High frequency quoting: 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)

The highest bid and lowest offer (over all market centers)

2

3

National Best Bid and Offer for AEPI during regular trading hours

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

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

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

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

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

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

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

A microstructure wavelet perspective

Ask prices over 8 “millisecond” intervals

A trader with arrival uncertainty over this interval buys (on average) at

Deviations:

14

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

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

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

etails

Detail varies only at scale j. Rough varies at scale j and finer scales.

18

Decomposition into

A detail varies over time scale Details are orthogonal:

19

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

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

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

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

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

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

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

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

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

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

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

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

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

33

Bid-ask correlations (by time-scale)

34

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

A plot of the first differences …

50

… of this time series

51