especially since the company in question hasn’t yet, by definition, gone bankrupt and therefore the statistical sample size is zero?

You can see where I’m heading with this. Finance doesn’t meet the basic requirement of science: repeatable results. The models aren’t capable of any great level of precision. In finance, when models are calibrated, they always have to be recalibrated a week later. But those parameters are supposed to remain fixed for evermore. If they have to be changed, then the model either was wrong before, is wrong now, or more likely both.

I’m not saying that we’ll ever find a perfect finance model, but we should be aware of the limitations -- that is to say the model error -- of whatever model we do use. And by calibrating we throw out all objective measure of model risk. Risk has been very effectively hidden.

An objective test of the accuracy of a model is how well the theoretical value matches market prices for traded instruments. And in a calibrated model it does that perfectly, but it only appears correct at that one instant in time. And that appearance is very deceptive. Next week, or even tomorrow, or just an hour later, theory and practice will inevitably diverge. But if you are forever recalibrating, you never see this. Yet the very act of recalibration negates the model value that you thought was correct. Hence my comment that appearances can be deceptive. The value wasn't even correct at that one original instant.

Recalibration means that risk managers remain in blissful ignorance of the errors in their model and hence the risk. If anything ever gave a false sense of security, this is it. All that risk management has done is to hide the risk, making it harder to spot, to estimate and to hedge.

I visited a regulator (who shall remain nameless) in Washington recently. People say that regulators don’t have enough bite, so I went there to offer a set of teeth. My goal was to arm them with one simple, surefire way to frighten the pants off any bank. My advice was to ask the banks one simple question: "So, how stable are your calibrated parameters?" The bankers would then find some respect for the regulators. Instead, I found myself surrounded by quants praising calibration, not even appreciating the negating effect of recalibration.

It doesn’t take a rocket scientist to figure out the fallacy in calibration, but it does take someone who can look beyond the math.

Occupy Wall Street? I Never Heard Such A Thing!

I've been popping downtown to Zucotti Park, near Wall Sreet, over the last few days. Did you know there's a protest going on, against bankers, corporate greed, corrupt politicians? You'd never guess if you got all your news from the US media. On CNN this morning they devoted almost eight seconds to the story of 700 protesters being arrested. Top news story was a man who'd fallen down an embankment. Second story was "American man found living in Portugal." The horror, the horror.

The protesters seem mostly harmless. There's a very 1960's feel about them, including a topless young lady. "She doesn't have implants," a friend observed. Clearly she's spent too much of her life demonstrating bra-less. (The demonstrator, not my friend, I hasten to add!) The protesters have a system of public speaking whereby a person says a few words and the crowd repeats them so others can hear. This is forced on them by the banning of loudspeakers. Approval of a speaker is expressed by making wiggly rain signs with your hands. I followed one General Assembly meeting. After an hour they'd democratically agreed to set up two more committees. All very "Life of Brian." After that I went off to give a lecture on derivatives to some bankers.

When in the States I sometimes like to watch Fox News. It reminds me how lucky I am to live in a country where the broadcast media isn't incentivized to manipulate the news. I also like to watch old men in make-up ranting about homosexuals.

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Quant Lessons From The Royal Wedding

I like to teach certain quant finance ideas by reference to real life, often involving supermarkets and tins of baked beans (see for example The Role of Mathematics in Finance: Relevance, Reliance, Robustness). This is a great way to dispel embedded foolish ideas and to open minds.

I have this knack of connecting otherwise disjointed topics. Genius? Stupidity? Such a fine line.

So naturally I’d like to point out a couple of aspects of the royal wedding that have quant implications!

Theory vs Practice

Something as blatantly unmeritocratic as the royals cannot possibly work according to any political theory. Obviously they are trivial to criticize, and to find fault with, but on balance the royals in practice are almost certainly a positive force for the UK. Then there are political theories. One from the mid 19th century springs to mind. Looking good on paper (even had a catchy manifesto!), the implementation didn’t quite pan out. Ok, a few million people died, but, hey, nothing’s perfect. Precisely. Nothing is perfect. And that applies to quant finance models. If perfection is not possible, just stick with what works. Aim for better not best. President Blair, President Brown? Less dogmatism in the theorizing, please. Pretty mathematics might be appealing in physics, the mind of god and all that, but not in finance. (Although I do know of a nice Manifesto.)

Fear of Arbitrage

A lot of people are bothered by the cost of the royal family. They cost a pound per UK taxpayer per year. It's costing you a pound! A pound! Look down the back of the sofa, you could fund your contribution for the next five years. The fact is that the existence of the royals is not materially hurting you personally. This reminds me of people who worry about the existence of arbitrage. They have it in their heads that it is somehow wrong. They worry to such an extent that they change and destroy otherwise reasonable quant models by forcing them to calibrate to every traded instrument. I call this the Fear of Arbitrage. But the strange thing is that they might not be trading some of these instruments. If you aren't trading them why do you care whether or not they are correctly priced? It’s not rational. It’s emotional. If people want to misprice things, let them. It might not be any of your business.

Sorry to be so deeply uncool but I believe that variety is the spice of life! Congratulations, Catherine and William!

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HIQLEQ

In 1983 Howard Gardner proposed a theory of 'multiple intelligences,' and to date has listed eight different types: Spatial; Linguistic; Logical-mathematical; Bodily-kinesthetic; Musical; Interpersonal; Intrapersonal; Naturalistic. The interesting point about this is not the concept, which is itself reasonably obvious. The interesting point is the list itself, those specific eight areas of intelligence. A simplified version of this theory breaks intelligence down into just the two categories, the classical IQ and a measure of 'Emotional Intelligence' or EQ.

In many walks of life, especially those associated with highly technical skills such as physics, programming, mathematics, law, and increasingly certain aspects of banking such as risk management and derivatives, it is common to find people who have very high IQs but low EQs: High IQ, Low EQ, or hiqleq (pronounced hick-leck).

The jobs in modern investment banking have become very technical, requiring advanced mathematical and programming skills, and at the same time these bankers are having less interaction with customers, people from a wide variety of backgrounds with diverse personalities. Banks have become a safe haven, if perhaps not a breeding ground, for hiqleqs.

I enjoy conversations with people who can bring together many disparate subjects and weave them to make an illuminating, entertaining, and fun, wide-ranging and free-flowing discussion, typically those people with both high IQ and high EQ. However, hiqleqs seem to feel uncomfortable when any discussion begins to stray in an unexpected direction or if conversational parameters are not defined to their satisfaction.

In discussing research I similarly find that some people 'get it' and can improvise with an idea, being very creative, while others do the exact opposite and seem to stifle any originality. I don't mean they do it at all deliberately or maliciously, but just because they want rules or structure when there doesn't have to be any. Or to be more precise, discussion and exploration of ideas should be fluid and do not have to be as constrained as if they were a branch of rigorous mathematics.

When speaking about risk or valuation ideas to mathematicians in investment banks, I often feel as if I am trying to explain the beauty of a red rose or the colours of the rainbow to someone who only sees in black and white.

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Rewarding Mathematics

We hear a lot about how talent will leave the major financial centres if taxes or regulations become unacceptable. That people move to more favourable locations is more or less plausible. But what seems to not ever be asked is how much talent does this "talent" really have?

Combine this with what I have often said, that the mathematics of quant finance is straightforward if approached properly, and the following idea immediately suggests itself: Measure the ratio of typical salary in a quantitative field to the difficulty of the mathematics in that field. How much better off is the quant compared to the aeronautical engineer?

And does salary correlate with talent?

Quantifying the math difficulty, for the denominator in the ratio, is the hard part. Inspired by the kind of differential equations seen in many physical sciences as well as in finance we could start as follows.

Parabolic equations 5 points; elliptic 10; hyperbolic or mixed 15.

Four or fewer dimensions 5 points; five or more 10 points.

Linear no points; nonlinear 10 points.

The aero engineer might have a ratio of 5 (after rescaling by 1,000 to make the numbers neater), the quant a whopping 30.

In other words the aero engineer ought to be on the quant's salary and vice versa.

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The "Inbox Test for Stability of the Global Financial Market"

Another day, another email in my inbox announcing another High Frequency Trading conference. I have nothing against the emails (we send quite a few of them ourselves) and I have nothing against HFT per se. But a large number of emails on the same subject in a short space of time is a sure sign of a bandwagon. And bandwagons are often bad news for the markets. More specifically bad news for shareholders, but often the cause for bumper bonuses for bankers.

The last time my inbox was bombarded with emails of such monotony was during the heyday of credit derivatives. At the time I said that the credit derivatives models were stupid but unfortunately I hadn't fully realized the size of the market, and therefore the potential for systemic risk. The state of my inbox should have warned me.

Now I know better. So according to my inbox there is far too much algo/hf/computerized trading. The minimal benefits this confers in terms of supposed "efficiencies" is far outweighed by the potential it has for causing chaos. Penny wise, pound foolish.

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Cyberterrorism

Cyberterrorism is in the news so I thought I'd share this little story with you.

A year or two ago I was at a dinner of the Great and the Good. I sat next to an Ambassador. We chatted broadly about the threats facing the world: Terrorism (I said it could be much worse if terrorists had any imagination); Finance (there will be another crisis unless governments bite the bullet and simplify); Viruses/pandemics (a big one eventually but not for a while); etc. My general theme being the Global Village, everything being linked, no more survival of the fittest since there is in effect only one organism, etc. I dismissed global warming on the grounds that there are many threats with much shorter timescales. I also threw in a few left-field suggestions such as a world in which half the population spends all its disposable income on health insurance thanks to a poor result in a genetic test.

And then I mentioned cyberterrorism. Many people downplay this, citing firewalls, encryption, etc. and saying that governments have better ways of causing trouble. But this underestimates the human role in setting up such firewalls, encryption, etc. and ignores the role of the lone hacker with a grudge or a mental problem, there doesn't need to be any government sponsorship.

The Ambassador said he wasn't worried. He then gave the unfortunate example of flight. "If computers went down my plane ticket could very easily be printed out the old-fashioned way," he said. I asked if he would really feel safe flying when the plane's computer went down. He stared at me for a few seconds with a confused look on his face. He then turned to the man on his other side and didn't speak to me for the rest of the dinner.

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High-frequency Trading: Where are we and how did we get here?

"The truth is the high-frequency traders create volatility and create liquidity," said John Damgard, president of the Futures Industry Association.

What he apparently meant to say was that they reduce volatility, not create it. And this was just a slip of the tongue. As Sigmund Freud observed, such slips can reveal the reality.

I am concerned about High-frequency Trading (HFT) for two main reasons: Reduction of the relationship between value and price; Potential for positive feedback.

Markets exist to enable businesses to raise money, to expand, to thereby employ people, and so on, for the benefit of society. This only works if the market does a decent job of revealing the true value of a company via its share price. Otherwise the market is no different from a casino, a share price may as well be given by the spin of a roulette wheel. Fundamental analysis is supposed to do a similar job. You analyze a company, study its customers, research the management, etc., and come to a conclusion. But fundamental analysis is hard work.

Much easier is to run a data feed into a black box containing some algorithm, then optimize that algorithm. Your HFT black box doesn't care a hoot about the true value of a company, it only cares about what happens to the price over the next few seconds. You may spend a few months setting up this black box the first time, but thereafter you can apply it to a wide variety of markets with relatively little effort. Just re-optimize for that market. (And we know from how market players are compensated that the question of whether or not the result is long-term profitable is of second-order importance.) Not so with fundamental analysis, each market is different, each requiring the same weeks of hard work.

The above wouldn't matter if the HFT boys didn't dominate the market. Is it now 70% of trades on some exchanges are HFT trades?

Whenever you have a bandwagon, such as HFT now is, then you have the potential for systemic risk and feedback. Remember the last bandwagon…the credit products. How did that one turn out for the world economy?

To get feedback you need a quantity of traders following similar strategies.

"They all have different strategies," you say. Perhaps true for a while, but nor for long. Traders copy each other mercilessly, and since people in finance change jobs every two years it doesn’t take long for ideas to diffuse widely.

But feedback can be positive or negative.

Negative feedback is when an up move in a stock leads to a sell signal, and thus a fall in the price, and a down leads to a buy, and thus a rise in the price. This dampens volatility.

Positive feedback is when an up begets a buy, which causes the stock to rise again, causing another buy, etc. etc. And when a fall begets a sell, causing another fall, and further selling, and…

So which is it? Does HFT result in a reduction of volatility via negative feedback or an increase via positive feedback? This is an easy one. If you are a hedge fund manager which of the following would you prefer? A or B?

A. Low volatility. Shares go up or go down fairly predictably. No skill is required to make money, even by the man on the street. Hedge funds can’t charge large fees.

B. High volatility. Very difficult markets, experts needed and can charge large fees. If a fund does well they make a killing because of the enormous profit they have made for their clients. But they are just as likely to lose all their clients' money, in which case…nothing bad happens to the fund manager.

Yes, we are in that familiar territory of moral hazard. Of course the funds want to increase volatility and they have found themselves in exactly the place they want to be to make this happen.

(BTW If you want the mathematics of feedback see PWOQF2 or read the paper The feedback effect of hedging in illiquid markets, (P.Schoenbucher and P.Wilmott.) SIAM J. Appl. Math. 61 232-272 (2000). It's all about the gamma of a strategy.)

How did we find ourselves in this place? Because the HFT boys cleverly played the "liquidity card" at the right time. The argument goes along these lines: "When Mom and Pop want to sell off some of their portfolio to fund their retirement then they'll get a better price if there's more liquidity. So liquidity is good." True! For the shares they've held onto for 20 years they will indeed get an extra cent. Whoohoo! Break out the champagne! So you mustn't argue with the liquidity card. The more the merrier, right? Well, no. The fact that during those 20 years their shares have lost 50% of their value thanks to the Great HFT Crash doesn't ever get mentioned. One extra cent versus a 50% fall? Hmmm.

Everything in moderation. The more liquidity there is, the more you rely on its providers, and the worse the collapse when that liquidity dries up. And who is in the position to both cause this drying up, and to benefit from it? Why, it's the HFT boys again!

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Out With The New, In With The Old

Goodbye, New Labour, you won't be missed. And the fondest of fond farewells to Peter Mandelson, please don't keep in touch.

Back to Old-style politics in which MPs and cabinet ministers have their say, no more is policy going to be dictated by a cabal of non-elected spin doctors with no understanding of the concept of 'content.'

I believe that Cameron has given away more than he needed to, but the end result is a sensible compromise...

Cuts to bring deficit under control: Conservative policy wins, emphasis on sooner rather than later. Good.

Tax for low earners: LibDem policy to eliminate tax for those earning less than £10,000. Good.

Inheritance tax: Conservatives wanted to drop this, how many times can you tax the same money? LibDems get their way, IHT tax stays. Bad.

Capital Gains Tax: This could have been very, very bad. Labour eliminated the taper relief whereby tax paid depended on how long an asset had been held. But Labour never did understand how businesses work. LibDems wanted to make CGT rates more like Income Tax. That would have killed all entrepreneurial activity in the UK. Would you rather a) have a safe job, no possibility of losing money and a pension or b) risk your entire worth, risk losing your home and family and have no pension? CGT is supposed to be lower than Income Tax to compensate for the difference between being an employee and being an employer, and so encourage people to start businesses. Fortunately the LibDems did not get their way entirely. Instead CGT will rise on non-business assets such as shares and second homes. Makes a lot of sense since businesses are not discouraged. Could have been far, far worse. I still want to see the details just in case...

Voting reform: LibDems want Proportional Representation, and more resulting power for them but woolly government for us. Conservatives want the status quo. Conservatives have given away a referendum on the Alternative Voting system. This is the weakest possible negotiating point they could have given away, but maybe it was a LibDem dealbreaker. We need to the see details on this. Is the resulting referendum binding in some way?

Immigration: Conservatives want caps on numbers from outside the EU, LibDems want an amnesty on all illegal immigrants. This did not go down well with voters, once they started to examine LibDem policies after Clegg's game-changing TV appearance. Conservatives get their way on this one, obviously.

Fixed-term parliaments: Next election scheduled for May 2015. Can't see the point in this.

Mansion tax: I'll finish on this one because it has a nice quanty element to it. LibDems had wanted a 1% annual tax on the value of homes above £2m. So on a home worth £3m you'd pay £10k p.a. Fortunately this silly idea has been dropped. Why is it silly? Let's do the math on the £3m house. With interest rates so low, what is the Present Value of an annual £10k? What might happen to the value of that house? Now repeat the calculation for a house worth an arbitrary X.

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Politics, Panic and Poker

The Conservatives have offered the LibDems a referendum on electoral reform (albeit only on a very weak version of reform). Clearly a panic move, they didn't even wait to get a sense of people's reactions to Brown's earlier speech.

I've long said that bankers ought to be forced to play poker in order to understand their own relationship with risk and return. I now think that politicians ought to play so that they can appreciate the strength of their hands and, crucially, learn to walk away from a hand to play another day. The Tories have something to learn.

In classical Modern Portfolio Theory we also learn to weigh up risk and expected return. Similar principles apply in politics. Nick Clegg has to decide between low risk with the Conservatives, with a resulting majority of seats, and high risk with Labour, for who would trust them. But how high will the expected returns be? The Conservatives have offered more than they should have. I can only assume that Clegg has photos of Cameron in a compromising position.

And does anyone know why this haggling is happening in public instead of behind closed doors?

If this is the quality of horse trading we can expect from the current crop of British politicians then Lord help us when we have to haggle with the wider world.

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Desperate Times, Desperate Measures - How Desperate Can You Get?

Brown graciously offers to run the country as PM for a few more months with a LibLab pact, and then will step down after Labour has chosen a new leader. Thanks, Gordon, but do you mind awfully if we pass on this one?

This is all highly disgusting and highly predictable. Brown and a few of his inner circle come up with this cunning plan, no consultation with the cabinet, just him and his favourite spin doctors. You only need to watch the 5.30pm Sky News interview with Alastair Campbell by Adam Boulton to see the Labour party imploding. Embarrassing. You expect such nonsense from banana republics.

That's the bad news. There is good news, at last. What wasn't predictable about all this was that Brown would announce this decision to the public. If it was an appeal to Clegg then I think it was a big mistake. Brown is clearly flailing around, desperate to cling to power.

I'm hoping that this lessens the probability of a LibDem-Labour relationship, the more natural of the two possible coalitions. Not that I'm keen on a LibDem-Conservative pairing up, I'm almost as worried by the thought of Proportional Representation as I am by the thought of higher taxes!

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Brown Out

Following the election result (not that there has been an actual 'result') and while waiting for the horse trading to lead somewhere, there are only two things that are absolutely certain:

1. Brown will not be PM for much longer. Whether the LibDems do a deal with the Conservatives or with Labour or whether the Conservatives go it alone, Brown will be out. This will be a condition of any LibDem-Lab deal.

2. Even as I type, Labour politicians are speaking to their agents about publishing deals. There are so many of them with knives still sticking in their backs, aching to tell their side of the story of the last 13 years. I am particularly looking forward to hearing the truth about the bullying, temper tantrums and personality disorders of the Brown years. Keep your DSM IV to hand!

BTW if you've enjoyed the last few days then you'll love Proportional Representation. Under such a system every election will be like this.

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The Labour Manifesto - the Deniability Quotient

I’d never bothered to read a political manifesto before today. But I suspected that some fun could be had with them. If you know that someone has a tendency to be economical with the truth then a lot of amusement can be had from figuring out how they have phrased their words to maximize the Deniability Quotient (DQ) in anticipation of accusations of lying.

The DQ of the Labour Manifesto is pretty high.

Take this example from Page 11 of the manifesto:

“We will not raise the basic, higher and new top rates of tax in the next parliament and we renew our pledge not to extend VAT [sales] to food, children’s clothes, books, newspapers and public transport fares.”

Superficially it sounds great, doesn’t it? The casual reader interprets this as “taxes won’t go up.” If you believe that Labour are to be trusted then you might be right in that interpretation. Ok it doesn’t exactly say that but we can trust them, no?

How many advisers, lawyers and spin doctors had an input into that sentence?

A more realistic assumption is that they cannot be trusted, they are political animals after all, and that sentence must be read through the eyes of a lawyer. There is enough room for weaseling around that a proper reading of this would be the exact opposite.

What the sentence means is that

- the percentages of income tax won’t change (i.e. the 20%, 40%, 50%)

- the threshold at which they each come into effect will change, i.e. decrease

- Capital Gains Tax will increase

- Other taxes will also go up

- The rate of VAT will increase

Notice how the sentence does not specifically refer to “income” tax. By missing out the word “income” the effect is to suggest that all taxes are being referred to. But that can’t be the case because it’s only income tax that has “basic, higher and new top rates” of tax. All taxes besides income tax and VAT are excluded from this sentence. This gives Labour the required deniability.

I am looking forward to the Conservative manifesto!

Greed Is Good But Envy Is Bad

"Greed is good," said the Ivan Boesky-inspired Gordon Gecko in the first "Wall Street" movie. And greed certainly is one of the prime movers behind many a successful business, along with altruism, curiosity, necessity, etc.

Greed is absolute. Wanting more for the sake of it.

But "Envy is bad," says yours truly.

Envy is relative, and all the nastier for it. It's about wanting more than your neighbour, even at a cost to yourself.

There's too much envy in finance. (No kidding, Paul, what an insight!) And this has led to an escalation in salaries and, in consequence, risk taking; an unspoken conspiracy in which senior management encourage gambling by their traders so that they all get 'rewarded.'

You know what though? Just divide all bankers' pay packets by ten. And since envy is relative no feelings will be hurt!

I don't really do envy myself, see my Cheese blog in which I explained my retirement needs as cheese, wine, books (mostly fiction), oh yes, and a swimming pool ;-)

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Hoping For One L Of A Recovery

A few months ago I was speaking at a conference at which Nouriel Roubini gave a talk about his view on the future of the world economy. He spoke about V-shaped recovery, U shaped, W shaped, and, the horror, the horror, the L-shaped version. An L-shaped recovery is one in which there is essentially no recovery at all. Japan in the 1990s was held up as the poster child and, I hope there are no Japanese reading this, was just about the worst thing that could possibly happen to a country, to be avoided at all costs, even if it means throwing money into the system (quantitative easing) or starting another war. (That's my interpretation, not his, I hasten to add!) I gave my talk after his and, improvising, said something like this...

Have you any experience of Japan in the 1990s? Well I have. And it didn't seem too bad to me. Were there hordes of people begging on the subway? Not that I recall. Was it dangerous roaming the streets for fear of being mugged? No, it seemed safe enough when I was there. Was there high unemployment and general desititution? No. More on this anon.

Japan in the 1990s was, as it still is, a safe, enjoyable place, with a very high standard of living, and at the cutting edge technology wise. Not the hell hole that economists like to paint. And so I really cannot imagine what Japan would be like now if they'd had a V-shaped recovery. They'd all be communicating by telepathy and travelling via matter transporter I guess.

To me the important point about the economy is not what letter of the alphabet best represents it, nor its percentage growth. After all, is it really necessary to grow at x percent per annum in order to maintain the feeling of status quo? Like the shark, which supposedly has to keep moving forward in order to stay alive. What sort of life is that? I believe what is most important is the well being of the people, and that's not the same as GDP. It is, however, closely linked to rate of employment. And that's where Japan does remarkably well. That's what governments should focus on, to L with growth!

I'm a simple person. (Easy now!) I take holidays in the Isle of Man and frequent thrift shops, for god's sake! So rampant growth really doesn't do it for me. I confess that I was kind of looking forward to a world with a little bit more of something beginning with L. But it looks like we are back on the treadmill, back to the bumper bonuses. And I believe we've just missed a great opportunity for making the world a better place. (Mind you, if we get the double dip maybe we should treat that as a second chance!)

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Valuation Versus Risk Management

Valuation and risk management, two sides of the quant business, must be treated with equal sophistication, with equal respect, and with equal suspicion. And there must be closer interaction between them.

In education, valuation should not be the domain of the most abstract of mathematicians with risk management its more primitive partner. In practice, quants must not produce models that risk managers cannot understand.

At every stage of valuation and model development you must be asking questions about risk and robustness. It is dangerous to come up with some fancy model and only afterwards start asking questions about model error. Anyone who has ever calibrated a model knows that the methods used to mitigate model risk almost come as an afterthought, and are totally inconsistent with the original model. This need not be the case.

In the CQF we treat valuation and risk management as equals. The structure of the CQF is unashamedly mathematical. Module by module we add mathematical flexibility, and in each lecture you will see model risk and model robustness discussed alongside the theory of valuation. This is how quantitative finance ought to be taught. This is the mature approach to the subject, and it will help to resolve many of the discrepancies between finance theory and finance practice.

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Policing The Police

I was at the G20 protests in London on 1st April. I took this photograph of the 'charming gentlemen' who were supposed to be keeping the peace. As we know they were instead beating people up, and slapping women around, hence their disguises. I mention this now because I've just seen a BBC story in which an MP is reported as saying that "police must modify their behaviour in an age where their actions were easily filmed by the public." Translated this means that if they are not being photographed then they can do what they like. A bit like MPs and their expenses, if no one can see what they are up to then they should be expected to get away with what they can.

It seems to old-fashioned me that police, MPs, anyone with a position of responsibility in public life, should have the personality and self control to stay within the letter and spirit of the law and be role models for everyone else. This is Britain, not Italy!

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FSA: It's Worse Than I Feared

Remember my blog about Magicians and Mathematicians in which I complained about the lack of imagination in risk management? If you don't, then please take a look otherwise the rest of this blog won't make any sense to you at all!

Well, I just had a very frightening experience at a conference. I used the magician example to get the audience to open up to the idea of thinking beyond the simple mathematics. I started with "What is the probability of...," and received the usual "One in 52" reply. Then the location (the magic show) was pointed out, and people changed their answer to 100%. Except that some people didn't. There were three people in the audience of maybe 100 who stuck to their original 1/52 answer and refused to budge.

So far so typical.

Now the frightening bit. The audience consisted almost entirely of actuaries. (That's not the frightening bit!) Except for three people from the FSA. And two of those were ones who insisted on the 'math' answer 1/52. (That's the bit that scared me!)

One of them explained his reasoning. I cannot remember the details, it was quite lengthy, but the essence was that "The answer should have been one in 52 except that the magician was tricking us and so really we should ignore this factor..." (I apologise if I have got this wrong, but from the reaction of the audience I don't think I have!)

Now forgive me but isn't the FSA supposed to be operating in the real world in which things are just not about pure mathematics? A world in which risk managers hide risk, moral hazard is rife and magicians do, er, magic. Isn't that sort of the entire point? If it was all about the maths then we wouldn't have the FSA, we'd use someone like the EdExcel examiners to give banks marks out of a hundred at the end of term.

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Buffett and Derivatives: Enthusiasm, Anger, Disbelief, Acceptance

Denial, anger, bargaining, depression, acceptance, according to Elizabeth Kübler-Ross the five stages of dealing with personal tragedy. I wonder if there's something similar we are going through with financial derivatives? If so, I think Warren Buffett is at the anger stage. "If you need to use a computer or a calculator to make the calculation, you shouldn't buy it," is his view on investing, famously calling derivatives "Weapons of mass destruction" a few years ago. I sympathize, and I speak as one of the mathematicians who works with derivatives for a living.

In my experience there are just four stages of dealing with derivatives, and they are: naive enthusiasm, as one experiences the glorious possibilities of derivatives in one's portfolio, then righteous anger as one suffers horrendous losses, followed by confused disbelief, as one realises that no one fully understood the risk in these dastardly creations, least of all the bankers, and finally a reluctant acceptance as one admits that these things are here to stay. Let's go through these stages one by one, while I explain what each means in terms of risk.

Naive enthusiasm: Derivatives are wonderful financial contracts, they allow you to finely tune your investment portfolio to benefit from your market views, assuming they turn out to be correct. My bank manager has recently been trying to sell me a contract that will give me over 5% return in one year if gold stays within a certain trading range. In market parlance this is called a double knockout quanto option. Or derivatives can be used to hedge risk from other business activities. If you regularly sell widgets to Japan you are exposed to dollar/yen exchange-rate risk. A derivative can be designed to reduce that risk for you. So far so good.

Righteous anger: Who wouldn't be angry after the trillions of dollars that have been lost thanks to CDOs, MBSs, and all the other acronyms? The problem though is not the derivatives themselves, rather the way that the derivatives have swamped the market for simple stocks and shares. The notional outstanding of all derivatives globally is over a quadrillion dollars. What, you thought trillions was bad enough? You, ain't seen nothing yet!

So rather than derivatives existing to help you manage risk, or profit from precise market views, the market has grown so much that derivatives seem to be there just to allow crazy leverage, risk taking on levels never seen before. And at this point the risk-management quants step in to say, don't worry we've got our fancy mathematical models that show there is actually no risk.

Buffett's right-hand man, Charlie Munger, has said about higher mathematics in finance "They teach that in business schools because, well, they've got to do something." Now that really hits the nail on the head. When your competitor university across the river is charging 50, 60, 70 thousand dollars for a one-year Masters course in Financial Engineering, what are you going to do? Are you going to say you don't have any faculty that understand derivatives? Hell, no. You are going to get your smartest mathematicians together and make up a syllabus. Are your 23-year old victims, sorry I mean students, going to know any better? In 2000 I warned about the dangers of a "mathematician-led market meltdown" after seeing what had happened at LTCM and how identikit risk managers were being churned out from Masters programs, and how Groupthink was beginning to dominate risk research and derivatives valuation. I sympathize totally with Warren Buffett and Charlie Munger.

Confused disbelief: I'm a great believer in education playing a bigger role in derivatives in future. But not the sort of education that we've got at the moment. I understand Warren Buffett when he says "The more symbols they could work into their writing the more they were revered." Universities are churning out many thousands of 'experts' in the analysis of derivatives but sadly they know more about the math and the symbols than they do about the markets. But again it's not the symbols themselves that are to blame, for we happily fly on airplanes designed using similar symbols, rather it's the lack of financial empathy exhibited by the multiple-PhD'd analysts, the quants, that worries me. Remember this is a mathematician writing this, but one who has been saying less is more for over a decade now.

Reluctant acceptance: I've blogged in the past about the "mathematics sweet spot" for finance, where the models are not dumbed down, but equally they are not fantastically over complicated (to impress, as I expect Buffett would say). I don't think we can go back to a dark ages before derivatives and quantitative finance, but I do believe that we desperately need to rethink the type of education that those 23-year olds, soon to be in charge of your pension, are getting. Less math, fewer symbols, more commonsense, and more market know-how.

And in this respect I think I'm a few stages ahead of Mr Buffett.

Avoiding Swine Flu: A Lesson From The Porn Industry

A couple of years ago I damaged my right hand trying to hold open the door of a London Underground train. For about 18 months I was unable to shake hands, especially with Americans. I just happened to be reading the autobiography of Ron Jeremy, legenday porn star, at the time, a book I would very highly recommend, in which he mentioned the "porn handshake." Apparently, and I emphasise that I only have his word for this, that when two porn stars meet on set instead of shaking hands, for who knows where those hands have been, they touch right elbow to right elbow. So I started doing this, because of my damaged hand, and for a while this became known as the "quant handshake." It only really caught on within a very small circle and then died out.

Time to bring it back for the general population...

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Celebrity Death Test

It is almost impossible for the layperson to rationally determine the seriousness of any new disease and whether it has the potential to be the next Black Death. I'm thinking of the new Swine 'Flu, which has replaced the old Bird 'Flu as the latest Terror. It's impossible to judge because of the modern tendency to dismiss science in favour of tree hugging, hippy, holistic nonsense. And the commercial needs of newspapers who have to make mountains out of molehills to sell in this internet age. Not to mention the internet itself which encourages fear and belief in conspiracy theories. And ambulance-chasing lawyers causing us to overreact to everything to avoid lawsuits.

I have no doubt that a new human virus is of more danger than global warming, and for the record I'd like to add other things that are of more pressing concern than global warming: terrorism; cyber attacks; computer viruses; (even worse) global financial meltdown; everything really thanks to the 'global village' problem.

So I have my own way of determining the seriousness of any new threat to human life, it's called the Celebrity Death Test, and I hope you find it useful. The way it works is simple, if a Celebrity dies from the Threat then it is to be taken Seriously, if they don't then it's probably nothing to worry about. Bird 'Flu, fine. AIDS, not fine. I can remember when Rock Hudson died, that was the moment when AIDS became real for me. (I'm also a fan of Doris Day, read into that what you will!) You see how it works? It's just a statistics thing. If a Celeb suffers from it (and assuming it's not something that has a natural correlation with Celebrity or is self inflicted) then it is statistically significant for the rest of us.

BTW your intrepid reporter is due to lecture in Mexico City in a few weeks. All being well I shall give you news from the frontline, possibly from behind a face mask.

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Tax, Cut, Sell, Or...

First my standard disclaimer, Economics Makes My Brain Hurt. I am but a mathematician, and businessman, I suppose. And although I cannot and do not claim to know anything about running a country (which is at least an honest position, one I wish were shared by those temporarily in power), I can draw on my own experiences and on simple logic.

It seems to me that the choices facing the UK government now are not dissimilar to those that might be faced by anyone running a household or a business, e.g. me.

When in debt you have limited choices:

a) Make more money. For the individual this means getting another job. For the government it means increasing tax revenues, which may be the same as increasing taxes (or it may not, depending on disincentives so introduced). Keeping the numbers simple, the goverment/IMF is talking about £200billion debt. Divided across the UK population not such a big number, but still enormous for the man in the street, divided across the rather smaller 200,000 high earners that the government has in its sights, hmmm, not such a small number. However you divide it up though it's all quite frankly impossible (unless you believe Darling's forecasts for growth in 2010, which I don't think even he can believe).

b) Cut spending. Painful for a Labour government (or New Nasty, as I now call them after the scandal of the attempted email slurs), but at least there is lots of waste they've introduced and which they could cut out. But no, cutting waste and public spending is not what Labour do, it's a vote loser.

c) Sell off the silver. Any foreigners want to buy a piece of the UK right now? Going cheap. But wait a while, the country will be even cheaper.

But there's one thing that the public cannot do, and which only governments can, and that is make the debt disappear like a David Copperfield trick. No mirrors, no distracting bright lights, no body doubles or revolving stages (sorry if I'm giving away his secrets!), just simple inflation.

d) Inflate, reduce the value of the pound. Debt disappears (compound interest acts remarkably quickly). And a vote winner among all the borrowers who started this mess. Of course there is the slight problem that the 'independent' Bank of England (made so by Gordon Brown in 1997 remember) has a specific remit to control inflation. So watch out for subtle changes in the BoE rules.

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Numbers People And Symbols People

Are you a numbers person or a symbols person? You should instinctively know the answer. Let’s step back a bit, are you a cat person or a dog person? A cat person? Like me then. You can’t be both. Again, numbers or symbols? Do you like your mathematics done with examples involving numbers or more abstractly with symbols? If you have a maths degree then you are definitely a symbols person, also probably if you have a hard-science background. But accountants prefer numbers.

Numbers are great for illustrating how things work. Add, subtract, multiply, divide, raise to a power, etc., you can’t fool anyone with numbers. If it can be done with numbers then it must be easy. On the other hand with numbers you can’t see structure. If the number 7 appears in some calculation you won’t necessarily know what it means. And is it the same “7” each time it appears? Maybe one is an interest rate and another is a maturity. To get to a deeper level of understanding you need symbols.

Symbols are great for showing structure, abstraction is always necessary if you are to go beyond mere arithmetic. The problem with symbols is that some people are frightened by them. And if you and I are used to using different types of symbols it may take some time before we fully understand each other. One could even be accidentally or deliberately confusing, throw in a symbol without a proper explanation and before you know it everyone is lost.

This is relevant to the teaching of mathematics in schools. People can become terrified of the subject at an early age if taught badly, with the result that they are probably forever lost. (Unless it’s possible to get therapy?) How often at dinner parties have we mathematicians heard the ever-so-original response to what we do for a living “I was terrible at maths at school, me!”? I read recently that the part of the brain that does maths is right next to the part that registers fear. I don’t know whether it’s true but it certainly makes sense.

I am forever hearing politicians wittering on about how maths education in schools needs to be made more fun, and more, what’s the word? Practical! Misguided fools! Not a single GCSE maths above grade D among them. The point of mathematics is that it is supposed to be abstract. If all your maths comes from counting apples then you are going to be stymied by the real thing. Mathematics is abstract, that is the beauty of it. And that’s what actually makes it fun. Teach mathematics properly, don’t terrify children by asking them how long it takes ten politicians to dig themselves into ten holes, explain to the young the beauty of the abstract.

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Society Has Finally Risen To The Level Of Its Own Incompetence

The Peter Principle (named after Dr Lawrence Peter) is the idea that people “rise to the level of their own incompetence.” Originally it was proposed in a humorous book published in 1968 but has since become accepted as giving genuine insight into how humans interact. According to Wikipedia “It holds that in a hierarchy, members are promoted so long as they work competently. Sooner or later they are promoted to a position at which they are no longer competent (their ‘level of incompetence’), and there they remain. Peter’s Corollary states that ‘in time, every post tends to be occupied by an employee who is incompetent to carry out his duties’ and adds that ‘work is accomplished by those employees who have not yet reached their level of incompetence.’” This is related to the concept that everything interesting happens at the margins.

The same is now clearly true of larger organisms, and I am obviously thinking of western society as a whole. The evidence is unambiguous: Bonus-bewitched bankers destroy institutions that had been around for centuries, politicians rescue their rich friends and ensure they get handsomely rewarded for their catastrophic failures, then people protest peacefully at the G20 summit where the police are the aggressors.

This has been made possible by ‘progress’ thanks to technology, the Ponzi scheme that is the world economy, the lawyer-led victim culture, the abandonment of common sense because of political correctness, the advance of globalization so that we are all tied together in one giant global-village/shopping-mall and the ubiquitous career politicians having no productive real-world experience but who know how to crawl their way to the top, lining their pockets all the way, over the bodies of the hard working and what are now called the ‘coping class.’

Senior management being paid in inverse proportion to their achievements; Personal Identification Numbers everywhere so that we are forced to use the same one every time therefore increasing the security risks they were meant to reduce; Health and safety rules that mean we are not permitted to experience the small pains that stop us from suffering from the deadly; There being so much new legislation that most people commit a petty, trivial crime each day, while real criminals go unpunished; No one being allowed to fail, all students must be given an A grade so it is impossible to tell who is fit for a job, while simultaneously lying on CVs is encouraged; The BBC being unable to spell its news announcements correctly, they happen so quickly; Over-paid professors proposing that spelling be relaxed because children find it too hard; Children unable to play in the streets because of hysteria over paedophilia; Children unable to learn contact sports properly because teachers are not allowed to touch them; People allowed to drown because ‘rescuers’ didn’t have the right ‘certificates’; People vying to be in minorities so as to get special treatment; Bins too heavy for binmen; Fines for not sorting rubbish; Homeopathy; Creationism;…

On my street recently a man was deliberately run into by a car and carried around the neighbourhood on the bonnet. The man suffers from MS. The police did nothing, even though they have a CCTV camera in the spot and it recorded the whole incident including the car’s number plate. But they manage to use the same CCTV on the same road to record parking violations and issue tickets without any problem. The reason is obvious, fining people for parking is profitable, solving crimes is not. And according to en vogue theories every part of society must be a self-sufficient, profit center, mustn’t it? Utter madness.

Society has risen to the level of its own incompetence and at the same time the means to return to a more sensible world has been legislated out of existence. The above we all know. But only some of us really care. If you are one of us, you will already know the solution, but you are perhaps understandably afraid to carry it out. The solution is this…I ask please do your best to bring back freedom of speech and expression; Please be politically incorrect at every opportunity; Tell jokes that are in bad taste; Travel on trains without a ticket, and then for your court appearance hire Cherie Blair as your barrister. Laugh in the faces of health and safety personnel! Edmund Burke, the political philosopher, is attributed with the saying “All it takes for evil to triumph is for good men to do nothing.” I’m not worried about evil, it’s stupidity that is soon going to be victorious. But the world can only continue its descent into madness if you let it.

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The New Empress's Clothes

I apologize in advance for this mini blog. But you all now expect me to get things off my chest, and I do like to tell it how I see it. Nevertheless this still pains me. (And I think I may have resisted temptation, but the title of this blog was just too good an opportunity to pass up.) So here goes...sequins, Argyle check and a pearl necklace...Michelle Obama, what were you thinking? There, said it. Let's move on.

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G20 End Of Term Report: B Minus, Could Do Better - See The Teacher

As I write this I have not seen details of the G20's agreement and related events. So I'm going by soundbites and rumours that I've heard in the last few hours. Nevertheless, I can't resist a few quick comments.

First, Gordon Brown has talked vaguely about only rewarding bankers for positive performance. Well, believe it or not, apart from packages paid to the likes of Fred Goodwin, that is exactly the current situation! And it is this that encourages risk. Compensation needs to be tied to maturity of contracts. And diversification within institutions needs to be encouraged. We have to align the interests of bank employees with the interests of depositors. I'm still not convinced that those in power get this yet.

I understand that mark-to-market is being relaxed in parts. I approve. I just wish that banks had been nationalized first so that the taxpayer would have benefitted from this. Again banks have "upside exposure with no downside risk" as they say in the prospectuses. For the taxpayer it is the opposite, so no change there.

And finally, they are going to be publishing a list of bad tax havens in order to shame them. Isn't that rather like telling teenagers where to buy the cheap alcohol? At the moment we have no idea where to put our money, since once-respectable banks are no longer safe. But this time tomorrow we'll all know exactly where to go!

I'm being harsh, you say. They mean well. Oh, yes, I'm sure they do!

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Good Risk Management Techniques Do Already Exist

In the popular press I keep reading about how quant models need to be improved. It's not as simple as that, but nor is it so subtle for the journalists to have to dumb down.

There was an article in the Financial Times last week that said we need more maths, yes, more, lots of it, until we are stuffed to the very brim. No mention of what sort of maths, no mention of the relevance of the maths or the robustness of the resulting models. Just "we need more maths." I have to disagree that it is just a case of more is better. The wrong models are partly responsible for the current mess, and many of them are too mathematical. Well, I've said that many times over the years.

There's also the perception that there are no good models out there. Again, I have to disagree strongly. There are plenty of models that are better than the established models. Some of them are better by virtue of being more accurate in a scientific sense, some are better by virtue of their simplicity. Given that financial models are never going to be perfect it surely makes sense to have models that are transparent and easy to understand (and mend when they go wrong) rather than complex and impenetrable.

One error that keeps being repeated is that there are no models for crashes, when all instruments move together in sync. Well, the much-maligned-and-rightly-so copulas are meant to do that. Clearly they didn't do a great job. There is also the model that Philip Hua and I designed in the mid to late '90s, CrashMetrics.

CrashMetrics ticks all the important boxes: a) accuracy, b) correct level of mathematics, c) understandability, d) robustness, e) flexibility, f) ease of use. We came up with the idea because it was clear that Value at Risk would only work during rather dull markets, that is, perversely at times when it almost wasn't important to measure risk! So something had to be done about the bank-destroying events, the crashes for example. Extreme Value Theory was supposed to do that, but that's just "rearranging the deck chairs on the Titanic." CrashMetrics is a worst-case scenario model, designed to tell you how bad the crash would be for your portfolio, with no reliance on probabilities. Once you know what the worst could be you then decide whether you want to protect yourself against it, and then, thanks to "Platinum Hedging," the methodology also tells you how to do this in the optimal, most cost-effective manner.

Sadly CrashMetrics fails to tick the most important box of all, the so-complicated-that-only-a-handful-of-people-with-17-PhDs-each-can-understand-it box. Silly us!

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Control Reversal

There's a well known phenomenon in aerodynamics in which a plane's flight controls appear to do the opposite of what is intended. This can happen at high speed, for example. (I have a vague memory of a movie supposedly about Chuck Yeager breaking the sound barrier, and there being a tense moment in which our hero had to decide which way to move the controls. Should he pull them the traditional way as advised by all his colleagues? Or do the opposite as his instinct said? Obviously he followed his instincts! I don't know how true any of that is!) This inspires the obvious thought...

Raise interest rates.

I'm not suggesting that there is any link between economics and aerodynamics. And my position on economics has been documented. So don't necessarily believe anything I say on the subject. However, there can be no doubt about the pointlessness of continuing to decrease interest rates. It has become a joke; 1%, 0.5%,... This strategy is about as effective as a visit to a witchdoctor.

If governments are in the business of bailing out more and more banks, and if they are about to start printing money/quantitative easing then raise interest rates at the same time. Bring back some semblance of normality for the man in the street.

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Copulas and Cults

Felix Salmon has written an interesting piece on the copula model. Naturally the model does not come out well. He quotes me, accurately, as disapproving, to put it mildly, of models that depend on correlations between companies.

But that's only part of the problem. Far more serious, because it extends to all of finance not just to a single model, is the poor education that people get in university financial engineering programs and also the blind-following-the-blind behaviour that is so common throughout the industry.

The copula model is not robust to changes in model assumptions. Black-Scholes is. Did you know that? Or maybe I'm wrong. Would you like to know the truth?

Yes, I could tell you. I could spoonfeed you. You've got used to being spoonfed, haven't you? But you're passing the buck there, putting an awful lot of responsibility on my shoulders. I can cope, as I'm sure David Li can cope. But you're a big boy/girl now, you should be able to think for yourself. Isn't that part of your job description?

It's getting quite tedious me telling people to get off their backsides and test the models for themselves. Don't believe anything I say, don't believe anything Nassim, also quoted in the Salmon article, says. Question everything. Switch your brains back on.

In the late 1970s I had the dubious pleasure of attending a Billy Graham evangelical event for the followers of the christian cult, as a guest of some born-again nutters. Over the last decade I have had the equally dubious pleasure of attending many conferences on credit, listening to various academics, let's say "Professor X," for example, preaching about the copula cult. I use the word 'cult' in this context because of the similarities between the unthinking adoration I witnessed at both types of event. I found the Billy Graham event hilarious, I found the credit events disturbing. In both cases the audiences were intelligent people, in both cases there was only one non-sheep among them: me.

Paul Volcker recently spoke about financial engineering and it being, er, not quite what it's made out to be. Setting aside the obvious discussion of what took him, and so many others, so long to realise this, he did make one point that matches my experience. And that is the use of the "Nuremberg Defence" by financial engineers, "Don't blame me, I was only following orders." I agree with Volcker that this is pathetic. And I've heard the same excuse from hundreds of people over the years, well before the recent crisis. I will be teaching people about the boundless possibilities of mathematical modelling, far beyond anything in most textbooks and certainly beyond anything in university programs, or I'll be explaining the dangers of Value at Risk, etc. and the audience will almost invariably say that they'd like to try out the new ideas when they get back to their office...but...but...but they won't be allowed to because the bank's policy is to use 'here insert name of stupid model that they've never properly tested.'

Gentlemen, and ladies, look in the bottom drawer, or wherever it is that you put them, and get out and dust off your cojones. Stand up, be counted, and stop bleating.

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How Are Those Toxic Contracts Coming Along, Guys?

When it was first proposed that banks should put all their troubled or toxic assets into separate banks or vehicles I bet some of you smarter quants were jumping for joy. Up until then you’d been playing that harmless game of “Invent a toxic contract that gives you a big bonus after one year but which blows up as soon as you have moved to another bank.” A pleasant enough game, but one that, it could be argued, had become just a little too easy, perhaps not as challenging as it had once been.

Anyway, along come the politicians who quite frankly know nothing about derivatives and risk management and they propose this plan that on the face of it looks reasonable. But to the quant it’s a very similar game to the one that they’d played before. All you have to do is invent new contracts that are sufficiently complicated that they might pose a danger, they don’t even have to be contracts with any meaningful economic justification anymore. The contract has to be ‘difficult to value.’ But what’s difficult to a government accountant is going to be easy for you guys! Once you’ve come up with a suitable contract, just sell it to a friend at another bank. Pocket the money. And then your friends says “Ohmigod, what have I bought?” And he puts it into the troubled-asset depository. Then you swap roles so he gets to trouser the cash. Result…everyone’s a winner. I leave you to work out the details. You may want to speak to a lawyer first.

There are a couple of plans on the table. Which do you think is better?

Plan A: Put all toxic contracts into separate banks/vehicles. Winners: Bankers. Losers: Taxpayer.

Plan B: Nationalize banks and change accountancy rules. Winners: Taxpayer. Losers: Bankers. (See Moral Hazard for the Masses.)

I think I can guess which one the UK government will go for, judging by their past record!

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In Praise of Ponzi

Well not really, of course. But there are some people quietly sitting pretty...

As it becomes generally accepted that the economy of the west is a giant Ponzi scheme, one should reflect on its positive aspects. The last fifty years, from "We have never had it so good" to the calm-before-the-storm's "No more boom and bust," have been considered by many to be golden years compared with the world war-torn decades before, and the iniquities of times before that.

We know all about those who suffered at the hands of Bernie Madoff's Ponzi scheme, those such as Steven Spielberg, Kevin Bacon, and Zsa Zsa Gabor. But where are all those who made money? It wouldn't be a Ponzi scheme if some people didn't profit.

There must be a few celebs who are feeling uncomfortable right now. They are keeping very quiet. But why? They are the lucky ones who are simply benefitting from the Modern Economics, as espoused by many Modern Politicians and Modern Economists.

The secret to benefitting from a Ponzi scheme is knowing when to get out, and who to leave behind to pick up the mess. Just ask multi-millionaire, style without substance, form without function, Tony Blair. I hear that he's looking very cheerful these days.

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P.S. It wouldn't surprise me in the run-up to the Oscars if a few rumours started appearing about some nominees being winners in the Madoff affair, such is the dirty-trickery that now accompanies this event!

Bailouts, Ponzi Schemes and Green Issues

The Lord of Darkness, Peter Mandelson, and I went to the same college, I am embarrassed to admit. (No, I could not have taken the opportunity to push a stake through his heart because he was there a few years before me and our paths did not cross. A pity.) He is now keen to spend billions bailing out our mainly foreign-owned car industry. Seems like yet another waste of money. Funny how you get used to them. “Bailout fatigue”? Looking along the streets it seems that we have more than enough cars already. I know I do, having three myself. Never mind when they are being driven around, you can hardly move for all the space they take up when parked. At least my cars are gorgeous to look at! I can’t help thinking that the car industry, like so much of the economy of the first world, is another Ponzi scheme. We have to keep buying and buying in order to maintain a status quo. We stop buying and everything collapses. There’s an argument here for spending less on ‘stuff’ and more on services, especially those services which are not harmful to the environment as opposed to the manufacture of the stuff that is. I pretty much already have all the possessions I will ever need.

Stop all manufacturing of cars now, unless they meet serious green criteria. And I don’t mean the tiny increases in miles per gallon that you might get from some hybrid over a petrol engine, I mean order of magnitude decreases in pollutants. Not that I particularly care about global warming, I think there are far worse things going to happen in the next decade that will make the global-warming fuss look a bit silly. But I do object to the use of global warming as justification for producing more cars. Stop making new cars until they are truly green, and just mend the old ones if they break down. Until you’ve owned a classic car you can’t fully appreciate the joys of driving for just 15 minutes before having to call out a mechanic!

This reminds me of the Scottish author Iain Banks, a famous petrolhead, who recently sold his collection of classic cars and replaced them with a single hybrid. He used to have a Porsche 911 Turbo, a Porsche Boxster S, a BMW M5 and a Land Rover Discovery. And he bought a Lexus SUV hybrid instead.

Am I alone in thinking this counterproductive?

First he says that he’s getting about 28.5mpg out of the Lexus as opposed to the “low 20s” he got from Porsches and the BMW. See what I mean? The marginal improvement probably did not outweigh the damage caused by the manufacture of the Lexus in the first place.

And, second, it is not humanly possible for Iain Banks, brilliant author though he may be, to drive more than one car at a time. So now there are five gas-guzzling cars on the roads, possibly all at the same time, when before there was just one.

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Financial Modelers' Manifesto

The Financial Modelers' Manifesto

Preface

A spectre is haunting Markets – the spectre of illiquidity, frozen credit, and the failure of financial models.

Beginning with the 2007 collapse in subprime mortgages, financial markets have shifted to new regimes characterized by violent movements, epidemics of contagion from market to market, and almost unimaginable anomalies (who would have ever thought that swap spreads to Treasuries could go negative?). Familiar valuation models have become increasingly unreliable. Where is the risk manager that has not ascribed his losses to a once-in-a-century tsunami?

To this end, we have assembled in New York City and written the following manifesto.

Manifesto

In finance we study how to manage funds – from simple securities like dollars and yen, stocks and bonds to complex ones like futures and options, subprime CDOs and credit default swaps. We build financial models to estimate the fair value of securities, to estimate their risks and to show how those risks can be controlled. How can a model tell you the value of a security? And how did these models fail so badly in the case of the subprime CDO market?

Physics, because of its astonishing success at predicting the future behavior of material objects from their present state, has inspired most financial modeling. Physicists study the world by repeating the same experiments over and over again to discover forces and their almost magical mathematical laws. Galileo dropped balls off the leaning tower, giant teams in Geneva collide protons on protons, over and over again. If a law is proposed and its predictions contradict experiments, it's back to the drawing board. The method works. The laws of atomic physics are accurate to more than ten decimal places.

It's a different story with finance and economics, which are concerned with the mental world of monetary value. Financial theory has tried hard to emulate the style and elegance of physics in order to discover its own laws. But markets are made of people, who are influenced by events, by their ephemeral feelings about events and by their expectations of other people's feelings. The truth is that there are no fundamental laws in finance. And even if there were, there is no way to run repeatable experiments to verify them.

You can hardly find a better example of confusedly elegant modeling than models of CDOs. The CDO research papers apply abstract probability theory to the price co-movements of thousands of mortgages. The relationships between so many mortgages can be vastly complex. The modelers, having built up their fantastical theory, need to make it useable; they resort to sweeping under the model's rug all unknown dynamics; with the dirt ignored, all that's left is a single number, called the default correlation. From the sublime to the elegantly ridiculous: all uncertainty is reduced to a single parameter that, when entered into the model by a trader, produces a CDO value. This over-reliance on probability and statistics is a severe limitation. Statistics is shallow description, quite unlike the deeper cause and effect of physics, and can’t easily capture the complex dynamics of default.

Models are at bottom tools for approximate thinking; they serve to transform your intuition about the future into a price for a security today. It’s easier to think intuitively about future housing prices, default rates and default correlations than it is about CDO prices. CDO models turn your guess about future housing prices, mortgage default rates and a simplistic default correlation into the model’s output: a current CDO price.

Our experience in the financial arena has taught us to be very humble in applying mathematics to markets, and to be extremely wary of ambitious theories, which are in the end trying to model human behavior. We like simplicity, but we like to remember that it is our models that are simple, not the world.

Unfortunately, the teachers of finance haven’t learned these lessons. You have only to glance at business school textbooks on finance to discover stilts of mathematical axioms supporting a house of numbered theorems, lemmas and results. Who would think that the textbook is at bottom dealing with people and money? It should be obvious to anyone with common sense that every financial axiom is wrong, and that finance can never in its wildest dreams be Euclid. Different endeavors, as Aristotle wrote, require different degrees of precision. Finance is not one of the natural sciences, and its invisible worm is its dark secret love of mathematical elegance and too much exactitude.

We do need models and mathematics – you cannot think about finance and economics without them – but one must never forget that models are not the world. Whenever we make a model of something involving human beings, we are trying to force the ugly stepsister’s foot into Cinderella’s pretty glass slipper. It doesn't fit without cutting off some essential parts. And in cutting off parts for the sake of beauty and precision, models inevitably mask the true risk rather than exposing it. The most important question about any financial model is how wrong it is likely to be, and how useful it is despite its assumptions. You must start with models and then overlay them with common sense and experience.

Many academics imagine that one beautiful day we will find the ‘right’ model. But there is no right model, because the world changes in response to the ones we use. Progress in financial modeling is fleeting and temporary. Markets change and newer models become necessary. Simple clear models with explicit assumptions about small numbers of variables are therefore the best way to leverage your intuition without deluding yourself.

All models sweep dirt under the rug. A good model makes the absence of the dirt visible. In this regard, we believe that the Black-Scholes model of options valuation, now often unjustly maligned, is a model for models; it is clear and robust. Clear, because it is based on true engineering; it tells you how to manufacture an option out of stocks and bonds and what that will cost you, under ideal dirt-free circumstances that it defines. Its method of valuation is analogous to figuring out the price of a can of fruit salad from the cost of fruit, sugar, labor and transportation. The world of markets doesn’t exactly match the ideal circumstances Black-Scholes requires, but the model is robust because it allows an intelligent trader to qualitatively adjust for those mismatches. You know what you are assuming when you use the model, and you know exactly what has been swept out of view.

Building financial models is challenging and worthwhile: you need to combine the qualitative and the quantitative, imagination and observation, art and science, all in the service of finding approximate patterns in the behavior of markets and securities. The greatest danger is the age-old sin of idolatry. Financial markets are alive but a model, however beautiful, is an artifice. No matter how hard you try, you will not be able to breathe life into it. To confuse the model with the world is to embrace a future disaster driven by the belief that humans obey mathematical rules.

MODELERS OF ALL MARKETS, UNITE! You have nothing to lose but your illusions.

The Modelers' Hippocratic Oath

~ I will remember that I didn't make the world, and it doesn't satisfy my equations.

~ Though I will use models boldly to estimate value, I will not be overly impressed by mathematics.

~ I will never sacrifice reality for elegance without explaining why I have done so.

~ Nor will I give the people who use my model false comfort about its accuracy. Instead, I will make explicit its assumptions and oversights.

~ I understand that my work may have enormous effects on society and the economy, many of them beyond my comprehension.

       

Emanuel Derman and Paul Wilmott January 7 2009

Please join in the discussion of this Manifesto here.

Economics Makes My Brain Hurt

A friend of mine, you may know him, you certainly know ‘of’ him, has called for the return of a couple of economics Nobel Prizes. It’s Nassim Nicholas Taleb, in case you didn’t know. (I mention his name because it may increase the number of times this blog is read thanks to Google!) I’m not fussed one way or the other whether or not they get to keep their prizes, I don’t really see much difference between their work and that of many of the others awarded the economics Nobel. (Yes, I know, it’s not a proper Nobel, blah, blah, blah, Bank of Sweden, blah, blah, we can take that much as read!) Or even those awarded the prize in other fields. The Nobel Prize for Literature seems to be political (political meaning either greasy pole, or as in politically correct), the Peace Prize is downright perverse, so the Economics Prize is no different for being pointless. In contrast, we probably all respect laureates in medicine, chemistry and physics for mostly decent work that has stood the test of time.

Economics is a queer subject. I like to boil things down to the very basics whenever I am trying to learn something new, doing research or teaching, as the students on the CQF can attest—think of some of my stranger analogies, guys! But this doesn’t work with economics. Starting with a couple of blokes in a cave, one of whom has just invented the wheel, try to imagine the exchanges that take place and how that turns into General Motors. No, it makes my brain hurt. No matter how much red wine I’ve drunk it doesn’t seem to work.

And I’m supposed to be clever. Why am I incapable of understanding economics, a straightforward enough subject that it’s even taught in schools?

My failure led me to think about economists, as opposed to economics, and they’re much easier to figure out. This is how it works. An economist starts with a few axioms, ones that bear a vague similarity to a small part of the human condition under restricted situations and in an idealized world. (You get my drift here?) From those axioms follows a theorem. More often than not this will be a theorem based upon rational behaviour. That theorem gets a name. And that’s the point I identify as being the problem: The jargonizing of complex ideas based upon irrelevant assumptions into an easily used and abused building block on which to build the edifice of nonsense that is modern economics.

Small assumption by small assumption, the economist builds up his theories into useless gibberish. By acceptance of each step he is able to kid himself he is making progress. And that’s why I struggle with economics. It is not mathematics where, barring mistakes, each step is true and indisputable and therefore you can accept it, even forget it, and move on. And others can do the same, using everyone else’s results without question. This you cannot do in a soft science. I’ve mentioned this in another blog, beware of anyone talking about ‘results’ in finance or economics, it says more about them and their perception of the world than it does about the subject.

Not so long ago Alan Greenspan famously said he had found a flaw in the “critical functioning structure that defines how the world works.” “I don't know how significant or permanent it is but I have been very distressed by that fact.” Ohmigod! His naivety and lack of self knowledge is staggering. He has fallen into the same trap as other economists. By believing the theories he has believed the axioms on which they are based. The edifice of nonsense has collapsed on top of one of its builders.

You beautiful, complex, irrational people! Please, promise me that you will continue to violate every axiom and assumption of economics, maybe not all the time, that would be too predictable, but now and then, just so as to keep those pesky economists on their toes!

Greenspan also said that risk models and econometric models are still too simple. Lord, help us!

Let me tell you a story.

A decade or so ago I was browsing through the library of Imperial College, London, when I happened upon a book called something like “The Treasury’s Model of the UK Economy.” It was about one inch thick and full of difference equations. Seven hundred and seventy of them, one for each of 770 incredibly important economic variables. There was an equation for the rate of inflation, one for the dollar-sterling exchange rate, others for each of the short-term and long-term interest rates, there was the price of fish, etc. etc. (The last one I made up. I hope.) Could that be a good model with reliable forecasts? Consider how many parameters must be needed, every one impossible to measure accurately, every one unstable. I can’t remember whether these were linear or non-linear difference equations, but every undergrad mathematician knows that you can get chaos with a single non-linear difference equation so think of the output you might get from 770. Putting myself in the mind of the Treasury economists I think “Hmm, maybe the results of the model are so bad that we need an extra variable. Yes, that’s it, if we can find the 771st equation then the model will finally be perfect.” No, gentlemen of the Treasury, that is not right. What you want to do is throw away all but the half dozen most important equations and then accept the inevitable, that the results won’t be perfect.

A short distance away on the same shelf was the model of the Venezuelan economy. This was a much thinner book with a mere 160 equations. Again I can imagine the Venezuelan economists saying to each other, “Amigos, one day we too will have as many equations as those British cabrones, no?” No, what you want to do is strip down the 160 equations you’ve got to the most important. In Venezuela maybe it’s just one equation, for the price of oil.

We don’t need more complex economics models. Nor do we need that fourteenth stochastic variable in finance. We need simplicity and robustness. We need to accept that the models of human behaviour will never be perfect. We need to accept all that, and then build in a nice safety margin in our forecasts, prices and measures of risk.

Happy New Year!

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Ponzi Schemes, Auditors, Regulators, Credit Ratings, And Other Scams

There are honest people, and there are dishonest people, a whole spectrum. I like to think I'm near the honest end, I would have worn a white hat in the old cowboy movies. And I've had the misfortune to have met a few from right up close to the other extreme, with the black hats. Most people wear hats of various shades of grey. High finance is a business which encourages people to shift towards the dishonest end of the spectrum by putting temptation in their way, and the dishonest are drawn to this field by its quick and easy rewards.

Nothing that I have ever seen in investment banking and fund management has impressed me as a disincentive to crooked behaviour, absolutely nothing.

As a keen observer of human behaviour I have been fascinated watching people's attitude towards money. In academia they struggle with their mixed feelings, on the one hand hating the filthy stuff since they are supposed to be above such worldly matters, but on the other hand rather liking what they can do with it. The really rich see it as nothing more than a measure of their success in life, a score. Some balanced people, few and far between, realise they need it, and that more is better than less, but it's not the main focus in their lives. Then there is the common greed that we see in our business, nasty and unpleasant. And nasty, unpleasant greed is so easy to feed, it is encouraged in banking, but it has some unpleasant side effects.

The Madoff affair has highlighted several things, brought some corrupt practices to light, but we haven't really learned anything new from all of this. The old lessons, the ones that should have been learned years ago, are just as valid. As I keep saying, there is little reason for regulators to do anything: People have short memories; People are easily distracted; The legal system is now much better at protecting the guilty than protecting the innocent.

Just like the Social Services in the UK, regulators do such a useless job that they are now permanently on the defensive. I bet you that few people working for regulators are doing their jobs right now, I bet most of their day is spent figuring out how to protect themselves against the growing backlash.

Quite frankly I don't see much difference between Madoff's Ponzi scheme and naive auditors, self-serving regulators and morally corrupt ratings agencies. They are all part of a financial system that encourages scams, scams that may then take years to sort out and years before the culprits are punished, meanwhile out on comfortable bail. The US legal system is particularly easy to 'play' so as to drag proceedings out so long that the accused dies of natural causes before justice is done.

There is no disincentive for dishonest behaviour in investment banking at the moment, in fact the opposite. If someone wants to invest with a manager they think might be dishonest but successful then they will ignore the dishonesty. If the investor loses their shirt then tough, serves them right. (Of course, it won't be their money, so anyone found not having done their full due diligence ought to be arrested.) I know of several people who manage money who have broken serious laws, lawbreaking that would prevent them managing money. And I know of some investors who know that I know, but who, when considering investing with these people, deliberately do not ask for my opinion as part of their due diligence. Why not? Because once they hear what I have to say then they would no longer be able to invest with the crooked, but oh-so-smooth and convincing manager. If you've ever bought a dodgy DVD at the market, or a hi-fi from a man in the pub, then you are just as culpable. And you therefore might find some sympathy for a lot of people being blamed at the moment. I haven't, and I don't.

When I first realised, several years ago, that due diligence is deliberately not being done I proposed that formal psychometric testing be part of the process of setting up a hedge fund or managing money. I know this is easy to criticize or trivialize, especially by all the 'left-brainers' working in finance. But equally I'm not a great fan of having to pass multiple-choice exams to get letters after your name showing how many regulations you know, I don't think this has much relevance today. But in this business trust is so important. In a world where we never get to know the people looking after our life savings, as we might have done in the old days, I can think of no other simple indicator of testing trustworthiness. Some people are dishonest, some can't be trusted. Do you care? I do, and always have. Maybe other people don't, that's greed at work, but they will eventually, perhaps only after they've lost lots and lots of money.

P

Magicians And Mathematicians

Quantitative finance and risk management are not just about the numbers. Numbers play a part, but so does the human side of the business. When analyzing risk it is important to be able to think creatively about scenarios. Unfortunately the training that most quants get seems to actively discourage creativity.

Some of the following appeared on the BBC website in December 2008.

We've learned the hard way how important it is to measure and manage risk. Despite the thousands of mathematics and science PhDs working in risk management nowadays we seem to be at greater financial and economic risk than ever before. To show you one important side of banking I'd like you to follow me in an exercise with parallels in risk management.

You are in the audience at a small, intimate theatre, watching a magic show. The magician hands a pack of cards to a random member of the audience, asks him to check that it's an ordinary pack, and would he please give it a shuffle. The magician turns to another member of the audience and asks her to name a card at random. "Ace of Hearts," she says. The magician covers his eyes, reaches out to the pack of cards, and after some fumbling around he pulls out a card. The question to you is what is the probability of the card being the Ace of Hearts?

Think about this question while I talk a bit about risk management. Feel free to interrupt me as soon as you have an answer. Oh, you already have an answer? What is that, one in fifty two, you say? On the grounds that there are 52 cards in an ordinary pack. It certainly is one answer. But aren't you missing something, possibly crucial, in the question? Ponder a bit more.

One aspect of risk management is that of 'scenario analysis.' Risk managers in banks have to consider possible future scenarios and the effects they will have on their bank's portfolio. Assign probabilities to each event and you can estimate the distribution of future profit and loss. Not unlike our exercise with the cards. Of course, this is only as useful as the number of scenarios you can think of.

You have another answer for me already? You'd forgotten that it was a magician pulling out the card. Well, yes, I can see that might make a difference. So your answer is now that it will be almost 100% that the card will be the Ace of Hearts, the magician is hardly going to get this trick wrong. Are you right? Well, think just a while longer while I tell you more about risk and its management.

Sometimes the impact of a scenario is quite easy to estimate. For example, if interest rates rise by 1% then the bank's portfolio will fall in value by so many hundreds of millions. But estimating the probability of that interest rate rise in the first case might be quite tricky. And more complex scenarios might not even be considered. What about the effects of combining rising interest rates, rising mortgage defaults and falling house prices in America? Hmm, it's rather looking like that scenario didn't get the appreciation it deserved.

Back to our magician friend. Are those the only two possible answers? Either one in 52 or 100%? Suppose that you had billions of dollars of hedge fund money riding on the outcome of this magic trick would you feel so confident in your answers? When I ask this question of finance people I usually get either the one in 52 answer or the 100%. Some will completely ignore the word 'magician,' hence the first answer. Some will say "I'm supposed to give the maths answer, aren't I? But because he's a magician he will certainly pick the Ace of Hearts." This is usually accompanied by an aren't-I-clever smile! Rather frighteningly, some people trained in the higher mathematics of risk management still don't see the second answer even after being told.

This is really a question about whether modern risk managers are capable of thinking beyond maths and formulas. Do they appreciate the human side of finance, the herding behaviour of people, the unintended consequences, what I think of as all the fun stuff. And this is a nice question because it very quickly sorts out different types of thinkers.

There is no correct answer to our magician problem. The exercise is to think of as many possibilities as you can. For example when I first heard this question an obvious answer to me was zero. There is no chance that the card is the Ace of Hearts. This trick is too simple for any professional magician. Maybe the trick is a small part of a larger effect, getting this part 'wrong' is designed to make a later feat more impressive...the Ace of Hearts is later found inside someone's pocket. Or maybe on the card are written the winning lottery numbers that are drawn randomly 15 minutes later on live TV. Or maybe the magician was Tommy Cooper. Or it was all the magician's performance-anxiety dream the night before. When I ask non mathematicians this is the sort of answer I get.

The answer one in 52 is almost the answer least likely to be correct! Magicians only rarely rely on probability. Clue: How many times did Houdini die during his Water Tiorture trick? (Unless the magician was using an ordinary deck of cards, was aiming to pull out a different card but accidentally pulled out the Ace of Hearts instead! Accidentally not making the intended 'mistake.')

A member of wilmott.com didn't believe me when I said how many people get stuck on the one in 52 answer, and can't see the 100% answer, never mind the more interesting answers. He wrote "I can't believe anyone (who has a masters/phd anyway) would actually say 1/52, and not consider that this is not...a random pick?" So he asked some of his colleagues the question, and his experience was the same as mine. He wrote "Ok I tried this question in the office (a maths postgraduate dept), the first guy took a fair bit of convincing that it wasn't 1/52 !, then the next person (a hardcore pure mathematician) declared it an un-interesting problem, once he realised that there was essentially a human element to the problem! Maybe you have a point!" Does that not send shivers down your spine, it does mine.

Once you start thinking outside the box of mathematical theories the possibilities are endless. And although a knowledge of advanced mathematics is important in modern finance I do rather miss the days when banking was populated by managers with degrees in History and who'd been leaders of the school debating team. A lot of mathematics is no substitute for a little bit of commonsense and an open mind.

How can we get quants and risk managers to think beyond the mathematics? I'm afraid I don't think we can, the way the majority of them are currently educated.

P

Frustration

As you will no doubt know, I have been frustrated by quants for a long, long time. Their modelling of markets is a strange combination of the childishly naïve and the absurdly abstract.

On a one-to-one basis many people working in banks will complain to me about the models they have to implement. They will complain about instability of the Heston volatility model for example. I will explain to them why it is unstable, why they shouldn't be using it, what they can do that's better and they will respond along the lines of "I agree, but I don't have any choice in the matter." Senior quants are clearly insisting on implementations that those on the front line know are unworkable.

And a large number of people complain to me in private about what I have started calling the 'Measure Theory Police.' These 'Police' write papers filled with jargon, taking 30 pages to do what proper mathematicians could do in four pages. They won’t listen to commonsense unless it starts with 'Theorem,' contains a 'Proof,' and ends with a 'QED.' I'll write in detail about the Measure Theory Police at a later date, but in the meantime will all those people complaining to me about them please speak up...you are preaching to the converted, go spread the word!

For several years I tried to argue scientifically, in papers, book, seminars, etc. about all the abysmal modelling I saw. Of all the conferences that I speak at, you would think that quant events would be the ones at which the audience would have the best appreciation of good versus bad modelling. Frustratingly, quant conferences have audiences with great technical skills but the least imagination. If you're not lecturing about the wonders of correlation, but about the stupidity of correlation, then expect a hostile ride. But I battled on, I have a very tough skin!

Then I thought I'd try a different tack. If data, scientific explanations and commonsense won't get the truth across then something else was required. (It turns out that the 'something else' was losses of trillions of dollars and a global recession!)

So I started introducing audiences to relevant aspects of human psychology. I explained about the famous experiments in peer pressure to highlight why people were adopting the same models as everyone else. I explained about the famous experiments in diffusion of responsibility, mentioned recently in an article by Taleb and Triana, so that people would understand why they were sitting around not doing anything about the terrible state of affairs. Perhaps a little bit of cognitive behavioural therapy might help them understand their own motives and this would bring about a change of practice in finance. Of course, I was overambitious. Audiences were entertained and amused, a good time was had by all. And then they went back to their day jobs and the implementation of the same old copula nonsense.

Combine peer pressure with diffusion of responsibility and fear for their jobs and most people will keep quiet. Sad, but expected and, reluctantly I will admit, understandable.

What is not understandable is the role in recent events played by regulators and rating agencies. Their jobs are not to toe the party line. The job of the regulator is to hold up the yellow card to banks with bad practices and the job of the rating agencies is to give an honest assessment of creditworthiness. In neither case should they have been effectively colluding with banks in increasing the amount of risk taken.

I have an analogy for you.

A rating agency or a regulator visits a bank. They are being shown around the premises, looking at all the products they have and how they are managed. They come to one desk on which there is a pile of nuclear material. "That's a large pile of nuclear material. How much does it weigh?" they ask. "Oh, nothing to worry about, only half the critical mass," comes the reply. They go on to the next desk and see a similar pile. "Nothing to worry about, only half the critical mass." They go next door to another bank, and they see the same story. It doesn't take a genius to see the potential risks. The regulators and the credit rating agencies saw something similar, with CDOs and the like being the explosive material.

In the early days of the current crisis the talk was of blame. That was precisely the wrong thing to consider at that time. Shore up the financial system asap, that was the most important thing to do. A quick response was what mattered, the details didn't. Now is the time to start considering blame and punishment. And yes, there has to be punishment. You cannot have obscene rewards for those working in banking, salaries tens or hundreds of times the national averages without expecting and demanding corresponding responsible behaviour. It is both morally objectionable and financially dangerous to not have the huge upside balanced by a matching downside for irresponsible actions. And so I point the finger at rating agencies and regulators as those near the top of those who must take the blame.

Realistically I expect further frustration and a return to business as usual.

P

Myers Briggs And Quants - A Survey

We are curious to find out about the personality types working within quantitative finance, risk management, development, etc. So we'd like you to tell us your type!

Take the test here http://www.humanmetrics.com/cgi-win/JTypes2.asp, it will only take 5 minutes. When you've finished return to us here http://www.wilmott.com/mbti.cfm and put your result in the box. (You must be logged on to wilmott.com.)

Thanks for your help! We will report the results (keeping you anonymous, of course!) as soon as we have sufficient data.

About Myers-Briggs: According to wikipedia, the Myers-Briggs Type Indicator (MBTI) assessment is a psychometric questionnaire designed to measure psychological preferences in how people perceive the world and make decisions.

Actuaries Versus Quants

The following article was written in August 2008 for The Actuary magazine. I was reminded of it by the responses to our Name and Shame Blame Game.

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Those working in the two fields of actuarial science and quantitative finance have not always been totally appreciative of each others’ skills. Actuaries have been dealing with randomness and risk in finance for centuries. Quants are the relative newcomers, with all their fancy stochastic mathematics. Rather annoyingly for actuaries, quants come along late in the game and thanks to one piece of insight in the early ‘70s completely change the face of the valuation of risk. The insight I refer to is the concept of dynamic hedging, first published by Black, Scholes and Merton in 1973. Before 1973 derivatives were being valued using the “actuarial method,” i.e. in a sense relying, as actuaries always have, on the Central Limit Theorem. Since 1973 and the publication of the famous papers, all that has been made redundant. Quants have ruled the financial roost.

But this might just be the time for actuaries to fight back.

I am putting the finishing touches to this article a few days after the first anniversary of the “day that quant died.” In early August 2007 a number of high-profile and previously successful quantitative hedge funds suffered large losses. People said that their models “just stopped working.” The year since has been occupied with a lot of soul searching by quants, how could this happen when they’ve got such incredible models?

In my view the main reason why quantitative finance is in a mess is because of complexity and obscurity. Quants are making their models increasingly complicated, in the belief that they are making improvements. This is not the case. More often than not each ‘improvement’ is a step backwards. If this were a proper hard science then there would be a reason for trying to perfect models. But finance is not a hard science, one in which you can conduct experiments for which the results are repeatable. Finance, thanks to it being underpinned by human beings and their wonderfully irrational behaviour, is forever changing. It is therefore much better to focus your attention on making the models robust and transparent rather than ever more intricate. As I mentioned in a recent wilmott.com blog, there is a maths sweet spot in quant finance. The models should not be too elementary so as to make it impossible to invent new structured products, but nor should they be so abstract as to be easily misunderstood by all except their inventor (and sometimes even by him), with the obvious and financially dangerous consequences. I teach on the Certificate in Quantitative Finance and in that our goal is to make quant finance practical, understandable and, above all, safe.

When banks sell a contract they do so assuming that it is going to make a profit. They use their complex models, with sophisticated numerical solutions, to come up with the perfect value. Having gone to all that effort for that contract they then throw it into the same pot as all the others and risk manage en masse. The funny thing is that they never know whether each individual contract has “washed its own face.” Sure they know whether the pot has made money, their bonus is tied to it. But each contract? It makes good sense to risk manage all contracts together but it doesn’t make sense to go to such obsessive detail in valuation when ultimately it’s the portfolio that makes money, especially when the basic models are so dodgy. The theory of quant finance and the practice diverge. Money is made by portfolios, not by individual contracts.

In other words, quants make money from the Central Limit Theorem, just like actuaries, it’s just that quants are loath to admit it! Ironic.

It’s about time that actuaries got more involved in quantitative finance. They could bring some common sense back into this field. We need models which people can understand and a greater respect for risk. Actuaries and quants have complementary skill sets. What high finance needs now are precisely those skills that actuaries have, a deep understanding of statistics, an historical perspective, and a willingness to work with data.

Cheese and Globalization

A couple of years ago, at the dinner after one of the courses I teach with Nassim Taleb, I asked the multicultural group of delegates a question that I'd been thinking about and suspected I knew the answer to. Or rather I suspected I knew what certain people's answers would be, the correct answer I still don't know. The question was "How many different types of cheese are there in the world?"

Now when I just said that I suspected I knew what certain people would say, those certain people are Americans. Around the table were folk from all over Europe, Australia, one from Iceland, and some Americans. So I asked the question of one of the Americans. He did not disappoint, and he gave the answer that I expected, but feared. His answer was "Seven or eight."

Had I asked for the names of the seven or eight I would probably have got the answer "Cheez Wiz, cheese slices,...and Monterey Jack." If you are from Europe you will have a better idea of the correct answer, which I suspect is in the thousands.

Now I love America and Americans so much that I married one. But the uniformity of the tastes of this large, rich country, or any, large, rich country, has the potential to damage smaller producers of niche products. Combine uniform tastes with easy global transport and hypermarkets within reach of everyone and you've got a recipe for evolution towards blandness. We are told that French wines are suffering from globalization. But then we also hear about record years for French wines. So what is happening?

Timescales are very important here, and we have the competing effects of globalization on the one hand and education on the other, together with the natural timescale for businesses to grow or collapse. Which will win?

It would be a shame if cheese or wine were to suffer, since I fully intend my retirement years to be spent sitting by a pool, somewhere warm, catching up on my reading, while working my way through the wines and cheeses of the world!

Finally, a question for you, how many varieties of apple are there? (Not that I care much for fruit or veg, where I come from chips count as one of my five portions per day!)

P

Hedge Funds: The Future

Word on the street and common sense suggest the following short- and medium-term future for hedge funds:

1) On average hedge funds will probably have done not much better or worse than the market as a whole. However, that average performance will hide a lot of extremes. Many funds, thanks to lady luck and leverage will be up record amounts. But that means many funds will be down record amounts too, and the downside is severely limited by zero! Therefore expect to see many funds announcing blow ups soon, maybe 30% of funds will close up shop for one reason or another.

2) After the blow ups expect to see the lawsuits. There will be many managers who have broken the terms of their prospectuses, many will have taken risks that they ought not to have taken. If they made money then they'll get away with it, if they've lost money then they will be on the wrong end of suits for damages. (Not that there's ever really a right end of a lawsuit!) And there will also be opportunistic suits in cases where no wrong has been done. In the US anybody can sue anyone for anything remember. There will be a three- to six-month delay between the big losses and the big lawsuits. They will take many years before they are completed.

3) When the dust has settled expect to see small, boutique funds being popular. They will have managers with very specialised experience and they will work closely with investors. There will necessarily be more transparency. Because investors will have the upper hand in negotiations leading up to investments expect to see investors taking a shareholding in hedge funds.

The above is what probably will happen. Now for something I personally would like to see happen.

For several years now I have been advising that potential investors in funds really need to take their due diligence far more seriously than they do at the moment. Current practice is that if an investor is very keen on a particular fund, perhaps because of a very persuasive salesman, then they tend not to perform as many background checks as they ought. The reason is simple, if they do the checks then they might find something that means they are unable to invest, therefore they reckon it's better if they don't do the checks. This leaves them the freedom to invest where they want. This is naive and dangerous.

In any random walk through life one encounters people who should not be left in charge of a pair of scissors never mind billions of dollars. These are people who, following formative experiences, are excessively risk seeking, or panic in a crisis, or who have a false idea of their own talents or who are simply dishonest. You may be unlucky enough to meet one person with all of these characteristics! Put this person in a sharp suit, send them to how-to-be-a-fund-manager finishing school and, hey presto, you’ve got a front-page Wall Street Journal scandal. There are a lot of clever people out there, people of talent, but how can you tell them from the disasters in waiting? I would very strongly advise that investors take the background checking far more seriously than at present. Speak to managers' colleagues, partners in previous funds, previous employers and previous employees, etc. Double and triple check CVs and qualifications.

I doubt whether it will catch on, sadly, but I’ve also been advocating for years that there should be a process of psychometric testing, along the line of Myers-Briggs, for fund managers. This is actually not uncommon in other business scenarios involving large loans, buyouts, etc. and ought to be standard practice for any position of serious responsibility.

P

Hedge Fund Blow Ups - Any Day Now!

Yesterday I was speaking at a hedge fund conference. On a discussion panel with me were some very eminent hedge fund managers. When asked their returns all of them said ten, 15, 20 percent this year. Perfectly normal numbers. It seemed strange to hear such normal numbers at a time of such abnormal markets.

Maybe that was because the specially picked panel was made up of sensible and respectable managers, those who would do well, and importantly, act conservatively, whatever the state of the markets.

But such managers are unfortunately rather rare.

While highly regulated banks can collapse any day of the month, hedge funds tend to report their performance on a monthly basis and can sometimes cling on to life, limping along until they can keep the sorry state of their business secret no longer. With the wild swings in the market of late it seems reasonable that it won't be too long before we start hearing about the collapsing of hedge funds, and maybe some big names among them.

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Serial Autocorrelation And Derivatives

Very, very few people have published on the subject of serial autocorrelation (SAC) and derivatives pricing and hedging. Being a specialist in doing things that are important rather than doing what everyone else does, I am obviously one of those few!

The figure shows the 252-day rolling SAC for the Dow Jones Industrial index. It is clear from this that there has been a longstanding trend since the late 1970s going from extremely positive SAC to the current extremely negative SAC. (I imagine you’ve all noticed this lately!) Positive SAC is rather like trend following, negative SAC is rather like profit taking. (I use ‘rather like’ because technically speaking trending is, in s.d.e. terms, the function of the growth or dt term, whereas SAC is in the random term.) The current level has been seen before, in the early thirties, mid 1960s and late 1980s. (Note that what I have plotted here is a very simplistic SAC measure, being just a moving window and therefore with all the well-known faults. The analysis could be improved upon dramatically, but the consequences would not change.)

As far as pricing and hedging of derivatives is concerned there are three main points of interest (as I say, mentioned in very, very few quant books!).

1) The definition of ‘volatility’ is subtly different when there is SAC. The sequence +1, -1, +1, -1, +1, has perfect negative SAC and a volatility of zero! (The difference between volatility with and without SAC is a factor of SQR(1 – rho^2), where rho is the SAC coefficient.

2) If we can hedge continuously then we don’t care about the probability of the stock rising or falling and so we don’t really care about SAC! (A fun consequence of this is that options paying off SAC always have zero value theoretically.)

3) In practice, however, hedging must be done discretely. And this is where non-zero SAC becomes important. If you expect that a stock will oscillate up and down wildly from one day to the next, like the above +1, -1, +1, -1, example, then what you should do depends on whether you are long or short gamma. If gamma is positive then you trade to capture the extremes if you can. Whereas if you are short gamma then you can wait, because the stock will return to its current level and you will have gained time value. Of course this is very simplistic, and for short gamma positions requires nerves of steel!

That’s just a brief introduction to a much-ignored topic. I hope it will inspire some discussion!

P

Moral Hazard for the Masses!

The current situation is rather like a cross between the two movies Trading Places and Ocean's Eleven. And now that I've finally got (most of) my AIG money back (see this NY Times article for that story!) I can sit back and enjoy the tragedy/comedy as it unfolds.

The old gang is brought together for one last caper (ok, this only makes sense to UK readers who will have seen the Devil himself, Peter Mandelson, returning to slimy power, so forget this bit!), bring down Wall Street fat cats, destroy the financial system, and then heroically restore order while pocketing loads of money.

The timing will have to be perfect, but it can be done.

Step 1: Encourage greed to grow unfettered by regulation, to such an extent that the markets themselves are in danger.

Step 2: Make sure accounting rules, mark to market, encourage feedback and instability.

Step 3: When the inevitable crash occurs just buy up (if you are private sector) or nationalize (if you are public sector) those banks with the right class of assets, those that are most affected by the accounting rules.

Step 4: With the public clamouring for a change of rules and regulation, abandon mark to market in favour of something more 'responsible.' But make sure that the new rules are such that you make an instantaneous killing as they are implemented across all those banks that you rescued.

Result: A big fat profit for all those 'in the know,' and everyone else feels relief that they mostly still have jobs. A win-win situation!

Roll credits.

P

Name and Shame in Our New Blame Game!

We are running a survey.

As a break from blaming anonymous men in suits for the current crisis, can you tell us which quants and which models ought to take some of the responsibility for recent events?

We are collecting names of blameworthy researchers and models here. (You must be logged in to wilmott.com to see this page.) Include as much information as you can about which of the models or methods you think are the most dangerous or just plain useless. Include citations as well if you can! But even if you haven't got the details to hand, please feel free to just give us a name together with any 'advice' for them, polite or otherwise! This can be constructive, we can use this opportunity to promote good modelling, research and numerical methods. But it can also be a way to release tension, especially if you've just lost your job or your savings!

The motivation behind this survey was seeing the usual suspects still speaking at conferences, running workshops, etc. as if nothing has happened. (See an earlier blog.) I will give these people the benefit of the doubt, that maybe they believe their work is of good quality. But there are a lot of people, perhaps the majority, who take the research of these 'leaders in their field' as gospel, they are the poor souls who end up suffering. In the interests of good research please join me in saying that the Emperor has no clothes.

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Congress Fights Over Matters of Great Consequence

Oblivious closely followed by oblivion.

Seen on a Post-It Note in Congress

There are some tough decisions ahead. Not!

Nurse, Hand Me That Scalpel

We all know that the relationship between credit-ratings agencies and the clients they rate is a corrupt one, reeking of moral hazard. Some of us have even laughed when told that a company is triple-A rated. “How much did they have to pay for that worthless piece of paper?” we’ve joked.

I have an analogy for you. This scandalous situation would be rather like having a doctor being rewarded for finding you ill. Unscrupulous doctors might imagine that you are suffering from all sorts of serious maladies, when in fact all you’ve got is an allergy to cats. Unfortunately, this mild condition only comes to light after many thousands of dollars worth of tests and treatments, paid for by you or by your insurance, i.e. you, or by the taxpayer, i.e. you. That would be a crazy system, wouldn’t it?!

What’s that I hear you say? This is how the medical system works in the US? Now I love America but it does have a hopeless medical structure: America has the highest per capita expenditure on healthcare in the world yet is 70th in level of health. Americans have lived, and died prematurely, with moral hazard for a long time. But as they realize how badly off they are compared with others countries so they are bound to change. Undoubtedly one day the US will adopt a less abused and more efficient and beneficial healthcare system.

One day I hope also that the financial world will end the many examples of moral hazard that permeates this organism. I think we are all fed up with the pin-striped billionaires in smoke-filled rooms making up self-serving regulations, aided and abetted by out-of-touch academics, then setting their 24-year old, rottweiler traders to “rip the faces” off each other, meanwhile simultaneously ripping the faces off unwitting third parties in the process.

P

Where's Hamlet?

We've seen the deaths of Polonius, Claudius, and Laertes, otherwise known as house-price falls, commodity-price rises and bank collapses. There still remains the death of Hamlet himself, the final double-digit percentage stock market crash. That is all that is missing from the Shakespearean drama that is the current financial crisis.

Despite the events there have still been many people who have profited from the current compensation system: "Our indiscretion sometime serves us well/ When our deep plots do pall/ And that should learn us/ There's a divinity that shapes our ends/ Rough-hew them how we will."

A little introspection by regulators (I will omit the rather obvious Hamlet quote!) would be appreciated.

In the final scene Horatio says "And let me speak to the yet unknowing world/ How these things came about. So shall you hear/ Of carnal, bloody and unnatural acts/ Of accidental judgments, casual slaughters/ Of deaths put on by cunning and forced cause/ And, in this upshot, purposes mistook/ Fall'n on the inventors' heads."

Sadly one letter in the above must be changed, it is not the "inventors" who suffer at the end of this modern-day tragedy, but instead the "investors."

Something is rotten, and not just in the state of Denmark.

P

The Same Old Same Old

Events of the last year seem to have passed a lot of researchers by. I find it both amusing and disturbing that the same people are still giving the same lectures about the same models at the same conferences without any sign of embarrassment whatsoever. It’s like a parallel universe!

You can fool some of the people all of the time.

Sadly the easy ones to fool are people doing Finance PhDs and MFEs. On the forum there’s always plenty of discussion about which qualifications people should go for, and how many. I find that the people who pick up new ideas fastest are those with a mathematics or science background, those actually with little hard-core quant education. They still have an open mind, something which is surely needed now more than ever before. The more time spent in academia learning the ‘received wisdom’ of quant finance the more one’s brain atrophies it seems. As has been said on the forum many times, a finance PhD is for someone who wants to be a finance professor. You are better off getting a job, any job, in a bank or fund asap, start earning asap, move up the food chain as quickly as possible and leave your degree-collecting friends behind. This business will not be this lucrative forever.

I worry that people just can’t distinguish between good and bad quant finance. There’s plenty of evidence for this in journals, at conferences and in textbooks. People will certainly spot a mathematical error in a paper, but can they make the more subjective distinction between a good paper that advances the subject and a bad paper that sets it back?

There is nothing new in this, journals have almost always preferred to publish the ‘reliable,’ the “brilliant new research by Professor X” that is really “the same old stuff by a has-been plodder.” At this point a plug for our magazine is in order. Portfolio magazine was very flattering in its recent article about our magazine, saying “Paul Wilmott, publisher and editor in chief of Wilmott, is looking pretty smart these days. Wilmott and his magazine, which is aimed at the quantitative-finance community—the math geeks at banks and hedge funds—foresaw many of the problems that dominate the headlines today. He and the contributors to the magazine, whose influence far outstrips its small circulation, were railing about the limits of math and financial models far in advance of the meltdown.”

It’s not hard to find good research, our magazine seems to be particularly talented at this. The difficult part is knowing the difference between the good and the bad. This skill can be learned, but an open mind is needed. And they are increasingly hard to find.

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Science in Finance X: Dynamic hedging and further defence of Black-Scholes

I continue to find myself in the middle of the argument over validity of Black-Scholes. On one side are those who we might call “the risk neutrals.” Those heavily invested in the concepts of complete markets, continuous hedging, no arbitrage, etc. Those with a relatively small comfort zone. On the other side there are those who tell us to throw away Black-Scholes because there are so many fallacious assumptions in the model that it is worthless. Let’s call them the “dumpers.” And then there are a tiny number of us saying yes, we agree, that there are many, many reasons why Black-Scholes should not work, but nevertheless the model is still incredibly robust to the model assumptions and to some extent you can pretend to be a risk neutral in practice.

A good example of this is the subject of discrete hedging. The theory says that to get the Black-Scholes model you need to hedge continuously. But this is impossible in practice. The risk neutrals bury their heads in the sand when this topic is discussed and carry on regardless, and the dumpers tell us to throw all the models away and start again. In the middle we say calm down, let’s look at the maths.

Yes, discrete hedging is the cause of large errors in practice. I’ve discussed this in depth in PWOQF2. Hedging error is large, of the order of the square root of the time between rehedges, it is path dependent, depending on the realized gamma. The distribution of errors on each rehedge is highly skewed (even worse in practice than in theory). But most analysis of hedging error assumes the simple model in which you rehedge at fixed time intervals. This is a very restrictive assumption. Can we do better than this? The answer is yes, if we are allowed a certain number of rehedges during the life of an option then rehedging at fixed intervals is not at all optimal. We can do much better.

The figure above shows a comparison between the values of an at-the-money call, strike 100, one year to expiration, 20% volatility, 5% interest rate, when hedged at fixed intervals (the red line) and hedged optimally (the green line). The lines are the mean value plus and minus one standard deviation. All curves converge to the Black-Scholes complete-market, risk-neutral, price of 10.45, but hedging optimally gets you there much faster. If you hedge optimally you will get as much risk reduction from just 10 rehedges as if you use 25 equally spaced rehedges.

You can see how this puts me firmly between the risk neutrals and the dumpers. The risk neutrals won’t go too far wrong as long as they know how to hedge well, and the dumpers are right if it turns out that the risk neutrals don’t know the maths of discrete hedging.

I suspect that the ratio of the number of papers on complete-market volatility models to the number of papers on discrete hedging is probably about a hundred to one, so I think the risk neutrals need to focus their attention elsewhere if they want to win this battle!

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Rule #1 of quant finance seems to be 'Make this as difficult as we can'

I got a great response to my maths sweet spot blog. Great in the sense of numbers of people writing to me and great in the sense that every single one of them agreed with me!

But it’s still going to be years before the tendency for people to make quantitative finance as difficult as they possibly can is eradicated. And that’ll be years while money is lost because of lack of transparency and lack of robustness in pricing and risk-management models. (But on the other hand, there’ll be lots of research papers. So not all bad news then!)

There’ve been a couple of recent forum threads that perfectly illustrate this unnecessary complexity. One thread was a brainteaser and the other on numerical methods.

The brainteaser concerned a random walk and the probability of hitting a boundary. Several methods were proposed for solving this problem involving Girsanov, Doleans-Dade martingales, and optimal stopping. It must have been a really difficult problem to need all that heavyweight machinery, no? Well, no, actually. The problem they were trying to solve was a linear, homogeneous, second-order, constant-coefficient, ordinary differential equation! (Really only first order because there weren’t even any non-derivative terms!) The problem was utterly trivial (although, if you look at the thread, I did still manage to make a sign error, typical!). Talk about sledgehammers and nuts.

The other thread was on using non-recombining trees to price a simple vanilla option. People were really helpful to the person asking for advice on this topic. But no one, except for me, of course, asked the obvious question “Why on Earth are you doing such a silly thing?” I can hardly imagine a more cumbersome, slow, and generally insane way to solve a simple problem.

It disturbs me when people have been educated to such a level of complexity that they can throw about references to obscure theorems while at the same time being unable to think for themselves. To me, mathematics is about creativity in the use of tools not about being able to quote ‘results.’ Even knowledge of the names of mathematicians and what they are famous for is something I find a bit suspect. If you know the names of all the theorems but don’t know when to use them then you are an historian not a mathematician. Perhaps maths is an art, and I’m not impressed with painting by numbers.

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Coming to a Wall Near You!

I just did a photoshoot for Portfolio magazine with the great Jason Bell (photographer to the stars!). He and his team of three (yes, three!) assistants set me up for all sorts of glam shots around London. There was even a, thankfully short-lived, plan to reproduce the famous American Beauty scene of Mena Suvari with rose petals, but with me and pages from the magazine instead!

I'm mentioning this here because the shoot took us to Farringdon where I was photographed defacing a wall with quant finance. If you happen to be in the neighbourhood (near the Guardian's offices) the equations may still be there, so you'll get to see a model for jump-diffusion with stochastic volatility, with optimal static and dynamic hedging with friction before it is published in the more traditional medium!

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It's what people want - In that case it's what they deserve

A recent thread started by Herd ("One who doesn't understand X is best qualified to talk about it") reminded me of the following events, which are even worse than Herd's point.

A couple of years ago I went to see my doctor about a torn ligament in my shoulder. She was away and so I saw a locum instead. This locum was an elderly lady but presumably sufficiently qualified, and up to date, to practice for the NHS. I told her the problem and she gave me her solution. It was to take a homeopathic medicine. Obviously I was appalled. And had she not been such a sweet old thing I would have given her a piece of my mind!

I went back a few weeks later, saw my usual doctor, and told her what had happened. She said that she sympathized, she was obviously 'scientifically' trained herself. "But," she said, "this is what people want these days."

And this was more frightening than the old dear with her quack remedies.

What does it matter what people 'want'? We aren't talking brand of mobile 'phone here. How can untrained laypeople ever understand the meaning of ‘science’ and the ‘scientific method’ when even the scientists are colluding in this nonsense?

Well, Darwin will prevail in the end and with a bit of luck practitioners of homeopathy and all their patients and advocates will eliminate themselves from the gene pool.

BTW the proper doctor arranged for some physio for my shoulder and I’m fine now, thanks for asking.

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Bringing High Finance into Disrepute… yet again

I filled up my car’s petrol tank at the weekend. The cost was just a couple of pounds shy of £100. We’ve all heard the reasons behind the recent oil price rises, demand from China, concerns over supply from unstable parts of the world, dollar weakness, speculation, etc. Of course, this is just economists doing what they do best, blathering on without having a clue. I’d really like to know some numbers behind all this. Although I’m sure all of the above reasons have a role to play, just as I’m sure high oil prices are going to be more important in the short to medium term than global warming, but for most of those reasons the timescale is wrong. The dollar isn’t falling that fast, the suppliers have always been in dodgy parts of the world, China’s demand may be growing but let’s keep a sense of proportion here. (The 1970s rise in oil price was dramatic too, but that oil crisis can be unambiguously blamed on OPEC.) So, I’d really like to know how much of the rise is due to speculation? Speculation, as seen in bubbles throughout history can cause prices to rocket in a very short period of time.

I’d like to know about the role of speculation because the man in the street is being affected by what goes on in the world of high finance. A few greedy mortgage lenders in the US make a fast buck, the idea catches on, clever quants then repackage the loans, pass them on to all and sundry, at every stage people in expensive suits take out a nice profit, thank you very much. Next thing you know we are in a recession, all lending dries up, and house prices fall. It will be pretty disgusting if it turns out that those people in the expensive suits are to blame for the oil price rise as well.

Next thing you know, the banks will be telling us that all those investments that they’ve written down to zero over the last few months have value after all! "Sorry, man in the street, the crisis was all a false alarm. Your house price has just collapsed and you owe more that it’s worth? Never mind, I’ll buy you a beer with the big fat bonus I've just got from the windfall CDO profit!"

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Results and Ideas: Two classical putdowns

I spoke recently at a very academic conference. I usually prefer trader and fund events because of their focus on practical matters. But this was in a place that I’d never visited and so I accepted. My lecture began in the traditional way of academic events with the audience being a bit hostile in their questioning. Being an old hand at this, I told myself not to rise to their baiting, but to see if I could win them over. It was clear that they knew little of the markets and practical finance, and so my ‘winning them over’ took the form of gently pointing out certain realities, certain constraints, and how interesting this subject is precisely because it is not a science. Getting them on my side turned out to be rather easier than usual, the hostility of most of them evaporated once they became intrigued.

However, one person in the audience was not impressed with my efforts. A well-known academic, he was quite aggressive, and not just with me but with the speakers before and after me as well. His reasons for this may never be known, but his behaviour was sadly not atypical of senior academics. He used two very famous putdowns on me, one of them is common only in academic circles and the other common in all circles.

The academic putdown was used in response to me talking about possibilities of arbitrage and whether the exploitation of arbitrage would make it go away. The putdown is to simply say “There is a result about that.” Now I’m perfectly happy with people talking about ‘results’ in mathematics, in statistics, in particle physics, or in a hard science generally, but the use of the word ‘result’ in the context of a discussion about quantitative finance says more about the person using the word than anything about the subject matter. Human beings have this annoying habit of stubbornly not obeying theoretical ‘results’ (or indeed laws). As I keep saying, this subject is not a hard science and is somewhat more ephemeral than can be captured in a set of results. So although saying “There’s a result about that” can be aggressive and arrogant it can also be very naïve, suggesting that whoever says it believes that finance is equivalent to a set of axioms. It is not, and to believe that it is can be very dangerous. This putdown is best just laughed off.

The other putdown came while I was explaining strategies that may be exploited for profit. The putdown is the simple “If this works then why are you telling us about it and not doing it yourself?” There are many responses to this including:

1. I don’t have the ability to do it myself, this is my marketing pitch, want to back me?

2. Ideas are cheap, I know which ones are good or bad but not everyone can tell the difference

3. Do you know all the barriers to entry? $1million in lawyers fees to set up a fund, months of software writing, years of knocking on doors trying to raise money. Forget it!

4. This is a great idea, but I’ve got better

5. I don’t want to spend the rest of my life doing this, even if it is profitable, variety is the spice of life

6. I did, and now I’ve retired or, more simply, I’ve got enough money already

7. My lawyer/doctor/wife says I mustn’t

And many more…

I was expecting this putdown from the well-known academic (he of the ‘results’) because of what happened in his lecture, which was earlier in the day than mine. He was talking about his model for something or other and right at the end he made the throw-away remark “Of course, if this worked in practice I wouldn’t be telling you about it.” I confess to being shocked. (My turn to be naïve!) This is a man who lectures on finance at a respected university, to students paying a lot of money, and here he was admitting that he lectures on things that do not work, that he keeps some of the good stuff to himself. Let me tell you that when I lecture, for example on the CQF, I keep nothing back (for at least one of the reasons listed above!). And unless I’ve signed some NDA, I will tell you everything.

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Science in Finance IX: In defence of Black, Scholes and Merton

There’s been a lot of criticism of the Black-Scholes model of late, on our Forum, in our blogs, in the magazine (see Haug & Taleb, Wilmott magazine, January 2008) and in other media. Most is warranted, but perhaps not all. I would now like to speak in its defence! This may seem perverse since I have been highly critical of this model for the last 15 years. But as I will explain, Black-Scholes is a remarkably robust model that copes very well even when its underlying assumptions are violated, as they inevitably are in practice. Before detailing my views on this matter, I’d like to explain how my personal relationship with the Black-Scholes model has evolved.

I was introduced to options in around 1987, well before the October crash, while I was a postdoc researching in various problems of industrial/applicable maths. For a while I researched in several areas of finance simultaneously: technical analysis; chaos theory; stochastic calculus. (Thanks to the technical analysis I was short the market coming into the crash of ’87 but sadly only on paper!). I quickly dropped the TA and chaos theory, the latter seemed like a dead end, it was too easy to construct ‘toy models’ that looked plausible but were useless in practice. And so I began to focus on classical quant finance. Being in a maths department before most maths departments had heard of quant finance I had to rely on reading the literature in order to learn the subject. There were no courses for me to attend and no one more experienced to speak to. In those days whenever I read a paper I tended to believe everything in it. If the paper referred to volatility as a constant then I would believe that it was a constant. Black-Scholes was to me a good model, which just needed a minor bit of tweaking. My research from that era was on making small improvements to Black-Scholes to allow for transaction costs, and on the pricing of exotic derivatives in a constant-volatility world. This was the first phase in my relationship with Black and Scholes.

The second phase was as a consultant working for various investment banks, hedge funds and software companies. I was still in academia but moonlighting on the side. In this new capacity I finally got access to real data and was now speaking to practitioners rather than academics. (Fischer Black himself contacted me about the possibility of working for Goldman Sachs, and at this time I got to know Emanuel Derman. For a while I was sorely tempted to join them, but ultimately such a position would not have suited my personality.) It didn’t take long for me to realise how unrealistic were the assumptions in the Black-Scholes model. For example, volatility was certainly not constant, and the errors due to discrete hedging were enormous. My research during the mid and late ’90s was on making more dramatic improvements to the models for the underlyings and this was also the era when my interest in worst-case scenarios began. I worked with some very talented students and postdocs. Some great ideas and new models came out of this period. This was the height of my anti-Black-Scholes views.

A couple of years after leaving academia I became a partner in a volatility arbitrage hedge fund, and this was the start of phase three. In this fund we had to price and risk manage many hundreds of options series in real time. As much as I would have liked to, we just weren’t able to use the ‘better’ models that I’d been working on in phase two. There just wasn’t the time. So we ended up streamlining the complex models, reducing them to their simplest and most practical form. And this meant using good ol’ constant volatility Black-Scholes, but with a few innovations since we were actively looking for arbitrage opportunities. From a pragmatic point of view I developed an approach that used Gaussian models for pricing but worst-case scenarios for risk management of tail risk. And guess what? It worked. Sometimes you really need to work with something that while not perfect is just good enough and is understandable enough that you don’t do more harm than good. And that’s Black-Scholes.

I had gone from a naïve belief in Black-Scholes with all its simplifying assumptions at the start of my quant career, via some very sophisticated modelling, full circle back to basic Black-Scholes. But by making that journey I learned a lot about the robustness of Black-Scholes, when it works and when it doesn’t, and have learned to appreciate the model despite its flaws. This is a journey that to me seems, in retrospect, an obvious one to take. However, most people I know working as quants rarely get even half way along. (As discussed elsewhere, I believe this to be because most people rather like being blinded by science.)

My research now continues to be aimed at questioning commonly held beliefs, about the nature of ‘value,’ about how to use stochastic calculus to make money rather than in a no-arbitrage world, about the validity of calibration (it’s not valid!), and how people price risk (inconsistently is how!). All the time I strive to keep things understandable and meaningful, in the maths sweet spot that I’ve mentioned before.

That’s my journey. But what about the criticisms of Black-Scholes? There are several main ones: Black-Scholes was known well before Black, Scholes and Merton; traders don’t actually use Black-Scholes; Black-Scholes doesn’t work.

I will happily accept that the Black-Scholes formulae were around well before 1973. Espen Haug (“Collector”) has done an excellent job hunting down the real history of derivatives theory (see his Models on Models). Ed Thorp plays a large role in that history. In the first issue of our magazine (Wilmott magazine, September 2002) the cover story was about Ed Thorp and his discovery of the formulae and their use for making money (rather than for publication and a Nobel Prize!). Ed wrote a series of articles “What I Knew and When I Knew it” to clarify his role in the discovery, including his argument for what is now called risk-neutral pricing. I particularly like the story of how Fischer Black asked Ed out to dinner to ask him how to value American options. By the side of his chair Ed had his briefcase in which there was an algorithm for valuation and optimal exercise but he decided not to share the information with Black since it was not in the interests of Ed’s investors! Incorrect accreditation of discoveries is nothing new in mathematics, but usually there’s a quid pro quo that if you don’t get your name attached to your discovery then at some stage you’ll get your name attached to someone else’s!

They say traders don’t use Black-Scholes because traders use an implied volatility skew and smile that is inconsistent with the model. (Do these same people complain about the illegitimate use of the ‘bastard greek’ vega? This is a far worse sin.) I think this is a red herring. Yes, sometimes traders use the model in ways not originally intended but they are still using a model that is far simpler than modern-day ‘improvements.’ One of the most fascinating things about the Black-Scholes model is how well it performs compared with many of these improvements. For example, the deterministic volatility model is an attempt by quants to make Black-Scholes consistent with the volatility smile. But the complexity of the calibration of this model, its sensitivity to initial data and ultimately its lack of stability make this far more dangerous in practice than the inconsistent ‘trader approach’ it tries to ‘correct’!

The Black-Scholes assumptions are famously poor. Nevertheless my practical experience of seeking arbitrage opportunities, and my research on costs, hedging errors, volatility modelling and fat tails, for example, suggest that you won’t go far wrong using basic Black-Scholes, perhaps with the smallest of adjustments, either for pricing new instruments or for exploiting mispriced options. Let’s look at some of these model errors.

Transaction costs may be large or small, depending on which market you are in and who you are, but Black-Scholes doesn’t need much modification to accommodate them. The Black-Scholes equation can often be treated as the foundation to which you add new terms to incorporate corrections to allow for dropped assumptions. (See anything by Whalley & Wilmott from the 1990s.)

Discrete hedging is a good example of robustness. It’s easy to show that hedging errors can be very large. But even with hedging errors Black-Scholes is correct on average. (See PWOQF2.) If you only trade one option per year then, yes, worry about this. But if you are trading thousands then don’t. It also turns out that you can get many of the benefits of (impossible) continuous dynamic hedging by using static hedging with other options. (See Ahn & Wilmott, Wilmott magazine, May 2007 and January 2008.) Even continuous hedging is not as necessary as people think.

As for volatility modelling, the average profit you make from an option is very insensitive to what volatility you actually use for hedging (see Ahmad & Wilmott, Wilmott magazine, November 2005). That alone is enough of a reason to stick with the uncomplicated Black-Scholes model, it shows just how robust the model is to changes in volatility! You cannot say that a calibrated stochastic volatility model is similarly robust.

And when it comes to fat tails, sure it would be nice to have a theory to accommodate them but why use a far more complicated model that is harder to understand and that takes much longer to compute just to accommodate an event that probably won’t happen during the life of the option, or even during your trading career? No, keep it simple and price quickly and often, use a simpler model and focus more on diversification and risk management. I personally like worst-case scenarios for analyzing hedge-fund-destroying risks. (See anything from the 1990s by Hua & Wilmott.)

The many improvements on Black-Scholes are rarely improvements, the best that can be said for many of them is that they are just better at hiding their faults. Black-Scholes also has its faults, but at least you can see them.

As a financial model Black-Scholes is perfect in having just the right number of ‘free’ parameters. Had the model had many unobservable parameters it would have been useless, totally impractical. Had all its parameters been observable then it would have been equally useless since there would be no room for disagreement over value. No, having one unobservable parameter that sort of has meaning makes this model ideal for traders. I speak as a scientist who still seeks to improve Black-Scholes, yes it can be done and there are better models out there. It’s simply that more complexity is not the same as better, and the majority of models that people use in preference to Black-Scholes are not the great leaps forward that they claim, more often than not they are giant leaps backward.

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Science in Finance VIII: The Maths Sweet Spot

Maths is fun. Many people reading this blog and the Forum get a real kick out of maths and problem solving. I’ve had many jobs and careers in the last three decades, and started various businesses, but the one thing that I keep coming back to is mathematics. There’s something peaceful and relaxing about an interesting maths problem that means you can forget all your troubles, just get totally absorbed in either the detail of a formulation, calculation or solution, or lie back and think of deep concepts.

I wonder if that’s one of the reasons quantitative finance is in such a mess.

I’m going to let you in on the big secret of quantitative finance, and you must keep this secret because if word got out then that would be the end of all masters in financial engineering programs. And universities make a lot of money from those.

Ok, the big secret...Quantitative finance is one of the easiest branches of mathematics.

Sure you can make it as complicated as you like, and plenty of authors and universities have a vested interest in so doing. But, approached correctly and responsibly, quant finance is easy.

Let’s talk about the different levels of maths you see in quant finance.

Some people try to dumb the subject down. There are plenty of textbooks that kid you into thinking that there is almost no mathematics in the subject at all. These books may dabble in the binomial model but go no deeper. Now anyone with a second-year undergraduate knowledge of numerical methods will recognise the binomial model for the inadequate and cumbersome dinosaur that it is. I like the binomial method as a teaching tool to explain delta hedging, no arbitrage and risk neutrality. But as a way of pricing derivatives for real? No way! Watching the contortions people go through on the Forums in order to make their binomial code work is an illuminating experience. Dumbing the subject down is not good. You cannot price sophisticated contracts unless you have a decent mathematical toolbox, and the understanding of how to use those tools. Now let’s look at the opposite extreme.

Some people try to make the subject as complicated as they can. It may be an academic author who, far from wanting to pass on knowledge to younger generations, instead wants to impress the professor down the corridor. He hopes that one day he will get to be the professor down the corridor who everyone is trying to impress. Or maybe it’s a university seeing the lucrative QF bandwagon. Perhaps they don’t have any faculty with knowledge of finance, certainly no practical knowledge, but they sure do have plenty of people with a deep knowledge of measure theory. Hey presto, they’ve just launched a masters in financial engineering! Making this subject too complicated is worse than dumbing it down. At least if you only work with the binomial method you can’t do much harm, simply because you can’t do much of anything. But with all those abstract math tools at your command you can kid yourself into believing you are a derivatives genius. Never mind that you don’t understand the markets, never mind that the people using your models haven’t a clue what they are doing. I believe that the obscenely over-complicated models and mathematics that some people use are a great danger. This sort of maths is wonderful, if you want to do it on your own time, fine. Or become a finance professor. Or move into a field where the maths is hard and the models are good, such as aeronautics. But please don’t bring this nonsense into an important subject like finance and where even the best models are rubbish. Every chain has its weakest link. In QF the weakest links are the models, not the maths, and not the numerical methods. So spend more time thinking about your models and their robustness and less on numerical inversion of a transform in the complex plane.

Here’s a true story that illustrates my point quite nicely. Not long ago I was approached by someone wanting to show me a paper they hoped to get published. The paper was about 30 pages long, all maths, quite abstractly presented, no graphs. When I’d read the paper I said to the author that I thought this was a good piece of work. And I told him that the reason I thought it was good was because, unfortunately for him, I’d done exactly the same piece of research myself with Hyungsok Ahn a few years earlier. What I didn’t tell him was that Hyungsok and I only took four pages to do what he’d done in 30. The reason for the huge difference in derivations was simply that we’d used the right kind of maths for the job in hand, we didn’t need to couch everything in the most complicated framework. We used straightforward maths to present a straightforward problem. Actually, what he had done was worse than just unnecessarily obscure the workings of the model. There was a point in the paper where he trotted out the old replacement-of-drift-with-the-risk-free-rate business. He did this because he’d seen it done a thousand times before in similarly abstract papers. Furthermore, because the paper was about incomplete markets, the whole point of the model was that you were not allowed to make this substitution! He didn’t understand the subtle arguments behind risk-neutral valuation. That was the place where his paper and ours diverged, ours started to get interesting, his then followed a well-worn, and in this case incorrect, path.

If you look through the various Forums on wilmott.com you will see that we have some areas for people to talk about mathematics, research papers, etc., and then there are areas to talk about trading, general finance, etc. You will notice that the majority of people are comfortable in only either the maths areas or the trading areas. Not so many people are comfortable in both. That should tell you something, the overlap of skills is far less than one would expect or hope. Who would you trust your money to? A mathematician who doesn’t know the markets or a trader who doesn’t know maths? Ideally, find someone who is capable in both areas.

And so to the middle ground, not too dumb, not too clever for its own good. Let’s start with the diffusion equation. As every mathematician knows there are three important classes of partial differential equation: Elliptic; Hyperbolic; Parabolic. There are various standard techniques for solving these equations, some of them numerical. The diffusion equations that we see so often in QF are of parabolic type. Rather conveniently for us working in QF, parabolic equations are by far the simplest of the different types to solve numerically. By far the simplest. And our equations are almost always linear. Boy, are we spoiled! (I’ve thought of publishing the “Wilmott Ratio” of salary to mathematical complexity for various industries. Finance would blow all others out of the water!)

Or take the example of some fancy exotic/OTC contract. You start with a set of model assumptions, then you do the maths, and then the numerics. Most of the time the maths can be 100% correct, i.e. no approximations, etc. Given the assumptions, the pricing model will follow as night follows day. Then you have to crunch the numbers. Now the numerics can be as accurate as you like. Let’s say you want the value and greeks to be 99% accurate. That’s easy! It may take a few seconds, but it can usually be done. So where’s the problem? Not the maths, not the numerics. The problem is in the model, the assumptions. Maybe you get 70% accuracy if you are lucky. It seems odd therefore that so many people worry about the maths and the numerics, when it is very obvious where the main errors lie!

There is a maths sweet spot, not too dumb, not too smart, where quants should focus. In this sweet spot we have basic tools of probability theory, a decent grasp of calculus, and the important tools of numerical analysis. The models are advanced enough to be able to be creative with new instruments, and robust enough not to fall over all the time. They are transparent so that the quant and the trader and the salesperson can understand them, at least in their assumptions and use.

Because the models are necessarily far, far from perfect, one must be suspicious of any analytical technique or numerical method that is too fiddly or detailed. As I said above, the weakest link in the chain is not the maths or the numerics but the model assumptions. Being blinded by mathematical science and consequently believing your models is all too common in quantitative finance.

This is to me the reason why QF is interesting and challenging, not because the mathematics is complicated, it isn’t, but because putting maths and trading and market imperfections and human nature together and trying to model all this, knowing all the while that it is probably futile, now that’s fun!

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Science in Finance VII: Risk Management – What is the point?

Another day, another financial institution collapses. Bear Stearns, fifth largest US investment bank, has gone. I’ve worked closely with Bear brokerage in the past and quite enjoyed the experience. It’s the prime brokerage that JP Morgan is presumably after. I’m a quant not an accountant so was surprised to see that Bear’s assets were just 2-3% higher than their liabilities. If this is standard practice in this sector then crikey, we really are doomed! Who in their right mind would run a business that way? Sorry if I seem awfully naïve, but as someone who has himself run a few businesses in his time, albeit on a somewhat smaller scale, to me this does seem highly irresponsible.

Investments (although that hardly feels like the right word) in mortgage-backed products and over-zealous lending combined with one particular scenario are at the bottom of this. This scenario is that of falling house prices. But isn’t scenario analysis supposed to spot this sort of exposure? It’s not as if falling property prices are totally unheard of. As those of you who have heard me lecture will know, I always like to boil things down to everyday experiences. And according to my experience there is a one in three chance of losing money in property! (Like most people with similar experiences it was the early 90s to ‘blame’ in my case.) And a one in three chance is not exactly the 10 standard deviation excuse du jour! It has been suggested that many bank employees are too young to have experienced negative equity and therefore it is off their radar, but if that is the case then what is the point of risk management at all? What is the point of all those risk management qualifications that are springing up like mushrooms? It has also been suggested that senior people don’t have a clue about the instruments that their bank is trading. So I really would like to know how they fill their days, whatever they are doing it is clearly not productive.

Are those in positions of responsibility at Bear Stearns blameless? Did senior management really think that their downside was tolerable, that Value at Risk and stress testing were giving an accurate picture of potential losses and their probabilities? Again we come back to that old problem, if there’s no downside then irresponsible people will prosper at the expense of the rest of us. And it seems that only the irresponsible rise to positions of responsibility in this business. Ironic.

Or maybe they are so lawyered up as to feel invincible. I am sure there will be civil suits in some of these cases because you can guarantee that the lawyers will, as always, be the big winners. They are paid to ensure that your back is covered no matter how unethical your behaviour, and then they are paid again when you are inevitably sued.

On the subject of ethical behaviour, don’t some of these risk management courses teach about ethics? Or does understanding ethics these days amount to knowing who are the best lawyers? Personally, if I know someone had to go on a course to learn business ethics then I would ask myself whether that’s a person I can trust. A risk management qualification is just another preventative measure against being sued, just like the “Mind the Step” signs in restaurants? What, you broke your leg? Not our fault, mate, didn’t you see the sign? (I was disappointed to discover recently, but not surprised, that they’ve taken peanuts out of Revels chocolates. Some people suffer from allergies, and presumably can’t read, so we all have to do without.)

Risk management must be consistent with protecting the wider interests of the institution rather than being easy to manipulate towards the narrow interests of some employees. At present the concept of risk management only exists to make it easier for people to take risks that common sense would suggest are stupid, but risks that people still want to take because of the huge upside for these same people in terms of bonus. Let’s face it, that’s what rules and regulations are for. As Madness said in Baggy Trousers “All I learnt at school was how to bend not break the rules.”

I’d now like to explain how I think risk management should work. It’s a simple combination of standard practices that I have used very successfully in the past. It’s not exactly earth shattering, but it shows how to focus your attention on what matters. I will also finish with a small proposal for how to approach scenario analysis.

Roughly speaking, I tend to think in terms of three different levels or classes of risk management. These are

Level 1: Probabilities and VaR

Level 2: Worst-case scenarios

Level 3: Invasion by aliens, “It’s the end of the world as we know it, and I feel fine” (REM this time!)

Level 1: Typical day-to-day markets for which it is acceptable to work with probabilities and even possibly normal distributions. Correlations, while never exactly trustworthy, will not be a deciding factor in survival or collapse. Use probabilities and talk about Value at Risk by all means. This is really just classical mid 1990’s risk management, with not too much worrying about fat tails. To some extent trust in a decent amount of diversification. The rationale behind this is simply that you never know what your parameters or distributions really are and so you are better off with simple calculations, more instruments and plenty of diversification. You may not make a profit but at least you won’t be killed during a quiet day in the market.

Level 2: Situations which will cause your bank or hedge fund to collapse. Test your portfolio against a wide range of scenarios and see the results. But since these are situations resulting in the collapse of your institution you must never, ever talk about probabilities, except in terms of how many centuries before such events may happen. I would much prefer you work with worst-case scenarios (as in the very simple concept of CrashMetrics). I sometimes use the example of crossing the road. Imagine it’s late, it’s dark, and it’s raining. If you cross the road there is a 5% chance of being hit by a bus and killed. That does not mean that tomorrow 95% of you goes to work! No, you assume the worst, because it is so bad, and cross the road elsewhere.

Certainly there is little role for Extreme Value Theory (EVT) in its fiddly, detailed sense. Consider these two statements about the same portfolio: “According to Gaussian distributions the expected time to bank collapse is 10^25 years” and “According to EVT the expected time to bank collapse is 50 years.” The difference between these statements should only be of academic interest. Such a portfolio must be protected asap. Of course, many people would be happy with such a portfolio because 50 years is still longer than a trading career. Such people should not be in positions of responsibility. As I said above, “risk management must be consistent with protecting the wider interests of the institution rather than being easy to manipulate towards the narrow interests of some employees.” To recap, if it’s bad enough to cause bank/fund collapse you don’t look at probabilities. Handle extreme events with worst-case scenario analysis.

Level 3: Scenarios which are so dire as to affect the world directly. I always use the example of invasion by aliens as an example, since there are whole bodies of literature and movies that have explored the effects of such an event, but we have little idea of the probability! If your hedge fund will collapse in the event of invasion by aliens, or drying up of oil supplies, or decimation of the world’s population by bird flu, then I wouldn’t necessarily change your portfolio! You’ll have other things to worry about!

Finally, a small proposal. I would like to see risk management forced to engage in the following task, the reverse engineering of a bank collapse. Start with your current portfolio and imagine being called into the big boss’s office to be told that the bank has lost $50billion. Having put yourself in the frame of mind of having already lost this amount, now ask yourself what could have caused this to happen. As Einstein said “Imagination is more important than knowledge.” This should be the mantra for those in risk management. There is always going to be something that will come as a surprise at the time but with hindsight you realise could have been expected (if not necessarily predicted). Once you have figured out what could have caused this loss then you ask about the likelihood of this happening. The result of that analysis then determines what you should do with the portfolio. If, for example, the answer is simply that a fall in property prices caused the loss then you must get out this very instant, before it actually happens. You see the idea, work backwards from the result, the loss, rather than pick (possibly convenient) scenarios and look at the effects. Then estimate the likelihood of the chain of events happening, and act accordingly. Going the other way is more open to abuse. Scenario testing is a beautiful concept, if one gets to choose the scenarios to test. And those of weak character will not, of course, test any scenario that might jeopardize a juicy trade.

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This is No Longer Funny

I’ve been critical of much of quant modelling for many years. I don’t like the assumptions, the models, the implementations. I’ve backed this up with sound reasons and wherever possible tried to find alternative approaches that I think are better. I don’t honestly expect to change the world, much, but, hey, I do what I can. Human nature is such that very often things have to go from bad to worse to bloody awful before the necessary paradigm shift happens. I hope we are close to that point now.

Who am I kidding? As another hedge fund disappears thanks to mishandling of complex derivatives, I predict that things are going to get even worse.

When it was just a few hundred million dollars here and there that banks were losing we could all have a good laugh at the those who had forgotten about convexity or whatever. But now the man in the street has been affected by these fancy financial instruments. It’s no longer a laughing matter.

Part of the problem is that many of the people who produce mathematical models and write books know nothing about finance. You can see this in the abstractness of their writing, you can hear it in their voices when they lecture. Sometimes they are incapable of understanding the markets, mathematicians are not exactly famous for their interpersonal skills. And understanding human nature is very important in this business. It’s not enough to say “all these interacting humans lead to Brownian Motion and efficient markets.” Baloney. Sometimes they don’t want to understand the markets, somehow they believe that pure mathematics for its own sake is better than mathematics that can actually be used. Sometimes they don’t know they don’t understand.

Banks and hedge funds employ mathematicians with no financial-market experience to build models that no one is testing scientifically for use in situations where they were not intended by traders who don’t understand them. And people are surprised by the losses!

I realized recently that I’ve been making a big mistake. I’ve been too subtle. Whenever I lecture I will talk calmly about where models go wrong and where they can be dangerous. I’ve said CDO models are bad because of assumptions about correlation. I’ve pointed out what you can do to improve the models. I’ve talked about hidden risks in all sorts of instruments and how sensible use of mathematics will unveil them. I’ve explained why some numerical methods are bad, and what the good methods are. But, yes, I’ve been too subtle. I now realise that one has to shout to be heard above the noise of finance professors and their theorems. Pointing people in the right direction is not enough. Screaming and shouting is needed.

So here, big and bold, gloves off, in capital letters (for this seems to help), are some fears and predictions for the future.

THERE WILL BE MORE ROGUE TRADERS: While people are compensated as they are, while management look the other way to let the ‘talent’ do whatever they like, while people mistake luck for ability, there will be people of weak character who take advantage of the system. The bar is currently at €5billion. There will be many happy to stay under that bar, it gives them some degree of anonymity when things go wrong. But that record will be broken.

GOOD SALESMEN WILL HOODWINK SMART PEOPLE: No matter what you or regulatory bodies or governments do we are all a pushover for the slick salesman.

CONVEXITY WILL BE MISSED: One of the more common reasons for losing money is assuming something to be known when it isn’t. Option theory tells us that convexity plus randomness equals value.

CORRELATION PRODUCTS WILL BLOW UP DRAMATICALLY: This means anything with more than one underlying, including CDOs. Stop trading these contracts in quantity this very minute. These contracts are lethal. If you must trade correlation then do it small and with a big margin for error. If you ignore this then I hope you don’t hurt anyone but yourself. (I am sometimes asked to do expert-witness work. If you blow up and hurt others, I am very happy to be against you in court.)

RISK MANAGEMENT WILL FAIL: Risk managers have no incentive to limit risk. If the traders don’t take risks and make money, the risk managers won’t make money.

VOLATILITY WILL INCREASE ENORMOUSLY AT TIMES FOR NO ECONOMIC REASON: Banks and hedge funds are in control of a ridiculous amount of the world’s wealth. They also trade irresponsibly large quantities of complex derivatives. They slavishly and unimaginatively copy each other, all holding similar positions. These contracts are then dynamically hedged by buying and selling shares according to mathematical formulae. This can and does exacerbate the volatility of the underlying. So from time to time expect to see wild market fluctuations for no economic reason other than people are blindly obeying some formula.

TOO MUCH MONEY WILL GO INTO TOO FEW PRODUCTS: If you want the biggest house in the neighbourhood, and today not tomorrow, you can only do it by betting OPM (other people’s money) big and undiversified. There are no incentives for spreading the money around responsibly.

MORE HEDGE FUNDS WILL COLLAPSE: You can always start a new one. Hell, start two at the same time, one buys, the other sells!

POLITICIANS AND GOVERNMENTS WILL REMAIN COMPLETELY IN THE DARK: Do you want to earn £50k p.a. working for the public sector, or £500k p.a. working for Goldman Sachs? Governments, who are supposed to set the rules, do not even know what the game is. They do not have the slightest clue about what happens in banks and hedge funds. Possibly, for the same reason, London will lose out to New York as a world financial centre.

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Science in Finance VI: True Sensitivities, CDOs and Correlations

One of the more quantie aspects of recent financial crises has been the valuation of CDOs, the highly complex credit instruments depending upon the behaviour of many, many underlyings.

Now your typical quant favours just one tool to capture the interaction of two assets, and that tool is correlation. Of course, this is a very unsubtle tool which is being used to capture the extremely subtle interactions between companies. And when you have 100 underlyings the number of correlations will be 100x99/2=4,950. All of them unstable, all of them meaningless. Yet you will often find complex derivatives being priced using such wildly nonsensical data. Sometimes, in the interests of simplicity, some instruments are priced assuming all correlations are the same. The rationale behind this might be to return some robustness, in the sense that you might be more sure of one parameter than of 4,950 of them. If only it were that simple!

Much more on correlation in a later blog.

Returning to the subject of CDOs. I conducted a simple experiment on a CDO with just three underlyings. Really just a toy model to illustrate some important issues. I started by assuming a single correlation (instead of three) to capture the relationship between the underlyings, and a ‘structural model.’ I then looked at the pricing of three CDO tranches, and in particular their dependence on the correlation. Look at the figure above, but ignore the exact numbers. First observe that the Senior Tranche decreases monotonically with correlation, the Equity Tranche is monotonically increasing, with the Mezzanine Tranche apparently being very insensitive to correlation.

Traditionally one would conduct such sensitivity experiments to test the robustness of ones prices or to assist in some form of parameter hedging. Here, for example, one might conclude that the value of the Mezzanine Tranche was very accurate since it is insensitive to the correlation parameter. For a single correlation ranging from -0.25 to +0.5 the Senior Tranche value ranges from 0.643 to 0.797, the Equity Tranche from 0.048 to 0.211, and the Mezzanine Tranche from 0.406 to just 0.415. (Remember, don’t worry about the numbers in this toy model, just look at the structure.) If you are confident in your valuation of the Mezzanine Tranche, then so will the next bank, and with competition being what it is, bid-offer prices will converge.

Such an analysis could not possibly be more misleading, such a conclusion could not possibly be more incorrect and such a response could not possibly be more financially dangerous.

Consider a more interesting, and more realistic, world in which correlation is state-dependent. Now allowing correlation to vary from -0.25 to +0.5, but not constant, and depending on ‘state,’ you will find that the Senior Tranche still varies from 0.643 to 0.797, the Equity Tranche still varies from 0.0408 to 0.211, but now the Mezzanine Tranche varies from 0.330 to 0.495, a factor of 18 in the sensitivity compared with the traditional naïve analysis. The reason is simple, inside the Mezzanine Tranche structure there is a non-monotonic sensitivity to correlation which is masked when calculating the value; sometimes more correlation is good, sometimes more correlation is bad. (For the Senior Tranche correlation is always bad, for the Equity Tranche correlation is always good.)

Why on earth people thought it a good idea to measure sensitivity to a parameter that has been assumed to be constant escapes me still.

The moral of this example is simple, there is far more risk inside some of these instruments than you could ever hope to find with classical analyses. Stop using such convoluted models, use more straightforward models and start thinking about where your models’ sensitivities really lie. Your models can fool some of the people all of the time, and all of the people some of the time, but your models cannot fool all of the people all of the time.

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Science in Finance V: Diversification

One of the first lessons in any course on quantitative finance will be about portfolio construction and the benefits of diversification, how to maximize expected return for a given level of risk. If assets are not correlated then as you add more and more of them to your portfolio you can maintain a decent expected return and reduce your risk asymptotically to zero. (Risk falls off like the inverse square root of the number of different uncorrelated assets.) Colloquially, we say don’t put all your eggs into one basket.

Of course, that’s only theory. In practice there are many reasons why things don’t work out so nicely. Correlations never behave as they should, the relationship between two assets can never be captured by a single scalar quantity. We’ll save discussion of correlation for another time! For the moment I’m more worried about people or banks not even attempting to diversify.

Part of the problem with current mechanisms for compensation is that people are encouraged to not diversify. I don’t mean “not encouraged to,” I do mean “encouraged to not.” Imagine you have just graduated from a respectable Ivy League university with a thorough academic understanding of risk and return but without a similar level of appreciation of politics in an employment environment. You start your job as a junior trader determined to help your bank, and yourself, make money. You thus look for opportunities that diversify some of the bank’s risk while maintaining a good, solid return. Now if, as a result of the diversification you find yourself either losing money when the others make it, or making it when they lose it, then you are stuffed. Lose money when all around are making it, you’re fired. Make money when all around are losing it? Expect a big bonus? No way! Your profits will help to bail everyone else out and no one gets a bonus, even you. No, you should do the same as everyone else. As Keynes said, “It is better to fail conventionally than to succeed unconventionally.”

There are many ways to diversify, across contracts, asset classes, time horizons, what letter of the alphabet the contract starts with, etc. Even across models. I am in two minds about diversifying using different models possibly for the same contract. The scientist in me obviously wants to see each bank trying to find the best model, but I can appreciate that less harm might be done if people pick prices and greeks at random (my slightly cynical view of using multiple models!).

My scientist within would prefer each bank/hedge fund to have ‘one’ model, with each bank/hedge fund having a different model from its neighbour. Gives Darwin a fighting chance! I see so many banks using the same model as each other, and rarely are they properly tested, the models are just taken on trust. (And as we know from everyone's problems with calibration, when they are tested they are usually shown not to work but the banks still keep using them. Again, to be discussed later.)

There are fashions within investing. New contracts become popular, profits margins are big, everyone piles in. Not wanting to miss out when all around are reaping huge rewards, it is human nature to jump on any passing bandwagon. Again this is the exact opposite of diversification, often made even worse because many of those jumping on the bandwagon (especially after it’s been rolling along for a while) don’t really have a clue what they are doing. To mix metaphors, many of those on the bandwagon are in over their heads.

The key point to remember is something that every successful gambler knows (a phrase I use often, but shouldn’t have to), no single trade should be allowed to make or break you. If you trade like it is then you are doomed.

We all know of behavioural finance experiments such as the following two questions. First question, people are asked to choose which world they would like to be in, all other things being equal, World A or World B where

A. You have 2 weeks’ vacation, everyone else has 1 week

B. You have 4 weeks’ vacation, everyone else has 8 weeks

The large majority of people choose to inhabit World B. They prefer more holiday to less in an absolute sense, they do not suffer from vacation envy.

But then the second question is to choose between World A and World B in which

A. You earn $50,000 per year, others earn $25,000 on average

B. You earn $100,000 per year, others earn $200,000 on average

Goods have the same values in the two worlds. Now most people choose World A, even though you won’t be able to buy as much ‘stuff’ as in World B. But at least you’ll have more ‘stuff’ than your neighbours. People suffer a great deal from financial envy.

In banking the consequences are that people feel the need to do the same as everyone else, for fear of being left behind. Again, diversification is just not in human nature. Now none of this matters as long as there is no impact on the man in the street or the economy. (Although the meaning of ‘growth’ and its ‘benefits’ are long due a critical analysis.) And this has to be a high priority for the regulators, banks clearly need more regulatory encouragement to diversify.

Meanwhile, some final quick lessons. Trade small and trade often. Don’t try to make your retirement money from one deal. And work on that envy!

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Science in Finance IV: The feedback effect

For every buyer there is a seller and vice versa. So at a first glance derivatives is a zero-sum game, someone wins and someone loses, and the amounts are identical. Therefore there can be no impact on the rest of us or on the economy if two adults want to bet large sums on money on the outcome of what may just be the roll of a dice. Well, it isn’t that simple for at least two reasons.

First, many of those trading derivatives are hedging with the underlying and this can affect the behaviour of the underlying: hedging positive gamma can decrease volatility and hedging negative gamma can increase volatility. When hedging positive gamma (i.e. replicating negative gamma) as the price rises you have to sell more of the underlying, and when the price falls you buy back, thus reducing volatility if your trades are in sufficient size to impact on the market. But hedging negative gamma is not so nice, you buy when the price rises and sell when it falls, exacerbating the moves and increasing volatility. The behaviour of stocks on which there are convertible bonds is often cited as a benign example, with the rather more dramatic '87 crash, replicating a put i.e. hedging negative gamma, as the evil version. (See Wilmott, P. and Schonbucher, P 2000 The feedback effect of hedging in illiquid markets. SIAM J. Appl. Math. 61 232—272, also PS’s dissertation.) You will probably find some reluctance for people to sell certain derivatives if they are not permitted to dynamically hedge. (Not that it works particularly well anyway, but that is what people do, and that is what most pricing theory is based on. Static hedging with other derivatives is better, and does not cause such (in)stability problems.)

(We’ve had newspaper headlines about damage done by excessive risk taking, whether by single, roguish, individuals or by larger institutions such as hedge funds, or banks and corporates investing in products they don’t fully understand. I expect it won’t be long before the attempt to reduce risk is the cause of similar headlines!)

Second, with the leverage available with derivatives it is possible, and actually rather simple, for people to trade so much as to get themselves into a pickle when things go wrong. This has many consequences. For example a trader loses his bank so much money that the bank collapses or is taken over, job losses ensue and possibly the man in the street loses his savings. Is wealth conserved during this process, as would be the case in a zero-sum game? I think not.

Of course, we don’t know what proportion of derivatives trades are being used for hedging, speculation with leverage, etc. and how many are being dynamically hedged. But while derivatives trading is such a large business and while pricing theory is underpinned by dynamic hedging then we can say that the game of derivatives is not zero sum. Of course, this should spur on the implementation of mathematical models for feedback…which may in turn help banks and regulators to ensure that the press that derivatives are currently getting is not as bad as it could be.

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Science in Finance III: Model accuracy in different markets

Some models are better than others. Sometimes even working with not-so-good models is not too bad. To a large extent what determines the success of models is the type of market. Let me give some examples.

Equity, FX and commodity markets: Here the models are only so-so. There has been a great deal of research on improving these models, although not necessarily productive work. Combine less-than-brilliant models with potentially very volatile markets and exotic, non-transparent, products and the result can be dangerous. On the positive side as long as you diversify across instruments and don't put all your money into one basket then you should be ok...at least as long as the market overall is going up!

Fixed-income markets: These models are pretty dire. So you might expect to lose (or make) lots of money. Well, it's not as simple as that. There are two features of these markets which make the dire modelling less important, these are a) the underlying rates are not very volatile and b) there are plenty of highly liquid vanilla instruments with which to try to hedge model risk. (I say "try to" because most model-risk hedging is really a fudge, inconsistent with the framework in which it is being used.)

Correlation markets: Oh, Lord! Instruments whose pricing requires input of correlation (FI excepted, see above) are accidents waiting to happen. The dynamic relationship between just two equities can be beautifully complex, and certainly never to be captured by a single number, correlation. Fortunately these instruments tend not to be bought or sold in non-diversified, bank-destroying quantities. (Except for CDOs, of course, see below.)

Credit markets: Single name instruments are not too bad. Again problems arise with any instrument that has multiple 'underlyings,' so the credit derivatives based on baskets...you know who you are. But as always, as long as the trades aren't too big then it's not the end of the world.

Where's the 'science' in this? The science comes in accepting right from the start that the modelling is going to be less than perfect. It is not true that one makes money from every instrument because of the accuracy of the model. Rather one makes money on average across all instruments despite the model. These observations suggest to me that less time should be spent on dodgy models, meaninglessly calibrated, but more time on models that are accurate enough and that build in the benefits of portfolios.

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Science in Finance I Revisited: Supply and demand, and spoon bending

I attended some of the recent Savoy auction by Bonhams this week and I couldn't resist observing the events from a quant perspective! In particular, I was drawn back again to the question of valuation versus supply and demand. We are taught that value comes from some complicated mathematical analysis involving lognormal random walks and stochastic calculus. However, we all ought to know that value comes about by a more obscure and more interesting and usually ad hoc procedure, often involving little logic and certainly no maths, and sometimes quite a lot of emotion. (Think women and shoes.) All of this was seen at the Savoy auction.

Yes, there were people tut-tutting at the amount some were willing to pay for an ashtray, but they weren't those doing the buying. Those who bought the ashtrays probably had some doubts at the time, and also shortly afterwards, even this morning and maybe when they collect the ashtrays, but in the long run they'll at least have a funny story about themselves. (The latter not so easy to assign a value to, and certainly not risk neutral!)

Near the end of the three days there was a boring patch with 50 Savoy double beds going under the hammer, one after another. To amuse myself and in the spirit of scientific curiosity, I wrote down the 'time series' of prices for these identical items. Now here was a room full of the same people, bidding for identical items with a known and limited supply, but even in this rather dull scenario the results were interesting, the plot of the times series is shown. Observations: the price did settle down to a value around £50, but that wasn't exactly stable; absentee bids mostly caused dramatic increases in the price (I'm sure economists will get excited about 'information' at this point, but this was the least interesting observation); later absentee bids were very low, people perhaps hoping for drying up of demand(?); a few lucky or clever people even got the price down below the £50; individual bidders did not seem to show consistency in their bidding; losing bidders often took a break for a few lots before coming back in. None of this is other than perfectly obvious (and much already covered in auction theory, I hope) but in my experience you really have to keep reminding quants that they are human beings as well, and that they should draw inspiration from the mundane.

I bumped into Uri Geller at the auction. He had just successfully bid for...you guessed it, spoons! He's a very nice gentleman, and very kindly gave a few of us a private display of spoon bending!

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Science in Finance II "...ists"

A century or two ago, finance was the career for the less talented members of the family. Sons of the aristocracy would eventually go to sit in the House of Lords, while overseeing their property. One son would join the military, Catholic families would send a son off to the church. Perhaps if they were of an enquiring mind one son might become a scientist. But if a son turned out to be intellectually challenged he would be sent off to be 'something in the City.' This didn’t require any more brains than that required for an arts degree. This was the finance-is-for-artists (and long lunches) period, now long gone.

More often one now finds proper scientists working in finance. They have the analytical skills needed by investment banks and hedge funds. I imagine some must start out being frustrated by the lack of an established rigorous foundation for the subject. Where are the conservation laws? Where are the experimental results and the hypotheses? Quantitative finance has a well-used set of tools, but the popular models are essentially ad hoc.

Those in trading are undoubtedly pragmatists who really don’t care for the port-and-cheese side of finance, nor for compact theories. Can it be put in a spreadsheet and does it make money? That’s all that matters.

Unfortunately, most of the theory is built by axiomatists who really seem to believe in their models. These are the ones to be really frightened of. Speaking to them is like speaking to a god botherer, "there is but one stochastic volatility model and its name is Heston." (News flash: God and complete markets are simplifying assumptions that make life easier for the unimaginative, you aren't meant to believe in them once you've grown up!)

My feeling is that the best type of 'ist' working in finance is a pragmatic scientist, combining the curiosity and the scepticism of the scientist with the get-the-job-done attitude of the pragmatist.

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Science in Finance I: Supply and demand

That's it in a nutshell, supply and demand. Everything is driven by supply and demand. And if you want any financial principle as the foundation for a (scientific) theory then this is it, just like we have conservation laws in the physical sciences.

Of course, quantifying this may not be that easy. Attempts to explain asset prices by modelling interacting agents have not been fantastically successful, whereas simply saying that the end result of all those interactions is a stochastic differential equation, has been.

I do sometimes wonder if the typical etiolated quant has ever been into a shop and experienced supply and demand first hand by buying a pint of milk. Whenever a quant calibrates a model to the prices of options in the market he is saying something about the information content of those prices, often interpreted as a volatility, implied volatility. But really just like the price of a pint of milk is about far more than the cost of production, the price of an option is about much more than simple replication. The price of milk is a scalar quantity that has to capture in a single number all the behind-the-scenes effects of, yes, production, but also supply and demand, salesmanship, etc. Perhaps the pint of milk is even a 'loss leader.' A vector of inputs produces a scalar price. So, no, you cannot back out the cost of production from a single price. Similarly you cannot back out a precise volatility from the price of an option when that price is also governed by supply and demand, fear and greed, not to mention all the imperfections that mess up your nice model (hedging errors, transaction costs, feedback effects, etc.).

Supply and demand dictates everything. The role of assumptions (such as no arbitrage) and models (such as the continuous lognormal random walk) are to simply put bounds on the relative prices among all the instruments. For example, you cannot have an equity price being 10 and an at-the-money call option being 20 without violating a simple arbitrage. The more realistic the assumption/model and the harder it is to violate in practice the more seriously you should treat it. The arbitrage in that example is trivial to exploit and so should be believed. However, in contrast the theoretical profit you might think could be achieved via dynamic hedging is harder to realize in practice because delta hedging is not the exact science that one is usually taught. Therefore results based on delta hedging should be treated less seriously.

To summarize: Supply and demand dictate prices, assumptions and models impose constraints on the relative prices among instruments. Those constraints can be strong or weak depending on the strength or weakness of the assumptions and models.

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Science in Finance: Introduction

Having for most of my quant career attacked the majority of mathematical modelling in finance for being 'unscientific' (in the sense that the theories are rarely tested before being used, and when tested usually fail miserably) I feel somewhat heartened by the recent anti-Black-Scholes movement.

Unfortunately this countermovement, although healthy in provoking debate, also does not quite match my (presumably rather high!) standards of rigour. With the aim of putting some science back into the quant debate I'm going to spend a few blogs highlighting what I think are the weaknesses of financial modelling, and its strengths. I will even be defending Black-Scholes at times! Being scientific does not mean being without emotion, so although my reasoning will be logical my language will almost certainly, and as always, get quite demonstrative.

Topics to look out for, in no particular order: supply and demand; accuracy in different markets; distributions and fat tails; volatility and robustness; hedging errors; diversification; correlation; etc.

In the meantime, listen to the recording of BBC Radio 4's recent More or Less programmme which discusses what quants do in the context of recent market upsets. The podcast of this programme may be found here. (The quant section starts after 9mins 25 secs.)

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It is and it isn't

I couldn't resist this rather trivial blog, just a comment really on happenings at a recent quantie dinner. In attendance, going clockwise around the table at Union Square Cafe, PW, Bruno Dupire, Salih Neftci, Peter Carr, Jim Gatheral and Emanuel Derman.

Discussing the validity of all this Black-Scholes stuff that has got so much bad press recently, JG says "I have a nice apartment in **** thanks to Black-Scholes being correct" to which yours truly responded "Well, I have a nice flat in **** thanks to it being wrong!" Now, you can sort of see how that can be! It depends upon a) to what use you put BS and, crucially, b) how much profit margin you can add to any deal!

Not naming any more names, it was clear from the rest of the conversation (which concerned numerical integration in infinite-dimensional spaces!) that, if this sample is to be trusted and extrapolated, a) half of all quants actually believe all this math finance modelling nonsense, b) one third of all quants don't, and are rather concerned for the mental health of the first half, and c) one sixth of all quants either don't care or have maybe been enjoying the excellent wine list at Union Square Cafe too much!

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Priests and Applied Mathematicians

Nassim Taleb and I were lecturing in Mexico City at the weekend (thanks, RiskMathics!). In our free time we visited Teotichucan with its two impressive pyramids. The larger (Pyramide del Sol) is the third largest pyramid in the world by volume. The two pyramids and the surrounding temples, buildings, arenas, etc. were constructed about two thousand years ago and took two hundred years to complete.

Pyramide del Sol

The people of Teotichucan were divided into three castes. The lowest being the farmers, the middle being the builders (15,000 involved in the construction of pyramids and temples), and the highest being the priests and the applied mathematicians. Yes, our guide really did specify that they were applied mathematicians!

A priest and an applied mathematician.

Labour Gets A Head

Watching Gordon Brown speaking at the Labour Party conference I was reminded of that quotation by the insightful Georges Clemenceau, "Not to be a socialist at 20 is proof of want of heart, to be one at 30 is proof of want of head." So perhaps Labour's transformation over the last ten years has not been a cynical ploy to get power but instead a perfectly natural maturing that comes with age.

Mexican Wave

Entirely unoriginal, but I couldn't resist taking this photo from the dais before my recent lecture at the HSBC Global Markets Conference, Latin America, held at Los Cabos, Mexico. (One of the audience members suggested it should be entitled "Hands up if you thought Wilmott's talk was the best of the conference?" But he suggested that before I spoke.)

Los Cabos is a desert-like resort near the tip of Baja Sur. Multi-million dollar properties are being snapped up by retiring Americans. Call me old fashioned, but with global warming isn't a desert the last place you would want to buy a retirement home?

A very warm climate, and an even warmer audience. Thank you, HSBC!

Swedish Message

And so my travels take me to the OMX in Stockholm where I had been invited to give a few lectures (fear and greed, blackjack and vol arb). The other two speakers were Joe Corona and Marc Faber, both of whom were foretelling the imminent collapse of global stockmarkets. It seems that at the moment we all want to hear that the end is nigh. Certainly, it makes for an entertaining speech, and nothing brings people together better than knowing that everyone is going to suffer, and not just you. 'Hope' is the trouble, as John Cleese says in Clockwise "I can take the despair. It's the hope I can't stand." My own view is equally pessimistic, but rather than blaming house prices and climate change, I tend to favour the 'global village' villain, i.e. thanks to easy long-distance travel and technology/telecoms we can no longer rely on Darwin to get us out of a mess. Survival of the fittest is not going to work when we all live or die as a single organism. (Mind you, this won't be an argument that will worry Americans, since only 50% of them believe in evolution. Praise the Lord, and pass the ammunition.)

The moderator for some of the lectures was Jon Briggs, famous as the voice of The Weakest Link. A true professional, he was totally unperturbed by the audience's refusal to laugh at his jokes. Don't get me wrong, they were a keen and bright audience (for example, no snoring even after a particularly heavy session the night before), but they were very shy and would not ask questions about the lecture nor would they laugh unless a joke contained a reference to suicide or sex.

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Cannes Film Festival

The Cannes Film Festival, of sorts, began in 1939 as a palatable alternative to the Venice Film Festival which had by then developed a nasty habit of giving all its awards to chums of Hitler and Mussolini. The Festival as we now know it began in 1946, and this year is the 60th Cannes (lack of money meant that there was no festival in 1948 and 1950). Last week I was lucky enough to attend the opening days as a guest of one of the few British films in any of the main competitions.

To draw similarities with more familiar terrain, the festival is not unlike a larger version of a major quant conference, but with more sun, sand and sex. There are the big premieres and innumerable smaller movies. The celebs attend only the biggest screenings, but will often sneak off as soon as they can. You can see the parallels. (I personally am more tolerant of boring, unimaginative films than I am of boring, unimaginative quant research!)

Being one of the plebs, I did actually see a few movies (as well as doing a decent amount of partying). Michael Moore's Sicko was excellent. I am sure it will be easy to pick holes in his data, but the big picture is spot on. I was at the premiere of Leonardo di Caprio's Al-Gore-without-the-science-but-with-a-real-Native-American-chief-instead 11th Hour. Daryl Hannah sat in front of me, you can see the back of her head in the photo below. (I know what you are thinking!)

Another film I must mention is the French Heros. Thirty minutes too long, it really drags, but then the main protagonist puts on the clown makeup, a Gene Kelly song, and some drum'n'bass and suddenly it's a whole new film. Worth sitting though the first 90 minutes for some memorable images towards the end.

Paul's Tips for Cannes:

1. Spend a few hours early on familiarizing yourself with all the venues and the system generally. Don't believe anything that anyone tells you, no matter how official they are. Printed info is usually correct however.

2. To get into the more exclusive screenings you must be a producer, director or someone on the buy side. (You need a pass with an 'R' on it.) Actors, editors, DOPs, etc. can get into many events, but PR people can't get into anything!

3. For the ladies, wear flat shoes whenever possible. You will spend many hours doing "the walk", up and down La Croisette, from screenings, to parties, etc. and back.

4. Cannes is surprisingly inexpensive. Except for taxis, that is. There is neither rhyme nor reason to the pricing, all that is certain is that they cost an arm and a leg.

5. In the screenings the celebs have reserved seating about one quarter of the way back from the screen. That's except for DH, who always sits in front of me. She must like younger men!

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Blackjack podcast

At Espen Haug's recent book launch I gave a lecture on how to win at Blackjack, and the Kelly criterion for money management. The MP3 of that lecture, introduced by Einar Bonnevie, is attached (see 'Download' link below). In a few weeks' time we will probably put the Powerpoint lecture on wilmott.com as well.

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Espen Haug book launch

Espen was kind enough to invite me to speak at the launch of his Derivatives: Models on Models at the Oslo Stock Exchange last week.

My talk was on Blackjack (I hope to have it on the site soon) and Espen spoke about the missing history of derivatives (his lecture also to be posted shortly).

This was followed by lots of very nice and free (NNT, are you reading this?!) food and drink, and an exhibition of some derivatives art.

The evening ended for some of us at around 2am, shortly after a visit to "Zinatra's" for karaoke. (Fortunately Mrs W was there to sing Smells Like Teen Spirit, I swear I was only miming!)

Life in the tail

Had dinner with Nassim Taleb last night, at Carluccio's off Russell Square. I realise now how he got into this Black Swan thing...his entire life is lived in the tail, every time we meet there is some major event happening. Last night it was his entry into the New York Times bestseller list at an impressive (even to him!) number 5. The photo was taken a couple of minutes after him getting the news from his publisher.

I only see NNT a few times a year, but always there is excitement. Unfortunately, not always of the good kind. We were walking along Bishopsgate a few years ago when a couple of planes flew into the WTC. Our discussions had to be cut short since he was managing a hedge fund which had a lot of tail exposure...long, of course. Another time we were giving one of our famous training courses together when we almost had to evacuate the building...it was the 21 July failed bombings in London.

I thought my life was quite unusual but I can't compete! And he seems to get younger as he gets older, clearly this life is good for him. (And, yes, Nassim, you are even getting slimmer!)

Nassim Nicholas Taleb's The Black Swan is available from all good online bookshops, such as here.

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Quantitative Finance in China

Paul Shaw (CEO of 7city Learning) and I have just returned from a week in China, starting in Shanghai and then going on to Beijing. We were invited there to explain about the Certificate in Quantitative Finance. I spoke at various exchanges, at universities and with government officials. We met with Mr Xia Bin, Director General and Research Fellow of the Financial Research Institute, which is the finance arm of the Development Research Center of the State Council of the P.R.C. The FRI will be endorsing the CQF as the best-practice financial engineering qualification for those working in or wanting to work in the emerging derivatives market in China.

As well as being a very successful business trip it was also an impressive social whirl. I have never eaten so much so consistently in all my life. Every day we had at least one 'banquet' (usually two) of typically a dozen courses. These banquets would sometimes take place in what I can only describe as Chinese versions of country estates, just a few of us and the staff in the middle of acres of lakes and lawns. What surprised me was that in eight days we only had two, small, bowls of rice. Given the vast amount we ate, with so few carbs, I think I can now vouch for the Atkins diet! The photo shows me having a late-night snack of scorpion, bought at a street food stall in Beijing.

If all goes well I hope to return to China later this year.

Fear and Greed: The Market Price of Risk

The Market Price of Risk is a much-neglected quantity. It is a concept that you'll find in models of incomplete markets. In a nutshell, if a market is incomplete and you can't hedge away some risk then you have to say how that risk is valued. The Market Price of Risk (MPR) quantifies this, and allows you to price all derivatives on the same underlying(s) consistently with each other. (If they have the same source(s) of risk then those risks ought to be treated alike.)

You don't see it discussed much because we tend to talk about the risk-neutral world alone, whereas the MPR defines the difference between the real and risk-neutral worlds. (You'll find the MPR in the drift of the stochastic variables.) And once you calibrate to the market prices of derivatives you won't see it anymore. (That's why it's hard to spot in the HJM and BGM models which calibrate right from the start.)

Nevertheless this quantity is very important since it levels the playing field for all investments, no matter how complex. You see it in Markowitz's Modern Portfolio Theory, and the MPR for each source of randomness and the correlations between them can be used to choose optimal portfolios.

But what does the MPR look like? Is it a time-stable constant, representing the compensation for taking risk of rational investors. Is it slowly varying representing the changing attitude towards risk of different generations? No, neither of these. The figure above shows what the MPR looks like for US interest rates. (Technically, this is the Market Price of Spot Interest Rate Risk.) It appears random. The spikes can be interpreted as over or undercompensation for taking risk, fear versus greed.

Details of how to find this MPR and how to use it for modelling as a second stochastic factor (incidentally, introducing the Market Price of Market Price of Risk Risk!) and also for trading, as in stat arb, can be found in Ahmad, R & Wilmott, P 2007 The Market Price of Interest-rate Risk: Measuring and Modelling Fear and Greed in the Fixed-income Markets. Wilmott magazine, January 64-70

Frequently Asked Questions in Quantitative Finance

The book FAQs in QF (FAQQF, pronounce it how you will!) has just been released. You can hear and 'see' me read the preface in the attached MP4 video. (If I sound a little tired in the video it's because I was just recovering from a head cold.)

The book can be bought here.

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Decline of the West: 1a

Following on from Emanuel's Continental Airlines spelling-error blog...

Virgin Atlantic is the worst airline for such errors, The Independent newspaper now matches The Grauniad typo for typo, even the BBC's standards have dropped so that on news bulletins you will, fortunately still only occasionally, find mistakes on their 'tickertapes.'

Now here's my favourite.

I was at a music festival this summer. There I saw a young gentleman sporting a fluorescent green Mohican. His chest was bare, and on it, in a very large gothic font, were the words:

"Life Wont Wait"

Indeed, nor will apostrophes. At least, you can't accuse him of not practising what he preaches.

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History of Monte Carlo Methods - Palisade Conference

Earlier this year, I gave the keynote speech at the Palisade Conference in exotic Heathrow (Monte Carlo itself has gone terribly downmarket of late, dahlings). This speech is now available as an audio podcast. Palisade incorporate Monte Carlo simulation tools as part of their powerful risk analysis software.

Download the attached.

Connaught Square Squirrel Hunt

The Connaught Square Squirrel Hunt is the world’s only urban hunt and the first hunt club founded after the 2004 hunting ban. Their recent meet was on Sunday, 17th September, starting, as they usually do, with a glass of port at the Duke of Kendal pub, Connaught Street.

The CSSH drag-hunt squirrels across Hyde Park, meaning that one member runs through the park with an old sock on a string, and the dog chases after this pretend 'squirrel.' Close on the paws of the dog are the hundred or so sweating followers, trying to keep up. After no more than thirty seconds the dog catches the sock, has a good chew, and after a short break for everyone to catch their breath, it all starts again.

Here's Dillon and master, on 'horseback.' On the way to Hyde Park we all stop outside 29 Connaught Square, the retirement home for Tony Blair, for a photo opp for the horde of media. The hunt say they named themselves after this square to remind TB about what they call his worst piece of legislation.

The 'squirrel' is just an old sock, but Dillon still seems to enjoy the chase.

Your fearless reporter gets trampled by the mob. And Dillon gets his breath back for a repeat performance.

The purpose of the hunt is explained on their website as follows.

It is absurd that the Hunting Act prohibits you from encouraging a dog to chase a squirrel. More than that, it is frightening that your dog could be put down and you could be fined £5,000 for saying “Go on Rover, get after it!”.

What is really sinister though, is that if a policeman thought you might want your dog to chase a squirrel in the future, he could raid your home and confiscate evidence.. All this without a warrant from a Magistrate: even a suspected burglar has more rights than a suspected Squirrel-Hunter!

When we realised that the innocent habits of most dog-owners were illegal, it was clear that this should be publicised as much as possible. People should be made aware of the law and how to act within it. And the more people that think the Hunting Act is an ass, the more people will support its repeal.

Top of the world, Ma!

Not wanting to compete with the Collector's 'The World is My Office,' of course, but even on top of a volcano one can check one's emails.

This is Haleakala, the volcano on the East of Maui. Haleakala hasn't erupted since 1790. (Kilauea on neighbouring Big Island has been in a state of eruption for twenty years, and you can see the lava running into the ocean.) The summit of Haleakala is just over 10,000 feet above sea level, but if it weren't for the other 20,000 feet being submerged this volcano would be taller than Mount Everest.

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Volatility arbitrage, some results

As promised, here is some of the mathematics behind hedging options when you think that there is an arbitrage opportunity.

Let's keep the problem simple. You are in a Black-Scholes world. Volatility is constant. But the market is pricing an option using the wrong volatility, implied volatility is lower than actual volatility, so the option is cheap. You buy the option, but then to make money you must hedge away market risk using the underlying. Do you use a delta based on the actual volatility or on implied volatility?

Case 1: Hedge using actual volatility

If you use actual volatility then you make a guaranteed profit, whose present value is the difference between Black-Scholes using actual volatility and Black-Scholes using implied:

where is actual volatility and is implied. This is the guaranteed profit, regardless of how the stock behaves, it is path independent. Unfortunately, you get wild P&L swings hedging this way.

Case 2: Hedge using implied volatility

It is more common to hedge using implied volatility. Now the profit is path dependent, but at least there aren't the wild swings from day to day. Each time step you make a profit of

This is always positive (as long as actual volatility is greater than implied) but the total by expiration depends on how the stock behaves.

The expected profit is then

This depends on the growth rate of the stock . Note that this is the expected profit. Although you won't lose money hedging this way you will not know a priori how much profit you will make.

So would you rather have a known profit but with daily P&L swings, or a positive daily P&L but random final profit? Perhaps the deciding factor is that when you hedge with implied volatility you will make a profit whenever you are on the right side of the trade (buy when implied vol is lower than actual and sell when it is higher). You can see this from the above formula for the profit each time step.

All of the details are contained in Ahmad & Wilmott 2005 "Which free lunch would you like today, Sir?" Wilmott magazine, November issue.

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Volatility arbitrage

I continue to be staggered by the depth and detail of some people's understanding of complicated quant models while these same people have absolutely no appreciation of the bigger picture. A case in point is that of volatility modelling.

If you really get into the Heston stochastic volatility model you will find yourself having to do some numerical integration in the complex plane (thanks to the transform methods used to solve the governing equation). This can be quite tricky to do in practice. Is all that effort worth it? Well, in part this depends on how good the model is. So you might think people would test the accuracy of the model against the data. Do they do this? Rarely. It is deemed sufficient to calibrate to a static dataset of option values regardless of the accuracy of the dynamics of that dataset. Yes, I know you then hedge with vanillas to reduce model risk, but this is a fudge that is completely inconsistent with the initial modelling. The cynic in me says that the benefit of modelling in such oblivion is truly tested by the state of your bank balance at the end of the year. If you get a bonus, does it matter? I don't have too much of a problem with that, depending on where you are in the management structure. However, I suspect that this is not most people's justification for their inaccurate modelling. I suspect that people really do believe that they are doing good work, and the more complicated the mathematics the better.

So, many know all the ins and outs of the most advanced volatility models based in the classical no-arbitrage world. Well, what if your job is to find volatility arbitrage opportunities? "There's no such thing as a free lunch" is drummed into most quants, thanks to academics and authors who take an almost axiomatic approach to our subject (see Derman’s recent blog). Those who know the details of volatility arbitrage are few and far between. Take the example of how to hedge when you think that options are mispriced.

You forecast volatility to be much higher or lower than current implied volatility. Clearly this is an arbitrage opportunity. But to get at that profit you must hedge stock risk. Now, working within an otherwise very simple Black-Scholes world but with two volatilities, implied and forecast, how should you hedge and how much profit will you make?

I have attached an audio recording (MP3) of the lecture I gave on this topic at a recent conference in Amsterdam.

In my next blog I will give some of the details of this problem.

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The brown acid is back...

Or maybe it really happened. Well, here are the photos to prove it. Hedgestock 2006.


Knebworth House, and some flash motors.


David Harding of Winton Capital. Winton Capital had one of the more laid-back tents.


The Credit Suisse tent. Thanks to them for inviting me to Hedgestock to give a little speech.


Jimi Hendrix is doing somersaults in his grave.

All together now, "One, two, three, what are we fighting for?"

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Celebrating Derivatives

"Celebrating Derivatives" was name of the conference I attended in Amsterdam on Thursday. (I will upload an audio file of my lecture shortly, assuming the recording is acceptable.) I arrived towards the end of the conference so missed almost all of the talks except for Jim Gatheral speaking on volatility forecasting. This seems to be all the rage at the moment. I don't mean being late or Jim Gatheral are all the rage, anyway no more or less than usual, rather vol forecasting is.

The panel discussion (John Hull, Claudio Albanese, JG, Antoon Pelsser and me, overseen by Ton Vorst) was great fun. My favourite bit was John Hull trying to persuade the audience of the value of an MBA above more mathematical programmes. Now JH is a lovely man, but even he couldn't convince this audience! (Do you really get more interpersonal and business skills on an MBA than you should have picked up naturally by the age of six? I don't think so.)

JH had been talking about CDOs and CDO^2s, mentioning that he knew of some CDO^3s that had been done. Exp(CDO) anyone?

The photo above is of the gift I was given by the organizers. All of the speakers were given their own personalized cartoon...as JG said "of a lot of bald guys."

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Certificate in Quantitative Finance Open Evening presentation

I have attached an audio recording of a recent open evening for the CQF in New York. This may be of interest to anyone who would like to but can't make the final open evening for the June programme, in London on Thursday 25th May.

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Volatility forecasting, option trading and CrashMetrics

In April 2006 I spoke at an IQPC conference in London on Correlation Trading. My contribution concerned three topics, all of which I have used successfully in practice:

- The first is a useful technique for backing out reliable stochastic models for random financial variables. It uses the increments in the variable to estimate the volatility structure (in this case, the volatility of volatility) and the steady-state distribution to back out the drift structure. It's a technique I've used for modelling volatility, interest rates and commodity prices.

- Second is the profit you make from buying/selling and hedging incorrectly priced options, simple volatility arbitrage.

- Third, CrashMetrics, the ever so simple stress test for extreme markets when assets become very highly correlated.

I'll be speaking on the second of these subjects in detail at a conference in Amsterdam on June 1st.

The attached (rather large, 17Mb) file is the audio recording of my London lecture.

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Why?

Dear All,

I'm going to use this blog to give people access to miscellaneous research lectures of mine, to keep them abreast of my current areas of research, to give some subtle publicity for various projects, of mine and of friends and colleagues, and to propose informal social events.

The photo should give you a ballpark idea of what I look like, should you want to accost me. Although I don't usually have that silly look on my face - that photo was taken at a book launch party, and all the attention clearly went to my head - sometimes I smile, but more usually I'm scowling. Don't take it personally!

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