很多人都知道CDO（抵押债务债券）摧毁了华尔街, 引发了全世界的金融危机, 改变了世界格局, 但很少人知道创造发明CDO的是一个中国人, 他的名字叫李祥林，英文名David X Li，当时在摩根大通工作。危机爆发后, 他安全回到祖国的怀抱, 现任中金公司首席风险官。

　　危机爆发前, 所有全球金融精英人士对David X Li构建的金融计量模型几乎像圣经一样顶礼膜拜，人们此前总认为像David X. Li这样有数学天才者可能在某日会得到诺贝尔经济学奖的眷顾，因金融经济学者，甚至华尔街的这类人才的确此前也获得过诺奖。DavidX. Li的开创性工作是度量投资风险。与以前获得诺奖学者的贡献相比，他的办法更有影响力、更快速。但就在晕头转向的银行家、政治家、监管者和投资者整肃自大萧条以来最严重的金融残局时，Li可能更感庆幸的是自己还有一份金融业的工作。

　　David X. Li从事的研究是确定资产间的相关性(correlation)，或称之为一些全异的事件似乎如何有关联，并以简单和规范的数学模型做描述。他构建的被称之为线性相依关系(Gaussian copula function)的模型几乎像是金融界毫无疑义的突破，是一项令巨大而极其复杂的风险，能以数学手段比以前更容易和精确地进行描述和度量的新型金融科技。

　　Li的方法能够让数量巨大的新型证券进行交易，将金融市场扩展至几乎不可思议的水平。他的方法被广泛使用，从债券投资者到华尔街，从评级机构和监管者。它已深深地植根于业内，并让一些人赚到了钱。但不幸的是精英们忘却了模型的限制条件的警告，最终使它失效。当因金融系统基础动摇而爆发的危机吞噬了数万亿美元，使全球银行体系处于严重危险之中时，David X. Li的模型变为纯粹的废物。如同给世界金融体系带来一落千丈的无底亏损的创新一样，他的模型也创新性地沦落至历史的底部。

　　令人们惊诧的问题是，一个计量模型怎会给金融界带来如此毁灭性的结果。答案在于让养老基金、保险公司和对冲基金向企业、各国家和购房者发放数万亿美元贷款的庞大债券市场。企业若想发行债券借款，投资者会严密审查公司账目，以确认公司能有足够资金偿还贷款。若放款人认为贷款的风险很高，他们索要的利息率也会更高。

　　债券投资者通常也对由数百乃至上千个住房按揭贷款构成的资产池进行投资。现在涉及的这类活动总规模大得惊人：美国购房人所欠下总债务已达11万亿美元。然而，按揭贷款资产池的情况比债券市场更混乱。这类投资中，因购房者每月集体偿还的现金量，是取决于已获得再融资的购房人数量和因违约未还款人的函数，因此投资不存在保证性的确定利率。同样，如此借贷活动也无固定的还款到期日。因购房人以无法预测的时间偿还按揭，例如购房者决定出售房产，池内的还款总数也是无规律可循。最令人头痛的问题是，尚无法找到给违约出现机会确定一个单个概率值的办法(即概率越高、贷款损失风险越大)。

　　华尔街解决的办法是，通过一个称之为划分等级(tranching)的办法，它将整个池内各类资产进行分级，创建以标注3A评级的无风险的安全债券。位于第一级别的投资者能够最先获得偿还债息，其他类别投资者虽因违约风险较高而评级稍低，但可收取更高的利率。

　　评级机构和投资者之所以对3A级的债券感到放心是因为他们相信，成百上千的贷款购房者不会在同一时间内发生违约行为。某人可能会丢掉工作，其他人可能生病。但这些都是不会给按揭贷款资产池整体带来重大影响的个体不幸事件。但所有的灾难性事件并非都是个体性，等级划分作法并未解决资产池风险的全部问题。

　　如房价可能下跌的事件会在同时影响到一大批人。如某购房者家附近住房价值下跌，此人住房的资产净值也同样会下降，他(她)周边邻居的房产会跟着下跌的可能性更大。一旦此购房人还款违约，周边邻居违约的可能性也更大。这就是所谓的相关性，即一个变量变化与另一些变量的关系和影响程度，度量此关系和关系程度高低是确定按揭贷款债券风险大小的重要部分。

　　只要投资者能够对风险定价，他们一定喜欢它。他们厌恶的是不确定性，即无法确定风险大小。正因如此，债券投资者、按揭贷款放款者拼命地想要找到能够度量、模拟相关性，并对其进行定价的方法。在计量模型应用于金融市场前，令投资者对按揭贷款资产池中投资感到安全的唯一时刻是不存在风险，即这类债券都是由联邦政府通过房地美和房利美两家企业进行隐形担保。

　　随着全球金融市场在1990年代快速扩张，数以万亿计美元要进入市场，若投资者能够找到确定任何资产间的相关关系的方法，这些资金便能顺利进入市场。但这是个折磨人的痛苦问题，特别是考虑到成百上千类资产在时刻不停波动和变化。无论是谁解决了这样一个问题不仅会赢得华尔街永恒的感谢，而且非常可能会引起诺贝尔奖委员会的关注。

　　此时巧合的是，在摩根大通工作的David X. Li2000年在《固定收益杂志》(Journal of Fixed Income)上发表了一份名为“On Default Correlation: A Copula Function Approach”的论文。论文以相对简单的数学方法，在不用参考历史默认数据(historical default data)情形下，以一种非常聪明方式构造了违约相关性的模型。取而代之，他使用信用违约调期产品(creditdefault swap，CDS)价格的市场数据。

　　由于针对每个借款人发行的CDS数量可以无限，调期产品供应并不制约债券供应方式，所以处于开创阶段的CDS市场以异乎寻常速度增长，所向披靡，规模大大地超过了其作为基础的债券市场。

　　在现实金融世界中，太多金融分析人士只看到他们眼前的毫无生命的数字，而忘却了这些数字所代表的有形和真实的现实。他们认为，能够仅靠只有数年价值的数据来模拟计算，再定出那些每10000年才可能发生一次事件的概率。人们此后就以如此概率进行投资，而不思考一下这些数据究竟是否有实际意义。正如Li本人对自己的模型的表态，最危险的事情莫过于人们相信模型能给他们带来所盼的结果。

Recipe for Disaster: The Formula That Killed Wall Street

In the mid-'80s, Wall Street turned to the quants—brainy financial engineers—to invent new ways to boost profits. Their methods for minting money worked brilliantly... until one of them devastated the global economy.

A year ago, it was hardly unthinkable that a math wizard like David X. Li might someday earn a Nobel Prize. After all, financial economists—even Wall Street quants—have received the Nobel in economics before, and Li's work on measuring risk has had more impact, more quickly, than previous Nobel Prize-winning contributions to the field. Today, though, as dazed bankers, politicians, regulators, and investors survey the wreckage of the biggest financial meltdown since the Great Depression, Li is probably thankful he still has a job in finance at all. Not that his achievement should be dismissed. He took a notoriously tough nut—determining correlation, or how seemingly disparate events are related—and cracked it wide open with a simple and elegant mathematical formula, one that would become ubiquitous in finance worldwide.

For five years, Li's formula, known as a Gaussian copula function, looked like an unambiguously positive breakthrough, a piece of financial technology that allowed hugely complex risks to be modeled with more ease and accuracy than ever before. With his brilliant spark of mathematical legerdemain, Li made it possible for traders to sell vast quantities of new securities, expanding financial markets to unimaginable levels.

His method 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.

Then the model fell apart. Cracks started appearing early on, when financial markets began behaving in ways that users of Li's formula hadn't expected. The cracks became full-fledged canyons in 2008—when ruptures in the financial system's foundation swallowed up trillions of dollars and put the survival of the global banking system in serious peril.

David X. Li, it's safe to say, won't be getting that Nobel anytime soon. One result of the collapse has been the end of financial economics as something to be celebrated rather than feared. And Li's Gaussian copula formula will go down in history as instrumental in causing the unfathomable losses that brought the world financial system to its knees.

How could one formula pack such a devastating punch? The answer lies in the bond market, the multitrillion-dollar system that allows pension funds, insurance companies, and hedge funds to lend trillions of dollars to companies, countries, and home buyers.

A bond, of course, is just an IOU, a promise to pay back money with interest by certain dates. If a company—say, IBM—borrows money by issuing a bond, investors will look very closely over its accounts to make sure it has the wherewithal to repay them. The higher the perceived risk—and there's always some risk—the higher the interest rate the bond must carry.

Bond investors are very comfortable with the concept of probability. If there's a 1 percent chance of default but they get an extra two percentage points in interest, they're ahead of the game overall—like a casino, which is happy to lose big sums every so often in return for profits most of the time.

Bond investors also invest in pools of hundreds or even thousands of mortgages. The potential sums involved are staggering: Americans now owe more than $11 trillion on their homes. But mortgage pools are messier than most bonds. There's no guaranteed interest rate, since the amount of money homeowners collectively pay back every month is a function of how many have refinanced and how many have defaulted. There's certainly no fixed maturity date: Money shows up in irregular chunks as people pay down their mortgages at unpredictable times—for instance, when they decide to sell their house. And most problematic, there's no easy way to assign a single probability to the chance of default.

Wall Street solved many of these problems through a process called tranching, which divides a pool and allows for the creation of safe bonds with a risk-free triple-A credit rating. Investors in the first tranche, or slice, are first in line to be paid off. Those next in line might get only a double-A credit rating on their tranche of bonds but will be able to charge a higher interest rate for bearing the slightly higher chance of default. And so on.

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