1. High Frequency Quoting: Short-Term Volatility in Bids and Offers Big Data Finance Conference May 3, 2013 Joel Hasbrouck Stern School, NYU 1

2. Disclaimers  I teach in an entry-level training program at a large financial firm that is generally thought to engage in high frequency trading.  I serve on a CFTC advisory committee that discusses issues related to high frequency trading.  I accept honoraria for presentations at events sponsored by financial firms.

3. What does quote volatility look like?  In US equity markets, bids and offers from all trading venues are consolidated and disseminated in real time.  The highest bid is the National Best Bid (NBB)  The lowest offer is the National Best Offer (NBO)  Next slide: the NBBO for AEPI on April 29, 2011 3

4. Figure 1. AEPI bid and offer, April 29, 2011 4

5. Figure 1. AEPI bid and offer on April 29, 2011 (detail) 5

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12. Quote volatility: the questions  What is its economic meaning and importance?  How should we measure it?  Is it elevated? Relative to what?  Has it increased along with wider adoption of high-speed trading technology? 12

13. Economic consequences of quote volatility  Noise due to flickering quotes  Execution price risk  For marketable orders  For dark trades  Intermediaries’ look-back options  Quote-stuffing  Spoofing 13

14. Descriptive statistics: computation and interpretation 14

15. Local variances about local means 15 n = length of averaging interval. Depends on trader’s latency and order strategies: we want a range of n

16. Interpretation  To assess economic importance, I present the (wavelet and rough) variance estimates in three ways.  In mils per share  In basis points  As a short-term/long-term ratio 16

17. Mils per share 17

18. Basis points (One bp = 0.01%) 18

19. The short/long variance ratio 19

20. The empirical analysis 20 CRSP Universe 2001-2011 In each year, chose 150 firms in a random sample stratified by dollar trading volume 2001-2011 April TAQ data with one-second time stamps 2011 April TAQ with one- millisecond time stamps High-resolution analysis Lower-resolution analysis

21. Table 1. Summary Statistics, 2011 Dollar trading volume quintile Full sample1 (low)2345 (high) No. of firms15030 NYSE470571619 Amex622011 NASDAQ972823 1310 Avg. daily trades1,331314311,1263,47816,987 Avg. daily quotes23,9289677,70624,02653,080181,457 Avg. daily NBBO records7,1383283,0297,54316,02646,050 Avg. daily NBB changes1,2451205111,3512,4154,124 Avg. daily NBO changes1,1641034601,3612,4214,214 Avg. price$15.62$4.87$5.46$17.86$27.76$51.60 Market capitalization of equity, $ Million$683$41$202$747$1,502$8,739

22. (1)(2)(3)(4)(5)(6)(7) Time scale Variance ratio Bid-Offer Corr < 50 ms0.280.164.22 50 ms0.390.223.990.270.153.760.32 100 ms0.550.313.790.380.213.580.36 200 ms0.760.433.530.530.303.270.41 400 ms1.050.593.210.730.412.880.44 800 ms1.460.832.901.010.572.590.47 1,600 ms2.021.142.641.400.792.380.51 3.2 sec2.801.582.401.941.092.160.55 6.4 sec3.902.182.122.711.491.840.60 12.8 sec5.432.991.883.772.041.650.64 25.6 sec7.544.101.705.232.791.510.69 51.2 sec10.485.611.547.253.821.390.74 102.4 sec14.537.681.4210.045.221.290.79 3.4 min20.1210.511.3213.877.141.210.83 6.8 min27.8814.401.2319.229.781.150.86 13.7 min38.5519.701.1626.4513.331.080.88 27.3 min52.8426.791.0835.7317.911.000.90 Table 2. Time scale variance estimates, 2011

23. Figure 2. Wavelet variance ratios across time scale and dollar volume quintiles 23

24. The 2011 results: a summary  Variance ratios: short term volatility is much higher than we’d expect relative to a random-walk.  In mils per share or basis points, average short term volatility is economically meaningful, but small. 24

25. Historical analysis 25 CRSP Universe 2001-2011 In each year, chose 150 firms in a random sample stratified by dollar trading volume 2001-2011 April TAQ data with one-second time stamps 2011 April TAQ with one- millisecond time stamps High-resolution analysis Lower-resolution analysis

26. Table 5. Summary statistics, historical sample, 2001-2011 (only odd numbered years are shown) 26 200120032005200720092011 No. firms146150 NYSE1085148555647 Amex221181456 NASDAQ168894818997 Avg. daily trades1421874259701,7901,331 Avg. daily quotes1,0781,2995,82812,52139,37823,928 Avg. daily NBB changes1032035967721,6181,210 Avg. daily NBO changes1032137297891,7311,126 Avg. price$18.85$14.83$16.10$15.81$10.72$15.62 Market equity cap $ Million$745$189$325$480$316$683

27. Table 5. Summary statistics, historical sample, 2001-2011 (only odd numbered years are shown) 27 200120032005200720092011 No. firms146150 NYSE1085148555647 Amex221181456 NASDAQ168894818997 Avg. daily trades1421874259701,7901,331 Avg. daily quotes1,0781,2995,82812,52139,37823,928 Avg. daily NBB changes1032035967721,6181,210 Avg. daily NBO changes1032137297891,7311,126 Avg. price$18.85$14.83$16.10$15.81$10.72$15.62 Market equity cap $ Million$745$189$325$480$316$683 25% CAGR 36% CAGR

28. What statistics to consider?  Long-term volatilities changed dramatically over the sample period.  Variance ratios (normalized to long-term volatility) are the most reliable indicators of trends. 28

29. Table 6. Wavelet variance ratios for bids and offers, 2001-2011 29 Time scale20012002200320042005200620072008200920102011 50 ms5.227.166.0310.286.698.576.966.064.527.084.70 100 ms5.446.585.289.696.518.076.275.384.126.264.32 200 ms5.286.285.139.036.227.345.334.643.685.403.74 400 ms4.595.235.008.165.756.304.253.843.214.533.07 800 ms3.124.043.935.575.035.103.413.112.763.712.56 1,600 ms2.112.553.254.114.144.052.892.592.433.042.23 3.2 sec1.982.242.933.383.483.372.562.292.172.532.01 6.4 sec1.942.112.622.912.932.922.352.081.952.161.82 Panel A: Computed from unadjusted bids and offers

30. No trend in quote volatilities?  Maybe …  “Flickering quotes” aren’t new.  Recent concerns about high frequency trading are all media hype.  The good old days weren’t really so great after all.  What did quote volatility look like circa 2001? 30

31. Figure 4 Panel A. Bid and offer for PRK, April 6, 2001. 31

32. Compare 32

33. Figure 4 Panel B. PRK, April 6, 2001, Rough component of the bid 33

34. Table 6. Wavelet variance ratios for bids and offers, 2001-2011 34 Time scale20012002200320042005200620072008200920102011 50 ms1.602.373.157.026.098.246.565.834.206.794.46 100 ms1.572.323.096.825.897.765.895.173.836.004.07 200 ms1.562.273.036.485.617.044.994.453.415.183.57 400 ms1.552.232.945.905.166.023.963.682.974.363.00 800 ms1.572.192.835.004.474.823.132.982.563.582.52 1,600 ms1.642.202.713.993.603.792.632.512.272.942.20 3.2 sec1.812.302.623.443.023.162.332.232.042.462.00 6.4 sec2.112.512.593.202.652.752.152.041.862.111.82 Panel B. Computed from denoised bids and offers

35. So has quote volatility increased?  Apples vs. oranges  The nature of quotes has changed.  Quote volatility has changed  From infrequent large changes to frequent (and oscillatory) small changes.  Possibly a overall small increase,  But nothing as strong as the trend implied by the growth in quote messaging rates. 35