Was Wall Street killed by a formula?

February 25, 2009

In the current issue of Wired, Felix Salmon argues that it was a formula, not bonuses or institutions, that led to the current credit crisis.

Can formulas kill economies?

10 Responses to “Was Wall Street killed by a formula?”

  1. […] Wall Street Paul Wilmott: Copulas and Cults Eric Falkenstein: Don’t Blame The Quants, Felix Was Wall Street killed by a formula? Email this […]

  2. jck Says:

    “Can formulas kill economies?”
    No, it’s always the people, not the models. Felix knows that but as he said (and I hope he does mind if I quote him) “..it is Wired.”
    BTW, greatly enjoyed your piece in “material markets”

  3. danielbeunza Says:

    JCK — well put. I guess my question was an easy comeback to a genuinely catchy article headline by Salmon.

    That a formula was involved in the credit crisis is, I think, well established by this article and MacKenzie’s piece on LBR. The real point is, how did humans and formulae combine to bring about the disaster?

    Here, I’d like to offer a related idea. Rather than accusing bank managers of inept or mathematically slow, as Salmon suggests, the fieldwork done by David and I suggests that the VaR formula had a big hand at this.

    VaR in hand, global risk managers at large banks did not need to understand the details of individual businesses. Now we know that what value-at-risk really did was to put banks-at-a-fatal-risk.

  4. jck Says:

    Mostly in agreement, VaR can be useful for traders if dealing in highly liquid markets like say, bond futures, but it falls apart when used by management and when dealing in illiquid markets with unknown or at very least highly skewed distributions like credit trading. People are the problem and I mean by that people far removed from the daily nitty-gritty of the business that is to say management. But don’t agree with your view on risk-managers, they are not guilty in my view, risk-management is seen as a cost center and their view count for nothing against the views of profit-center crowd. So I would blame management because they are always happy with simplistic risk metrics, as are regulators and the “Authorities”.
    Will try to get some “insider” to comment on this.

  5. danielbeunza Says:

    JCK – I meant “risk manager” in a broad sense: anybody who is making decisions about capital allocation. Formal risk management departments, by contrast, are interesting places; I spent time in one. Their peculiar logic of action is, I would say, administrative in the sense coined by Simon: it makes sense in the context of the bureaucratic organization they belong to.

    The problem I wished to highlight about VaR, however, is not that it does not represent the territory well in its entirety. Any model suffers from that. The problem is instead that it is used for commensuration across strange things. VaR is used to aggregate positions taken by traders based on their own models. And whereas deciding whether your own model works or not is a tough but doable task, deciding whether the model-based positions of ten desks are too risky in the aggregate… is quite something else.

  6. Jan Simon Says:

    What makes a formula powerful on Wall Street? Acceptance! Over the past 40 years academics and practitioners have developed 1000s of formulas (concepts and ideas), but only a few (YTM, Beta, BSM, Gaussian Copula,VaR), stick. Why? Because they are intuitive, elegant and relatively easily understood by the people who have to apply/program them. In a world of uncertainty they give something to hold on to, just like a climber uses a rope.

    An accepted formula is often what holds the system together. Through devices such as spreadsheets, Bloomberg terminals and RiskMetrics people at different sides of a trade or sometimes in different functions make their business decisions based on ‘the formula’. Actually on that 1 variable of the formula which is ‘the unknown’. It is as if all climbers would be climbing on the same rope, a practice often applied in military operations by commandos as it speeds up the process.

    Commandos do climb up the rock or mountain as fast as possible and assume that the rope is safe. It are the Premiers de Cordee (military climbing instructors) who are responsible for safety who assure that the rope is safe and that all nuts and hexes are well connected. In the same fashion risk managers should be the ones who make sure that ‘the formula is still safe’. I.e. that the assumptions on which the formula is based are still valid.

    Put like this the role of the risk manager, as the role of the Premier de Cordee, becomes vital. Premiers de Cordee have absolute authority and take absolute responsibility for safety. It seems to me that the risk managers were often subordinate to other decision groups and that to be aligned with those they were solely focused on the formula, not its assumptions. In other words they were also on the rope and were not aware that the nuts and hexes had come loose. Indeed, a rope which pulls 66 trillion of CDOs needs stronger hexes than one which pulls 1 trillion.

    Coming back to Salomon’s article and jck’s original comment: I think that responsibility always should be given the people, and consequently the formula can not be blamed. However, what we need are more powerful risk managers and hopefully for those risk managers to understand SSF better.

  7. danielbeunza Says:

    This is a fascinating metaphor. Quantitative trading as climbing on a single rope. Does the practice have a name? My own research on prop trading is very consistent. When one goes arbitrageur down, chances are everyone will go down together.

    What is even more interesting is that this “shared destiny” extends outside a single bank. Here’s how it works. Different arbitrage teams at different desks typically use the same formula. Because of that, they can validate their own estimates simply by looking at prices, and “backing out” from them the estimates that rival traders have developed. It is called “arbitrage disasters.”

    For a fascinating paper on these disasters see:

    Click to access Officer_JCF_13(5).pdf

  8. Aaron Brown Says:

    I’m sorry it took me so long to get to this. I’ve been busy, and I have so much to say about these issues that it’s hard to compress it into a manageable post.

    The biggest problem with this article, and the general charge that models or narrow-minded modelers caused disasters, is that Wall Street doesn’t use pricing models. Wall Street interpolates.

    If I have a bunch of bonds, I use the “yield to maturity pricing model” to convert prices to “market implied YTM.” I graph them versus time and find they line up in neat curves by credit quality. So if I want to price a new bond, I check the “market implied YTM’s” of bonds with similar duration and credit quality, interpolate a YTM and use it to generate a price.

    I do exactly the same with with Black-Scholes, only I get a market implied volatility, and interpolate from options of similar time to expiry and moneyness.

    As long as I’m interpolating, the model makes very little difference. I could just draw a freehand curve and get pretty much the same result with no theory at all (in fact, people used to do precisely that, for both bonds and options, and the prices worked fine). What does make a difference is that I’ve graphed the correct dimensions. If I stick some tax-free bonds, callable bonds and convertible bonds in my sample, bonds won’t line up so well. I’ll have to add dimensions to get a clean picture. The more dimensions, the riskier interpolation is (“the unbearable emptiness of multidimensional space”).

    Wall Street does use models for hedging and risk management. These are dynamic models of how things might move in the future, like interest rate models, not pricing models.

    There are four easy ways to blow up, none of which involve having bad pricing models.

    1. Leave out a key dimension when graphing prices of market instruments and fail to notice that securities that are close together have very different prices.

    2. Include too many dimensions when graphing prices, so you don’t have enough reference securities to interpolate reliably.

    3. Extrapolate beyond the range of market securities and assume you have the same range of errors as when you interpolate.

    4. Use a bad dynamic model of what might happen so either things move a lot more than you expected, or hedges work a lot worse than you expected.

    The Gaussian copula was a silly model from the start, not because it’s bad math or bad finance, but because it includes too many dimensions (one per security, which makes it contentless), and was always extrapolating (with that many dimensions, it’s virtually impossible for one security to be between two others), and it was not paired with any dynamic model at all. That’s 2, 3 and 4 above. These were well-known and often-remarked, from the day the models were introduced. GC models frequently blew up without any great market events. The one thing that was not generally known about them was that they also made the error (1) of leaving out a key dimension of credit risk, which can be loosely described as leverage-derived credit risk.

    Saying this model blew up Wall Street is like saying people are getting too fat because the nutrition labels on food are written in too small type.

  9. Aaron Brown Says:

    Now to VaR. I’m a big fan of it. I wrote an article looking at the publicly reported VaRs of the big financial institutions, and the metric came off quite well. It started climbing in early 2005, and often doubled in short periods of time. Not only did VaR increase, but the number and size of VaR breaks (days with losses greater than VaR) grew.

    There were some exceptions. Bank of America reported a flat VaR one quarter, but if you read the notes you saw it was because they stopped including VaR on credit default swaps.

    I maintain anyone who read the full risk disclosures had a pretty good idea of both the nature and size of the risks. All the banks and dealers reported VaR’s that suggested significant probability of insolvency. The ones that reported higher risks than the ones that have survived to date.

    Why did people not cut risk sooner? The securities that changed this from a normal credit downturn to a global financial meltdown were written in 2006 and especialy 2007 and 2008; long after the troubles had become clear.

    There are two main reasons. First, people had faith in the equity value of financial companies. These companies have billions of dollars of real cash that flows in reliably every year, regardless of investment losses. We figured AIG could sell its operating businesses for $80 billion if its CDS portfolio went bad. We were wrong, it couldn’t have gotten more than 10% of that. We figured similar things for Citigroup and Morgan Stanley.

    Second, people had faith that the off-balance sheet securitizations would stay off balance sheet. Personally, I didn’t believe that one, but a lot of other people did (I was wrong about other stuff that other people were right about, this is just one I got right).

    Risk managers were not ignored in general. I hashed out these issues many times in considerable detail. My views got respect (I would have quit if they didn’t). Other people had different views, which I respected as well. I don’t think people did stupid things so much as they did untested things in too large size. A lot of the untested stuff worked, but you knew at least some of it wouldn’t, and the sizes were large enough that you had a train-wreck instead of a temporary detour.

    The criticism that VaR allowed risk managers to not learn the businesses is misplaced. Front-office risk managers know their businesses, some use VaR, some don’t, but those that do use business-specific computations. It’s middle-office risk managers that all use VaR, they are charged with managing the risks that appear at the firm level, not the business level. They need something that abstracts from the specific risks of individual businesses to focus on systemic risks to the firm, like counterparty credit, or every business making the same bet in different guise. Back office risk managers, the ones who compile the reports, use VaR as well, but it’s supplemented with a lot of business-specific measures.

    VaR tells you the border between everyday, normal market events where you can rely on specific recent data, and the tails where you can rely on nothing (but general long-term observation provides the closest thing to a guide we have). You need to know that border to know where the risk manager has to step in and restrict the freedom of the risk-taker.

    It’s also useful because changes in VaR, or excessive VaR breaks, are often signs of regime changes. You get a lot of false alarms, but rarely does a significant change occur without a VaR warning. This isn’t something you can prove in theory or be sure will occur in the future, it’s just something risk managers have noticed and put mild confidence in.

  10. danielbeunza Says:

    Aaron — that’s a fascinating comment. And my research on equity derivatives findings agree with your core point: that models cause problems in risk management, not pricing or valuation.

    What I have found — and your comment — confirms is that the crux of the problem lies with “backing out.” It introduces a circular logic in that it takes existing prices to be good. This links up a bank with its rivals, creating an interdependency that might cause systemic risk. The paper is here:


    Ok, on to the Gaussian cupola. You seem to point out that the cupola was so bad it is irrelevant as a cause of the credit crisis. But this is not consistent with what I understand from Donald MacKenzie’s article…


    According to Donald, that the cupola really became useful in 2004 when additional instruments such as iTraxx came up and allowed traders to back out the implied correlation in a CDO tranche. Donald then argues that it was the sheer usefulness of this machinery –including the cupola– that led to ever-lower debt quality.

    Is this what you had in mind? I would be very curious to know more, and to better understand your “leverage-derived” credit risk.

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