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In recent weeks, high-frequency trading (HFT) skeptics have turned their febrile imaginations to the issue of "excessively high" order cancellation rates, suggesting they constitute “evidence” of gaming or manipulation on the part of HFTs, or “proof” that the liquidity these strategies provide is of inferior quality. The fact that the detractors never specify a rate of cancellations they'd deem satisfactory, nor any material criteria for determining such a threshold, belies the fact that cancellation rates are, in fact, a false issue.

Cancellation rates in excess of 90 percent arise quite naturally from the operation of perfectly legitimate and valuable liquidity-providing strategies. For instance, cross-sectional mean-reversion (i.e. the tendency of abnormally wide spreads between correlated stocks to converge) is the among the oldest and most widely practiced of all liquidity-enhancing quantitative strategies. A common technique for executing a mean-reverting spread trade is to post a bid on a stock believed to be “cheap,” and then attempt to actively hedge oneself by hitting the bid on another stock that is reckoned to be "expensive."

The efficacy of such an approach depends on the continuous availability of shares on the bid of the stock used as a hedge. If shares on the bid of the hedging instrument disappear (because the hedge ticked down), then the trader will seek to cancel his bid on passive leg of his trade, since the effective spread between the rich and cheap stocks will have changed. Though such strategies can entail extremely high cancellation rates, their value to the market is well-understood and non-controversial, as they serve as effective mechanisms to transfer liquidity from stocks where it is abundant to those where it is in demand.

Claims that high cancellation rates are symptomatic of low-quality liquidity are similarly spurious. Quite the opposite is true – elevated cancellation rates are evidence of robust competition between market makers vying for priority during the price-formation process. Most electronic markets observe strict price-time priority. In such markets, time priority at each price level is extremely important, because it determines the extent to which an order is likely to experience “adverse selection” when filled. Thus, each time a new price is formed, liquidity providers rush to submit orders to secure their place in line at the new price. Participants who wind up at the end of a very large queue will be more inclined to cancel their orders, in order to avoid adverse selection. Discouraging such players from canceling their orders will deter them from trying to compete for time priority, which will result in far less competition among market makers to participate in the formation of prices.

A common sleight-of-hand used by detractors to "demonstrate the growing problem" of increasingly large cancellation rates is to plot a time series of cancellation rates over the past ten years or longer. These transparently cynical attempts to pin blame neglect to mention that the growth in cancellation rates is linked mostly to factors unrelated to HFT. One such factor is the overall number of price changes per unit of time; price changes lead naturally to cancellations, as traders must cancel old orders in order to participate at current prices. The frequency of price changes depends on the prevailing level of volatility in the market, as well as the size of the minimum quoting increment. Thus, it is entirely unsurprising (and not at all the fault of HFTs) that upon the advent of decimal pricing, cancellation rates show a huge and permanent spike upward, and that during periods of heightened volatility (e.g. 2008-2009), cancellation rates temporarily surge as well.

Another important factor is increasing market fragmentation. After the final implementation of Reg NMS in 2007, new exchanges quickly proliferated, and there are over a dozen exchanges that are now “protected” by Reg NMS. This affects cancellation rates because a passive trader will often post orders on multiple venues in order to maximize the odds of getting filled. As a result, the total shares posted at a price across all venues often significantly exceeds the amount that traders are willing to buy or sell at that price. Consequently, when a trader's allotted size is filled at some subset of venues, he must cancel all open orders at the remaining venues. The more such venues, the greater the cancellation rate. Unsurprisingly, charts of cancellation rates over time show another sharp and permanent shift upward shortly after the passage of Reg NMS, but again, this has nothing to do with HFT and everything to do with the fragmentation created by this flawed regulation.

Such duplicity is not only used to exaggerate the trend in cancellation rates, but to "demonstrate" false consequences as well. For instance, a recent blog post from the anti-HFT site zerohedge.com asserts that since 100,000 to 200,000 NBBO quotes per day are received on average for Dow Jones stocks in 2010, that the "quote" therefore changes 600+ times each minute, preventing any “true investor” from ascertaining the real price. The post further claims that the average “quote duration” has thus gone from well over a second in 2004, to 0.1 seconds or less in 2010. This contention is sheer nonsense – the average quote duration is still well over one second, just as it was in 2004.

The authors not only ignore the effect of Reg NMS and increased market fragmentation on overall message traffic, but they engage in a manipulative use of the term "quote" in order to conduct their false derivation. The Credit Suisse article the authors source for their quotes-per-day figures uses “quote” to refer to an order – in other words, 100,000 to 200,000 orders at the NBBO arrive each day for DJIA stocks. The author then conflates this with the NBBO (nationwide best bid/offer) quotation, leading the reader to believe that the NBBO changes 600+ times per minute.

Unfortunately, the two concepts have nothing to do with each other, and the conclusion is false. In fact, the average duration of quotes can easily be measured directly, without convoluted derivations. For all of 2010, the average NBBO on the most rapidly traded stock in the world (SPY) had an average duration of over 3 seconds. Stocks in the DJIA, which have considerably lower prices and volumes than SPY, have far longer mean NBBO durations than SPY.

Bad Medicine

HFT detractors fail to demonstrate any compelling evidence that prevailing cancellation rates are problematic, yet this has not deterred them from proffering myriad cures for the presumed ailment. One such remedy is to impose a "speed limit" on trading by imposing a minimum time-in-force for orders before cancellations are allowed. The stupidity of such a measure is so obvious that it is alarming that regulators are even entertaining it. Such a measure may indeed curb cancellation rates, but it would also be a sheer windfall for HFTs, because it would lead inexorably to a proliferation of riskless arbitrage opportunities for fast traders as a direct result. Every time the E-Mini S&P futures contract ticks up in value, a fast trader will be able to lock in a riskless payoff by shorting the futures and lifting the frozen offer on SPY. Similar arbs will arise in highly but imperfectly related stocks, and between stocks vs options. At the most basic level, passive traders cancel orders to avoid getting "picked off." Absent the ability to do so, market-makers will have no choice but to widen out their spreads to compensate for the additional adverse selection.

Another proposed remedy is that HFTs should pay a penalty for excess cancellations or message traffic. The premise is that HFTs generate the lions share of message traffic to the exchanges, far in excess of their share of volume traded, and should therefore pay a “tax” for clogging up the exchanges and slowing everyone else down. There are two main fallacies for this argument. First, there is no empirical evidence that the day-to-day cancellation rates on exchanges have any role in slowing the exchanges down. The exchanges themselves are best positioned to understand the impact of cancellation rates and message traffic on their matching engines, and are not among the people making such claims.

More importantly, the complaint is moot because the the exchanges already tax participants on the basis of their message traffic. To connect to an exchange, such as Nasdaq or BATS, you must connect to it through a “port,” which is essentially a participant's private connection to the exchange. If you send multiple messages into a port, they queue up in the port and are processed sequentially. The next message in the queue is not processed until the first one has received an acknowledgment. These exchanges use a round-robin system to process messages from the myriad inbound ports used by all the clients connected to the exchange. Because of this architecture, a large volume of messages on any one port has absolutely no bearing on the exchange's ability to function at its normal rate. Put simply, if you send too many messages, you will clog up your own connection to the exchange, but not the exchange itself. The only way a participant can increase his message throughput to the exchange by purchasing more ports – which are billed at a per-month rate per port.

In other words, the fee that the detractors wish to impose already exists. How, then, to explain the criticism? Either the detractors are blissfully unaware of the finer details of how the market actually works (such as the existence of ports to throttle and constrain traffic), or they are cynically taking advantage of the lack of knowledge of market structure on the part of the public or policy makers, in order to promote their own self-interested agendas.

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