Profiting from bubbles: divergence trades and the problem of resonance

August 6, 2010

I’m now getting ready for the Academy of Management conference. Getting ready, that is, for the strange hotel existence of the conference attendant. Featuring: the continuous use of a name tag, the foraging for food in academic receptions, and the attempts not to doze off in the after-lunch PowerPoint presentations. But not all is lost. The Academy is inspiring at its best. And this year I am very hopeful for the session that Michael Jacobides has put together on the credit crisis.

If there is one message coming out of the crisis, it is that we live in a bubble economy. Bubbles are, as I see it, the central intellectual challenge of our time. And instead of telling the government to go and fix it for us, I’d rather devise strategies that allow actors to deal with bubbles on an individual basis. I am offering some ideas here, based on my research with David Stark. (This, by the way, is the second of a series started here).

Bubbles and the problem of resonance

My latest paper with David identifies a new problem in the capital markets, which we call resonance. Resonance, I would argue, is one of the ways in which bubbles come about. Understanding what resonance is, and how some traders exploit it, provides ideas for profiting from bubbles – and ameliorating them in the process.

What, then, is resonance? Our paper traces the case of a merger arbitrage desk, and a so-called “arbitrage disaster.” Merger arbitrageurs use models and databases to bet on the probability that two firms that announce their merger will indeed merge. But the traders, we found, not only relied on their own estimates; they also used models to find out what their rivals were collectively thinking about the trade. As we show, this typically works very well… except for situations in which everyone is similarly mistaken. In those cases, everyone is falsely reassured that they are correct, bet the house, and lose the shirt. This mechanism, which we call “resonance,” was at play in the case of the GE-Honeywell merger. See paper for details.

So what? The lesson we draw is that attending to the social context (“the market”) is only helpful in situations where that market context contains enough diversity. If not enough rivals hold a certain risk to be relevant, a trader that relies on a combination of his/ her own model and “the market” will dismiss the most damning evidence about it, down to press reports that write it on the front page.

Divergence trades

The lack of diversity makes for a trading opportunity. A trader can actively look for situations in which there is a great measure of agreement among market participants, and consider whether the agreement is genuine or an artifact of the precautionary mechanism. If it is, a trader might hypothesize that most of its rivals are wrong, and profit from it.

For an example, return to the case of GE-Honeywell and consider how an entrepreneurial trader found a way to exploit disasters in merger arbitrage. According to the Financial Times, the renowned New York hedge fund Atticus Global developed a strategy to exploit arbitrage disasters such as the GE-Honeywell deal, before they happen. Atticus proceeded by betting on the reverse of the outcome that its rivals were anticipating. As we saw above, merger arbitrageurs bet on merger success and the subsequent convergence in the prices of GE and Honeywell. By contrast, Atticus bet on merger cancelation and a subsequent divergence in the prices of the two stocks. As the journalist described, “Most risk arbitrage managers followed their usual strategy of going long the target, Honeywell, and short the buyer, GE. Atticus shorted Honeywell and bought GE, making a 10 per cent return on its investment”. By assembling a trade that was the negative image of what its competitors did, Atticus managed to profit from their losses. Because the original trade is known as a convergence trade, Atticus strategy is known as a divergence trade. In general, “divergence trading” is a form of being contrarian.

Divergence trades such as performed by Atticus are unconventional and rare. While betting on convergence allows traders to rely on their rivals for reassurance, betting on divergence does not allow for that possibility. Divergence trades are therefore riskier and rarely put in practice — not even considered to be an integral part of the strategy. However, Atticus understood that there is one instance in which divergence trades might be profitable enough to be worth the risk – when something is not going happen and everyone else thinks it will. E.g., the more traders bet on convergence, the narrower the price difference, and the grater the returns from betting that the prices will widen.

In short, understanding the role that resonance and the lack of diversity plays in the market provides the basis for a trading strategy. Traders exploit cognitive diversity among their rivals. When this is missing, those same traders will be misleadingly reassured and potentially very wrong. This can be exploited with a convergence trade, by betting that the misled will lose out. As Gregory Zuckerman explains in his terrific book, this is exactly what John Paulson did in the credit crisis. And in a recent meeting with a hedge fund strategist in Paris this past May, I learnt that he was also focusing more and more on divergence trades. This should give us cause for optimism. If enough traders take on this approach, perhaps the next bubble will be less virulent as the last.

10 Responses to “Profiting from bubbles: divergence trades and the problem of resonance”

  1. Chris Jefferis Says:

    Daniel, this is interesting stuff! You could say the concept of resonance applied to the LTCM collapse and the chaos experienced by fixed income convergence traders in August 2007 too. .

  2. danielbeunza Says:

    Chris — right on. That’s exactly the question that I’m asking myself now: What other instances of resonance are there out there? There would be huge gains in establishing that resonance was at play in these two crises.

    Note, however, that not any crisis is necessarily a case of resonance. For it to be one, you need to have arbitrageurs who are reverse engineering prices to make judgments about their competitors, and you need a large risk factor that proved disastrous and that was ignored despite the availability of information about it.

    Interestingly enough, one paper by Donald MacKenzie in the London Review of Books on “The end of the world trade” does argue that traders confirmed their estimates of the low correlation in the default rates of mortgage bonds by calculating the “implied correlation” from the prices of CDSs.

    As for Long Term Capital, one would need evidence that the Russian crisis was not altogether unexpected, that it hit the business press well in advance of August 1998, but that it did not register in the spreads.


  3. Daniel,

    It’s fortuitous you posted this, as I’ve spent the last couple of weeks thinking about what a “material sociology of asset bubbles” might look like. I think you provide a valuable perspective here to complement the herding/imitation literature, as you essentially open up the “black box” of traders’ beliefs. In that literature, beliefs are simple Bayesian probabilities, and that literature generally assumes that traders’ private beliefs are independent from each other — the reason being that in the culture of economics it makes for a stronger theoretical claim to show that herding can arise *even when* traders have independent, uncorrelated beliefs. From a practical perspective though, this literature ignores the fact that traders’ beliefs *do* tend to be systematically correlated. Behavioural economists justify attention to correlated beliefs using the psychology of individual biases. I think a valuable linkage the SSF can make is to tie those biases back to what we know about the diffusion of new technological artefacts via attention to distributed cognition. From your account with Stark, I’m left wondering: where do the traders’ databases come from? Are they produced independently by each hedge fund? Or is there an interesting process of diffusion one could track (perhaps via personal networks, industrial espionage) that changes the tool-set traders use when doing merger arbitrage? In terms of explaining the ABS CDO bubble (I would call it a bubble), the fact that the ratings agencies’ models were embedded in widely available desktop programs like S&P’s CreditMetrics seem to have played an important role in generating the “resonance” necessary for widespread adoption of ABS CDOs. For this reason, I think you’re right to focus on the dangers of what one might call “calculative monoculture.” New assets — like ABS CDOs — necessitate new valuation tools and models. When these tools are new, most practitioners lack the capabilities necessary to engage in bricolage. Thus models are too similar, which can lead to resonance.

    I like your concept, but I think we need to be more clear about what a bubble is before we apply the concept of resonance to it. It’s a fuzzy boundary that isn’t without controversy, but I think it’s safe to say a bubble isn’t merely an instance where markets “get it wrong.” Instead, there needs to be a structural feature or incentive issue that encourage investors to “time the market” instead of acting immediately on their beliefs. Brunnermeier (2004) provides compelling evidence that hedge funds timed the market during the technology bubble of the 90s; they profited from its rise, but were able to get out in time to prevent serious losses. This is the important difference between an arbitrage disaster and a bubble. In other words, with equity or real estate bubbles you often see that gradually there is recognition among some traders that a bubble exists, but they fail to act on those beliefs in order to capture the profits that arise from holding onto assets whose value continues to inflate. The main strategic question a bubble investor faces is not simply “Does a bubble exist?” but also “Assuming a bubble does exist, when should I dump my shares?” In merger arb, as far as I can tell, everyone is interested in the question of “Is this deal going to happen?” and not “When will everyone realise this deal won’t happen?”

    In other words, trader strategy in a bubble depends not only on their beliefs about an asset’s value, but their meta-beliefs about other investors’ beliefs. Sophisticated traders can’t “back out” those meta-beliefs from the prices since the prices are thought to be wrong in the first place. My hunch is that traders’ beliefs-about-beliefs are shaped by the interpersonal and inter-firm networks in which they are embedded. So while a trader may suspect that market prices are out-of-whack, he uses his network of contacts to ascertain whether other people have similar doubts and how widespread those doubts are. But because there’s an incentive to “time the market”, members of these networks have little incentive to act quickly on their beliefs, thus keeping them from being rendered visible to other participants. In fact, if they are really convinced that the asset is over-valued, they have every incentive to manipulate other traders to go long, even as they are slowly taking out short position on the asset in question. I suspect that those networks are crucial for creating and sustaining the private doubts that guys like Paulson had about the sub-prime market. Thus, for studying bubbles it might be useful to expand the focus from just the relationship between traders, their tool-set and scopic systems like prices to include their network of personal ties as well. It seems like Yuval is using a quantitative methodology in his paper on hedge fund connectedness that could be adopted to the study of bubbles to understand these personal networks.

    1. Markus K. Brunnermeier and Stefan Nagel, “Hedge Funds and the Technology Bubble,” The Journal of Finance 59, no. 5 (October 2004): 2013-2040.  

  4. danielbeunza Says:

    Taylor — I have three comebacks on your superb comment.

    First, i really like the expression “calculative monoculture.” This is, i think, the problem that Andy Lo uncovered in his research on the “quant mini crisis” of summer 07. Interestingly enough, our traders in Tools of the Trade actually *rented* some of their trading algorithms. No, I’m not kidding you. The rented them like you rent a Toyota Corolla. So that’s even more grounds for mono culture.

    As for the bubble — you are picking up on the fact that most investment situations suffer the beauty contest problem… it’s not right or wrong, but about anticipating other financiers. I agree. This is where my “ultimate bottleneck” strategy (see post of that title) can work — you assume that the bubble will continue for as long as all the links in the chain are there. And you predict the end of it by identifying when the weakest link will break. I.e., at what point in the deterioration of credit will new home buyers not even be able to make the first mortgage payment?

    As you suggest, once you are in a beauty contest and dissenters are gone because they recognize they cannot time it, backing out is not going to work. This is a great and original insight. Thank you. What Michael Lewis shows very well in The Big Short is that networks is the ideal complement. But still, it does seem as if traders were still feeling reassured by implied correlation and other asset prices.

  5. Chris Jefferis Says:

    Another reference to throw into the mix – I would say that the concept of resonance describes the crash in 1987 as captured by Richard Bookstaber in a demon of our own design. He attributes the 1987 crash to the implosion of portfolio insurance trades which were a “calculative monoculture”.

    Daniel – are there then two types of resonance? One which, traders may not be aware of which comes from using a common model and another more deliberate type of resonance trade, where traders are reflexive about the calculative monoculture and try to get one step ahead of it – I’ve heard this is what Renaissance capital do.

  6. danielbeunza Says:

    Not sure I agree. The notion of resonance, as David and I have coined it, has to do with backing out. Although 1987 was indeed the outcome of calculative monoculture, I don’t think that what happened entailed any backing out. As far as I know, portfolio managers knew at all times that prices were off, but they were just not fast enough to correct the program trading mispricing.

    On your second point, I did not know that Renaisance was explointing resonance. Very interesting. I’d love to see any link to article on it. My sense is that there is only one form of resonance, but it leads to trades that lose money, and others that make money — when they exploit it.

    By the way, great expression, “resonance trade”.


  7. I think 1987 is more of a “backing out” story than it is a “monoculture” story. According to Shiller (1988), only about 6% of investors were using program trading at the time of the ’87 crash. As far as I know, that estimate is fairly reliable — at least MacKenzie cites that figure in “An Engine Not A Camera.”

    So 1987 wasn’t caused by a “monoculture” per say. Instead, that small group of portfolio insurers sent a faulty signal to other market participants that fundamentals had changed, who then acted by selling. This caused the program trading programs to sell more, and so on. Because all of the trades were made over-the-phone, this caused a break-down in market liquidity, and eventually nobody’s orders could get through.

    So I do agree with Chris that there is an element of “backing out” — at least initially — with the 1987 crash, but it’s the inverse of what Daniel saw with merger arbitrage. Instead of inferring “nothing has changed” from price convergence when the merger was becoming increasingly less likely, traders in 1987 inferred “fundamentals have changed” when they really hadn’t.


  8. So, I went back and read your post on the “ultimate bottleneck strategy”, and it made more sense to me this time around. But I think that the event around which you should design a bottleneck strategy depends critically on the sophistication and diversity of the other financial actors in the market in question. As we’ve said, sophisticated financial actors reflexively “back out” information about other agents’ beliefs from stock price movements. Whenever a financial agent “backs out” information from a price, she must make strong assumptions about the nature of other financial actors — their information-processing capabilities, the information they possess, the decision-routines they follow and heuristics they employ, etc. In a market where agents are all sophisticated and equipped to be rational (in the neoclassical sense), a seemingly insignificant event or announcement can cause a bubble to pop.

    The following is at the tail-end of a good economics paper on currency crises. It concerns a theoretical model, but if we follow Callon and accept the idea that real neoclassical actors can be constructed, at least to a certain extent, I think it’s a good indicator of how sensitive markets can be when agents are enacted and equipped to act rationally:

    ‘A “grain of doubt,” allowing that others may believe that the economy is, in fact, unstable, will lead to a currency crises even if everyone knows that the economy is not unstable. In predicting when crises will occur, average opinion or even extreme opinion need not precipitate a crisis. Rather, what matters is the higher order beliefs of some participants who are apprehensive about the beliefs of others, concerning the beliefs of yet further individuals, on these extreme opinions’ (Morris and Shin 1998).

    Now for the strategy. Imagine a spectrum: on one hypothetical extreme, you have an “ideal” market of fully-enacted, neoclassical financial agents. For all intents and purposes, they are perfectly rational in the sense that they act on information, and their actions are informative to other agents. In this market, choosing the “weakest link” in the chain will probably get you burned because the bubble might pop with something as simple as a credible central banker announcing the bubble’s existence. On the other extreme, you have something like the real estate market. A wide cross-section of the population buys real estate, some for speculative purposes but many just to have a place to live. They have a wide range of calculative capabilities, beliefs, and reasons for action. It’s not really possible to “back out” people’s beliefs from the prices, so bubbles are more resistant to bursting. As you said, the bubble will keep on growing even after informed agents become aware of it because they believe there exist suckers who remain ignorant of the bubble. In these cases, it literally takes people failing to make their payments for the bubble to pop. In between those two extremes you have most bubbles, and which event you choose to build a bottleneck strategy depends on the calculative capabilities and motivations of other actors in the market.

  9. danielbeunza Says:

    Taylor — I agree with your point, but only partially. I read your excellent comment and actually went back and checked. I read “The Big Bad Wolf and the rational market,” Donald’s article on the 87 crash on which Chapter 6 of his book is based.

    You are right that a movement in prices led to a change in the implied magnitude — in this case, the cash S&P 500. Here is what MacKenzie writes:

    “The breakdown in arbitrage permitted futures prices to plunge far below the theoretical values implied by the apparent level of the index” p. 315

    “The fact that futures prices plunged far below even the huge falls on the stock market exacerbated fears on the latter, because they were taken as indicative of further declines yet to come.” p. 316

    However, I would need to know more details about the investors who were active on the index. Did they have a model or elaborate negative view of the market that then got confirmed? Or were they trying to ride the fall in prices, like chartists? Only in the former case can we say that there is resonance.

  10. danielbeunza Says:

    Taylor (on trading strategies): what you just offered is a very nice step towards a taxonomy of sociologically-induced strategies to profit from bubbles. Certainly, one dimension should be the degree of positive feedback that prices create. Bottleneck works with low feedback, divergence works with high feedback.

    As you point out, the feedback depends on the sophistication of the actors, and the degree of similarity in their strategies (i.e., speculation vs. direct use of the asset). To this, I would add the degree of agreement on the model used to back out: in the absence of a shared model, it is difficult to make inferences.

    Finally, one caveat to your argument that inferring is difficult is that professional arbitrageurs can find out the identity of those responsible for price movements. As my paper with David shows, the trader at the desk called the floor broker at the Amex.

    In sum… this is terrific. I wonder if we should be trading at our own hedge fund rather than blogging about it…


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