Sunday, 22 March 2009

SHARES AT POSTAGE STAMP PRICES;WHY NOT GO FOR THE REAL THING?

No-one is sure when the bottom will bottom in shares, lower new highs, lower lows, and no-one wants to overpay even when getting back into the market at obviously historical lows far below net book values. Our bank shares are now postage stamp prices, so I say why not buy the real thing? I favour stamp investments when they are like Bonds, but also a great inflation hedge and recession-proof investments. And, of course, no stamp-duty when buying 'forever' postage stamps. For those investors ignorant of the 'forever' jargon, this means a postage stamp stating first class or second class but not the class-price! Only 'forever stamps' are investment-grade! I just wish our banks paid as much as the annual gain on 'forever stamps' in retail deposit rates? The cost of sending a letter in UK will go up next year. First and second-class stamps are being increased by 3p to 39p and 30p from April. That's a heady 7.7% and 10% return if you buy now. This will be the second set of rises in 12 months after similar increases last April well above the rate of inflation never mind stratospherically above stock market returns. First class stamps back then went up by 2p to the current 36p and second class by 3p to the present 27p. Business customers will see average price rises of 4.2% (worth in total over £200m). The Royal Mail said that even after the rises, UK stamp prices would remain among the lowest in Europe. That means plenty more scope for rises. If you are a US$ dollar investor now might be a great time to buy UK stamps in expectation of additional currency exchange rate gain sometime later this year. In the UK, around five million fewer letters are being delivered every day compared with two years ago. Therefore, post offices will have many spare sheets, good as cash, better as they rise in value. This is a liquid market with less uncertainty than Gold. Stamps must have a big and ready market of willing buyers and willing sellers now that many post offices face closure threats. hence the prices have got to be 'fair value' and by buying stamps in their thousands it is a win-win for post offices and stamp-holder investors. In the USA, postage stamp rises are limited to the rate of consumer price infltion, hence the next rise like the last one is only about 2% (though 32% for a canny £ sterling investor back then) but for the US$ investor no currency gain. Long term if you could get Forever Stamps, not a bad return. Sending a letter will soon be a little more expensive in the U.S. Postal Service. The next 2% increase is effective May 11, 2 cents to 44 cents for a first class stamp. The total rise is worth about $billion, so not a market for big speculators. Stamps are like cash. Forever Stamps are like AAA bonds and franking machines are like treasury bills. You can buy "Forever Stamps" at the current 42-cent rate and make a 2% return in only 6 weeks or less guaranteed, even wait until the 10th and make the gain in 1 day. That's better than the banks are guaranteed to return on any day, but who knows when they might rebound and stay up?

Thursday, 5 March 2009

ACHILLES HEEL OF CDS DEUS EX MACHINA

Peter Paul Rubens - Achilles down at heel.
Following 2 blogs below, more on Gaussian copula and credit derivatives
In 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!

DAVID X. LI - Enter The Dragon


Enter Li, a star mathematician who grew up in Mao's Red Guards-led Cultural Revolution in rural China in the 1960s. He excelled in school and eventually got a master's degree in economics from Nankai University before leaving the country to get an MBA from Laval University in Quebec. That was followed by two more degrees: a master's in actuarial science and a PhD in statistics, both from Ontario's University of Waterloo. In 1997 he landed at Canadian Imperial Bank of Commerce, where his financial career began in earnest; later, via JPMorgan Chase, he moved to Barclays Capital and by 2004 was charged with rebuilding its quantitative analytics team.
Li's trajectory is typical of the quant era, which began in the mid-1980s. Academia could never compete with the enormous salaries that banks and hedge funds were offering. At the same time, legions of math and physics PhDs were required to create, price, and arbitrage Wall Street's ever more complex investment structures.
In 2000, while working at JPMorgan Chase, Li published a paper in The Journal of Fixed Income titled "On Default Correlation: A Copula Function Approach." (In statistics, a copula is used to couple the behavior of two or more variables.) Using some relatively simple math—by Wall Street standards, anyway—Li came up with an ingenious way to model default correlation without even looking at historical default data. Instead, he used market data about the prices of instruments known as credit default swaps.
David X. Li - Illustration: David A. Johnson - If you're an investor, you have a choice these days: You can either lend directly to borrowers or sell investors credit default swaps, insurance against those same borrowers defaulting. Either way, you get a regular income stream—interest payments or insurance payments—and either way, if the borrower defaults, you lose a lot of money. The returns on both strategies are nearly identical, but because an unlimited number of credit default swaps can be sold against each borrower, the supply of swaps isn't constrained the way the supply of bonds is, so the CDS market managed to grow extremely rapidly. Though credit default swaps were relatively new when Li's paper came out, they soon became a bigger and more liquid market than the bonds on which they were based.
When the price of a credit default swap goes up, that indicates that default risk has risen. Li's breakthrough was that instead of waiting to assemble enough historical data about actual defaults, which are rare in the real world, he used historical prices from the CDS market. It's hard to build a historical model to predict Alice's or Britney's behavior, but anybody could see whether the price of credit default swaps on Britney tended to move in the same direction as that on Alice. If it did, then there was a strong correlation between Alice's and Britney's default risks, as priced by the market. Li wrote a model that used price rather than real-world default data as a shortcut (making an implicit assumption that financial markets in general, and CDS markets in particular, can price default risk correctly).
It was a brilliant simplification of an intractable problem. And Li didn't just radically dumb down the difficulty of working out correlations; he decided not to even bother trying to map and calculate all the nearly infinite relationships between the various loans that made up a pool. What happens when the number of pool members increases or when you mix negative correlations with positive ones? Never mind all that, he said. The only thing that matters is the final correlation number—one clean, simple, all-sufficient figure that sums up everything. The effect on the securitization market was electric. Armed with Li's formula, Wall Street's quants saw a new world of possibilities. And the first thing they did was start creating a huge number of brand-new triple-A securities. Using Li's copula approach meant that ratings agencies like Moody's—or anybody wanting to model the risk of a tranche—no longer needed to puzzle over the underlying securities. All they needed was that correlation number, and out would come a rating telling them how safe or risky the tranche was.
As a result, just about anything could be bundled and turned into a triple-A bond—corporate bonds, bank loans, mortgage-backed securities, whatever you liked. The consequent pools were often known as collateralized debt obligations, or CDOs. You could tranche that pool and create a triple-A security even if none of the components were themselves triple-A. You could even take lower-rated tranches of other CDOs, put them in a pool, and tranche them—an instrument known as a CDO-squared, which at that point was so far removed from any actual underlying bond or loan or mortgage that no one really had a clue what it included. But it didn't matter. All you needed was Li's copula function.
The CDS and CDO markets grew together, feeding on each other. At the end of 2001, there was $920 billion in credit default swaps outstanding. By the end of 2007, that number had skyrocketed to more than $62 trillion. The CDO market, which stood at $275 billion in 2000, grew to $4.7 trillion by 2006. At the heart of it all was Li's formula. When you talk to market participants, they use words like beautiful, simple, and, most commonly, tractable. It could be applied anywhere, for anything, and was quickly adopted not only by banks packaging new bonds but also by traders and hedge funds dreaming up complex trades between those bonds. "The corporate CDO world relied almost exclusively on this copula-based correlation model," says Darrell Duffie, a Stanford University finance professor who served on Moody's Academic Advisory Research Committee. The Gaussian copula soon became such a universally accepted part of the world's financial vocabulary that brokers started quoting prices for bond tranches based on their correlations. "Correlation trading has spread through the psyche of the financial markets like a highly infectious thought virus," wrote derivatives guru Janet Tavakoli in 2006.
The damage was foreseeable and, in fact, foreseen. In 1998, before Li had even invented his copula function, Paul Wilmott wrote that "the correlations between financial quantities are notoriously unstable." Wilmott, a quantitative-finance consultant and lecturer, argued that no theory should be built on such unpredictable parameters. And he wasn't alone. During the boom years, everybody could reel off reasons why the Gaussian copula function wasn't perfect. Li's approach made no allowance for unpredictability: It assumed that correlation was a constant rather than something mercurial. Investment banks would regularly phone Stanford's Duffie and ask him to come in and talk to them about exactly what Li's copula was. Every time, he would warn them that it was not suitable for use in risk management or valuation.
In hindsight, ignoring those warnings looks foolhardy. But at the time, it was easy. Banks dismissed them, partly because the managers empowered to apply the brakes didn't understand the arguments between various arms of the quant universe. Besides, they were making too much money to stop.
In finance, you can never reduce risk outright; you can only try to set up a market in which people who don't want risk sell it to those who do. But in the CDO market, people used the Gaussian copula model to convince themselves they didn't have any risk at all, when in fact they just didn't have any risk 99 percent of the time. The other 1 percent of the time they blew up. Those explosions may have been rare, but they could destroy all previous gains, and then some.
Li's copula function was used to price hundreds of billions of dollars' worth of CDOs filled with mortgages. And because the copula function used CDS prices to calculate correlation, it was forced to confine itself to looking at the period of time when those credit default swaps had been in existence: less than a decade, a period when house prices soared. Naturally, default correlations were very low in those years. But when the mortgage boom ended abruptly and home values started falling across the country, correlations soared.
Bankers securitizing mortgages knew that their models were highly sensitive to house-price appreciation. If it ever turned negative on a national scale, a lot of bonds that had been rated triple-A, or risk-free, by copula-powered computer models would blow up. But no one was willing to stop the creation of CDOs, and the big investment banks happily kept on building more, drawing their correlation data from a period when real estate only went up. "Everyone was pinning their hopes on house prices continuing to rise," says Kai Gilkes of the credit research firm CreditSights, who spent 10 years working at ratings agencies. "When they stopped rising, pretty much everyone was caught on the wrong side, because the sensitivity to house prices was huge. And there was just no getting around it. Why didn't rating agencies build in some cushion for this sensitivity to a house-price-depreciation scenario? Because if they had, they would have never rated a single mortgage-backed CDO."
Bankers should have noted that very small changes in their underlying assumptions could result in very large changes in the correlation number. They also should have noticed that the results they were seeing were much less volatile than they should have been—which implied that the risk was being moved elsewhere. Where had the risk gone? They didn't know, or didn't ask. One reason was that the outputs came from "black box" computer models and were hard to subject to a commonsense smell test. Another was that the quants, who should have been more aware of the copula's weaknesses, weren't the ones making the big asset-allocation decisions. Their managers, who made the actual calls, lacked the math skills to understand what the models were doing or how they worked. They could, however, understand something as simple as a single correlation number. That was the problem.
"The relationship between two assets can never be captured by a single scalar quantity," Wilmott says. For instance, consider the share prices of two sneaker manufacturers: When the market for sneakers is growing, both companies do well and the correlation between them is high. But when one company gets a lot of celebrity endorsements and starts stealing market share from the other, the stock prices diverge and the correlation between them turns negative. And when the nation morphs into a land of flip-flop-wearing couch potatoes, both companies decline and the correlation becomes positive again. It's impossible to sum up such a history in one correlation number, but CDOs were invariably sold on the premise that correlation was more of a constant than a variable.
No one knew all of this better than David X. Li: "Very few people understand the essence of the model," he told The Wall Street Journal way back in fall 2005. "Li can't be blamed," says Gilkes of CreditSights. After all, he just invented the model. Instead, we should blame the bankers who misinterpreted it. And even then, the real danger was created not because any given trader adopted it but because every trader did. In financial markets, everybody doing the same thing is the classic recipe for a bubble and inevitable bust.
Nassim Nicholas Taleb, hedge fund manager and author of The Black Swan, is particularly harsh when it comes to the copula. "People got very excited about the Gaussian copula because of its mathematical elegance, but the thing never worked," he says. "Co-association between securities is not measurable using correlation," because past history can never prepare you for that one day when everything goes south. "Anything that relies on correlation is charlatanism."
Li has been notably absent from the current debate over the causes of the crash. In fact, he is no longer even in the US. Last year, he moved to Beijing to head up the risk-management department of China International Capital Corporation. In a recent conversation, he seemed reluctant to discuss his paper and said he couldn't talk without permission from the PR department. In response to a subsequent request, CICC's press office sent an email saying that Li was no longer doing the kind of work he did in his previous job and, therefore, would not be speaking to the media.
In the world of finance, too many quants see only the numbers before them and forget about the concrete reality the figures are supposed to represent. They think they can model just a few years' worth of data and come up with probabilities for things that may happen only once every 10,000 years. Then people invest on the basis of those probabilities, without stopping to wonder whether the numbers make any sense at all. As Li himself said of his own model: "The most dangerous part is when people believe everything coming out of it."
from: article by Felix Salmon (felix@felixsalmon.com) writes the Market Movers financial blog at Portfolio.com.

Wednesday, 4 March 2009

THE YOU COULDN'T INVENT IT SCANDAL - BUT DAVID LI DID


- taken from WIRED magazine.
David Li's formula, known as a Gaussian copula function was adopted by everybody from bond investors and Wall Street banks to ratings agencies and regulators. And it became so deeply entrenched—and was making people so much money—that warnings about its limitations were largely ignored. In 2000, while working at JPMorgan Chase, Li .came up with an ingenious way to model default correlation without even looking at historical default data. Instead, he used market data about the prices of instruments known as credit default swaps. When the price of a credit default swap goes up, that indicates that default risk has risen. Li's breakthrough was that instead of waiting to assemble enough historical data about actual defaults, which are rare in the real world, he used historical prices from the CDS market/ Li wrote a model that used price rather than real-world default data as a shortcut (making an implicit assumption that financial markets in general, and CDS markets in particular, can price default risk correctly).
The effect on the securitization market was electric. Armed with Li's formula, Wall Street's quants [i.e. math wizards] saw a new world of possibilities. And the first thing they did was start creating a huge number of brand-new triple-A securities. Using Li's copula approach meant that ratings agencies like Moody's—or anybody wanting to model the risk of a tranche—no longer needed to puzzle over the underlying securities. All they needed was that correlation number, and out would come a rating telling them how safe or risky the tranche was.
As a result, just about anything could be bundled and turned into a triple-A bond—corporate bonds, bank loans, mortgage-backed securities, whatever you liked. The consequent pools were often known as collateralized debt obligations, or CDOs. You could tranche that pool and create a triple-A security even if none of the components were themselves triple-A. You could even take lower-rated tranches of other CDOs, put them in a pool, and tranche them—an instrument known as a CDO-squared, which at that point was so far removed from any actual underlying bond or loan or mortgage that no one really had a clue what it included. But it didn't matter. All you needed was Li's copula function.
The CDS and CDO markets grew together, feeding on each other. At the end of 2001, there was $920 billion in credit default swaps outstanding. By the end of 2007, that number had skyrocketed to more than $62 trillion *reduced by net clearing today to just under $50 trillions). The CDO market, which stood at $275 billion in 2000, grew to $4.7 trillion by 2006.
At the heart of it all was Li's formula. When you talk to market participants, they use words like beautiful, simple, and, most commonly, tractable. It could be applied anywhere, for anything, and was quickly adopted not only by banks packaging new bonds but also by traders and hedge funds dreaming up complex trades between those bonds. "The corporate CDO world relied almost exclusively on this copula-based correlation model," says Darrell Duffie, a Stanford University finance professor who served on Moody's Academic Advisory Research Committee. The Gaussian copula soon became such a universally accepted part of the world's financial vocabulary that brokers started quoting prices for bond tranches based on their correlations. "Correlation trading has spread through the psyche of the financial markets like a highly infectious thought virus," wrote derivatives guru Janet Tavakoli in 2006.
David X. Li's Gaussian copula function as first published in 2000. Investors exploited it as a quick—and fatally flawed—way to assess risk. A shorter version appears on this month's cover of Wired. Probability Pr
Specifically, this is a joint default probability—the likelihood that any two members of the pool (A and B) will both default. It's what investors are looking for, and the rest of the formula provides the answer.
Survival times [T]
The amount of time between now and when A and B can be expected to default. Li took the idea from a concept in actuarial science that charts what happens to someone's life expectancy when their spouse dies.
Equality the = sign
A dangerously precise concept, since it leaves no room for error. Clean equations help both quants and their managers forget that the real world contains a surprising amount of uncertainty, fuzziness, and precariousness.
Copula the copula symbol bits
This couples (hence the Latinate term copula) the individual probabilities associated with A and B to come up with a single number. Errors here massively increase the risk of the whole equation blowing up.
Distribution functions the ((F))
The probabilities of how long A and B are likely to survive. Since these are not certainties, they can be dangerous: Small miscalculations may leave you facing much more risk than the formula indicates.
Gamma the Y symbol
The all-powerful correlation parameter, which reduces correlation to a single constant—something that should be highly improbable, if not impossible. This is the magic number that made Li's copula function irresistible.
Li's copula function was used to price hundreds of billions of dollars' worth of CDOs filled with mortgages. And because the copula function used CDS prices to calculate correlation, it was forced to confine itself to looking at the period of time when those credit default swaps had been in existence: less than a decade, a period when house prices soared and so risk priced only a one-way market - UP.