high frequency q uoting : short-term volatility in bid/ask quotes
DESCRIPTION
High frequency q uoting : short-term volatility in bid/ask quotes. Joel Hasbrouck. Now available at http://pages.stern.nyu/~jhasbrou. Illustration. AEPI is a small Nasdaq -listed manufacturing firm. Market activity on April 29, 2011 National Best Bid and Offer (NBBO) - PowerPoint PPT PresentationTRANSCRIPT
![Page 1: High frequency q uoting : short-term volatility in bid/ask quotes](https://reader036.vdocuments.us/reader036/viewer/2022062501/5681671f550346895ddba195/html5/thumbnails/1.jpg)
High frequency quoting: short-term volatility
in bid/ask quotes
Joel Hasbrouck
Now available at http://pages.stern.nyu/~jhasbrou
![Page 2: High frequency q uoting : short-term volatility in bid/ask quotes](https://reader036.vdocuments.us/reader036/viewer/2022062501/5681671f550346895ddba195/html5/thumbnails/2.jpg)
Illustration
AEPI is a small Nasdaq-listed manufacturing firm.
Market activity on April 29, 2011 National Best Bid and Offer (NBBO)
The highest bid and lowest offer (over all market centers)
2
![Page 3: High frequency q uoting : short-term volatility in bid/ask quotes](https://reader036.vdocuments.us/reader036/viewer/2022062501/5681671f550346895ddba195/html5/thumbnails/3.jpg)
3
National Best Bid and Offer for AEPI during regular trading hours
![Page 4: High frequency q uoting : short-term volatility in bid/ask quotes](https://reader036.vdocuments.us/reader036/viewer/2022062501/5681671f550346895ddba195/html5/thumbnails/4.jpg)
Discussion points
The features of the AEPI episode. Implications of short-term quote volatility. Price risk and order timing uncertainty. Time scale variance decompositions Analysis of millisecond-stamped TAQ data Dealing with truncated time stamps Analysis of historical second-stamped TAQ data Connections to existing studies Outstanding questions More pictures from the HFQ gallery
5
![Page 5: High frequency q uoting : short-term volatility in bid/ask quotes](https://reader036.vdocuments.us/reader036/viewer/2022062501/5681671f550346895ddba195/html5/thumbnails/5.jpg)
Short-term quote volatility …
Degrades the informational value of the quotes. Induces execution price risk for marketable orders.
And dark trades that use the bid and ask as reference prices.
Impedes monitoring of market performance. A dealer guarantees that he will sell to me at the
market’s prevailing ask price. Prevailing as of when? Short-term quote volatility increases the value of
the dealer’s look-back option. (Stoll and Schenzler) 8
![Page 6: High frequency q uoting : short-term volatility in bid/ask quotes](https://reader036.vdocuments.us/reader036/viewer/2022062501/5681671f550346895ddba195/html5/thumbnails/6.jpg)
Execution price risk for marketable orders
A buyer submits a marketable order at time . The limit price is “infinite”. Executed on arrival at the lowest offer.
Arrival is subject to a delay that is uniform random on
The execution price is random. The outcome is characterized by mean and
variance (risk) of price over
9
![Page 7: High frequency q uoting : short-term volatility in bid/ask quotes](https://reader036.vdocuments.us/reader036/viewer/2022062501/5681671f550346895ddba195/html5/thumbnails/7.jpg)
Connection to transaction cost analysis
Implementation shortfall imputation of trading cost is the difference between actual execution price and a benchmark price.
When there is timing uncertainty, a common benchmark is the value- or time-weighted price over a series of trades or an interval.
Usually the interval is an hour or a day.
10
![Page 8: High frequency q uoting : short-term volatility in bid/ask quotes](https://reader036.vdocuments.us/reader036/viewer/2022062501/5681671f550346895ddba195/html5/thumbnails/8.jpg)
Other sources of timing uncertainty
Information transmission lags There are about
17 “lit” market centers publish visible quotes
20 dark poolsdon’t publish quotes, do report trades
200 executing brokers don’t publish quotes, do report trades
11
![Page 9: High frequency q uoting : short-term volatility in bid/ask quotes](https://reader036.vdocuments.us/reader036/viewer/2022062501/5681671f550346895ddba195/html5/thumbnails/9.jpg)
Time-scale decompositions
A time series = sum of components Each component is associated with a
particular time scale (“horizon”) Each component is associated with a
variance. Horizons and components are constructed
systematically using wavelet transforms
12
![Page 10: High frequency q uoting : short-term volatility in bid/ask quotes](https://reader036.vdocuments.us/reader036/viewer/2022062501/5681671f550346895ddba195/html5/thumbnails/10.jpg)
Sources
Percival, Donald B., and Andrew T. Walden, 2000. Wavelet methods for time series analysis (Cambridge University Press, Cambridge).
Gençay, Ramazan, Frank Selçuk, and Brandon Whitcher, 2002. An introduction to wavelets and other filtering methods in finance and economics (Academic Press (Elsevier), San Diego).
13
![Page 11: High frequency q uoting : short-term volatility in bid/ask quotes](https://reader036.vdocuments.us/reader036/viewer/2022062501/5681671f550346895ddba195/html5/thumbnails/11.jpg)
A microstructure wavelet perspective
Ask prices over 8 “millisecond” intervals
A trader with arrival uncertainty over this interval buys (on average) at
Deviations:
14
![Page 12: High frequency q uoting : short-term volatility in bid/ask quotes](https://reader036.vdocuments.us/reader036/viewer/2022062501/5681671f550346895ddba195/html5/thumbnails/12.jpg)
𝑝𝑟𝑖𝑐𝑒=𝒮 h𝑚𝑜𝑜𝑡 +ℛ h𝑜𝑢𝑔
The wavelet smooth is
The wavelet rough is
“3” refers to time-scale (log base two): “ is constant over ms”
15
![Page 13: High frequency q uoting : short-term volatility in bid/ask quotes](https://reader036.vdocuments.us/reader036/viewer/2022062501/5681671f550346895ddba195/html5/thumbnails/13.jpg)
A faster trader has arrival uncertainty of 4 ms.
He will trade within one of two 4 ms. windows:
His average price is either , or
From his perspective where
Interpretation of “2”: “ is constant over ms.”
16
![Page 14: High frequency q uoting : short-term volatility in bid/ask quotes](https://reader036.vdocuments.us/reader036/viewer/2022062501/5681671f550346895ddba195/html5/thumbnails/14.jpg)
The fastest trader: arrival uncertainty of 2 ms.
He will trade within one of four two-ms. windows:
From his perspective Where
“ is constant over ms.”
17
![Page 15: High frequency q uoting : short-term volatility in bid/ask quotes](https://reader036.vdocuments.us/reader036/viewer/2022062501/5681671f550346895ddba195/html5/thumbnails/15.jpg)
etails
Detail varies only at scale j. Rough varies at scale j and finer scales.
18
![Page 16: High frequency q uoting : short-term volatility in bid/ask quotes](https://reader036.vdocuments.us/reader036/viewer/2022062501/5681671f550346895ddba195/html5/thumbnails/16.jpg)
Decomposition into
A detail varies over time scale Details are orthogonal:
19
![Page 17: High frequency q uoting : short-term volatility in bid/ask quotes](https://reader036.vdocuments.us/reader036/viewer/2022062501/5681671f550346895ddba195/html5/thumbnails/17.jpg)
Variance decompositions
The price risk of the fastest trader (2 ms) The price risk of the faster trader (4 ms) The price risk of the fast trader (8 ms)
20
![Page 18: High frequency q uoting : short-term volatility in bid/ask quotes](https://reader036.vdocuments.us/reader036/viewer/2022062501/5681671f550346895ddba195/html5/thumbnails/18.jpg)
Formally, this is the Haar discrete wavelet transform. One of a family of weighting/differencing
schemes Construct successive averages and differences in
averages over intervals of length 1, 2, 4, 8, 16, … Does N have to be an integer power of 2?
No. Received wisdom favors maximal overlap transforms (which don’t have this limitation).
21
![Page 19: High frequency q uoting : short-term volatility in bid/ask quotes](https://reader036.vdocuments.us/reader036/viewer/2022062501/5681671f550346895ddba195/html5/thumbnails/19.jpg)
Sampling properties
We can obtain asymptotic distributional results for difference-stationary processes.
A fifteen minute sample at ms. frequency has 900,000 observations.
But with discreteness and infrequent price changes, asymptotic validity is questionable.
I construct my estimates over 15-minute samples, and in panels.
22
![Page 20: High frequency q uoting : short-term volatility in bid/ask quotes](https://reader036.vdocuments.us/reader036/viewer/2022062501/5681671f550346895ddba195/html5/thumbnails/20.jpg)
An aside: should we work with price differences or levels?
Differencing at the resolution of the data obscures longer-term features.
“Differencing is a high-pass filter.”
23
![Page 21: High frequency q uoting : short-term volatility in bid/ask quotes](https://reader036.vdocuments.us/reader036/viewer/2022062501/5681671f550346895ddba195/html5/thumbnails/21.jpg)
Economic significance I
How large is the risk relative to other trading costs?
If we’re analyzing price levels, the units of are $ (per share) Rescale to mils (one mil = $0.001)
Access fees in US equity exchanges are capped at three mils.
What is compared to three mils?
24
![Page 22: High frequency q uoting : short-term volatility in bid/ask quotes](https://reader036.vdocuments.us/reader036/viewer/2022062501/5681671f550346895ddba195/html5/thumbnails/22.jpg)
Economic significance II
How large is the risk relative to share value? Some costs are measured as price relatives. “The relative bid-ask spread is 0.1%, which
is 10 basis points.” measures relative volatility
25
![Page 23: High frequency q uoting : short-term volatility in bid/ask quotes](https://reader036.vdocuments.us/reader036/viewer/2022062501/5681671f550346895ddba195/html5/thumbnails/23.jpg)
Economic significance III
How large is the risk relative to what we’d expect from a random-walk?
For , get The variance ratio between j and k is Where j corresponds to a short interval
(subsecond) and k to a longer interval (30 minutes)
26
![Page 24: High frequency q uoting : short-term volatility in bid/ask quotes](https://reader036.vdocuments.us/reader036/viewer/2022062501/5681671f550346895ddba195/html5/thumbnails/24.jpg)
Sample for cross-sectional analysis
For all CRSP firms present January through March of 2011, compute average daily dollar volume. Sort into decile groups. Take first ten firms in each group. Reported results collapsed into quintiles.
27
![Page 25: High frequency q uoting : short-term volatility in bid/ask quotes](https://reader036.vdocuments.us/reader036/viewer/2022062501/5681671f550346895ddba195/html5/thumbnails/25.jpg)
Bid and ask
Source: TAQ with millisecond time-stamps, All trading days in April 2011 Construct series for National best bid and
offer at one millisecond resolution. Wavelet variances calculated over 15-
minute intervals, 9:45-15:45
28
![Page 26: High frequency q uoting : short-term volatility in bid/ask quotes](https://reader036.vdocuments.us/reader036/viewer/2022062501/5681671f550346895ddba195/html5/thumbnails/26.jpg)
Summary statistics (excerpt from Table 1.)
29
Cross-firm median
N
Avg. no. daily
trades
Avg. no. daily quote
updates
Avg. no. daily
NBBO records
Full sample 100 1,061 23,347 6,897
Dollar volume
quintiles
1, low 20 30 960 362
2 20 404 6,288 2,768
3 20 873 20,849 6,563
4 20 2,637 45,728 11,512
5, high 20 13,057 179,786 37,695
![Page 27: High frequency q uoting : short-term volatility in bid/ask quotes](https://reader036.vdocuments.us/reader036/viewer/2022062501/5681671f550346895ddba195/html5/thumbnails/27.jpg)
NBBO volatility, mils per share(Table 2 Panel A excerpt)
30
Time scaleFull
Sample
Dollar volume quintiles
1 (low) 2 3 4 5 (high)64 ms 0.4 0.3 0.2 0.4 0.5 0.6
128 ms 0.6 0.4 0.3 0.6 0.7 0.9 256 ms 0.8 0.6 0.5 0.8 1.0 1.2 512 ms 1.1 0.8 0.6 1.2 1.4 1.7
1,024 ms 1.6 1.1 0.9 1.6 1.9 2.4 4.1 sec 3.0 2.1 1.6 3.0 3.6 4.8
32.8 sec 8.0 5.3 4.1 7.4 9.9 13.3
![Page 28: High frequency q uoting : short-term volatility in bid/ask quotes](https://reader036.vdocuments.us/reader036/viewer/2022062501/5681671f550346895ddba195/html5/thumbnails/28.jpg)
Table 2 Panel B excerpt basis points (0.01%)
Short-run volatility seems flatter across firms when it’s measured in mils per share
31
Time scaleFull
Sample
Dollar volume quintiles
1 (low) 2 3 4 5 (high)64 ms 0.3 0.6 0.4 0.3 0.2 0.1
128 ms 0.4 0.8 0.6 0.4 0.2 0.2256 ms 0.6 1.1 0.8 0.6 0.3 0.2512 ms 0.8 1.4 1.1 0.8 0.5 0.3
1,024 ms 1.2 2.0 1.5 1.2 0.6 0.54.1 sec 2.2 3.8 2.8 2.2 1.2 0.9
32.8 sec 5.6 9.5 7.1 5.7 3.3 2.5
![Page 29: High frequency q uoting : short-term volatility in bid/ask quotes](https://reader036.vdocuments.us/reader036/viewer/2022062501/5681671f550346895ddba195/html5/thumbnails/29.jpg)
NBBO variance ratios, “short/long”(Table 3, excerpt)
32
Time scale
Base Res
Full Sample
Dollar volume quintiles
1 2 3 4 51 ms ms 5.36 8.81 9.74 3.69 2.74 1.838 ms ms 4.18 5.86 8.05 3.33 2.12 1.53
64 ms ms 3.25 4.31 5.93 2.69 1.86 1.47128 ms ms 3.03 4.03 5.35 2.56 1.78 1.45
1,000 ms sec 2.56 3.63 4.13 2.19 1.51 1.312,048 ms ms 2.36 3.45 3.63 2.04 1.42 1.27
8.0 sec sec 1.97 2.87 2.69 1.75 1.30 1.2532.0 sec sec 1.60 2.13 1.99 1.47 1.18 1.224.3 min sec 1.24 1.54 1.33 1.18 1.08 1.09
34.1 min sec 1.00 1.00 1.00 1.00 1.00 1.00
![Page 30: High frequency q uoting : short-term volatility in bid/ask quotes](https://reader036.vdocuments.us/reader036/viewer/2022062501/5681671f550346895ddba195/html5/thumbnails/30.jpg)
33
![Page 31: High frequency q uoting : short-term volatility in bid/ask quotes](https://reader036.vdocuments.us/reader036/viewer/2022062501/5681671f550346895ddba195/html5/thumbnails/31.jpg)
Bid-ask correlations (by time-scale)
34
![Page 32: High frequency q uoting : short-term volatility in bid/ask quotes](https://reader036.vdocuments.us/reader036/viewer/2022062501/5681671f550346895ddba195/html5/thumbnails/32.jpg)
The cross-sectional results: a summary
In mils per share or basis points, short term volatility is on average small.
Variance ratios: short term volatility is much higher than we’d expect when calibrated to a random-walk.
Bid-ask correlations are often weak at sub-second time-scales.
These findings are particularly true for low-activity firms.
35
![Page 33: High frequency q uoting : short-term volatility in bid/ask quotes](https://reader036.vdocuments.us/reader036/viewer/2022062501/5681671f550346895ddba195/html5/thumbnails/33.jpg)
High-resolution analysis …… with low resolution data
TAQ with millisecond time stamps only available from 2006 onwards
TAQ with second time stamps available back to 1993.
Can we draw inferences about subsecond variation from second-stamped data?
36
![Page 34: High frequency q uoting : short-term volatility in bid/ask quotes](https://reader036.vdocuments.us/reader036/viewer/2022062501/5681671f550346895ddba195/html5/thumbnails/34.jpg)
Truncated time stamps
Assume that in a given second We have N quote records They are correctly sequenced. The one-second time-stamps are generated
by truncation of the millisecond remainder. The arrival rate over the second is constant-
intensity Poisson. Then relative to the start of the second, the
arrival time of the kth quote is distributed as the kth order statistic in a sample of variates.
37
![Page 35: High frequency q uoting : short-term volatility in bid/ask quotes](https://reader036.vdocuments.us/reader036/viewer/2022062501/5681671f550346895ddba195/html5/thumbnails/35.jpg)
A Bayesian imputation approach
Additional assumption The arrival times are independent of the
bid and ask realizations. Simulate the millisecond arrival times and
perform analysis on simulated data. Check: try it on millisecond-stamped data,
and see how results for simulated data match up with original data.
38
![Page 36: High frequency q uoting : short-term volatility in bid/ask quotes](https://reader036.vdocuments.us/reader036/viewer/2022062501/5681671f550346895ddba195/html5/thumbnails/36.jpg)
39
Dollar volume quintiles
Time Scale All 1 (low) 2 3 4 5 (high)
1 ms 0.991 0.997 0.985 0.991 0.995 0.989
…
16 ms 0.967 0.947 0.959 0.965 0.975 0.979
…
256 ms 0.975 0.960 0.962 0.973 0.984 0.990
…
4.1 sec 1.000 1.000 0.999 0.999 1.000 1.000
…
32.8 sec 1.000 1.000 1.000 1.000 1.000 1.000
Correlations between wavelet variances computed • Using the orginal ms. time stamps, and• Using simulation ms. time stamps
![Page 37: High frequency q uoting : short-term volatility in bid/ask quotes](https://reader036.vdocuments.us/reader036/viewer/2022062501/5681671f550346895ddba195/html5/thumbnails/37.jpg)
Why is agreement so good?
Time averaging implicit and explicit. When the quotes are sparse (within the
second), high-frequency variances are not highly sensitive to placement.
When the quotes are dense (within the second), the distribution of their arrival times is tight.
Agreement is weaker for correlations.
40
![Page 38: High frequency q uoting : short-term volatility in bid/ask quotes](https://reader036.vdocuments.us/reader036/viewer/2022062501/5681671f550346895ddba195/html5/thumbnails/38.jpg)
The historical sample
Construct dollar trading volume for all CRSP firms in the first quarter of each year 2001-2011
In each year, take three firms from each dollar vol decile (30/firms per year) 2001: only firms that traded in $0.01
Analyze April Monthly TAQ data, 9:45-15:45
41
![Page 39: High frequency q uoting : short-term volatility in bid/ask quotes](https://reader036.vdocuments.us/reader036/viewer/2022062501/5681671f550346895ddba195/html5/thumbnails/39.jpg)
Summary statistics, historical sample (Table 6, excerpt)
42
Year 2001 2003 2005 2007 2009 2011
No. of firms
30 30 30 30 30 30
Mkt Cap
$341 $165 $272 $445 $150 $484
Share price
$15.88 $9.45 $22.51 $16.65 $4.90 $16.23
Avg. daily
trades97 65 276 889 869 1,341
Avg. daily
quotes807 814 4,846 12,383 18,305 17,989
![Page 40: High frequency q uoting : short-term volatility in bid/ask quotes](https://reader036.vdocuments.us/reader036/viewer/2022062501/5681671f550346895ddba195/html5/thumbnails/40.jpg)
NBBO Volatility, mils ($0.001) / share; (Table 7, excerpt)
43
YearTime scale 2001 2003 2005 2007 2009 2011
64 ms 0.5 0.4 0.7 0.4 0.5 0.3 128 ms 0.7 0.5 1.0 0.5 0.7 0.5 256 ms 0.9 0.7 1.3 0.7 0.9 0.6 512 ms 1.3 1.0 1.9 0.9 1.2 0.9
1,024 ms 1.9 1.4 2.5 1.3 1.6 1.2
4.1 sec 3.6 2.8 4.6 2.3 3.0 2.2 32.8 sec 10.1 7.2 11.3 6.3 7.7 5.8
![Page 41: High frequency q uoting : short-term volatility in bid/ask quotes](https://reader036.vdocuments.us/reader036/viewer/2022062501/5681671f550346895ddba195/html5/thumbnails/41.jpg)
Given the increased quote traffic, why didn’t short-term quote volatility explode?
The good old days weren’t really that good. “Gapping the quote”
Maybe the bad new days aren’t so nasty. … At least between 9:45 and 15:45
44
![Page 42: High frequency q uoting : short-term volatility in bid/ask quotes](https://reader036.vdocuments.us/reader036/viewer/2022062501/5681671f550346895ddba195/html5/thumbnails/42.jpg)
Variance ratios, “short/long”(Table 8 excerpt)
45
Time scale 2001 2003 2005 2007 2009 2011
1ms 2.41 4.99 6.89 4.86 7.79 5.978 ms 2.41 4.98 6.86 4.72 7.61 5.62
64 ms 2.37 4.92 6.66 4.06 6.83 4.51512 ms 2.27 4.42 5.46 2.76 5.22 3.034.1 sec 2.22 3.67 3.48 2.07 3.68 2.18
32.8 sec 2.03 2.80 2.53 1.58 2.20 1.654.3 min 1.75 1.49 1.72 1.36 1.83 1.36
34.1 min 1.00 1.00 1.00 1.00 1.00 1.00
![Page 43: High frequency q uoting : short-term volatility in bid/ask quotes](https://reader036.vdocuments.us/reader036/viewer/2022062501/5681671f550346895ddba195/html5/thumbnails/43.jpg)
The elements of the story
There is a presumption that HF activity has increased over the 2000’s Strong trend in quote traffic
Short-term volatility (mils per share) does not show a clear increase.
Variance ratios show increase relative to 2001 (but not uniformly)
46
![Page 44: High frequency q uoting : short-term volatility in bid/ask quotes](https://reader036.vdocuments.us/reader036/viewer/2022062501/5681671f550346895ddba195/html5/thumbnails/44.jpg)
Connection to high frequency trading
Brogaard (2012), Hendershott and Riordan (2012) use Nasdaq HFT dataset: trades used to define a set of high frequency traders.
Hendershott, Jones and Menkveld (2011): NYSE message traffic
Hasbrouck and Saar (2012): strategic runs / order chains
General consensus: HF activity enhances market quality and lowers volatility.
Quote volatility results are less uniform.47
![Page 45: High frequency q uoting : short-term volatility in bid/ask quotes](https://reader036.vdocuments.us/reader036/viewer/2022062501/5681671f550346895ddba195/html5/thumbnails/45.jpg)
Connection to realized volatility literature
Realized volatility = summed (absolute/squared) price changes. Andersen, Bollerslev, Diebold and Ebens
(2001), and others Hansen and Lunde (2006) advocate pre-
averaging to eliminate microstructure noise. Present paper: “Don’t throw out the noise!”
48
![Page 46: High frequency q uoting : short-term volatility in bid/ask quotes](https://reader036.vdocuments.us/reader036/viewer/2022062501/5681671f550346895ddba195/html5/thumbnails/46.jpg)
Open questions
Analysis in this paper focuses on average HF volatility. But HFQ is marked by extreme and interesting
outliers. What are the strategies?
Are the HFQ episodes cases of “dueling algos”? Or Are they sensible strategies to detect and access
liquidity? Wavelet signal processing methods show great
promise in isolating strategic microstructure effects from long-term information noise.
49
![Page 47: High frequency q uoting : short-term volatility in bid/ask quotes](https://reader036.vdocuments.us/reader036/viewer/2022062501/5681671f550346895ddba195/html5/thumbnails/47.jpg)
A plot of the first differences …
50
![Page 48: High frequency q uoting : short-term volatility in bid/ask quotes](https://reader036.vdocuments.us/reader036/viewer/2022062501/5681671f550346895ddba195/html5/thumbnails/48.jpg)
… of this time series
51