几个星期前，博文“数学‘诺贝尔奖’揭晓：又没中国人啥事”引起不小的讨论。一些人在问那些数学顶尖的人才都去干什么了？其实，数理好的孩子是有很多职业道路可选的，有些选择了学术道路，读博当教授；有些转工程，计算机，进入高科技；有些学经济，MBA，走管理的道路；一些为CIA，FBI，NSA，DOD工作，摇身为间谍或网络安全专家；也有些进入华尔街街，成为了宽客(quants)。Quants是做定量分析(Quantitative Analysis)的人的昵称。

美国是自由国家，走哪条道路完全是个人的选择，本身并没有高低贵贱之分。认为去了华尔街就是出卖灵魂的看法也是一种偏见。可喜的是，美国孩子的选择还是相当多样的，这种多样性是社会均衡发展的重要保证。美国还有一个不算秘密的武器，那就是全世界的顶尖人才都来美国求学，学成后很多选择留在美国发展。这样也在一定程度上缓解了本土人才不足的问题。

那些在华尔街的宽客们又在做什么呢？我想起了小宝在高中时为一家英文报纸所写的专栏 “It’s not QUANTum physics anymore”，翻译出来，以餐读者。小宝的专栏涉及很广，但其中不少是写数学和科学的。

小宝对数学的兴趣在很早的时候就展示出来。在初中是曾经是北加州MATHCOUNTS的地区冠军(三个县)，数十年来第一位女生获此荣誉。她在高中时又花过两个暑假在夏令营学习数论，开始的时候小宝并不想去，宝爸只好说：“你不是喜欢密码学吗(cryptology)？加密要用到素数(prime number)，而数论则是研究素数的。” 当然数论不只是研究素数，她听了居然就去了。小宝对纯数学的兴趣不大，但数学夏令营的孩子们却是她喜欢的。按照她的说法，数学男孩多半有些怪，数学女孩却大多正常，只是很聪明。第二年她又去了，倒不是素数有这么大的魅力，和她那帮狐朋狗友们在一起很开心。

夏令营的一个后果是小宝对建立数学模型(Mathematical models)解决复杂的问题产生了兴趣，这种喜好也影响到她的专业选择，以及后面的职业选择。

是谁搞垮华尔街的？

小宝，写于2009年

在过去十几二十年里，粒子物理学家开始在所有的顶级金融机构里镇守摊位。他们不再研究大统一理论(General Unified Theory)，夸克，或粒子加速器。他们使用自己在数学和逻辑推理方面的专业知识来预测经济下一步会怎样运行。他们的目的不仅仅是买或卖 - 还包括分析相关性(correlations)和风险因素，解读钟形曲线，还有操纵细微的优势为他们的雇主和客户赚钱。

令人惊讶，是不是？如果我们回顾一下这些工作的来源，其实很正常。半个世纪前美国和苏联的冷战培育整整一代的数学和科学家...当冷战结束时，大学只能容纳这么多教授。于是许多科学家决定放弃纯科学的“美”，转而挺进向华尔街。他们成了“宽客”- 定量分析和风险管理的专家。

举个例子来说，伊曼纽尔·德曼(Emanuel Derman)，一个有哥伦比亚学位和在牛津大学工作过的学者，在高盛(Goldman Sachs)度过了17个春秋 [注一]。事实上近年来麻省理工学院的数学和物理的毕业生有很大比例在华尔街工作，像浮士德一样把灵魂换成钱了。

金融工程师利用复杂的，满是希腊字母的数学公式来梳通，理解股市 - 不幸的是，有时会有不曾预想到的后果。例如，李祥林(David X. Li)的高斯Copula函数，这使得非常复杂的风险，可以轻松和具有相当精度地进行建模。当它首先发明时被金融界视为天赐之物。因为这个方程式“可以让交易员卖出数量庞大的新证券，将金融市场扩大到无法想象的地步。”

李祥林几年前是列在诺贝尔经济奖的短名单上。然而今天，他据传躲在中国。一些人指责他的公式的巨大裂痕导致了2008年美国经济的次贷危机和随后的经济衰退的。

其实，这并不一定是李祥林和他的方程式的错，而是那些过度信任数学公式的交易员和金融大师们的错。就连李祥林本人，他已经不在华尔街工作，也说过，“最危险的部分是当人们相信从公式里出来的一切东西。”如今金融领域里宽客的作用的整个问题已引发了巨大的争议。一方面，部分人认为，如果被视为一种模型，作为一种指引，而不是刻在石头上的，金融工程师做的工作是非常有用的。在另一方面，我们有纳西姆·尼古拉斯·塔勒布(Nassim Nicholas Taleb)。

塔勒布是个有话就说的人，“我认为物理学家应该回到物理系去，别再缠着华尔街”。不同于许多宽客，他们对股市的假设是基于钟形曲线公式 – 平均值是最有可能的，这位前股票交易员认为我们国家的金融历史是更多地基于不可预测，无法建模的事件而非平均。富豪慈善家巴菲特显然同意这种说法，他在2008年查理·罗斯节目上(Charlie Rose Show )就说过 –“我能说的是，留神那些穿着公式的极客们”(beware of geeks bearing formulas)

这句话基本上总结了进口的物理学家在金融界的地位层次。他们做了很多工作，但他们并没有像交易员或经纪人受到公司的重视。而到了最后，经济不景气罪魁祸首的头衔又被放在他们身上。有些人说，他们应该能预测下沉的房地产和下沉的经济之间的相关性。“他们忘记了这些数字代表的具体的现实。”华尔街是在告诉宽客们：这些东西不是像高中微积分课程那么容易。

然而，这也许是问题的一部分。太多鼻孔朝天的银行家已经不记得了他们的高中微积分课程。他们不会让宽客做任何实际的决定，他们也不问这些数学模型在那些情况下可以适用。信用研究公司CreditSights的吉尔克斯(Kai Gilkes)说，“我们应该责怪那些误读它的银行家。”

整个情况就像坐在你身边的孩子抄了你所有的作业，也不问你是怎么得出结果的。当要考试的时候，他就死定了。

所以人们不应该把宽客们从华尔街赶出来，因为他们在做有价值的工作 – 大部分时间是对的。然而，宽客们对定量财务分析技术的信心应该有所动摇。一个很大的问题是当所有的人都同时使用李祥林的公式或者“宽客的黄金标准”，Black-Scholes模型 [注二]，当船破的时候，所有人都淹死。

缺少遗传多样性的物种不能活的长久。 也许华尔街需要更多的宽客和更多的数学模型，而不是更少。

白露为霜注：以下是李祥林毁掉华尔街的公式。他用高斯Copula函数来衡量事件的关系。用数学名词，随机的经济事件之间的相关性，可表示为：

通俗地说，他提出两件不同但有关的事件的关系，比如“楼A”违约和“楼B”违约可以用相关性来衡量。计算相关性的公式似乎在大部分时间是相当准确的，在某些特殊情况下则没有用。最根本的问题：过去的历史终究无法预测未来，数学模型的局限性通常只在最糟糕的时候才暴露出来。

注一：伊曼纽尔·德曼写过一本书“我的宽客生活”(My life as quants).

注二：Black-Scholes模型是常用的计算期权(option)价格的公式。

火辣的数学女

怪发的数学女

华尔街的宽客

李祥林

股票市场是不可预测的

It’s not QUANTum physics anymore

For more than two dozen years, there have been particle physicists manning the booths at all of the top financial organizations. They are no longer studying General Unified Theory, quarks, and particle accelerators. They are using their expertise with mathematics and logical reasoning to forecast what the economy is going to do next. Their game isn’t just buying and selling – it’s correlations and risk factors, interpreting bell curves and manipulating the slightest percentage of an advantage to make money for their employers and clients.

Surprising, isn’t it? Not so much, if we go back to the root of the job. America and Russia’s little Cold War half a century ago bred an entire math and science generation…when the Cold War ended, there were only so many professors needed. Many of the scientists decided to forgo the “beauty” of pure science and made their way to Wall Street. They became “quants”, masters of Quantitative Analysis and “risk management”.

Take, for example, Emanuel Derman, an academic with a degree from Columbia and a job at Oxford, who spent 17 years at Goldman Sachs. Indeed, a large percentage of M.I.T.’s math and physics graduates went on to work in Wall Street in recent years, bartering away their souls for money.

Quants utilize complicated mathematical equations involving the greek alphabet to detangle the stock market – unfortunately sometimes with the bad consequences. For example, David X. Li’s Gaussian copula function, which allowed hugely complex risks to be modeled with ease and supposed accuracy, was seen as a godsend by the Wall Street community when it was first invented. After all, the equation “made it possible for traders to sell vast quantities of new securities, expanding financial markets to unimaginable levels.”

Li was on the short list for a Nobel Prize just a few years ago. Today, however, he has gone into hiding in China; some are blaming the huge cracks in his function for the sub-prime mortgage meltdown and subsequent downturn of America’s economy.

Nevertheless, it was not necessarily the fault of Li and his equation, but rather the traders and financial gurus who placed an excess amount of trust in a mathematical formula. Even Li himself, who is no longer working in the field, said that “the most dangerous part is when people believe everything coming out of it”. Now the entire issue of having quants in the financial sector at all has sparked a giant debate. On one side, some argue that the work that quants do is useful if seen as a model, a guideline, not something set in stone. On the other hand, we have Nassim Nicholas Taleb.

Taleb is a man of set opinions: “I think physicists should go back to the physics department and leave Wall Street alone.” In contrast to many quants, who base their stock-market assumptions on the bell curve formula where the average is most likely, the former trader believes that our nation’s financial history is based far more upon unpredictable, unmodeled events than on the mean. The charitable Warren Buffet apparently agreed last fall on The Charlie Rose Show, when he said “All I can say is, beware of geeks bearing formulas”.

That sentence might best sum up the placing on the hierarchy of the imported physicists. They do a lot of work, but they do not get as much credit as the traders or the brokers who are the face of the company. And in the end, much of the blame for economic downturn is being placed on them. People say that they should have been able to perceive the correlations between the sinking housing market and the sinking economy. “They forget about the concrete reality the figures are supposed to represent.” Basically, Wall Street is telling the quants that stuff here isn’t as easy as it is in a high school calculus class.

However, this might be part of the problem. Too many bankers, who look down their noses on the quants, do not remember anything from their high school calculus classes. They don’t let any of the quants make the actual decisions, and they don’t ask questions about the applicability of the models in certain contexts. Kai Gilkes of CreditSights, a credit research film, says that “we should blame the bankers who misinterpreted it.”

The entire situation is like the kid who sat next to you and copied all your homework without asking how you got to that point. When the test comes around, he was totally screwed.

The quants should not be run out of Wall Street, because ultimately they were doing valuable work that was correct a majority of the time. However, their faith in tenets of quantitative financial analysis should be shaken a little bit. The main problem with force-feed equation’s like Li’s or “the quant’s gold standard”, the Black-Scholes Model, is that everyone started using it at once, so everyone sunk with the ship. A species can’t live on without genetic diversification.

Maybe what the Wall Street needs are more quants and more models, not less.