Peter Paul Rubens - Achilles down at heel.
Following 2 blogs below, more on Gaussian copula and credit derivativesIn 2005, a WSJ article described the 5-year old maths equation that ballooned the market for credit derivatives to a nominal value issued that briefly exceeded all of world GDP in 2007. In 2005 the value of contracts outstanding was only 1/30 of what it grew to over only the next 3 years. That heady ascent alone should have sufficed for regulators, central banks, and governments to call an emergency stop to the topsy turvey madness and take drastic action - they didn't.
Credit derivatives let banks, hedge funds and other investors trade the risk associated with credit defaults (i.e. bankruptcy of bond issuers). As with other derivatives products, market size didn't take off on rocket trajectories until a simple model for pricing was widely accepted. The model itself that did this was without a scintilla of doubt far too simple, yet academics were guarded in their condemnations, and used their critiques mainly to publish more academic papers rather than scream out "Emperor has no clothes!". So, somehow, the doubts were only ripples in the market pond-life. From market-traders and securitizing bankers' perspective it improved risk valuations by simplifying (in proprietary ways) and yet maintained the fiction of the necessity to pay large telephone number bonuses to "sophisticated, complex, structured product" traders and research analysts. On the plus side, credit derivatives appeared to make bond markets more liquid and efficient, allowing "risk to be transferred to those most willing to bear it". On the downside, by 2005 it was already in the public domain from the views of many clear-sighted thinkers that this was supporting an ill-understood casino playing with trillions of dollars. The earlier generation of models coming out of the Vasicek model for default probabilities (the basis of the KMV methodology) looked ragged and stochastically rough.
David Li's computerized financial model appeared to weigh the likelihood that a given set of corporate bond-issuers would default on their bond debt in quick succession, forming the long tail of a risk bell-shaped curve, the tail being the long downcurving end with a small % (unexpected, unlikely) probability of many simultaneous defaults (bankruptcies) occuring. Think of it as a produce scale that not only weighs a bag of apples but estimates the chance that they'll all be rotten in a week. The 2001 dot.com technology bubble burst was an example of this. And yet, that, and many other examples in previous years, was not enough to shed serious doubt on a simplistic risk algorithm, possibly because it appealed to financial mathematicians while financial economists were left entirely out of the loop.
The model fueled explosive growth in the market for credit derivatives: investment vehicles that based on corporate bonds to price and sell insurance protection against a default. This market that barely existed in the mid-1990s. By 2005 it seemed in WSJ's words "gigantic -- measured in the trillions of dollars -- and so murky that it has drawn expressions of concern from several market watchers. The Federal Reserve Bank of New York has asked 14 big banks to meet with it about practices in the surging market." This did lead to changes to Basel II regulations, but the practises nevertheless mushroomed incredibly.
The model David Li had devised helped estimate what return investors in certain credit derivatives should demand, how much they have at risk, and what strategies to employ to minimise the risk. Big investors started using the model to make trades that entailed giant bets (given, as with most derivatives, the opportunity to leverage hugely) i.e. with little or none of their cash-money tied up. By 2005, hundreds of billions of dollars were riding on variations of the model day by day.
In 2005, Darrell Duffie, a Stanford University professor, famous alongside Professors, Merton and Singleton for mathematical modeling of financial risks, said "David Li deserves recognition, he brought that innovation into the markets [and] it has facilitated dramatic growth of the credit-derivatives markets." But he recognised that the problem was that "the scale's calibration isn't foolproof. The most dangerous part." Hence the professors focused on more scalable version. Mr. Li himself said back then of the model, words that have been oft-repeated recently, the problem "is when people believe everything coming out of it." He knew that investors put too much trust in it or don't understand its subtleties (?) and may think they've eliminated their risks when they hadn't.
The story of Mr. Li (see next blog below) and his model illustrated, according to the WSJ in 2005, "the peril of today's increasingly sophisticated investment world... extends far beyond its visible tip of stocks and bonds and their reactions to earnings or economic news... the largely invisible realm of derivatives... investment contracts structured so their value depends on the behavior of some other thing or event... credit derivatives play a significant and growing role... Endless trading in them makes markets more efficient and eases the flow of money into companies that can use it to grow, create jobs and perhaps spread prosperity", which seemed on balance to condone the market. But the WSJ also said, "investors who use credit derivatives without fully appreciating the risks can cause much trouble for themselves and potentially also for others, by triggering a cascade of losses", and quoted David Hinman, of Ares Management LLC, "I think this is a baby financial mania... Like a lot of financial manias, it tends to end with some casualties."
David Li's model needed a fertile context. The context was investment banks trying to replicate a version of the german Pfandbriefe market of bank bonds, bonds covered by a bank's balance sheet of corporate loans. This became the concept of pooling corporate bonds and selling off pieces of the 'asset pool', of loan-receivable such as lease-finance loans, and including the value even of buying and selling the tax liabilities attaching to lease-finance asset pools, and extending this to corporate loans, just as they had done with mortgages. Banks called these bond pools collateralized debt obligations, CDOs. By cracking this market, investment banks could take a lot of corporate lending business away from traditional commercial banks, and did so.
CDOs made bond investing less risky through diversification across a pool of many borrowers of different sizes and business sectors. Invest in one company's bonds and you could lose all. But invest in the bonds of 100 to 300 companies and one loss won't hurt much.
The pools, however, didn't just offer diversification. They also enabled sophisticated investors to boost potential returns by taking on a portion of the pool if it can be divided into sub-pools with different risk probabilities or into theoretical slices each with different risk protections. Banks cut the pools into slices, called tranches, including one that bore the bulk (first loss %) of the default-risk and several more that were progressively less risky.
Say a pool holds 100 bonds. An investor can buy the riskiest tranche because it offers by far the highest % coupon return, but also bears the first 3% or 6%, say, of any losses the pool suffers from any defaults among its 100 bonds. The investor who buys this is betting there won't be any such losses, or not enough not to buy it for its double-digit % returns. The investor might be a trader or a broker who believes it can be sold-on to less sophisticated buyers who are mesmerised by the 12%, 15% or even higher coupon, and crazily even more so for some short-term gamblers when the spreads widened as a sure sign of the coming crash - why, because they might still book a big multi $million gain and could then maybe take their bonus and make a run for it?
Alternatively, an investor could buy a conservative slice, which won't pay as high a return but also won't face any losses until 10% or more of the pool's bonds default first, and in short to medium term that might appear unlikely. But, who knew? And, when looking for fee-spreads, when dealing with other people's money, who cared?
Investment banks, to figure the rates of return and thereby the price to offer each slice of the pool, they first had to estimate the likelihood of companies who debt is represented in the pool would all go bust at once and totally fail to honour their interest and repayment obligations? Their fates might be tightly intertwined, interdependent in the market, and secondarily the investors and financial firms involved might also be inter-networked. But that latter aspect failed to be quantified. If the corporate borrowers and bond issuers were all in closely related industries, such as automotive, they might fall like dominoes after some catastrophic event exclusive to the automotive industry. In that case, the riskiest slice of the pool would not offer a return much different from the more risk-protected slices, since anything that would sink two or three companies would probably sink many more. Such a pool would have a "high default correlation." But, if a pool had a low default correlation, a low chance of all its companies falling together, then the price gap between the riskiest and least-risky slices would be wide.
This is where Mr. Li made his contribution in 2001.
For four years, nobody knew how to calculate default correlations with precision. Mr. Li's solution drew inspiration from a concept in some actuarial life and pension policy risk research known as "broken heart", which observed that people tend to die faster after the death of a beloved spouse and this this death correlation could be quantitatively predicted, something quite useful to companies that sell life insurance and married-couple annuities. This kind of research has grown with many new companies entering the market for retailing health, life and pension policies. They wanted the agent-fees and faster growth from cherry-picking the least risky policy-holders. The essence of insurance is to build big enough pools that reflect the aggregate risks of what is known in national statistics. To improve on those meant growing faster. Building market share always has a cost a few years down the track of a sudden ballooning of claims. Cherry-picking seemed a way to mitigate this. The same thinking could be applied to CDS.
"Suddenly I thought that the problem I was trying to solve was exactly like the problem these guys were trying to solve," says Mr. Li. "Default is like the death of a company, so we should model this the same way we model human life." A fruitful context for this lateral way of thinking was the current fashion for finding zoological and biological metaphors to replace or augment the empirically-observed and testable precepts of Keynesian macroeconomic models that in the heyday of Monetarism were now politically abandoned if not discredited.
Li's colleagues' work gave him the idea of using copulas (correlated couplings): mathematical functions the colleagues had begun applying to actuarial science. Copulas help predict the likelihood of various events occurring when those events depend to some extent on one another. Among the best copulas for bond pools turned out to be one named after Carl Friedrich Gauss, a 19th-century German statistician. Li had moved to a J.P. Morgan Chase & Co. unit (before later joining Barclays Capital) where he published his idea in March 2000 in the Journal of Fixed Income. The model, known by traders as
the Gaussian copula, was born.
"David Li's paper was kind of a watershed in this area," said Greg Gupton in 2005, senior director of research at Moody's KMV, a subsidiary of the credit-ratings firm. "It garnered a lot of attention. People saw copulas as the new thing that might illuminate a lot of the questions people had at the time." To calculate the likelihood of coupled defaults in a bond pool, the model uses information about the way investors are treating each bond, how risky they're perceiving its issuer to be, if similar they may be linked. The market's assessment of the default likelihood for each company, for each of the next 10 years, is encapsulated in what's called a credit curve. Banks and traders take the credit curves of 9say) all 100 companies in a pool and plug them into the model.
The computer model runs the data through the copula function and spits out a default correlation for the pool - likelihood of all of its companies defaulting on their debt at once. The correlation would be high if all the credit curves looked the same, lower if not. But, of course, the correlations were abstract and unexplained and therefore entirely notional, predicated on s secondary or tertiary assumption that what looks the same is the same? By knowing the pool's default correlations, banks and traders can agree with one another on how much more the riskiest slice of the bond pool ought to yield than the most conservative slice. "That's the beauty of it," said Lisa Watkinson, who in 2005 managed structured credit products at Morgan Stanley in New York. "It's the simplicity." The irony of this is that what all those outside structured products considered opaquely complex, those inside thought of as beautifully simple. Those outside actually understood that the simplicity was inexplicable, but they were real bankers not mathematicians, and empirical economists, not theoretical drawers of curves, frontiers, and crossing points.
Because the model, by making it easier to create and trade CDOs, helped bring forth a factory mass-production of new products whose behaviour it can predict only abstractly and derivately, not with real-world precision, the effect was really to grow 'unknown' risk.
The Gaussian Copula Model managed to make Donald Rumsfeld, the Secretary of Defence at the time, sound supremely intelligent by comparison, when he said, "
There are known knowns. There are things we know that we know. There are known unknowns. That is to say, there are things that we now know we don’t know. But there are also unknown unknowns. There are things we do not know we don’t know."
The CD Swaps are like insurance policies. They insure against a bond default. Owners of bonds can buy credit-default swaps on their bonds to protect themselves. If the bond defaults, whoever sold the credit-default swap is in the same position as an insurer and has to pay up. AIG, one of the world's biggest insurers and the most ambitious jumped on the CDS market determined to dominate it and thereby become truly the world's largest insurer, which it did by an Irish country mile. The price of this protection naturally varies, costing more as the perceived likelihood of default grows. Some people buy credit-default swaps even though they don't own any bonds. They buy just because they think the swaps may rise in value. Their value will rise if issuers of the underlying bonds starts to look shakier. Hence, when in mid-2005 when housing prices started to fall and there was talk of a looming downturn, the prices of CDS took off and so too did the issuance, a case of excess supply growth not causing price deflation! Short term speculators outpaced insurance buyers. As spreads widened that in turn signaled to the markets that defaults and general economic downturn was increasingly imminent. This fed back into the CDS market and speculators weighed in even heavier. It was the equivalent of a massive short-selling signal, but the CDS speculators wanted desperately to make the biggest possible profits and that meant holding until just after the underlying stock markets and general economy would begin crashing.
Say somebody wants default protection on $10 million of GM bonds. That investor might pay $500,000 a year to someone else for a promise to repay the bonds' face value if GM defaults. If GM later starts to look more likely to default than before, that first investor might be able to resell that one-year protection for $600,000, pocketing a $100,000 profit. Hold on longer and the margin becomes 1,100bp i.e. $1.1m (as currently on many corporate bond CDS) but what's the value if the insurers look like they'll go bankrupt first, before claims are accepted and settled? AIG went bust and was shored up by the US Treasury in September 2008 just after Lehman Brothers failed.
Just as investment banks were pooling bonds into CDOs and selling off riskier along with less-risky slices, banks (beginning with ABN-AMRO) were pooling batches of CDS into Synthetic CDOs and sell slices of those. Because the SCDOs don't contain any actual bonds, only CDO insurance claims, banks can create them without going to the trouble of purchasing underlying bonds. And the more SCDOs they create, the more money the banks can earn by selling and trading them.
SCDOs have made the world of corporate credit very financially casino-sexy, high risk high return with little money up front.
Someone who invests in a SCDO's riskiest slice, agreeing to protect the pool against its first $10 m in default losses, say, might receive immediate payment up front of $5m plus $500,000 a year, for taking on this risk. He would get this $5m without investing anything, just for the pledge to pay in case of a default, like an insurance company does, with the insured trusting that the risk will be underwritten by sub-insurers. Some investors, to prove they can pay if there is a default, might have to put up some collateral, but that might be only 15% or so of the amount they're on the hook for, or $1.5 million, giving a clear short term profit.
This confidence-trick setup makes SCDO investment very tempting formany hedge-funds that are predicated on highly-leveraged risk-taking. "If you're a new hedge fund starting out, selling protection on the [riskiest] tranche and getting a huge payment up front is certainly something that's going to attract your attention," said Mr. Hinman of Ares Management. It's especially tempting given that a hedge fund's manager typically gets to keep 20% of the fund's bookable profit annually.
SCDOs were booming massively in late 2005, and largely displacing the older-fashioned CDOs. Whereas in 2001, SCDOs insured less than $400bn face amount value of U.S. corporate bonds, they covered $2tn by the end of 2005 (source: J.P. Morgan Chase).
By the end of 2008, the size of the CDO market was $50tn in December 2008 (source: IMF - down from $54.6tn in mid-2008, and from $62tn at end-2007). Hugh McLernon, IMF Director says, "This is a commonly stated figure - it's been stated by the banks, rating agencies, regulators". He did also say, "even if they are nearly accurate, it dwarfs the GDP of the entire world by a couple of times", which, er, it doesn't (world GDP = $62tn) but that's what happens with astronomical numbers.
CDOs are investment products that bundle debt into tranches with the same rating, which when highly-rated pay a 1-2% premium and are sold to investors in the form of credit swaps, contractual bets between two parties about whether a third party will default on its debt. The associated companies listed in many of these products include major US financial firms caught up in the credit crunch, such as Countrywide, Lehman Brothers, Bear Stearns, Fannie Mae and Freddie Mac. According to McLernon, if seven or more of the 100 associated entities fail, investors will suffer heavy losses that will trigger "unprecedented litigation" including class action suits. Hence, when several of the entities commonly listed in these contracts failed, they were immediately saved or resuscitated by the US Treasury and are now called 'zombie banks', with the exception of Lehman Brothers, the decision not to save it now being deeply regretted by the US Treasury and many others. Mclernon said, "It depends, but on average, if the number of defaults goes to seven you lose one-third of your money, if it goes to eight, you lose two-thirds and if it goes to nine, you lose the lot." He also noted that it would be difficult to predict the extent of the potential fallout because of the lack of transparency in the derivatives market. "This area is noted for the fact that it's not transparent. No-one has a clue around the world - including the banks or the regulators. No-one has a clue what the amount in value of CDOs is, who's got them, when they are due to mature, what the terms of them are, and what will cause a total loss," and "God only knows - or maybe even he doesn't. I certainly don't." Therefore, the solution being worked on for over a year is to bring all CDOs and SCDOS on exchange via major clearing houses in the USA and Europe.
"I wouldn't want to be sitting on a list of these companies wishing that three or four more don't fail... I mean, if it hadn't been for the US government intervention ... which turned out to be an extraordinary one, they'd have all failed already."
In 2005, the U.S. corporate-bond market has been stated by ratings agencies and others as $4.9tn and $3.6tn in early 2007 and $4tn in 2009. Actually, the truer figure is $13tn in 2005 and the European corporate-bond figure in 2005 was $7tn. These are both data source and definitional confusions. But, they show just how perplexing the analytics of the market can be. By mid-2006 for example the US Corporate bond market was said by some to be half the size of the European market, while US securitized bonds were 5 times the size of European securitized bonds. The confusion arises with defining what is a cash-market bond and what are derivative bonds such as CDOs. All tradable cash-market bonds must be registered on stock exchange even though most of the trading in them is off-exchange. Sometimes the confusion is between the size quoted for the trading volume estimates (secondary market), the value of the outstanding issues, and the value of new issues (primary market) or net new issues (issues less bonds that have matured).
Given all these problems of lack of transparency and in determining just the actual size of outstandings, turnover, and new issues, plus pricing, including the increasingly detached pricing of CDS and SCDS markets, even though these latter are used as proxies for the pricing of underlying bonds, and trying to track default rates, never mind too the downgrading of bonds by the ratings agencies, then all of that also causes confusion. Downgradings were running at less than 3% of issues, then about 3-4% and now 8-10% a year in some or all classes; we can't be absolutely sure.
Consequently, given the amount of conflicting noise, and despite the now well-recognised shortcomings of Mr Li's GCM, if in the credit crunch and recession all classes are correlating towards similar default rates as increasingly all debts appear inter-dependent, then ironically the GCM that caused much of the problem becomes more reliable, at least in the absence of any other reliably authoritative guides. The double-irony however is that CDS and SCDS spreads predicated on GCM are self-fullfilling i.e. have become part of a self-debilitating downward spiral, the ultimate short-selling
deus ex machina!
Much of the world's private and public financial assets are directly and indirectly riding on Mr. Li's model, which he freely conceded 4 years ago had important flaws. For one, it merely relies on a snapshot of current credit curves, rather than taking into account the way they move. It has limited historical data including no full-cycle data. We are getting that only now in extremis. The result: Actual prices in the market differ widely from what the model indicates they would or should be!
Investment banks try to compensate for the shortcomings of the model by cobbling copula models together with other, proprietary model adjustment methods. But, while this is especially active today, it has been going on for years! At J.P. Morgan, 4 years ago, Andrew Threadgold, Head of Market Risk reported, "We're not stupid enough to believe [the model] is omniscient... All risk metrics are flawed in some way, so the trick is to use a lot of different metrics." Bank of America and Citigroup representatives also said they were using various models to assess risk and constantly working to improve them. Deutsche Bank had no comment. Moody's woke up in early 2007 to the fact that their risk-grading models were indifferent to changes in default data! When they fixed that by mid-year, their ratings on ABS and CDO bonds on re-calculation dropped anything up to 17 risk grades, from top AAA to lowest junk-bond status!
As with any model, the forecasts investors, issuers, raters, traders make by using the model are only as good as the inputs and the economic scenarios and stress-tests. Someone asking the model to indicate how CDO prices will act in the future, for example, must first offer a guess about what will happen to the underlying credit curves, to not only the economic underpinnings, but to the market's risk-aversion, risk appetite, and to risk-signals that can include anything from currency exchange rates and inflation and LIBOR rates to corporate profits and length and depth of credit and economic cycles to arrive at not only defaults but also net recoveries! Perception of the riskiness of individual bonds affect shot-term investors wholly differently from long term investors and differently again in terms of the type balance sheet profit statements quarter by quarter or over several years. Trouble awaits those who blindly trust the model's output instead of recognising the differentiating impacts as well as questions about whether they are making a bet based only on what they told the model to calculate or on what else can happen? Mr. Li worried in 2005 that "very few people understand the essence of the model!"
Consider the trade that trips up hedge funds say, when selling insurance on the riskiest slice of a synthetic CDO and looking to the model for a way to hedge the danger that default risk will increase. Using the model, investors may calculate they can offset that danger by buying a double dose of insurance on a more conservative slice. That looks like a great deal. When everyone does it the insurers look insolvent and the pack of cards, the whole asset class, liable to total collapse. If selling protection on the riskiest slice and agreeing to pay as much as $10 million to cover the pool's first default losses, say, the protection-selling investor would collect a $3.5m upfront payment and an additional $500,000 yearly. Hedging the risk would pre-credit crisis cost that investor a mere $415,000 annually to buy protection on a $20 million conservative piece. Today, the cost can be $3-7m or in fact be impossible to buy!
Pre-credit crunch the model's hedge assumed only one possible future: prices of all credit-default swaps in the synthetic CDO move in sync. They don't. This has been clear, or should have been for years! When back May 5, 2005, when the outlook for most bond issues stayed steady, GM and Ford Motor Co., both were downgraded by S&P to below investment-grade. That event caused a jump in the price of protection on GM and Ford bonds. Within two weeks, the premium payment on the riskiest slice of a CDO containing them, the slice most exposed to defaults, leapt to $6.5m upfront. The r result: An investor who had sold protection on the riskiest slice for $3.5 million had a paper loss of nearly $3 million. That's because if the investor wanted to get out of the investment, he would have to buy a like amount of insurance from somebody else for $6.5 million, or $3 million more than he was getting.
The simultaneous investment in the conservative slice proved an inadequate hedge. Because only GM and Ford saw their default risk soar, not the rest of the bond world, the pricing of the more conservative slices of the pool didn't rise nearly as much as the riskiest slice. So there wasn't much of an offsetting profit to be made there by reselling that insurance. Also, this wasn't really the fault of the model, which was designed mainly to price the tranches, not to make predictions. The model assumed the various credit curves would move in sync. and allowed investors to adjust this assumption, an option that some ignored. Because numerous hedge funds made the same credit-derivatives bet, the turmoil they faced spilled over into stock and bond markets. Many investors worried hedge funds might have to dump assets to cover their losses, so they sold, too. Some hedge funds lost a separate bet that relied on GM's bond and stock prices moving in tandem; but went wrong when GM shares rallied when Kirk Kerkorian said he would bid for GM shares.
Writing to investors, fund manager Jean-Michel Hannoun called the market reaction to the GM and Ford credit downgrades too improbable an event for the hedge fund's risk model to capture.
Now, take that example and extrapolate it say 200-fold and we begin to approach the current crisis. Following these events, academics and central bank researchers all started writing paper on systemic risk and the credit default and off-balance sheet securitization markets, and double-default risk, all got extra attention under Basel II. But, BIS in 2005 said, "the events of spring 2005 might not be a true reflection of how these markets would function under stress." Stanford's Prof. Duffie disagreed, "The question is, has the market adopted the model wholesale in a way that has overreached its appropriate use? I think it has." David Li said, "it's not the perfect model. (But) There's not a better one yet." And that more or less is how matters were left until the full earthquake of the credit crunch hit!
Standard Bank asks customers for ideas on how it can improve servicE - surely an excellent idea and one that other banks embrace - but vociferously not Bank of America?
The contrast could not be greater than Bank of America, one of the world's very biggest banks. BoA specifically asks people not to contact it with ideas and suggestions for customer service improvement. It states, "unsolicited idea submission policy - Bank of America and its associates do not accept or consider unsolicited ideas, including ideas for new or improved products, processes or technologies, product enhancements, advertising and marketing campaigns, promotions or new product names. Please do not send any original materials, suggestions or other items," and "If, despite our request not to send us your ideas, you still do, then regardless of what your communication states, the following terms shall apply to your idea submission. You agree that: 
