Lessons for Risk Management - Wilmott and Rowe

Great event organised by PRMIA and IAFE last night at Goldman's London offices with a long title:

 "A Little Thought Goes A Long Way and Lessons for Risk Management from the Current Crisis".

The event was moderated by Giovanni Bellossi of FGS Capital, and featured speaking slots by Paul Wilmott and David Rowe of Sungard. Here are my notes on the evening, please forgive any innaccuracies, and please persevere through some of the techy quant stuff, as their general points are well worth understanding.

• Giovanni quoted from Nassim Taleb about how VAR is invalid and that mainstream financial mathematics should be banned (or words to that effect, see earlier post on Taleb)

• He added that whilst what Taleb says cannot be ignored, he said that despite the current crisis and its causes that we should not "throw the baby out with the bathwater" and added that Taleb "...is not only able to recognise a cow but also knows how to milk one."

• Giovanni said that financial mathematics has much to offer and that whilst VAR is simply a number, one of its great benefits has to make one measure of risk simple and compelling enough to get traders and risk managers talking.

Paul Wilmott then took the floor and put forward his thoughts:

On Taleb and the Black-Scholes Model

• Paul mentioned that he and Taleb were great friends, and whilst he agreed with much of what Taleb says he has areas of disagreement, particularly over the use of the Gaussian distribution in finance and its implications for "fat tail" events
• Paul Googled "Taleb" and found more entries for Taleb than for Stephen Hawkin which shows how much attention had come his way due to the "Black Swan" debate
• He thinks that he and Taleb are the "Marmite of finance" (for those of you not in the UK who do not know Marmite, it is a sandwich spread that you either love or hate, never anything inbetween)
• He suggested that every quant needs a much more fundamental and practically grounded understanding of financial mathematics.
• Paul refered to some work (mentioned by Giovanni) that Peter Carr of Bloomberg had done on discrete daily hedging that showed that this option replication technique could remove up to 85% of the risk and that all quants should know about this 15% error term when trying to calculate an option price to the Nth decimal place.
• He described how in the past he had set up a volatility arbitrage hedge fund, wanting to improve upon the flawed assumption of the Black-Scholes (B-S) model that volatility is constant and to build the world's best volatility model for option pricing.
• Paul said that he did build the world's best volatility model (?!), but soon found it took too long to calculate, so he reverted back to B-S and has become an unfashionable fan of the model and its assumptions.
• He added that many of the variants on B-S to overcome its limitations have made the model worse and harder to calibrate.
• In some part due to Taleb's opinions on fat tails of distributions, B-S and other models are now very unpopular but Paul claims that not many people have actually bothered to robustly test the B-S model or take a practical, evidence based approach such as that adopted by Peter Carr.

• Paul then showed some example charts and said that with a limited number of opportunities for regular time-period hedging it was not valid to use risk-neutral pricing whereas if the same number of hedges could be used optimally (implying at irregular time periods) then risk-neutral was valid and hedging could be more effective. He emphasised that this was the kind of practical stuff that a quant should know and that quants show know less about esoteric complex financial mathematics.

Correlation

• Paul said that of all of the issues that need addressing in mathematical finance, the one that he has very few answers on is correlation.
• He showed that even basic questions about correlation are poorly understood, even by quants - a question he asks some quants was that if two asset prices both start out at 100, and they have a correlation (of returns) of 1 (perfect correlation) what is the price of the second asset after a year if the first moves to 200. The answer is not 200, and he showed how assets could diverge in overall direction but still have a correlation of 1 or rise together with a perfect negative correlation of -1.
• Paul illustrated how correlation was a very blunt measure that is mis-used by people to summarise the highly complex and historically unstable relationships between assets driven for example by industry sector success (leading to +ve correlation) or competitive success (leading to -ve correlation)
• As a result, he said that financial products whose value depends on correlation should not be transacted in any great size and moved on to the example of CDOs, where a CDO with 1,000 underlying mortgages has been modelled with 1/2 million correlations all assumed to be 0.6. Why this assumption should be made was his main point.

Sensitivity to Parameters

• His main point here was that a constant should not be varied, otherwise it is not a "constant", in particular focussing on volatility used in the B-S model and the calculation of Vega as prices are moving.
• Paul added that sensitivity measures may apply locally and is such may look comparible from one situation to another, but quants need to understand how outputs respond over a wider range of inputs, and not to be inhibited by accepted practices and beliefs.

Complexity

• Models need to be robust and transparent, and that quants should aim for the mathematical sweet spot.
• Paul put forward the following analogy that at least when driving an old car over a long distance, you knew that the car was likely to break down at least once, but you also knew that it was likely that you could fix it. Contrast this with driving a modern sports supercar and finding that it has (unexpectedly?) broken down - you don't know how to fix it, you do not complete your journey and it costs you an ordinate amount of money to put things right...

Self-Referential Feedback

• Paul described here how the hedging of derivatives contracts in the underlying markets can cause price movements in underlying markets that cause derivatives contracts to re-price that cause more hedging in the underlying markets...
• He was critical of credit derivative pricing as being too complex and too "mathsy" (...but had to admit that he had also endorsed some of this work at the time)

Calibration

• Paul said that model parameter calibration is the devil's work...
• He refered us to inverse problems in mathematics as a background to this issue in mathematical finance.
• He emphasised how markets and price behaviour is fickle and driven by human opinions and behaviours
• He said that on-going and regular re-calibration of a model is very, very likely to mean that the model is wrong (he had a particular example of calibrating a particular model he hates where vol is a function of underlying price and time.

David Rowe, Sungard's specialist spokesman on risk management, then took over from Paul and set out his five topics for discussion:

• Statistical Entropy - fundamentally that information can only be extracted from data, with the emphasis on extraction of information (from that already in the data) rather than creation of new information.
• Structural Imagination - that we need to be aware of how the market assumptions we make are themselves a model and that we need to spend more time on thinking about what could happen outside our current understanding or market experience.
• Self-Referential Feedback - the feedback loops in pricing, risk management and economics
• Complexity and Dark Risk - when you add (untested) complexity of a model to limited data sets you get a recipe for disaster.
• Alternate Means of Valuation - when the primary means of valuing a security is not available (illiquid markets anyone?) then what is the secondary means of calculation value.

Some further notes from David's talk:

• AAA rating should imply a failing once every 10,000 years, with some super senior CDO tranches being rated as better than AAA - David pointed out that even as recently as the early 1990s there were problems in the US housing market that indicated that AAA did not mean what it was taken to mean.
• On structural imagination, David said that quants and risk managers must look for unrepresented variables in a model and track them early to monitor their effects
• On feedback he cited an example where increased returns drove product innovation which drove up (CDO) volumes, which caused underwriting standards to fall, that allowed further complexity, that then led to unreliable risk estimation which then led to more product innovation... and so on.
• He suggested that quants adopt the "second means of valuation" mantra in a similar way to credit specialists always having the mantra when assessing credit of "what is the second means of repayment" (e.g. a lien on a house) when the primary means (mortgage payments) goes away.
• David showed a nice classification from an IASB paper on classifying financial instruments:

Level 1: fair values measured using quoted prices in active markets for the same instrument.

Level 2: fair values measured using quoted prices in active markets for similar instruments or using other valuation techniques for which all significant inputs are based on observable market data

Level 3: fair values measured using valuation techniques for which any significant input is not based on observable market data

David additional proposed the interesting level of "Level ?" for some products, and said that obviously more attention needs to spent on Level 2 and 3 instruments under conditions of reduced (non-existant?) market liquidity.

Summary Session:

Paul and David then answered some questions from the audience:

• Paul said that some risk managers lacked the imagination necessary for good risk management, being confined in standard procedures, beliefs and ways of doing things. He wants risk managers who are good at thinking laterally.
• Paul said that risk management was often an afterthought, not part of the trading process.
• David said that VAR has proven useful despite its weaknesses, in his opinion preventing failures from non-extreme events regardless of the recent extremes
• David said that in answer to Taleb's criticism of using history in modelling, it quite frankly is all we have to go on. He quoted Mark Twain in that: "History does not repeat itself but it does rhyme"

The talks were interesting, and even on points that have been discussed elsewhere both speakers had some interesting slants and good analogies. But maybe I am biassed, as the wine afterwards wasn't bad either!...