Thursday, 5 July 2012

Haldane And MacKenzie On Gaussian Copulas

I had the privilege of hearing the Bank of England’s Executive Director of Financial Stability, Andy Haldane speak at the University of Edinburgh on the 8th June. Haldane presented his new paper. For those familiar with Haldane’s output, this continues his familiar style of jargon-free prose and ideas expressed with unerring simplicity and logic, supported by an impressive armature of complex empirical exhibits. This paper moves beyond previous concerns with the scale of bank balance sheets and the problems of interconnectedness in complex systems, and instead begins to unpack the theoretical assumptions that underpin dominant neoclassical theories of mathematical finance and form the skeleton of many financial products.

His argument is that the normal or Gaussian statistical distributions (the bell curve) that are at the heart of these assumptions do not accurately describe huge swathes of human and natural phenomena, whether it is the volume of monthly rainfall, earthquake intensity over time, the occurrence of unique words in novels, historical prices in rice spot markets or equity markets, or even annual growth in GDP or real bank loans. These examples are instead characterized by non-normal or ‘fat tailed’ distributions, where extreme events are much more likely to occur than Gaussian distributions imply.

Such ideas are not new: Nassim Taleb and Benoit Mandelbrot have argued this point for some time. But Haldane’s novelty lies in his history of ‘normality’, which outlines the migration of Gaussian principles from the physical sciences into economics and mathematical finance. Haldane’s view is that this migration is part memetic transmission across the sciences and part inspired by a kind of primordial desire for symmetry within the human brain which makes normal ‘bell curve’ distributions appealing in a very aesthetic sense. Breaking with normalcy is therefore difficult but essential if financial regulation is to do what is now done in meteorology, where complex computer systems using non-normal models have been better able to predict and prepare for weather system risks. Haldane’s conclusion was that it is only by using non-normal, fat-tailed models and mapping system risk that the effects of financial crisis will diminish over time.

Haldane’s work has again introduced many thought-provoking observations on the world of banking and finance, as well as practical solutions for how it might be better regulated. But I am still left with one misgiving, which was expressed in our earlier CRESC work on Haldane: that weather systems have neither the capacity nor the incentive to game those non-normal models or maps of system risk once introduced. Finance does, and therefore the extent to which the methods used to prepare for fat tail events in the natural world can be transposed effectively to the world of financial regulation remains moot. Perhaps for that reason I am more receptive to Taleb’s view – that there are limits to the predictive power of statistics in complex systems like finance, and so the job at hand is to make the system smaller and simpler.

Haldane’s convincing empirical exhibits demonstrate the prevalence of fat-tail distributions in many walks of life. But they do raise an interesting paradox: why do banks – or perhaps more accurately the quants working within banks - persist with Gaussian models if normal distributions in economic and financial systems are so very rare? This was the interesting start point for Donald MacKenzie, Professor of Sociology at Edinburgh University, whose paper followed Andy Haldane’s.

MacKenzie’s answer, based on a detailed ethnography of bank quants was that the majority simply do not believe in Gaussian copula models. MacKenzie’s story is one of quants married to the aesthetic of mathematical purity and rigour, who embrace the elegance of a model like Black Scholes, but hold little regard for the Gaussian copula. This is a problem when most financial risk measures like Value at Risk and the structuring and pricing of financial products, like CDOs are built upon Gaussian principles. So why continue using them? Here, MacKenzie argues, the reasons are rooted fundamentally in culture – an ‘evaluative culture’ with Gaussian copula models at their centre, where exit costs are high. Those exit costs relate specifically to the aim of securing ‘Day One P&L’ – the lump of risk free profit on a deal from which bonuses are allocated.

MacKenzie explains that if non-Gaussian rather than Gaussian assumptions were used in the measurement of risk, then Day One P&L would be much smaller and perhaps even impossible to calculate because many more risky scenarios and unanticipated events would need to be priced in: the lump of profit would not be ‘risk-free’.

This finding very much chimes with discussions and briefing notes that were passed around the secretive ‘dark pool’ exchange that is CRESC whilst writing our book. These ideas broadly suggested that the role of derivatives in banking had been misunderstood. That a Credit Default Swap was not necessarily a tool of risk management or an instrument of wanton speculation, but a vital component in underwriting bankers’ high pay. If securitization was always about bringing forward revenues from the future and realizing them in the present, then derivatives played a vital part in passing on the uncertainties of the future to another party. Thus various swaps would enable banking divisions to strip default risk, interest rate risk etc from the block of revenue on a deal, leaving behind a notionally risk-free lump. Locking in ‘arbitrage profits’ for example by holding AAA securities, financing them with a repo and selling on the default risk via a CDS, would enable the deal brokers to get the revenues onto the P&L and claim their bonus. Of course, this incentive encouraged the expansion of a vast transaction-generating machine, as mortgage volumes were ramped up and worked through the CDO mincer, while risk was passed on to naïve operators at AIG and monoline insurers. The result: system-wide counterparty risk that blew up spectacularly in the aftermath of Lehmans collapse.

Two things emerge from this for me. First, an intellectual question about where performativity theory goes from hereon in? My (albeit limited) understanding of Callonian influenced writing (with which MacKenzie has aligned himself in the past) is that economics performs the economy – it creates the economy in its own image, provided the correct assemblages can be mobilised to bring those assumptions into reality. What MacKenzie is now describing, it seems to me, is something quite different: that the desire to maximise Day One P&L (a financial incentive in other words) influences the models used within specific evaluation cultures, even though those models appear to bear little relation to empirical outcomes over time. This is not a million miles away from questions we have been asking for some time: why those models and why those models at that time?

Second, it also raises an interesting question about how you might regulate such institutions going forward. If that evaluative culture could change, and that non-normal models were used to price in fat tail events, it would remove many of the more pernicious incentives we currently see in the banking sector. If lawyer and accountancy costs were booked up front on deal and revenues were not realized immediately, those products would initially be loss making, and only become profitable after a period of years. It would therefore tie in bonus pay better to the long term performance of the particular products created. Structurers of those products might also have to contemplate counterparty risks going forward, and thus think reflexively about whether they were passing on ‘too much’ risk to others – rather than maximizing volume and passing off risk as ‘somebody else’s problem’. It may also resolve intra-firm moral hazard when many ‘innocent’ bankers are penalized by excessive risk taking in another banking division which causes the value of their bonus options collapse.