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http://www.pinggu.org/bbs/thread-439561-1-1.html 我说他们没有数学素养，说我乱说。下面我将给出mckinsey的2009年2月23日的一篇咨询报告。
无论关于任何，什么是风险管理？我们用一些词语尽管每个人都明白我们在讨论什么。但是生命不是那样简单！
风险意味着事情会发生比期望发生的要多-这就是说我们不知道将来会发生什么。如果我们不知道将来会发生什么，一些意外将使我们损失。但是其他将使我们获得比预期要多的财富。任何人对风险管理项目感兴趣，明白潜在损失和潜在收益是很重要的。所以我们可以明白，如果更多的风险管理经理能够完全的评估以往，现在的金融危机就不能发生。
在当今世界，对风险管理来说，数学分析已经成为流行和时髦的方法。这在wall-street是最明显的，在那里所谓的具有数学或者理论物理学博士的Quants利用他们的神秘（arcane）模型技术魔术般构建能够获利交易模型和新产品。非Quants对于这些新技术通常是非常怕的，但是喜欢他们产生的利润并躲避去争论这些模型是否可靠。
事实上，数学仅仅能部分的帮助我们进行风险管理。 它不能管理的是在风险核心的部分：不知道。利用单一数学方法，风险管理经理有完全不能正确的定义问题和问正确问题的风险。让我从另一个视角看同一件事情：风险管理实际上是试图优化在一个所有的结果可能不知道的情况来结果。数字在这种条件下将是非常脆弱的（frail reed）。
然而，我们该怎么管理风险当数学方法失败后？I begin the answer to this question with an anecdote from myexperience managing other peoples’ money back in the late 1960s. Thestory is interesting in its own right, but it also provides a profoundinsight into the essence of risk management. A marriedcouple came to see us at our offices one day, scruffily dressed and shyin manner. The man, John, opened the discussion by showing us theirportfolio, which was worth a couple of hundred thousand dollars andconsisted of only three stocks: AT&T, U.S. Steel, and Thiokol. Thewhole portfolio was on margin, but each position showed enormousprofits. We were nonplussed and asked John why he needed us. Then hetold us their story. He had been a reporter for the Brooklyn Eagle,but the paper had folded and he was now unemployed. At the time that hewas fired, the couple had $15,000 in the bank, just about the amountthey spent in the course of a year to meet their basic needs (don’tforget this episode took place over 40 years ago). John’s wife was aschool teacher, so they had some money coming in—but nowhere nearenough to cover their basic living expenses.
Unlike many people who hoard small accumulations of assets for fearof losing the little they have, John decided to go into the stockmarket and shoot the moon. “If I lose,” he figured, “I’ll just be brokea year earlier than I would be otherwise. If it works, though, we canbe comfortable for the rest of our lives.”
That logic iswhat made John a master risk manager. The key question in decisionmaking is, “What happens if I am wrong?” or, as in John’s case, “Whathappens if I lose?” In this instance, he could see that he and his wifewere in such bad shape that they had little to lose but much to gain bytaking this highly concentrated and leveraged risk in the stock market.(It did work. The problem John wanted my firm to help with was adifferent, though not uncommon one. John’s wife, who had been a firmcompanion while the great experiment was under way, now had highanxieties about the risk of losing their windfall. But John, transfixedby success, was psychologically incapable of unwinding his fantasticsuccess. That was the role they wanted us to play.)
Johnwas unaware of the hallowed history of his line of analysis, whichdated back nearly four centuries to one of English literature’s mostglorious achievements, Shakespeare’s Hamlet and Hamlet’s mostfamous soliloquy, “To be, or not to be.” There is a powerful connectionbetween the investment decision by an unemployed newspaper reporter andthe contemplation of suicide by the Prince of Denmark (which is what hemeant by the phrase, “To be, or not to be”).
Hamlet alwaysdeliberated at length before acting on his impulses. In this crucialscene in the play, he is considering what might happen to him if hedoes commit suicide: “To die: to sleep; no more; and by a sleep to saywe end the heartaches and the thousand natural shocks that flesh isheir to.” An end to heartache. That is the outcome Hamlet hopes he willachieve. But then he asks a critical question: can we be certain of “nomore”? Hardly. We can be certain of nothing that happens after death.
Thatbeing the case, suicide is not a riskless act. Suppose there is more tocome after death? “To die, to sleep; to sleep: perchance to dream: ay,there’s the rub; for in that sleep of death what dreams may come . . .There’s the respect that makes calamity of so long life.” Hamletprefers to suffer the immense pain of life rather than face theunknowable consequences of suicide: “to grunt and sweat under a wearylife” because “the undiscovered country from whose bourne no travelerreturns, puzzles the will, and makes us rather bear those ills we havethan fly to others that we know not of.” Hamlet left a perfect modelfor my client John to follow: what happens if I am wrong in taking thisstep? In John’s case, the consequences of being wrong were minorcompared with the transformation he could achieve if his decisionturned out to be the right thing to do. Hamlet’s choice of whether tobe or not to be was precisely the opposite, because not acting was thebetter selection. But both John and Hamlet asked the right question.
Anotherexample of the power of this line of analysis is Blaise Pascal, thegreat 17th century French mathematician who first articulated the useof probability in making estimates about the future. Despite thetremendous importance of Pascal’s work in the field of probability, hismore fundamental contribution to risk management is similar toHamlet’s, although I doubt that Pascal ever read any Shakespeare—or hadeven heard of Shakespeare. Like Hamlet, however, Pascal applied commonsense, rather than higher mathematics, in managing the risk he faced.
Pascalwas a deeply religious man, although he was also a skilledgambler—which is what led him to the study of probability in the firstplace. One day, in the silence of his room, Pascal asked himself atantalizing question: “If I had to make a bet on whether God is or Godis not, how should I respond?” He immediately recognized that “reasoncannot answer.” Nevertheless, this was clearly a question ofoverwhelming importance, even though he would have to wait until theend of eternity to find out how his bet on God’s existence had workedout.
Pascal finally turned to an indirect approach to thispuzzle, in which reason would help him decide which way he should beton whether God is or God is not. He could choose what kind of a life hewanted to live: a life of virtue, restraint, and unselfishness, or alife of lust and self-indulgence. Suppose he chose a life of virtue andabstinence and then found out at the end of time that God is not? Hewould have passed up some goodies unnecessarily, but it would not havebeen such a bad life. If, on the other hand, he chose a life of lust,deceit, and self-gratification, and then found that God is, he would bein big trouble. Therefore, Pascal decided he must bet that God is andchoose the virtuous life, even though he had no way of knowing whetherthe bet would pay off. One thing he did know: the consequences of beingwrong by betting that God is not and leading a life of sin could haveintolerable consequences.
The heart of the matter isdefining the choices. Shoot the moon or leave the $15,000 in the bank?To be, or not to be? God is or God is not? John, Hamlet, and Pascal allprovide the same framework for risk management: whichever road youchoose—whether you play it safe or take a risk—what are theconsequences of being wrong?
In our own time, let ussuppose that some of the people who took out subprime mortgages, orsome of the lenders, had stopped for a moment to ask themselves, “Whatif we are wrong about the outlook for housing prices? I am confidentthey will keep rising, but nothing is certain in this life. I betterthink through the consequences if I am wrong.” The consequence of beingwrong about the trend of housing prices would be disaster, as thedeclining value of the mortgaged homes would soon wipe out theborrowers’ paper-thin equities. This tragedy is precisely what didhappen when housing prices began falling in autumn 2006. If buyers orlenders had only taken the trouble to ask the question about beingwrong, the history of the world economy could have been entirelydifferent from the chaos that has overtaken us.
Thinkingthrough what might happen if things go wrong is also a useful approachin routine business decision making. In 1994, Avinash Dixit and RobertPindyck wrote a book called Investment Under Uncertainty,which emphasizes the inherent irreversibility of mostbusiness-investment decisions. Dixit and Pindyck suggest a method fordealing with the risks posed by irreversibility: wait before acting.Waiting is valuable because the passage of time can produce additionalinformation. This new information may have value that would not havebeen available if an irreversible decision had been made earlier. Thus,Dixit and Pindyck’s case has its roots in the deliberations of Hamletand Pascal, because taking the risk of not waiting can have negativeconsequences. Waiting to make an irreversible decision may lead to amore rational choice than not waiting. My client John, Hamlet, andPascal, each in his own way, laid out the fundamental principle of riskmanagement by defining the right problem and asking the right question.A purely mathematical approach would make sense only if the riskmanager were indifferent to the possible outcomes, in which case, therewould be no point to the exercise. There is always uncertainty. Nothingis 100 percent sure. While a 95 percent probability is statisticallysignificant, that still leaves us in the dark about the remaining 5percent; we may decide to accept that uncertainly and bet on the 95percent sure thing, but there is still a possibility of being wrong.The crucial question to ask is, “What would be the consequence if that5 percent chance comes to pass?”
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