What Role Did Mathematical Models Play in the Financial Crisis?

September 21, 2009

Addressing an audience made up for the most part of applied and computational mathematicians, I.E. Block Community Lecturer Andrew Lo considered the blame of those in the finance industry---including quants---who failed to see the looming crisis. Is it possible, he asked, pointing as an example to the large number of parties involved in issuing a single security, that a person focused on one aspect of a task will be oblivious to other aspects? His response featured a memorable demonstration of, among other things, the ability of mathematicians to focus intently on a task.

James Case

On the evening of July 8, during the 2009 SIAM Annual Meeting in Denver, Andrew Lo delivered the I.E. Block Community Lecture. Lo, the Harris & Harris Group Professor in the Sloan School of Management at MIT, titled his lecture "Kill All the Quants? Models and Mania in the Current Financial Crisis." It was about as informative and entertaining as a lecture of substance can be.

Lo, who is also director of the MIT Laboratory for Financial Engineering, began with a brief history of the crisis, the seeds of which were sown during the period of low interest rates in the late 1990s. The ensuing housing boom was sustained by a proliferation of adjustable-rate mortgages and subprime mortgages (a.k.a. "liar loans") extended to borrowers lacking the means to repay, as well as by the wholesale issuance of mortgage-backed securities (MBSs) by financial institutions, including the government-sponsored enterprises known as Fannie Mae and Freddie Mac. Such instruments could be leveraged---investors could use them as collateral against which to borrow more money to make more such investments, which could then be reused in the same fashion, and so on. Their acceptability as collateral was due in large part to the AAA ratings slapped on them by well-established credit-rating agencies, such as S&P, Moody's, and Fitch, and to the availability of default insurance in the form of credit-default swaps. But the wealth so created could not survive the interest rate increases of 2004 and the consequent decline of housing prices from 2006 highs. Default rates increased, inflicting losses on investors, dealers, insurers, and mortgage originators, which led to further declines in home prices, and so on. The resulting "death spiral" continues.

When it came to assigning blame, Lo named the usual suspects. Homebuyers deserve a share for assuming loans they couldn't hope to repay, as do the real estate agencies and mortgage companies that rewarded their brokers for persuading such buyers to assume unserviceable loans. The investment banks that purchased their contracts, bundled them into MBSs, and persuaded the rating agencies to label them AAA---the better to sell them to the proverbial "widows and orphans" funds---are surely at fault as well, as are the investors who failed to peer behind the ratings. Also blameworthy are the insurance companies that guaranteed payment; the rating agencies that gave apparently inflated ratings; the regulators (the SEC, the Fed) that looked the other way; the politicians and government-sponsored enterprises that promoted the "ownership society"; and the business media that (mostly) applauded the orgy of "wealth creation."

All this was familiar ground. Lo was really more interested in assessing the blame to be borne by risk managers and other quants. To that end, he had to explain how some of those quants had contrived to turn mortgages with unappealing risk/return ratios into MBSs that sold like hotcakes to investors of every description. That was an achievement worthy of Jimmy (The Greek) Snyder, who invented the point-spread wager as a way of enticing the betting public to gamble on football and basketball games in which---as is usually the case---one of the teams is a clear favorite to win. The packagers reduced the risk in part by spreading it geographically: On the basis of evidence that epidemics of homebuyer defaults tend to be regional, they assembled mortgages from every time zone into MBSs that were---or seemed to be---inherently less risky than the individual mortgages. Mainly, however, they did it by separating the underlying mortgages into "tranches" with different risk/return characteristics.

Lo explained the mechanics of the tranche system with an extremely simple model. The ingredients were a pair of identical $1000 IOUs, to be redeemed on a certain date in the not too distant future, each with a 10% chance of default. The expected value of each individual asset, which he equated with its price, is 90% � $1000 + 10% � $0 = $900. Under the assumption that defaults are statistically independent events, a portfolio containing both assets should be worth 81% � $2000 + 18% � $1000 + 1% � $0 = $1800, because either, neither, or both borrowers might ultimately default.

But there are other ways to package the same pair of assets. Modern financial institutions, Lo said, are more likely to create two dissimilar asset-backed securities (ABSs), one outranking the other. In his example, purchasers of the "senior-tranche" ABS stand to collect $1000 unless both borrowers default, while "junior-tranche" purchasers collect $1000 only if both borrowers repay. The expected value of the senior-tranche ABS is thus 99% � $1000 + 1% � $0 = $990, that of the junior-tranche ABS 81% � $1000 + 1% � $0 = $810.

The senior-tranche ABS is thus a low-risk/low-return investment, suitable for purchase for the benefit of widows and orphans, while the junior-tranche ABS is a high-risk/high-return opportunity attractive to hedge funds and the like. The "high rollers" who invest in such funds understand the need to bear extraordinarily high risk in order to obtain extraordinarily high returns on their investments, and they actively seek out opportunities to do exactly that. But what happens if the defaults cease to be statistically independent? If the two become perfectly correlated, either paying or defaulting together, they will have the same expected value: 90% � $1000 + 10% � $0 = $900. The senior-tranche investors have then paid $990 for an asset worth $900, while the investors in junior-tranche (and riskier) ABSs find themselves in possession of assets worth $900 for which they paid only $810!

Simple though his model was, Lo confirmed during the question-and-answer session that the illustrated effect is entirely real: Hedge funds that invested heavily in the high-risk tranches have (on balance) been hurt less than more risk-averse investors. That may seem unfair, but it is not inconsistent with the history of financial crises. Fortune smiles on those who buy low! Despite the large number of hedge funds shut down during the crisis, Lo said at the reception following his talk, he expects that new ones will form in coming months, taking advantage of the many high-risk/high-return opportunities so reliably spawned by disorderly markets.

Lo found no fault with the bundling of loans to create a more attractive line of financial products. He expressed concern, rather, with those in the industry---and here he specifically included quants---who were in a position to see, yet failed to see, the danger with which the industry was so obviously flirting. But he did not hasten to judge even then, on the ground that it isn't always easy to see the obvious while striving to observe something else. He emphasized this point by showing a well-known video (which about a tenth of the audience had seen previously) in which two teams of three students each---one dressed in white, the other in black---strove to pass a pair of basketballs back and forth without fumbling. The audience was to count the number of times the white team passed the ball successfully from one member to another, as Lo called out random numbers to confuse the counters.

When the action ceased, Lo asked for the white team's total, and for anything else the audience had seen. Many laughed when a voice from the back of the room asked whether he meant "the guy in the gorilla suit." For a surprising number of those present, intent as they were on counting passes, had failed to see anything unexpected. When Lo reran the video, however, it was impossible to miss the person in a gorilla suit walking brazenly out into the middle of the action, pausing to beat his chest several times before exiting stage right. It was a memorable way to make the point that it's easy to see what you expect to see, and surprisingly difficult to see the unexpected. Because people in the finance industry hear no end of talk about the heroic quantities of wealth they are creating, and little if anything about the danger they pose to the economy as a whole, it is hardly surprising that the latter should be all but invisible to them.

Lo quoted with approval Charles Perrow, a systems-behavior expert who, after studying the tragedies at Chernobyl and Bhopal, as well as the near tragedy at Three Mile Island, formulated a theory of "normal accidents" in high-tech industries. The gist is that catastrophic failures are to be expected in such industries: Complex nonlinear systems (which are famously hard to predict) abound, and the various subsystems are so tightly coupled that a failure in one is likely to produce failure in others. And, because they cannot be prevented, they should be planned for! To this, Lo would add that human failure is the main cause of such breakdowns, and that the absence of negative feedback (of the sort that results in the identification and correction of mistakes) over an extended time is a virtual guarantee of human failure. Finally, he said, all of these observations apply directly to the finance industry, in which investors, managers, legislators, and regulators receive little constructive feedback.

It's not a tragedy when hedge funds lose money, Andrew Lo pointed out in Denver; it is a crisis when banks or retirement funds lose money. The key to avoiding future crises? More training in financial mathematics and engineering, not less.

Wondering whether the crisis could have been avoided, Lo described the probable fate of various operatives, had they known with certitude in 2005 that a crisis was on the way. A Wall Street CEO might have shut down one or two groups in the firm that were earning money hand over fist, as were similar groups at rival firms. But the CEO would probably have been fired for doing so, as the groups at rival firms would have continued for two more years to record "supernormal" profits and bonuses. A credit-risk officer might have hedged the firm's exposure with investments designed to underperform MBSs while the boom lasted, but to offset losses from them during the bust to follow. But that officer too would probably have been fired, for leaving two years worth of extraordinary profits on the table. Lowly portfolio managers might have purged their clients' accounts of MBSs, thereby reducing their rates of return. But some if not all of those clients would then have requested different account managers, or moved to different firms, probably costing the managers their jobs! In short, there was hardly a desk on Wall Street from which it would have been safe to act on the knowledge that the housing bubble was ready to burst, without knowing the precise date on which it would do so. In Lo's opinion, the psychology of greed makes periodic crises unavoidable. That being the case, the prudent course would seem to be to prepare for them.

Lo closed with a 14-point program of preparations worth making in anticipation of the next crisis. Although most were couched in terminology too technical for inclusion here, a few are readily accessible. His suggestion that banks and brokerages that seem too big to fail be broken up into smaller units needs no explanation. Nor do two suggestions pertaining to education---that finance, economics, and risk management be taught in high school, and that a new discipline of "risk accounting" be created. Finally, his call for a small "derivatives tax" to fund university programs in financial engineering is straightforward. Because the rest of his suggestions seem equally worthy of consideration, one can only wish him success in bringing them to the attention of the appropriate authorities, regrettably few of whom are avid readers of SIAM News.

James Case writes from Baltimore, Maryland.

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