June 27, 2017

Did a denial-of-service attack cause the flash crash? Probably not.

Last June I wrote about an analysis from Nanex.com claiming that a kind of spam called “quote stuffing” on the NYSE network may have caused the “flash crash” of shares on the New York Stock Exchange, May 6, 2010. I wrote that this claim was “interesting if true, and interesting anyway”.

It turns out that “A Single Sale Worth $4.1 Billion Led to the ‘Flash Crash’“, according to a report by the SEC and the CFTC.

The SEC’s report says that no, quote-stuffing did not cause the crash. The report says,

It has been hypothesized that these delays are due to a manipulative practice called “quote-stuffing” in which high volumes of quotes are purposely sent to exchanges in order to create data delays that would afford the firm sending these quotes a trading advantage.

Our investigation to date reveals that the largest and most erratic price moves observed on May 6 were caused by withdrawals of liquidity and the subsequent execution of trades at stub quotes. We have interviewed many of the participants who withdrew their liquidity, including those who were party to significant numbers of buys and sells that occurred at stub quote prices. …[E]ach market participant had many and varied reasons for its specific actions and decisions on May 6. … [T]he evidence does not support the hypothesis that delays in the CTS and CQS feeds triggered or otherwise caused the extreme volatility in security prices observed that day.

Nevertheless … the SEC staff will be working with the market centers in exploring their members’ trading practices to identify any unintentional or potentially abusive or manipulative conduct that may cause such system delays that inhibit the ability of market participants to engage in a fair and orderly process of price discovery.

Given this evidence, I guess we can simplify “interesting if true, and interesting anyway” to just “interesting anyway”.

Did a denial-of-service attack cause the stock-market "flash crash?"

On May 6, 2010, the stock market experienced a “flash crash”; the Dow plunged 998 points (most of which was in just a few minutes) before (mostly) recovering. Nobody was quite sure what caused it. An interesting theory from Nanex.com, based on extensive analysis of the actual electronic stock-quote traffic in the markets that day and other days, is that the flash crash was caused (perhaps inadvertently) by a kind of denial-of-service attack by a market participant. They write,

While analyzing HFT (High Frequency Trading) quote counts, we were shocked to find cases where one exchange was sending an extremely high number of quotes for one stock in a single second: as high as 5,000 quotes in 1 second! During May 6, there were hundreds of times that a single stock had over 1,000 quotes from one exchange in a single second. Even more disturbing, there doesn’t seem to be any economic justification for this.

They call this practice “quote stuffing”, and they present detailed graphs and statistics to back up their claim.

The consequence of “quote stuffing” is that prices on the New York Stock Exchange (NYSE), which bore the brunt of this bogus quote traffic, lagged behind prices on other exchanges. Thus, when the market started dropping, quotes on the NYSE were higher than on other exchanges, which caused a huge amount of inter-exchange arbitrage, perhaps exacerbating the crash.

Why would someone want to do quote stuffing? The authors write,

After thoughtful analysis, we can only think of one [reason]. Competition between HFT systems today has reached the point where microseconds matter. Any edge one has to process information faster than a competitor makes all the difference in this game. If you could generate a large number of quotes that your competitors have to process, but you can ignore since you generated them, you gain valuable processing time. This is an extremely disturbing development, because as more HFT systems start doing this, it is only a matter of time before quote-stuffing shuts down the entire market from congestion.

The authors propose a “50ms quote expiration rule” that they claim would eliminate quote-stuffing.

I am not an expert on finance, so I cannot completely evaluate whether this article makes sense. Perhaps it is in the category of “interesting if true, and interesting anyway”.

Intractability of Financial Derivatives

A new result by Princeton computer scientists and economists shows a striking application of computer science theory to the field of financial derivative design. The paper is Computational Complexity and Information Asymmetry in Financial Products by Sanjeev Arora, Boaz Barak, Markus Brunnermeier, and Rong Ge. Although computation has long been used in the financial industry for program trading and “the thermodynamics of money”, this new paper applies an entirely different kind of computer science: Intractability Theory.

A financial derivative is a contract specifying a payoff calculated by some formula based on the yields or prices of a specific collection of underlying assets. Consider the securitization of debt: a CDO (collateralized debt obligation) is a security formed by packaging together hundreds of home mortgages. The CDO is supposedly safer than the individual mortgages, since it spreads the risk (not every mortgage is supposed to default at once). Furthermore, a CDO is usually divided into “senior tranches” which are guaranteed not to drop in value as long as the total defaults in the pool does not exceed some threshhold; and “junior tranches” that are supposed to bear all the risk.

Trading in derivatives brought down Lehman Brothers, AIG, and many other buyers, based on mistaken assumptions about the independence of the underlying asset prices; they underestimated the danger that many mortgages would all default at the same time. But the new paper shows that in addition to that kind of danger, risks can arise because a seller can deliberately construct a derivative with a booby trap hiding in plain sight.

It’s like encryption: it’s easy to construct an encrypted message (your browser does this all the time), but it’s hard to decrypt without knowing the key (we believe even the NSA doesn’t have the computational power to do it). Similarly, the new result shows that the seller can construct the CDO with a booby trap, but even Goldman Sachs won’t have enough computational power to analyze whether a trap is present.

The paper shows the example of a high-volume seller who builds 1000 CDOs from 1000 asset-classes of home mortages. Suppose the seller knows that a few of those asset classes are “lemons” that won’t pay off. The seller is supposed to randomly distribute the asset classes into the CDOs; this minimizes the risk for the buyer, because there’s only a small chance that any one CDO has more than a few lemons. But the seller can “tamper” with the CDOs by putting most of the lemons in just a few of the CDOs. This has an enormous effect on the senior tranches of those tampered CDOs.

In principle, an alert buyer can detect tampering even if he doesn’t know which asset classes are the lemons: he simply examines all 1000 CDOs and looks for a suspicious overrepresentation of some of the asset classes in some of the CDOs. What Arora et al. show is that is an NP-complete problem (“densest subgraph”). This problem is believed to be computationally intractable; thus, even the most alert buyer can’t have enough computational power to do the analysis.

Arora et al. show it’s even worse than that: even after the buyer has lost a lot of money (because enough mortgages defaulted to devalue his “senior tranche”), he can’t prove that that tampering occurred: he can’t prove that the distribution of lemons wasn’t random. This makes it hard to get recourse in court; it also makes it hard to regulate CDOs.

Intractability Theory forms the basis for several of the technologies discussed on Freedom-to-Tinker: cryptography, digital-rights management, watermarking, and others. Perhaps now financial policy is now another one.