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as to the future Borrowing from standard nance theory, it depends on two variables (standard deviations and correlations) that only make existential sense under normality It paints a picture of how dispersed (volatile) nancial markets have been during a prespeci ed prior period, and then translates that estimate into expected results going forward, using a very large degree of con dence but not quite yet 100 percent That is, VaR does not capture the more unlikely setbacks The problem with this is not just that the effects of rare events may be devastating, but that the normal world of VaR assumes an unrealistically low chance that those happenstances will happen In other words, the VaR number (generally purported to be a reliable guide to the market risks faced by a nancial institution) excludes the potentially most troublesome scenarios and assigns an unseemly high probability to the (selected) past repeating itself.



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prices declined for 29 consecutive months from their peak in July 2006 through December 2008 and there s no end in sight, so this makes buyers reluctant even when the price appears cheap and sellers desperate. Regarding the latter, there is a huge mismatch between supply and demand, due largely to the tsunami of foreclosures. In January 2009, distressed sales accounted for 45 percent of all existing home sales nationwide and more than 60 percent in California.1 As noted in 3, the shadow inventory of foreclosed homes already probably exceeds one year, and there will be millions more foreclosures over the next few years, creating a large overhang of excess supply that is likely to cause prices to overshoot on the downside, as they are already doing in California, as shown in Figure 5.7. Therefore, we expect home prices (using the S&P/Case-Shiller national index) to decline below fair value, which is roughly a 40 percent drop from the peak, and only bottom after a 45 to 50 percent decline.





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No wonder, then, that VaR models failed during the crisis Markets spectacularly revealed themselves to be non-normal, and the historical sample periods used in the calculation (which range from a few months to several years, depending on the institution) did not contain some of the things that uniquely took place beginning in the second half of 2007 Both volatility and correlation behaved in insultingly different ways from the recent past The risk forecast proved spectacularly lacking The of cial guiding light misguided aplenty Neither the likelihood nor the speed or the severity of the downfall were predicted But before we delve deep into the actual details of how VaR did not succeed during the crisis, let s anticipate a central theme of this book: VaR not only fails at measuring, preventing, or predicting humongous risks, it can actually help create them.

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basis of the observation of the value of the trait in a sample of the population Of course, if H0 is rejected, understanding the location of the gene will require, for example, some genetic marker information and the techniques of Section 44 To perform a test of the type we described in (435), (436), or (437), there exist two main classical techniques: 1 A test based on moments: in a rst approximation, expectation, variance, order-three moment 2 A test based on likelihood ratio The asymptotic distribution of the likelihood ratio test was established by Ghosh and Sen (1985) under a strong separation hypothesis: for example, | 1 2 | > > 0 for model (436).

We must have some agreement on the cryptographic primitives used among all participants implementing higher-level application protocols that layer on top of PKI (which in turn is layered on top of the mathematics of public key cryptography). We must describe what we plan to do with certificates in our applications. Will we authenticate users Will we publish software Will we protect communications Will we implement other higher-level protocols We must develop certificate practice statements that apply to our business domain that clearly state acceptable corporate use of certificates. We must have a corporate-wide security policy that governs certificate use. We have to select standards-compliant products for long-term interoperability over noncompliant, feature-rich solutions. The replacement cost of PKI must be considered. We must understand the legal implications of depending on the PKI. How will these affect our business

By leaving aside the extremes and operating from a philosophical platform that vastly underestimates the (real) probability of rare events, VaR can yield numbers that are so low that complacency is unmitigatingly bred and risk taking runs amok Trades can be shown to be almost negligibly risky at the 95 or 99 percent (or even 999 percent) con dence level, thus affording the perfect stamp of approval Not only would the trade be executed, little capital would be set against it, creating in effect a largely leveraged position for the institution In other words, the mathematics of VaR would have encouraged the rm to enter into situations where bad news (even slightly so) can cause a lot of damage and manufacture enormous losses, certainly way above those indicated by the glori ed risk radar These types of.

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