On Gaussian copula (cognitive limitations restrict attention to an obviously oversimplified model; big brains were worried from the start):
Correlation is by far the trickiest issue in valuing a CDO. Indeed, it is difficult to be precise about what correlation actually means: in practice, its determination is a task of mathematical modelling. Over the past ten years, a model known as the ‘single-factor Gaussian copula’ has become standard. ‘Single-factor’ means that the degree of correlation is assumed to reflect the varying extent to which fortunes of each debt-issuer depend on a single underlying variable, which one can interpret as the health of the economy. ‘Copula’ indicates that the mathematical issue being addressed is the connectedness of default risks, and ‘Gaussian’ refers to the use of a multi-dimensional variant of the statistician’s standard bell-shaped curve to model this connectedness.
The single-factor Gaussian copula is far from perfect: even before the crisis hit, I wasn’t able to get a single insider to express complete confidence in it. Nevertheless, it became a market Esperanto, allowing people in different institutions to discuss CDO valuation in a mutually intelligible way. But having a standard model is only part of the task of understanding correlation. Historical data are much less useful here. Defaults are rare events, and producing a plausible statistical estimate of the extent of the correlation between, say, the risk of default by Ford and by General Motors is difficult or impossible. So as CDOs gained popularity in the late 1990s and early years of this decade, often the best one could do was simply to employ a uniform, standard figure such as 30 per cent correlation, or use the correlation between two corporations’ stock prices as a proxy for their default correlations.
Ratings, indices and implied correlation:
However imperfect the modelling of CDOs was, the results were regarded by the rating agencies as facts solid enough to allow them to grade CDO tranches. Indeed, the agencies made the models they used public knowledge in the credit markets: Standard & Poor’s, for example, was prepared to supply participants with copies of its ‘CDO Evaluator’ software package. A bank or hedge fund setting up a standard CDO could therefore be confident of the ratings it would achieve. Creators of CDOs liked that it was then possible to offer attractive returns to investors – which are normally banks, hedge funds, insurance companies, pension funds and the like, not private individuals – while retaining enough of the cash-flow from the asset pool to make the effort worthwhile. As markets recovered from the bursting of the dotcom and telecom bubble in 2000-2, the returns from traditional assets – including the premium for holding risky assets – fell sharply. (The effectiveness of CDOs and other credit derivatives in allowing banks to shed credit risk meant that they generally survived the end of the bubble without significant financial distress.) By early 2007, market conditions had been benign for nearly five years, and central bankers were beginning to talk of the ‘Great Stability’. In it, CDOs flourished.
Ratings aside, however, the world of CDOs remained primarily one of private facts. Each CDO is normally different from every other, and the prices at which tranches are sold to investors are not usually publicly known. So credible market prices did not exist. The problem was compounded by one of the repercussions of the Enron scandal. A trader who has done a derivatives deal wants to be able to ‘book’ the profits immediately, in other words have them recognised straightaway in his employer’s accounts and thus in the bonus that he is awarded that year. Enron and its traders had been doing this on the basis of questionable assumptions, and accounting regulators and auditors – the latter mindful of the way in which the giant auditing firm Arthur Andersen collapsed having been prosecuted for its role in the Enron episode – began to clamp down, insisting on the use of facts (observable market values) rather than mere assumptions in ‘booking’ derivatives. That credit correlation was not observable thus became much more of a problem.
From 2003 to 2004, however, the leading dealers in the credit-derivatives market set up fact-generating mechanisms that alleviated these difficulties: credit indices. These resemble CDOs, but do not involve the purchase of assets and, crucially, are standard in their construction. For example, the European and the North American investment-grade indices (the iTraxx and CDX IG) cover set lists of 125 investment-grade corporations. In the terminology of the market, you can ‘buy protection’ or ‘sell protection’ on either an index as a whole or on standard tranches of it. A protection seller receives fees from the buyer, but has to pay out if one or more defaults hit the index or tranche in question.
The fluctuating price of protection on an index as a whole, which is publicly known, provides a snapshot of market perceptions of credit conditions, while the trading of index tranches made correlation into something apparently observable and even tradeable. The Gaussian copula or a similar model can be applied ‘backwards’ to work out the level of correlation implied by the cost of protection on a tranche, which again is publicly known. That helped to satisfy auditors and to facilitate the booking of profits. A new breed of ‘correlation traders’ emerged, who trade index tranches as a way of taking a position on shifts in credit correlation.
Indices and other tranches quickly became a huge-volume, liquid market. They facilitated the creation not just of standard CDOs but of bespoke products such as CDO-like structures that consist only of mezzanine tranches (which offer combinations of returns and ratings that many investors found especially attractive). Products of this kind leave their creators heavily exposed to changes in credit-market conditions, but the index market permitted them to hedge (that is, offset) this exposure.
Quants and massive computational power (one wonders whether the mathematics and computers did nothing more than lend a spurious air of technicality to untrustworthy basic assumptions):
With problems such as the non-observability of correlation apparently adequately solved by the development of indices, the credit-derivatives market, which emerged little more than a decade ago, had grown by June 2007 to an aggregate total of outstanding contracts of $51 trillion, the equivalent of $7,700 for every person on the planet. It is perhaps the most sophisticated sector of the global financial markets, and a fertile source of employment for mathematicians, whose skills are needed to develop models better than the single-factor Gaussian copula.
The credit market is also one of the most computationally intensive activities in the modern world. An investment bank with a big presence in the market will have thousands of positions in credit default swaps, CDOs, indices and similar products. The calculations needed to understand and hedge the exposure of this portfolio to market movements are run, often overnight, on grids of several hundred interconnected computers. The banks’ modellers would love to add as many extra computers as possible to the grids, but often they can’t do so because of the limits imposed by the capacity of air-conditioning systems to remove heat from computer rooms. In the City, the strain put on electricity-supply networks can also be a problem. Those who sell computer hardware to investment banks are now sharply aware that ‘performance per watt’ is part of what they have to deliver.
Collapse of rating agency credibility:
The rating agencies are businesses, and the issuers of debt instruments pay the agencies to rate them. The potential conflict of interest has always been there, even in the days when the agencies mainly graded bonds, which generally they did quite sensibly. However, the way in which the crisis has thrust the conflict into the public eye has further threatened the credibility of ratings. ‘In today’s market, you really can’t trust any ratings,’ one money-market fund manager told Bloomberg Markets in October 2007. She was far from alone in that verdict, and the result was cognitive contagion. Most investors’ ‘knowledge’ of the properties of CDOs and other structured products had been based chiefly on ratings, and the loss of confidence in them affected all such products, not just those based on sub-prime mortgages. Since last summer, it has been just about impossible to set up a new CDO.
Illiquid assets, difficulty of mark to market:
Over recent months, banks have frequently been accused of hiding their credit losses. The truth is scarier: such losses are extremely hard to measure credibly. Marking-to-market requires that there be plausible market prices to use in valuing a portfolio. But the issuing of CDOs has effectively stopped, liquidity has dried up in large sectors of the credit default swap market, and the credibility of the cost of protection in the index market has been damaged by processes of the kind I’ve been discussing.
How, for example, can one value a portfolio of mortgage-backed securities when trading in those securities has ceased? It has become common to use a set of credit indices, the ABX-HE (Asset Backed, Home Equity), as a proxy for the underlying mortgage market, which is now too illiquid for prices in it to be credible. However, the ABX-HE is itself affected by the processes that have undermined the robustness of the apparent facts produced by other sectors of the index market; in particular, the large demand for protection and reduced supply of it may mean the indices have often painted too uniformly dire a picture of the prospects for mortgage-backed securities. One trader told the Financial Times in April that the liquidity of the indices had become very poor: ‘Trading is mostly happening on interdealer screens between eight or ten guys, and this means that prices can move wildly on very light volume.’ Yet because the level of the ABX-HE indices is used by banks’ accountants and auditors to value their multi-billion dollar portfolios of mortgage-backed securities, this esoteric market has considerable effects, since low valuations weaken banks’ balance sheets, curtailing their capacity to lend and thus damaging the wider economy.
Josef Ackermann, the head of Deutsche Bank, has caused a stir by admitting ‘I no longer believe in the market’s self-healing power.’ ...
