In trying to find a WSJ article on David Li, I came up with David Hsu's website, which is very interesting. Let's look at his take on the David Li model:
"This
WSJ article describes a mathematical innovation that helped create the now huge market for credit derivatives. "
This will help create credit derivatives, but one can imagine other ways to essentially do the same thing.
"Credit derivatives let banks, hedge funds and other investors trade the risk associated with credit defaults (i.e. bankruptcy of bond issuers)"
This is correct. The derivative abstracts the risk from a bundle of bonds, say, and redistributes it to buyers of a particular level of risk. What's being bought is the level of risk. But, right off, you can ask yourself a very simple question. Couldn't I find a particular bond or series of bonds for the risk that I'm buying without having to create a bundle and the ensuing abstraction? Sure. Why not? What, then, is the benefit of abstracting levels of risk?
"Just as in previous derivatives markets, things didn't take off until a simple model for pricing became widely accepted."
This was the key innovation. A simpler model of pricing the various levels of risk.
"The model itself is almost certainly too simple, but is (hopefully) improved in proprietary ways by sophisticated traders and researchers."
The model itself needs to be adjusted and improved upon in the actual pricing of bonds.
"On the plus side, credit derivatives make bond markets more liquid and efficient, allowing risk to be transferred to those most willing to bear it."
Maybe. Let's see.
1) Easier to price and sell
2) Efficient
3) Focus on risk
But is that the real benefit?
"On the downside, we have yet another ill-understood casino running, with trillions of dollars in play."
This was my belief. But was it complexity and misunderstanding, or fraud, negligence, and fiduciary misjudgment?
"A few years ago I looked at the Vasicek model for default probabilities (which forms the basis of the KMV methodology), and boy did it look rough."
What is a Vasicek Model?
"In
finance, the
Vasicek model is a
mathematical model describing the evolution of
interest rates. It is a type of "one-factor model" (
short rate model) as it describes interest rate movements as driven by only one source of
market risk. The model can be used in the valuation of
interest rate derivatives, and has also been adapted for credit markets. It was introduced in 1977 by
Oldrich Vasicek."
A trajectory of the short rate and the corresponding yield curve
"Vasicek's model was the first one to capture
mean reversion, an essential characteristic of the interest rate that sets it apart from other financial prices. Thus, as opposed to
stock prices for instance, interest rates cannot rise indefinitely. This is because at very high levels they would hamper economic activity, prompting a decrease in interest rates. Similarly, interest rates can not decrease indefinitely. As a result, interest rates move in a limited range, showing a tendency to revert to a long run value."
So, the interest rates go up and down within a limited range, but revert to a mean.
"The main disadvantage is that, under Vasicek's model, it is theoretically possible for the interest rate to become negative, an undesirable feature."
Very negative, because, in the real world, people would hold cash.
On KMV methodology:
"Forecasting Default with the KMV-Merton Model
Sreedhar T Bharath and Tyler Shumway∗
University of Michigan
December 17, 2004
Looking at CDS implied default probability
regressions and bond yield spread regressions, the KMV-Merton probability does not appear to
be a significant predictor of either quantity when our naive probability, agency ratings and other
explanatory variables are accounted for. We conclude that the KMV-Merton probability is a
marginally useful default forecaster, but it is not a sufficient statistic for default.
We acknowledge that our implementation of the KMV-Merton model is different from that of
Moody’s KMV, and therefore the forecasts of Moody’s KMV might be better than those tested in
this paper."
So, we have two models, which have serious drawbacks for predicting CDS default rates.
"This all looks a lot like the CMO market, where traders blow up with regularity."
A CMO = Collateralized Mortgage Obligation
Not good.
From the WSJ now:
"The banker, David Li, came up with a computerized financial model to weigh the likelihood that a given set of corporations would default on their bond debt in quick succession. 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."
It gives a distribution of defaults over a short period of time.
"The model fueled explosive growth in a market for what are known as credit derivatives: investment vehicles that are based on corporate bonds and give their owners protection against a default. This is a market that barely existed in the mid-1990s. Now it is both so 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 this week about practices in the surging market."
They are an insurance policy on the default of a particular bond or bundle of bonds.
"The model Mr. Li devised helped estimate what return investors in certain credit derivatives should demand, how much they have at risk and what strategies they should employ to minimize that risk. Big investors started using the model to make trades that entailed giant bets with little or none of their money tied up. Now, hundreds of billions of dollars ride on variations of the model every day."
It helps assess risk and defuse it, and how much they should be priced. They are used in trades that involve little collateral.
"The problem: The scale's calibration isn't foolproof. "The most dangerous part," Mr. Li himself says of the model, "is when people believe everything coming out of it." Investors who put too much trust in it or don't understand all its subtleties may think they've eliminated their risks when they haven't."
This is IMPORTANT. Li, himself, understands that it is just a model. A tool for dealing with the real world, but only a tool. It needs Human Agency to assess its value and use.
"The story of Mr. Li and the model illustrates both the promise and peril of today's increasingly sophisticated investment world. That world extends far beyond its visible tip of stocks and bonds and their reactions to earnings or economic news. In 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."
Theoretically, since bonds fund companies in the real world, say, making them easier to trade and sell, should help the creation and funding of businesses, hence helping create jobs, etc.
"But 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. The GM episode proved relatively minor, but some experts say it could have been worse. "I think this is a baby financial mania," says David Hinman, a portfolio manager at Los Angeles investment firm Ares Management LLC, referring to credit derivatives. "Like a lot of financial manias, it tends to end with some casualties."
This is 2005, and some investors are being accused of not understanding them, thereby leading to a possible cascade of losses. 2005. It's being likened to a mania. 2005.
What's the GM episode?
"Delphi, GM & Rogue Events by Jim Willie CB
Jim Willie CB is the editor of the "HAT TRICK LETTER"
Oct 14, 2005
The Oracle of Delphi was once a venerable shrine, supposedly foretelling the future in ancient Greek times. The car parts maker Delphi might today foretell of not only a General Motors bankruptcy, but tectonic shifts beneath the foundations of our financial system. Full leverage puts the entire bond market at risk. It is no coincidence to me that on a single day, Delphi filed for bankruptcy, the Bank of America upped their estimated likelihood of eventual General Motors bankruptcy to 30%, and Standard & Poor's downgraded GM debt one level deeper in junk status. The next day GOLD TOUCHED 480 ON THE DECEMBER FUTURES CONTRACT. My viewpoint has it that gold is being purchased not so much as a price inflation hedge but for a HEDGE AGAINST SYSTEMIC RISK. The bond bubble is under siege.
Chart courtesy of ino.com The USFed is harping about price inflation, in a pathetic orchestrated public relations ploy, which is without a doubt intended to offer them political cover for hiking interest rates. Their hope is to prevent a run on the USDollar, and to continue to encourage foreigners to pay our bills. We have no discipline, no desire to halt waste, no concern even about fraud. Federal budgets are out of control. Monetary inflation unfettered is a valid risk, but systemic risk is a larger risk. Diversion is a key tactic from the Greenspan Fed.
The June episode for GM bond and credit default derivatives was unpleasant and highly disruptive. Gold then began its big rise, decoupled from the USDollar at that time also. Toss in the European Union votes against centralized power. Toss in the advent of euro and yen based carry trades to purchase gold. A witch's brew stirs gold in favorable turns within the cauldron. Tectonic shifts are taking place in the bond market at the foundation sub-basement level. The Delphi bankruptcy will have far-reaching effects to the corporate bond market, and to credit derivative swaps, where risk is offloaded to third parties. What will third parties sell when they take it in the shorts? The treacherous part about derivative risk is that, like an earthquake, it sneaks up on you. The foundation beneath your feet loses its structural integrity and strength. The additional debt downgrade is sure to deliver yet another lethal blow to the convertible debt arbitrage. GM will not go away quietly."
This is 2005.
"DELPHI BANKRUPTCY
The Delphi bankruptcy pulls General Motors back to the slaughterhouse. The rogue event has a clear loser, makers of inefficient obsolete SUV's. When was the last time you saw an SUV pull a boat? CNN pointed out that 50% of state governors drive an SUV. Our leaders are morons. Shock has reverberated to the bond market and surely to their credit derivatives, with damage unclear to date. Car sales are down big, but limited to General Motors and Ford, as Chrysler has been spared. The first economic domino is with car sales, in the movement from inefficient cars, trucks, and sport utility vehicles, toward smaller more efficient cars. The principal source of "better" cars is Asia. A hidden advantage of Asian cars is the lower cost from reduced overhead due to worker benefits. We are witnessing the death of a large segment of the US car industry before our eyes, the tragic consequence of global trade with unfettered lack of controls. National economic policy fails to recognize the threat to our entire manufacturing base.
September car sales were miserable, except for Chrysler. Sport Utility Vehicle sales plummeted 50%, no big surprise there. The ripple effects from gasoline cost shock extend beyond General Motors to its parts suppliers, notably Delphi, but also to some extent Dana. The Delphi insolvency has caused financial stress above with GM and below with its own suppliers, as the United Auto Worker union has become a principal player. Bank of America has raised its estimate from 10% to 30% for the likelihood of a GM bankruptcy. My number is 99% in an easy call. At the least comes a restructuring Ch 13 BK to rid themselves of their obligations for pensions and retiree health care costs, and to enable a debt writedown. The new bankruptcy laws screw individuals, but not corporations. Wage deflation continues to cut a deep swath. The GM stock price has descended below the Kerkorian rescue price of 31 per share. The GM pension system is badly under-funded, despite claims by officials. Market assumptions are the key to the deception, probably aided by bogus 10% annual gains built into formulas.
General Motors owns $11 billion in pension liabilities from Delphi, a major car parts supplier with 24k employees, which itself has 2000 parts suppliers and $1.9 billion in bills pending. They must be nervous. Delphi has filed for bankruptcy. It has shut some US plants, cut pay up to 60%, and abandoned pension obligation to workers. It has an estimated $10.8 billion in under-funded pension obligations. Any downstream supplier with over 20% dependence is at risk, as a dozen such suppliers have also filed for bankruptcy. Delphi has $750 million in 1H2005 losses. Delphi sees in its future the termination of health benefits for its retirees, however adorned by golden parachutes for its executive staff.
In 1999, GM guaranteed the Delphi pension obligations, as part of the GM subsidiary spinoff, in what has proved to be yet another albatross around the GM neck financially. GM derives $2500 in contents per vehicle from Delphi parts. The United Auto Workers are involved, which makes a certainty the long slow certain death, just like with General Motors. Delphi executives have complained that workers earn over $60 per our, 2 to 3x the norm for competitors. Don't get me wrong. My heart is with unions for improving worker conditions and finances. However, refusal to make deep concessions, along with foot dragging on plant closures, guarantees a continued burden of surplus workers and more importantly surplus car output. The end result is not only added overhead costs, but poor pricing power for the end product. More losses are assured. We have already seen a rash of profitless car sales. Furthermore, a $65/hr wage scale seems off by a factor of two, and 90% locked pay for furloughed workers seems overly generous. Delphi seems more like a socialist corporate entity, just like GM and Ford. A second GM parts supplier is also in trouble, namely Dana, which has accounting problems. They have postponed 3Q2005 earnings, and restated 2004 and 2205 earnings. Ford Motors has a similar parts supplier problem with Visteon."
The bankruptcy of GM. This is 2005.
"THE RISK FROM DERIVATIVES
The chain which locks excessive worker pay scales has become the leash leading the companies to ruin. Many are the dominos in Detroit from car makers, their debt burdens, their union obligations, their aging work force, their profitless operations, their heavy unwise reliance upon SUV sales, and the lethal linkage in limbo to credit market "financial sewage," as Warren Buffett calls derivatives.
We have not heard the last of the GM death throes. If the UAW is cooperative, GM might emerge from a restructuring sometime in the next year. If not, GM will endure the death of a thousand cuts, whittled to nothing in the end. The rogue event of twin hurricanes has numerous victims. Each contributes to the process of destabilizing the entire US financial system. Behind the scenes, credit derivatives will continue to fall like underground dominoes. Its underpinning is so dangerous fashioned, that nobody even can properly assess the risk, let alone monitor the status in real time. Heck, an army of 1500 accountants is required to accurately measure their status, another crippled financial giant. Let me save time, and guess that Fanny Mae's capital core is worth well south of $500 billion. The final number cannot be properly assessed until the housing bubble dissipates and resolves itself. The end tally might be somewhere between negative $1800 billion and negative $2500 billion. That figure is a raw estimate, a return of 35% of the $7 trillion in artificially lifted housing value nationally. A bubble giveth, a bubble taketh away.
What one should fear and prepare for is the unexpected. Earthquakes strike with little immediate warning, but often with some imprecise distinctive signals. The LongTerm Capital Management fiasco struck suddenly in autumn 1998, part of the ripple effects from the Asian Meltdown and the Russian debt default. Denials abound for assigning minimal systemic risk from the hurricane damage. Its reconstruction response is audaciously labeled as positive for the US Economy. How about the financial sector fallout? Is that positive also? Is everything positive? Wall Street might prefer a GM and Delphi restructuring over a drawn-out downfall. Last in line, share holders would lose their shirts and shoes. Controlling the strings, their executives might celebrate hefty bonuses and options with newly formed corporate formed entities. Creditors are first in line, while equity share holders pick up whatever does not vanish. Axed workers are not in line at all."
In 2005.
"THE EXTINCTION OF US LEGACY FIRMS
In conversations with people about the legacy Detroit car makers, strange irrational comments and perspectives are offered. An older family member has bought Chevy and Buick brand cars all his life. He secretly bristles at my disdain for US cars based years ago on poor quality and low reliability. My stream of purchases include Audi sedan, Ford pickup (lemon, never again), Toyota pickup, Nissan pickup, BMW sedan. Few believe that the Toyota, the Nissan, and the BMW have never had a major repair from a component failure. He is considering another Buick, even with low miles on his current 4-yr-old sedan. In response to my concern about whether GM will be around in a couple years, he says "I hope so" without concern. Another friend has no idea of the burden from retirees, nor their exorbitant pensions. Another buys Ford as an act of patriotism, with a decal to support the troops. A few are happy customers indeed. But one in particular complains chronically about steady repairs required for his GM sedan, with little indication of breaking ranks in an act of disloyalty. He hates Japanese cars, even though they might be more reliable. It is utterly amazing how many younger women prefer small Japanese sedans. By the way, the #1 stolen car in the USA in recent years has always been a Honda. An old roommate owned a sorry GMC truck, which did not survive 70k miles. A Philly friend owns an old Ford truck, pushing 200k miles, described as "indestructible" but a gas hog.
My viewpoint is that legacy US manufacturing firms are at great risk, since Asian competitors have much lower costs owing to absent fringe benefits like pensions, life insurance, workmen compensation, and short-term disability. Japan offers some benefits, but not China. The gain from half the total mfg hours to produce a Toyota sedan enables that cost advantage. Not a single person who has crossed my path and offered an exchange of views has been aware that China plans next year to export the Cheri, a fully loaded sedan in the $15,000 price range. It will be built with state of the art mfg equipment from Japan. That is the death blow for Detroit, the coup de grace. USGovt officials probably might in their myopia regard the Cheri importation as yet another benefit to our economy, another low-cost solution. Macro economic policy is abysmal in the United States. Not so much abysmal, as non-existent or extinct. US mfg is in line for an unnatural extinction."
This seems to all be coming true.
So, in 2005, the possible cascading effects of derivatives was understood, and, oddly, it was tied to the Automakers bailout.
"In 1997 he landed on the New York trading floor of Canadian Imperial Bank of Commerce, a pioneer in the then-small market for credit derivatives.
Investment banks were toying with the concept of pooling corporate bonds and selling off pieces of the pool, just as they had done with mortgages. Banks called these bond pools collateralized debt obligations."
This is quite simple. You bundle a bunch of corporate bonds, and then divide them up artificially by risk.
"They made bond investing less risky through diversification. 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 so much."
Yes. But you could do that by building a portfolio of bonds. So, what's the advantage? That's no more profound than saying you shouldn't buy only one stock. Put this way, it sounds like a mutual fund bond fund.
"The pools, however, didn't just offer diversification. They also enabled sophisticated investors to boost their potential returns by taking on a large portion of the pool's risk. Banks cut the pools into several slices, called tranches, including one that bore the bulk of the risk and several more that were progressively less risky."
So what? You could do this by buying individual bonds. Again, just build a portfolio of bonds at at certain risk level, and get paid the interest at that level of risk.
"Say a pool holds 100 bonds. An investor can buy the riskiest tranche. It offers by far the highest return, but also bears the first 3% 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, in return for a shot at double-digit returns."
Yes, and an investor can buy 100 bonds from various companies or a bond fund. All this pool does it artificially divide up the risk of this bundle and sell it.
"Alternatively, an investor could buy a conservative slice, which wouldn't pay as high a return but also wouldn't face any losses unless many more of the pool's bonds default."
Same thing, just buy a bunch of AAA bonds from different companies.
"Investment banks, in order to figure out the rates of return at which to offer each slice of the pool, first had to estimate the likelihood that all the companies in it would go bust at once. Their fates might be tightly intertwined. For instance, if the companies were all in closely related industries, such as auto-parts suppliers, they might fall like dominoes after a catastrophic event. In that case, the riskiest slice of the pool wouldn't offer a return much different from the conservative slices, since anything that would sink two or three companies would probably sink many of them. Such a pool would have a "high default correlation."
They might, or they might not. So diversify, just as you would with Fidelity Sector Funds in stocks. Diversify across them.
"But if a pool had a low default correlation -- a low chance of all its companies stumbling at once -- then the price gap between the riskiest slice and the less-risky slices would be wide."
So what? Except that it makes it easier to divide up. But you could do that on your own.
"This is where Mr. Li made his crucial contribution. In 1997, nobody knew how to calculate default correlations with any precision. Mr. Li's solution drew inspiration from a concept in actuarial science known as the "broken heart": People tend to die faster after the death of a beloved spouse. Some of his colleagues from academia were working on a way to predict this death correlation, something quite useful to companies that sell life insurance and joint annuities."
So one spouse dies and, what, you immediately raise the premium?
"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."
Call me skeptical, but I'm no math genius.
"His colleagues' work gave him the idea of using copulas: 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."
"Gaussian copula
Cumulative distribution and probability density functions of Gaussian copula with
ρ = 0.4 One example of a copula often used for modelling in finance is the Gaussian Copula, which is constructed from the bivariate normal distribution via Sklar's theorem. "
"In
statistics, a
copula is used as a general way of formulating a
multivariate distribution in such a way that various general types of dependence can be represented
[1]. Other ways of formulating multivariate distributions include conceptually-based approaches in which the real-world meaning of the variables is used to imply what types of relationships might occur. In contrast, the approach via copulas might be considered as being more raw, but it does allow much more general types of dependencies to be included than would usually be invoked by a conceptual approach.
The approach to formulating a multivariate distribution using a copula is based on the idea that a simple transformation can be made of each marginal variable in such a way that each transformed marginal variable has a uniform distribution. When applied in a practical context, such transformations might be fitted as an initial step for each margin, or the parameters of the transformations might be fitted jointly with those of the copula.
There are many families of copulas which differ in the detail of the dependence they represent. A family will typically have several parameters which relate to the strength and form of the dependence. However, it is possible to specify a dependency structure and for a copula to emerge using a conditioning technique such as the D distribution."
So, this will correlate how the defaults will relate to each other over a pattern of distribution.
1.2 Why are CDOs issued?
The possibility to buy CDO tranches is very interesting for investors to manage
credit risk. The investment in a CDO tranche with a specific risk-return profile is much more attractive for a credit investor or a hedger than to
achieve the same goal via the rather illiquid bond and loan market with high
bid/ask spreads.
However, it may not always be immediately clear why CDOs are issued at
all, since the costs of lawyers, issuers, asset managers and rating agencies
encountered when setting up a CDO can be very high. (For the role that
lawyers play in the CDO business see Wolcott [27]). Besides the reason
mentioned above, that by tranching one creates securities fitting very specific
risk appetites of investors, there are two main reasons why CDOs are issued,
which are discussed in the following."
Okay. Maybe, maybe, CDOs are easier to sell. But they are expensive to create and carve up. So what's the deal?
"1.2.1 Spread arbitrage opportunity
Imagine that the portfolio of a hypothetic CDO consists entirely of credit
default swaps (CDS in the following). The CDO issuer bought the single
name CDS and will receive on each name a premium. With these premia the
CDO issuer pays itself premia to the CDO tranche holders. The goal of the
spread arbitrage is that the total spread collected from the single name CDS
exceeds the total spread to be paid to investors of the CDO tranches. Such
a mismatch typically creates a significant arbitrage potential which offers an
attractive excess spread to equity and subordinated notes investors."
(Excess spread - Refers to the excess of the income inherent in the portfolio of receivables, over and above the SPV's discounting rate and the expenses of the transaction. Represents the profit of the originator in the securitisation transaction)
Well. The creator of the CDO can make more money by bundling, slicing, and selling, than with the simple CDSs. Who knew?
"1.2.2 Regulatory capital relief or balance sheet CDOs
Balance sheet CDOs are initiated by holders of securitizable assets, such as
commercial banks, which desire to sell assets or transfer the risk of assets.
The motivation may be to shrink the balance sheet, reduce regulatory capital,
or reduce required economic capital."
Let's be clear here. It allows lower capital/collateralization than regular bonds. They're more highly leveraged.
"In simple terms such a transaction works in the following way: In general,
loan pools require regulatory capital in size of 8% times Risk Weighted Assets
of the reference pool (according to Basel II standard model). After the
securitization of the pool, the only regulatory capital requirement the originator
has to provide regarding the securitized loan pool is holding capital for
retained pieces. For example if the originator retained the equity tranche,
the regulatory capital required on the pool would have been reduced from
8% to 50bp, which is the size of the equity tranche. The 50bp come from the
fact that retained equity pieces usually require full capital deduction."
The capital requirement for the creator is lowered because it only falls on the bond risk retained by the creator, which will be less the risk sold.
"As nice as this looks at first sight one has to keep in mind that the costs for capital relief are high. The originating bank has to pay premia to note holders, upfront costs for lawyers, rating agencies and structuring, and ongoing administration costs. A thorough calculation of the costs of issuing theCDO compared to the relief of reducing the regulatory capital (and thereby
maybe avoid a downgrading of the firm rating) is required to decide on such
a major transaction."
You need to be careful.
"Conclusion. By calculating this simple example of an equity tranche compared
to a CDS on the index it became immediately clear that an investment
in the equity tranche is highly leveraged. The loss after one credit event was
34 times higher for the equity tranche holders than for the holders of the
index CDS!This example was included to give a first gut feeling on the riskiness of CDOs.
The high leverage involved is one reason why the correct pricing of CDOs
is extremely important. Wrong risk assessment and identification can easily
result in huge losses."
I included this , as well, to give you a gut feeling of the risk.
"It should by now have become clear that the Gauss one factor model is not the
right model to price CDOs and that we are in desperate need for a convincing
alternative. In this thesis, three promising models for pricing synthetic CDOs
were for the first time compared to each other and to the Gauss one factor
model. Further tests using current market data are necessary before we can
conclude on a superiority of any of the three models."
Wow. Can you say "risky"?
"Synthetic CDO pricing using the
double normal inverse Gaussian copula
with stochastic factor loadings
Diploma thesis submitted to the
ETH ZURICH and UNIVERSITY OF ZURICH
for the degree of
MASTER OF ADVANCED STUDIES IN FINANCE
presented by
ANNELIS LÜSCHER
Supervisor: Prof. Dr. Alexander J. McNeil
(Department of Mathematics ETH Zurich)
December 2005"Once again, 2005.
"Mr. Li, who had moved over to a J.P. Morgan Chase & Co. unit (he has since joined Barclays Capital PLC), 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," says Greg Gupton, 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."
We've just learned that the basic models were inadequate.
"To figure out the likelihood of 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. 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 all 100 companies in a pool and plug them into the model."
Fine. Plug them in. Their info is the default rates of the individual bonds over the next ten years. Of course, that has to be reliable for any of this to work.
"The model runs the data through the copula function and spits out a default correlation for the pool -- the 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 they didn't. By knowing the pool's default correlation, 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."
It ranks default risk on a curve, which can then be sliced up, the risk evaluated for each slice, and then priced.
"That's the beauty of it," says Lisa Watkinson, who manages structured credit products at Morgan Stanley in New York. "It's the simplicity."
She's kidding? Right?
"Lehman Brothers’ pioneering spirit has put the firm at the forefront of credit derivatives product design and market development. By continuing to foster that spirit, it has secured this year’s award. In the past year, Lehman developed the first ever rated synthetic equity structure that enables traditional investors who need a rating to access cheap equity.
The structure takes advantage of the relative value of junior parts of the capital structure while providing protection to return against defaults. To date, $2bn of risk has been placed and the new issue pipeline is strong.
“With these kinds of products, we have made it easier for more traditional types of investors, such as money managers and insurance companies, to invest in the structured area for the first time,” says Lisa Watkinson, global head of structured credit business development at Lehman Brothers.
Lehman also pioneered the development of preferred credit default swaps, in which it has traded more than $8bn across more than 60 counterparties, and on which it has based a series of innovations. In September 2005, it introduced a new layer of the capital structure to the credit derivative index market with the launch of PDX, an index referenced to 40 issuers of preferred securities; it has broadened the investor base in the hybrid markets and created a homogenous and liquid pricing/hedging benchmark.
“The cornerstone of our business is the research platform,” says Ms Watkinson. “This enables Lehman Brothers to be prudent and conservative risk managers but innovative in our structuring. And this enables us to tap into new investor bases.”
Banker of the Year, 2006. For Lehman Brothers, you say. I've heard that name.
"It's also the risk, because the model, by making it easier to create and trade collateralized debt obligations, or CDOs, has helped bring forth a slew of new products whose behavior it can predict only somewhat, not with precision. (The model is readily available to investors from investment banks.)"
Not with precision.
"The biggest of these new products is something known as a synthetic CDO. It supercharges both the returns and the risks of a regular CDO. It does so by replacing the pool's bonds with credit derivatives -- specifically, with a type called credit-default swaps.The 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 -- he has to pay up.
The price of this protection naturally varies, costing more as the perceived likelihood of default grows."
We've talked about all this.
"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 the issuer of the underlying bonds starts to look shakier."
This is what people don't like or understand, as I argued on Derivative Dribble.
"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."
They're getting more because the likelihood of default, and payment, are going up.
"Just as investment banks pool bonds into CDOs and sell off riskier and less-risky slices, banks pool batches of credit-default swaps into synthetic CDOs and sell slices of those. Because the synthetic CDOs don't contain any actual bonds, banks can create them without going to the trouble of purchasing bonds. And the more synthetic CDOs they create, the more money the banks can earn by selling and trading them."
Why bother with the bonds? They're actually loans to an actual company. They're limited by the issue.
"Synthetic CDOs have made the world of corporate credit very sexy -- a place of high risk but of high potential return with little money tied up."
Sexy = Risky.
"Someone who invests in a synthetic CDO's riskiest slice -- agreeing to protect the pool against its first $10 million in default losses -- might receive an immediate payment of $5 million up front, plus $500,000 a year, for taking on this risk. He would get this $5 million without investing a dime, just for his pledge to pay in case of a default, much like what an insurance company does. Some investors, to prove they can pay if there is a default, might have to put up some collateral, but even then it would be only 15% or so of the amount they're on the hook for, or $1.5 million in this example."
Can you say "leverage"?
"This setup makes such an investment very tempting for many hedge-fund managers. "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," says 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 winnings each year."
Well, that's just self-explanatory.
"Synthetic CDOs are booming, and largely displacing the old-fashioned kind. Whereas four years ago, synthetic CDOs insured less than the equivalent of $400 billion face amount of U.S. corporate bonds, they will cover $2 trillion by the end of this year, J.P. Morgan Chase estimates. The whole U.S. corporate-bond market is $4.9 trillion."
There is no way to say that this wasn't hellishly risky. Period.
"Some banks are deeply involved. J.P. Morgan Chase, as of March 31, had bought or sold protection on the equivalent of $1.3 trillion of bonds, including both synthetic CDOs and individual credit-default swaps. Bank of America Corp. had bought or sold about $850 billion worth and Citigroup Inc. more than $700 billion, according to the Office of the Comptroller of the Currency. Deutsche Bank AG, whose activity the comptroller doesn't track, is another big player."
A couple of charts to look at.
"Much of that money is riding on Mr. Li's idea, which he freely concedes has important flaws. For one, it merely relies on a snapshot of current credit curves, rather than taking into account the way they move. The result: Actual prices in the market often differ from what the model indicates they should be."
That's not good. A static model for a moving market.
"Investment banks try to compensate for the shortcomings of the model by cobbling copula models together with other, proprietary methods. At J.P. Morgan, "We're not stupid enough to believe [the model] is omniscient," said Andrew Threadgold, head of market risk management. "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 said they use various models to assess risk and are constantly working to improve them. Deutsche Bank had no comment."
A lot of different metrics. Sure. I understand that.
"As with any model, forecasts investors make by using the model are only as good as the inputs. 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 -- that is, to the market's perception of the riskiness of individual bonds over several years.
Trouble awaits those who blindly trust the model's output instead of recognizing that they are making a bet based partly on what they told the model they think will happen. Mr. Li worries that "very few people understand the essence of the model."I'm getting more and more confident as Li tells me his method is deeply flawed for predicting the real world.
"Consider the trade that tripped up some hedge funds during May's turmoil in GM securities. It involved selling insurance on the riskiest slice of a synthetic CDO and then looking to the model for a way to hedge the danger that the default risk would increase. Using the model, investors calculated that they could offset that danger by buying a double dose of insurance on a more conservative slice."
A double dose of the conservative slice. That helps how?
"It looked like a great deal. For selling protection on the riskiest slice -- agreeing to pay as much as $10 million to cover the pool's first default losses -- an investor would collect a $3.5 million upfront payment and an additional $500,000 yearly. Hedging the risk would cost the investor a mere $415,000 annually, the price to buy protection on a $20 million conservative piece."
That helps how?
"But the model's hedge assumed only one possible future: one in which the prices of all the credit-default swaps in the synthetic CDO moved in sync. They didn't. On May 5, while the outlook for most bond issuers stayed about the same, two got slammed: GM and Ford Motor Co., both of which Standard & Poor's downgraded 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 the CDO, the one most exposed to defaults, leapt to about $6.5 million upfront.
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."
One possible future? Well, that's true. There will be only one outcome. Here, it wasn't the one planned on.
"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."
See, I saw that coming. The one level didn't necessarily correlate with the other level. I saw that right off the bat, which is why I didn't see how it helped unless the whole thing crumbled.
"This wasn't really the fault of the model, which was designed mainly to help price the tranches, not to make predictions. True, the model had assumed the various credit curves would move in sync. But it also allowed for investors to adjust this assumption -- an option that some, wittingly or not, ignored."
It was the fault of the people who use the model. See, the model doesn't have agency.
"Because numerous hedge funds had made the same credit-derivatives bet, the turmoil they faced spilled over into stock and bond markets. Many investors worried that some hedge funds might have to dump assets to cover their losses, so they sold, too. (Some hedge funds also suffered from a separate bad bet, which relied on GM's bond and stock prices moving in tandem; it went wrong when GM shares rallied suddenly as investor Kirk Kerkorian said he would bid for GM shares.)"
2005. Can you say "wake-up call"?
"GLG Credit Fund told its investors it lost about 14.5% in the month of May, much of that on synthetic CDO bets. 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. A GLG spokesman declines to comment."
Too improbable. Can you say "understatement"?
"The credit-derivatives market has since bounced back. Some say this shows that the proliferation of hedge funds and of complex derivatives has made markets more resilient, by spreading risk."
Some will come to reget having said that.
"Others are less sanguine. "The events of spring 2005 might not be a true reflection of how these markets would function under stress," says the annual report of the Bank for International Settlements, an organization that coordinates central banks' efforts to ensure financial stability. To Stanford's Mr. Duffie, "The question is, has the market adopted the model wholesale in a way that has overreached its appropriate use? I think it has."
I wonder?
"Mr. Li says that "it's not the perfect model." But, he adds: "There's not a better one yet."
Too bad it was not a particularly apt one for planet earth.
Now, why did I do this?
Simply to show that, in a couple of hours, with data from 2005, I , an autodidact, could understand the basics of these investments and how risky they were, even by not understanding much of the actual math. But I could see how the math was supposed to work, and I could see that this model was risky, and designed to be risky.
After all, as I showed, at least to myself. The products are riskier because the models are risky, and the leveraging is risky. The whole point is to increase risk. Period. And in one case, CDOs, by an incredible amount.
I also believe that I showed that the main motivation, far from market liquidity and efficiency, which now is laughable, as it was obviously so at the time, was the attempt to circumvent capital requirements, and earn more fees for the creators. I'll put my thesis plainly: I can see no advantage for buyers. You can get the same investments with a mutual fund or portfolio of bonds, whatever risk you want. This without even mentioning the risk of a housing price collapse with CDSs considered purely as insurance. When you add the secondary bets, it looks like lunacy on steroids.
My remaining question is really how much of this was fraud, negligence, and fiduciary mismanagement.
Now, can I see ways that CDSs and CDOs could work? Yes. But they would be much less risky, and so, I believe, that they would be much less interesting. It wasn't the investments. It was the investors. The instruments got them what they wanted, which was higher fees and lower capital requirements.
This strikes me as way off base. Now, conservative economic policymakers may have had something like a principle against selective intervention in the economy, which has subsequently been destroyed thanks to Hank Paulson's vertiginous lurching, but that's a different matter entirely.
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