High Frequency Quoting: Short-Term Volatility in Bids and Offers Joel Hasbrouck Stern School, NYU 1.

High Frequency Quoting: Short-Term Volatility in Bids and Offers Joel Hasbrouck Stern School, NYU 1

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.

Figure 1. AEPI bid and offer, April 29, 2011 3

Figure 1. AEPI bid and offer on April 29, 2011 (detail) 4

More pictures from the National (High Frequency) Portrait Gallery 5

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 over the recent past along with the utilization of advanced trading technology? 10

Context and connections  Analyses of high frequency trading  Volatility modeling  Methodology: time scale resolution and variance estimation 11

“HF traders are the new market makers.”  Provide valuable intermediation services.  Like traditional designated dealers and specialists.  Hendershott, Jones and Menkveld (2011): NYSE message traffic  Hasbrouck and Saar (2012): strategic runs / order chains  Brogaard, Hendershott and Riordan (2012) use Nasdaq HFT dataset in which trades used to define a set of high frequency traders.  Studies generally find that HFT activity is associated with (causes?) higher market quality. 12

“HF traders are predatory.”  They profit from HF information asymmetries at the expense of natural liquidity seekers (hedgers, producers of fundamental information).  Jarrow and Protter (2011); Foucault and Rosu (2012)  Baron, Brogaard and Kirilenko (2012); Weller (2012); Clark-Joseph (2012) 13

Volatility Modeling  ARCH, GARCH, and similar models focus on fundamental/informational volatility.  Statistically: volatility in the unit-root component of prices.  Economically important for portfolio allocation, derivatives valuation and hedging.  Quote volatility is non-informational  Statistically: short-term, stationary, transient volatility  Economically important for trading and market making. 14

Realized volatility  Volatility estimates formed from HF data.  average (absolute/squared) price changes.  Andersen, Bollerslev, Diebold and Ebens (2001), and others  Hansen and Lunde (2006) advocate using local averaging (“pre-averaging”) to eliminate microstructure noise.  Quote volatility is the microstructure noise. 15

Economics of quote volatility  Noise degrades the value of any signal.  Creates execution price risk for  marketable orders  dark trades  Creates and increases value of intermediaries’ look-back options 16

Execution price risk for marketable orders 17 Offer (ask) quote

18 A buyer who has arrival time uncertainty can expect to pay the average offer over the arrival period (and has price risk relative to this average).

Dark trading  “Dark” the market executing the order did not previously post a visible bid or offer at the execution price.  The trade itself is promptly reported.  Dark mechanisms  Hidden (undisplayed) limit orders  Internalized executions  Dark pools 19

Dark trades: internalized execution  A broker receives a retail buy order.  The order is not sent to an exchange or any other venue.  The broker sells directly to the customer at the National Best Offer (NBO)  Volatility in the NBO  volatility in execution price. 20

Dark trades: dark pools  Mechanism  Traders send buy and sell orders to a computer.  The orders are not displayed.  If the computer finds a feasible match, a trade occurs.  The trade is priced at the midpoint of the National Best Bid and Offer (NBBO)  Volatility in the NBBO causes volatility in the execution price. 21

Look-back options  Internalization: a broker receives a retail buy order and executes the order at the NBO.  Problem: how does the customer know what the NBO is or was?  Might the dealer take the highest price in the interval of indeterminacy?  Stoll and Schenzler (2002) 22

“Spoofing” manipulations  A dark pool buyer enter a spurious sell order in a visible market.  The sell order drives down the NBBO midpoint.  The buyer pays a lower price in the dark pool. 23

Analyzing quote volatility  Usual approach  parametric model for variance of price changes (ARCH, GARCH, …)  This study  Non-parametric analysis of variances of price levels 24

Variance about a local mean of a random walk 25

Computational definitions 26

Signal processing and time scale decompositions 28

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 30

Mils per share 31

Basis points 32

The short/long variance ratio 33

Variance ratios (cont’d) 34

The empirical analysis 35 CRSP Universe 2001-2011. (Share code = 10 or 11; average price $2 to $1,000; listing NYSE, Amex or NASDAQ) 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

Table 1. Summary Statistics, 2011 Dollar trading volume quintile Full sample1 (low)234 5 (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

Table 2. Time scale variance estimates, 2011  Variance estimates (across)  Time scale (down, shortest to longest) 37

(1)(2)(3)(4)(5)(6)(7) Level, j Time scale (mils per share) 2 (basis points) 2 Variance ratio (mils per share) 2 (basis points) 2 Variance ratio Bid-Offer Corr 0< 50 ms0.170.064.220.170.064.22 150 ms0.320.113.990.150.053.760.32 2100 ms0.610.223.790.290.103.580.36 3200 ms1.170.413.530.550.193.270.41 4400 ms2.190.753.211.030.342.880.44 5800 ms4.151.382.901.960.632.590.47 61,600 ms7.932.562.643.781.182.380.51 73.2 sec15.274.732.407.352.172.160.55 86.4 sec29.598.572.1214.313.851.840.60 912.8 sec57.6215.491.8828.036.911.650.64 1025.6 sec112.3828.031.7054.7612.541.510.69 1151.2 sec219.3151.171.54106.9223.141.390.74 12102.4 sec428.8194.111.42209.5042.941.290.79 133.4 min842.72174.701.32 413.9180.601.21 0.83 146.8 min1,668.69328.051.23 825.97153.351.15 0.86 1513.7 min3,287.68618.261.16 1,618.99290.211.08 0.88 16 (=J)27.3 min6,379.911,159.031.08 3,092.22540.771.00 0.90

(1)(2)(3)(4)(5)(6)(7) Level, j Time scale (mils per share) 2 (basis points) 2 Variance ratio (mils per share) 2 (basis points) 2 Variance ratio Bid-Offer Corr 0< 50 ms0.170.064.220.170.064.22 150 ms0.320.113.990.150.053.760.32 2100 ms0.610.223.790.290.103.580.36 3200 ms1.170.413.530.550.193.270.41 4400 ms2.190.753.211.030.342.880.44 5800 ms4.151.382.901.960.632.590.47 61,600 ms7.932.562.643.781.182.380.51 73.2 sec15.274.732.407.352.172.160.55 86.4 sec29.598.572.1214.313.851.840.60 912.8 sec57.6215.491.8828.036.911.650.64 1025.6 sec112.3828.031.7054.7612.541.510.69 1151.2 sec219.3151.171.54106.9223.141.390.74 12102.4 sec428.8194.111.42209.5042.941.290.79 133.4 min842.72174.701.32413.9180.601.210.83 146.8 min1,668.69328.051.23825.97153.351.150.86 1513.7 min3,287.68618.261.161,618.99290.211.080.88 16 (=J)27.3 min6,379.911,159.031.083,092.22540.771.000.90

Figure 2. Wavelet variance ratios across time scale and dollar volume quintiles 40

(1)(2)(3)(4)(5)(6)(7) Level, j Time scale (mils per share) 2 (basis points) 2 Variance ratio (mils per share) 2 (basis points) 2 Variance ratio Bid-Offer Corr 0< 50 ms0.170.064.220.170.064.22 150 ms0.320.113.990.150.053.760.32 2100 ms0.610.223.790.290.103.580.36 3200 ms1.170.413.530.550.193.270.41 4400 ms2.190.753.211.030.342.880.44 5800 ms4.151.382.901.960.632.590.47 61,600 ms7.932.562.643.781.182.380.51 73.2 sec15.274.732.407.352.172.160.55 86.4 sec29.598.572.1214.313.851.840.60 912.8 sec57.6215.491.8828.036.911.650.64 1025.6 sec112.3828.031.7054.7612.541.510.69 1151.2 sec219.3151.171.54106.9223.141.390.74 12102.4 sec428.8194.111.42209.5042.941.290.79 133.4 min842.72174.701.32 413.9180.601.21 0.83 146.8 min1,668.69328.051.23 825.97153.351.15 0.86 1513.7 min3,287.68618.261.16 1,618.99290.211.08 0.88 16 (=J)27.3 min6,379.911,159.031.08 3,092.22540.771.00 0.90 How closely do the bid and offer track at the indicated time scale?

Figure 3. Wavelet correlations between the National Best Bid and National Best Offer 42

Dollar trading volume quintiles Level, jTime scale Full sample1 (low)2345 (high) 0< 50 ms0.170.130.100.140.220.25 (0.01)(0.07)(0.02)(0.01) 150 ms0.150.120.090.120.200.23 (0.01)(0.07)(0.01) 3200 ms0.550.380.290.430.750.89 (0.04)(0.22)(0.03)(0.02)(0.04)(0.05) 5800 ms1.961.031.001.532.793.35 (0.09)(0.40)(0.09)(0.07)(0.14) (0.20) 13.42 73.2 sec7.353.333.455.4110.73 (0.28)(0.93)(0.30)(0.23)(0.57)(0.84) 1025.6 sec54.7615.2520.9934.8781.37117.44 (2.09)(2.41)(1.84)(1.50)(4.50)(8.22) 146.8 min825.97173.25242.94445.931,273.221,930.34 (42.96)(28.14)(21.87)(21.43)104.07)173.36) 1627.3 min3,092.22533.78798.241,665.485,425.586,786.46 (188.75)(87.40)(73.69)(82.94)(634.46)(639.18)

Dollar trading volume quintiles Level, jTime scale Full sample1 (low)2345 (high) 0< 50 ms0.060.200.060.030.020.01 (0.01)(0.07)(<0.01) 150 ms0.110.380.120.050.030.02 (0.03)(0.14)(0.01)(<0.01) 3200 ms0.411.330.440.190.110.06 (0.09)(0.47)(0.02)(0.01)(<0.01) 5800 ms1.384.261.580.700.400.23 (0.21)(1.15)(0.07)(0.03)(0.01) 73.2 sec4.7313.905.652.591.510.87 (0.49)(2.60)(0.26)(0.12)(0.04)(0.03) 1025.6 sec28.0371.5236.8517.3711.397.27 (1.46)(7.44)(1.74)(0.78)(0.34)(0.25) 146.8 min328.05694.55463.45225.57173.41119.32 (10.59)(44.14)(27.35)(11.01)(6.47)(4.60) 1627.3 min1,159.032,234.941,718.14815.77685.54446.54 (41.18)143.62)138.93)(42.03)(27.48)(18.25)

Table 3. Time scale variance estimates across $ volume quintiles, 2011 Panel C. Rough variance ratios Dollar trading volume quintiles Level, jTime scale Full sample1 (low)2345 (high) 0< 50 ms4.2212.723.452.621.761.37 (1.28)(6.96)(0.18)(0.07)(0.04)(0.02) 150 ms3.9912.013.232.441.691.35 (1.25)(6.81)(0.16)(0.06)(0.04)(0.02) 3200 ms3.5310.402.832.201.571.30 (1.06)(5.77)(0.11)(0.05)(0.03)(0.02) 5800 ms2.907.822.502.021.431.21 (0.66)(3.56)(0.08)(0.04)(0.03)(0.02) 73.2 sec2.405.872.171.821.321.15 (0.38)(2.08)(0.06)(0.04)(0.02) 1025.6 sec1.703.061.701.491.191.17 (0.12)(0.64)(0.04)(0.03)(0.02) 146.8 min1.231.581.241.171.041.16 (0.02)(0.12)(0.03) (0.02) 1627.3 min1.081.191.081.061.011.06 (0.01)(0.06)(0.03)(0.02)

Table 3. Time scale variance estimates across $ volume quintiles, 2011 Panel D. Bid-offer correlations Dollar trading volume quintiles Level, jTime scale Full sample1 (low)2345 (high) 150 ms0.320.050.230.310.410.56 (0.01) 3200 ms0.410.110.330.420.490.65 (0.01) (0.02) (0.01)(0.02) 5800 ms0.480.150.400.510.560.72 (0.01) (0.02) 73.2 sec0.550.190.470.590.660.82 (0.01)(0.02) 1025.6 sec0.700.270.610.750.850.95 (0.01)(0.02)(0.03)(0.02) (0.03) 146.8 min0.860.440.880.970.991.00 (0.02)(0.03)(0.04)(0.03) 1627.3 min0.900.510.960.991.00 (0.02)(0.04)(0.05)(0.03)(0.04)(0.03)

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. 47

Back to the empirical analysis 48 CRSP Universe 2001-2011. (Share code = 10 or 11; average price $2 to $1,000; listing NYSE, Amex or NASDAQ) 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

High-resolution analysis … … with low resolution data  TAQ with millisecond time stamps only available from 2006 onwards  TAQ with one second time stamps available back to 1993.  Can we draw inferences about subsecond variation from second-stamped data? 49

The problem  Where within the second did these quotes actually occur?  With a few simple assumptions, we know how they are distributed and how they may be simulated. Quote A10:01:35 Quote B10:01:35 Quote C10:01:35

Recall the constant intensity Poisson process … 51

52  Draw three U(0,1) random numbers  Sort them  Assign them as the millisecond remainders Quote A10:01:35 Quote B10:01:35 Quote C10:01:35 Quote A10:01:35.243 Quote B10:01:35.347 Quote C10:01:35.912  Compute variance estimates using the simulated time stamps.

Formalities  Assume that  The quotes are correctly sequenced.  Arrivals within the second are Poisson with (unknown) constant intensity.  The bid and offer process is independent of the within-second arrival times.  Then each calculated statistic constitutes a draw from the corresponding Bayesian posterior. 53

Does this really work? 54 2011 millisecond-stamped TAQ data Wavelet variance estimates using actual ms time-stamps Strip the millisecond portions of the time-stamps Simulate new ms stamps Wavelet variance estimates using simulated ms. time- stamps. Correlation?

Table 4. Correlations between statistics based on actual vs. simulated millisecond time stamps. 55 Dollar trading volume quintiles Level, jTime scaleFull sample1 (low)2345 (high) 0< 50 ms0.9520.9480.9600.9580.9160.979 150 ms0.9530.9440.952 0.9370.982 3200 ms0.9750.9650.9690.9750.9770.988 5800 ms0.9940.9910.9890.9950.9960.998 73.2 sec0.999 1.000 1025.6 sec1.000 146.8 min1.000 1627.3 min1.000

The correlations are terrific. Why? 56

Table 4. Correlations between estimates based on actual vs. simulated millisecond time stamps. 57 Dollar trading volume quintiles Level, jTime scale Full sample1 (low)2345 (high) 0< 50 ms0.7750.3330.7680.8960.9190.943 150 ms0.9000.6620.9260.9650.9720.978 3200 ms0.9790.9210.9860.995 0.998 5800 ms0.9990.9980.9991.000 73.2 sec1.000 1025.6 sec1.000 146.8 min1.000 1627.3 min0.7750.3330.7680.8960.9190.943 Panel B: Correlations for bid-offer wavelet correlation estimates

Table 5. Summary statistics, historical sample, 2001-2011 (only odd numbered years are shown) 58 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 capitalization of equity, $ Million$745$189$325$480$316$683

Table 5. Summary statistics, historical sample, 2001-2011 (only odd numbered years are shown) 59 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 capitalization of equity, $ Million$745$189$325$480$316$683 25% CAGR 36% CAGR

Table 6. Wavelet variance ratios for bids and offers, 2001-2011 60 Level, jTime scale20012002200320042005200620072008200920102011 150 ms5.227.166.0310.286.698.576.966.064.527.084.70 2100 ms5.446.585.289.696.518.076.275.384.126.264.32 3200 ms5.286.285.139.036.227.345.334.643.685.403.74 4400 ms4.595.235.008.165.756.304.253.843.214.533.07 5800 ms3.124.043.935.575.035.103.413.112.763.712.56 61,600 ms2.112.553.254.114.144.052.892.592.433.042.23 73.2 sec1.982.242.933.383.483.372.562.292.172.532.01 86.4 sec1.942.112.622.912.932.922.352.081.952.161.82 Panel A: Computed from unadjusted bids and offers

Table 6. Wavelet variance ratios for bids and offers, 2001-2011 61 Level, jTime scale20012002200320042005200620072008200920102011 150 ms5.227.166.0310.286.698.576.966.064.527.084.70 2100 ms5.446.585.289.696.518.076.275.384.126.264.32 3200 ms5.286.285.139.036.227.345.334.643.685.403.74 4400 ms4.595.235.008.165.756.304.253.843.214.533.07 5800 ms3.124.043.935.575.035.103.413.112.763.712.56 61,600 ms2.112.553.254.114.144.052.892.592.433.042.23 73.2 sec1.982.242.933.383.483.372.562.292.172.532.01 86.4 sec1.942.112.622.912.932.922.352.081.952.161.82 Panel A: Computed from unadjusted bids and offers

No trend in quote volatilities?  Maybe …  “Flickering quotes” aren’t new.  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? 62

Figure 4 Panel A. Bid and offer for PRK, April 6, 2001. 63

Compare  PRK in 2001 differs from AEPI in 2011  PRK: large amplitude, no oscillation.  AEPI: low amplitude, intense oscillation. 64

Denoising (filtering) “pops” 65

Figure 4 Panel B. PRK, April 6, 2001, Rough component of the bid 66

Table 6. Wavelet variance ratios for bids and offers, 2001-2011, Detail 67 Level, j Time scale2001 …2011 150 ms5.224.70 2100 ms5.444.32 3200 ms5.283.74 4400 ms4.593.07 5800 ms3.122.56 61,600 ms2.112.23 73.2 sec1.982.01 86.4 sec1.941.82 Panel A: Computed from unadjusted bids and offers Level, j Time scale2001 …2011 150 ms1.604.46 2100 ms1.574.07 3200 ms1.563.57 4400 ms1.553.00 5800 ms1.572.52 61,600 ms1.642.20 73.2 sec1.812.00 86.4 sec2.111.82 Panel B: Computed from denoised bids and offers

Table 6. Wavelet variance ratios for bids and offers, 2001-2011 68 Level, jTime scale20012002200320042005200620072008200920102011 150 ms1.602.373.157.026.098.246.565.834.206.794.46 2100 ms1.572.323.096.825.897.765.895.173.836.004.07 3200 ms1.562.273.036.485.617.044.994.453.415.183.57 4400 ms1.552.232.945.905.166.023.963.682.974.363.00 5800 ms1.572.192.835.004.474.823.132.982.563.582.52 61,600 ms1.642.202.713.993.603.792.632.512.272.942.20 73.2 sec1.812.302.623.443.023.162.332.232.042.462.00 86.4 sec2.112.512.593.202.652.752.152.041.862.111.82 Panel B. Computed from denoised bids and offers

Table 6. Wavelet variance ratios for bids and offers, 2001-2011 69 Level, jTime scale20012002200320042005200620072008200920102011 150 ms1.602.373.157.026.098.246.565.834.206.794.46 2100 ms1.572.323.096.825.897.765.895.173.836.004.07 3200 ms1.562.273.036.485.617.044.994.453.415.183.57 4400 ms1.552.232.945.905.166.023.963.682.974.363.00 5800 ms1.572.192.835.004.474.823.132.982.563.582.52 61,600 ms1.642.202.713.993.603.792.632.512.272.942.20 73.2 sec1.812.302.623.443.023.162.332.232.042.462.00 86.4 sec2.112.512.593.202.652.752.152.041.862.111.82 Panel B. Computed from denoised bids and offers

The facts  Pre-filtering, no trend in quote volatility.  Filtering to remove spikes/pops greatly diminishes quote volatility in the early years, but not later years.  Early years: volatility due to spikes  Later years: volatility reflects oscillations 70

Table 8. Wavelet bid and offer variances, 2001-2011 Level, j time scale 200120032005200720092011 150 ms0.050.070.230.080.250.07 (<0.01) (0.03)(<0.01)(0.03)(0.01) 3200 ms0.340.451.520.451.500.40 (0.01)(0.02)(0.17)(0.02)(0.19)(0.08) 5800 ms1.501.855.561.425.161.42 (0.05)(0.07)(0.53)(0.07)(0.42)(0.22) 73.2 sec6.826.7716.034.1916.454.74 (0.52)(0.22)(1.25)(0.16)(0.96)(0.49) 1025.6 sec80.4647.0384.1825.18109.4230.76 (16.17)(2.57)(5.75)(0.98)(13.16)(3.22) 146.8 min735.03489.43862.96302.161,638.73333.50 (30.23)(12.26)(73.94)(23.79)492.40)(12.05) 1627.3 min2,511.151,554.802,872.451,046.554,623.581,164.98 (80.99)(39.18)335.55)101.74)849.95)(41.65) Panel A. Rough variances, mils per share

Table 8. Wavelet bid and offer variances, 2001-2011 72 Level, jTime scale200120032005200720092011 150 ms1.603.156.096.564.204.46 (0.02)(0.11)(0.39)(0.40)(0.31)(1.42) 3200 ms1.573.065.765.473.653.84 (0.02)(0.10)(0.36)(0.30)(0.26)(1.16) 5800 ms1.562.914.943.872.912.94 (0.03)(0.09)(0.27)(0.17)(0.16)(0.69) 73.2 sec1.712.713.642.782.312.28 (0.09)(0.10)(0.15)(0.09) (0.35) 1025.6 sec2.362.602.422.031.741.70 (0.37)(0.29)(0.07)(0.05)(0.04)(0.12) 146.8 min1.371.501.491.371.321.23 (0.04)(0.03)(0.02) (0.03)(0.02) 1627.3 min1.121.16 1.121.111.08 (0.02) (0.01) Panel B. Rough variance ratios

SEC’s Reg NMS (“National Market System”)  Defined the framework for competition among equity markets.  Enhanced protection against trade-throughs  Example: market A is bidding $10 and market B executes a trade at $9.  For a market’s bid and offer to be protected, they have to accessible instantly (electronically)  This requirement essentially forced all markets to become electronic.  Timing: Proposed in 2004; adopted 2005; implemented in 2006. 73

Prior to SEC’s Reg NMS (2004-2006)  Most markets were manual and slow.  Few possibilities of automatic execution.  Dealers were supposed to display customer limit orders … but sometimes didn’t.  Bid and offer quotes were supposed to be firm … but sometimes weren’t.  Protection against trade-throughs was weak. 74

And now …  Quotes are firm, accessible, and (more strongly) protected.  But quote volatility has increased.  More questions  What strategies give rise to these patterns?  Are the HFQ episodes unstable algos?  Are they sensible strategies to detect and access liquidity? 75

High Frequency Quoting: Short-Term Volatility in Bids and Offers Joel Hasbrouck Stern School, NYU 1.

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