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# Other

# Quote Life Report Methodology 

                            Feb. 25, 2021                       

This report provides two distinct sets of analyses: conditional order lifetimes and conditional frequency plots, hazard, survivor and cumulative distribution functions. NYSE Ultra feed and NYSE MKT are hybrid exchanges that do not report individual order identification numbers. They are excluded from the conditional order lifetimes and conditional frequency plots, hazard, survivor and cumulative distribution functions sample.1 Beginning May 1, 2017, the MIDAS switched from the NYSE Ultrabook level feed to the NYSE Integrated Feed (NIF). This feed provides a mechanism for matching trades and modifications with the original resting orders.

The sample includes every order between 9:35 am and 4:00 pm. Amex, Arca, Nasdaq and NYSE conduct some form of open and/or closing auction. Most permit a mixture of normal orders with open- or close- specific orders. NSYE and Amex print the open with a special code. Frequently a series of trades and cancels are printed immediately thereafter and these orders are often at different prices. Nasdaq stocks frequently open within a few hundred milliseconds of 9:30 am, but not always. Filtering the first five minutes is a conservative effort to avoid some of the idiosyncrasies associated with the open.

Every message includes an exchange-generated timestamp as well as a single-collection-point timestamp generated by the collection system. Collection-point timestamps are accurate to the microsecond and can be used to time-sequence cross-exchange events, at least from the specific vantage of the collection point. Some exchange-generated timestamps are provided with microsecond granularity; others are provided with millisecond granularity. For the purpose of measuring the lifetime of individual quotes, cross-exchange time-sequencing is not needed. In the analyses below we use the microsecond collection-point timestamp for all exchanges except Nasdaq, for which we use the (microsecond) timestamp generated by Nasdaq.

The list of included stocks and exchange-traded products is sourced from the Center for Research in Security Prices (CRSP) daily stock database (SHRCD = 10, 11 for stocks; SHRCD = 73 for ETPs). This list is updated monthly with a 3 – 4 week lag from the final trading day of the previous month. Trades against hidden orders have no unique order identification (by construction). These are not included in the sample. For every exchange except Nasdaq, we take the timestamp as reported by Tradeworx. For Nasdaq, we use the exchange timestamp. We construct the following variables:
                                - Full Cancel lifetime  is recorded when the original order volume is reduced to zero by a single cancel order.
                                - Full Trade lifetime  is recorded when the original order volume is reduced to zero by a single trade.
                                - Partial Cancel lifetime  is recorded when the original order volume or remaining volume is reduced by a cancel order.
                                - Partial Trade lifetime  is recorded when the original order or remaining volume is reduced by a trade order.
                                - Cancels  = Full Cancel + Partial Cancel;  Trades  = Full Trade + Partial Trade;  All  = Cancels + Trades.
                                - Price  is the closing price for the day according to the CRSP database. When there is no closing trade, a quote midpoint is used in the absence of a close price.
                                - Market Capitalization (Size) : Price * shares outstanding. Shares outstanding are sourced from the daily CRSP files.
                                - Turnover : # of shares traded ÷ # of shares outstanding
                                - Volatility  is the daily standard deviation of 1-minute quote midpoint returns

For each stock and ETP in the CRSP universe, quote lifetime (duration) is calculated as the time difference between the event (Trade, Cancel) and the matching Add Order. If the order is not fully canceled or executed, it is treated as canceled at the close. Order lifetimes are binned (i.e., counted) by time interval and position relative to the spread, market capitalization, turnover, volatility or price, scaled to 1 (by dividing by the total count for all of the bins) and cumulated over the time intervals.

We use a subsample of stocks and ETPs for the conditional frequency plots, hazard, survivor and cumulative distribution functions analyses. There are three market capitalization sub-samples: small, mid-size and large. For stocks (ETPs), the large sample is the 100 (40) securities with the largest market capitalization on a particular day. The mid-size sample ranges from the 50 (20) stocks (ETPs) below the median to the 50 (20) securities above the median. The small subsample is the smallest set of 100 (40) stocks (ETPs) in the sample. Note that the securities composing each sub-sample may not be the same from day to day if relative market capitalizations change. For each stock and ETP in the size sub-samples, quote lifetime (duration) is calculated as the time difference between the event (Trade, Cancel) and the matching Add Order. If the order is not fully canceled or executed, it is treated as canceled at the close. For the hazards, each partial or full cancellation or trade is counted as an event. That is, the timer begins anew after each partial cancellation or trade. One potential interpretation is that following an incomplete fill or cancellation, the trader is presented with an opportunity to reevaluate the order decision. For the frequency plots, order lifetimes are binned (i.e., counted) by time interval and position relative to the spread, scaled to 1 (by dividing by the cumulative count for the bins) and plotted against duration. The hazard, survivor and cumulative distribution functions are computed using the continuous lifetable method with trades (cancellations) acting as the censoring event for cancellations (trades). For more information on hazard modeling in general see, for example, “The Statistical Analysis of Failure Time Data” by John D. Kalbfleisch and Ross L. Prentice.

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[1] In February 2014, an updated Arca direct feed was implemented on the MIDAS system. This feed is no longer amenable to the order-matching duration computations required for the current analyses and will be dropped from the analyses after January 2014.

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