Seasonality, Microstructure and Market Evolution:An Algorithmic Perspective

Kerr Hatrickkerr.hatrick@db.com

Danila Deliyadanila.deliya@db.com

Quantitative Products One, Global Markets Equity, Deutsche Bank AGThis paper was presented at the Northfield Research Seminar on 17 November 2008, Hong Kong

IMPORTANT: Statements and opinions regarding the Company’s investment case, positioning and valuationare not, and should not be construed as, an indication that Deutsche Bank will provide favourable researchcoverage of the Company or publish research containing any particular rating or price target for the Com-pany’s common stock. This presentation speaks only as of the date it is given, and the views expressed aresubject to change based upon a number of factors, including market conditions and the Company’s businessand prospects.

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1 Introduction

Over recent years, the ability to execute huge baskets of stocks with apparent ease has beena key factor in the growth of portfolio trading globally. This growth has in turn provided theclimate in which a variety of algorithmic trading models have evolved. Algorithmic tradinghubs can now be found in every sizeable brokerage — and they continue to push transactioncosts down to the limits imposed by market microstructure, and lack of alpha forecasts.

This process has resulted in changing seasonality characteristics, and in the evolution ofmicrostructure itself. We study some novel, previously unreported aspects of these changesin this paper. A review, and further material, can be found in [4], [5], [2], [3].

2 The evolution of size and speed in Global Equity

Markets

A commonly encountered pair of assertions are that algorithmic trading has significantlydecreased the typical order size observed on an exchange, and that trading frequency hasincreased. We examine exactly how this has happened in key markets, from the US to Korea.

A number of metrics are indicative of changes in microstructure. Here we will concentrateon three of them, specifically:

� The distribution of inter-trade durations (time between arrivals of consequtive trades),

� The distribution of trade sizes (logged),

� The average number of trades per minute, per day.

These measures are calculated over a rolling window of 200 days to get a picture of howmarkets evolve. We limit our analyses to the most liquid stocks.

Throughout this paper most of the results will be presented in form of animated graphs.These allow the reader to scroll through time, and observe microstructure change at theirleisure. The top panel of the graph represents our probability density estimate of the tradeduration distribution. The bottom left panel represents the evolution of the logarithm ofsize distribution, and the bottom right panel corresponds to changes in the average numberof trades per day per minute.

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2.1 The US and the UK: size & speed in the world’s most liquidmarkets

First of all, we consider the evolution of size and speed in the world’s most liquid markets —the US and the UK. These markets have exhibited massive changes in market microstructureduring the last 10 years. For the US (figure 1), typical trading duration has compressedsteadily, so that the majority of trades happen within 1 second. The typical trade size hasshrunk from 1000 shares to 100 shares.

In the UK (figure 2), whilst duration has compressed steadily, the chief size mode has notshifted significantly. The number of trades in both the US and the UK increases significantlyover the last year.

In summary,

� Typical inter-trade duration has shrunk for both markets,

� The size distribution has shrunk in the US, but not necessarily in Europe,

� Regional patterns are apparent in trade frequency seasonality.

In the next section we will study if this occurs in other English speaking markets, eg.Australia.

2.2 Australia: more of the same?

Australia (figure 3), like the US & the UK, shows expected duration to be an almost mono-tonically decreasing function. However, there is a small peak at two seconds. One hypothesisas to why this might be involves the existence of an automated trading system which reactsto, or schedules, events, with a two second period. Note that this system need not tradeevery two seconds; the simple presence of a system which has the option to trade every twoseconds would be sufficient to guarantee the small peak observerd. This is still visible in2002, and possibly later. Then, in conjunction with a change in size distribution, where themedian becomes smaller, it’s signal is swamped by higher frequency ‘noise’. Major peaks intrade size shift to smaller peaks over the course of the period.

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Figure 1: US (liquid) market evolution. Use the arrow button to play animation forward, <

and > buttons to switch animation slide-by-slide, the back arrow button to play animationbackwards. Data sourced from Reuters.

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Figure 2: UK (liquid) market evolution . Use the arrow button to play animation forward, <

and > buttons to switch animation slide-by-slide, the back arrow button to play animationbackwards. Data sourced from Reuters.

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Figure 3: Market Microstructure Redux: Australia. Use the arrow button to play animationforward, < and > buttons to switch animation slide-by-slide, the back arrow button to playanimation backwards. Data sourced from Reuters.

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2.3 Japan: inter-trade durations are not monotonic!

In Japan (figure 4), during the late 1990’s, on trading, you would be significantly more likely,to have a trade follow three seconds after your trade, than any other period. After that,the likelihood of a following trade peaks on integral seconds after the trade. The typicalperiodicity between trades changes as we pass through the years in our analysis. In 2000 itbriefly changes to 5 seconds between trades, before reverting back to a single second. Onepotential reason is different calibrations of the dominant higher frequency trading systems inthe Japanese market. Two trading systems with different periods, for instance, might resultin the marked dual period Japanese inter-trade durations appear to exhibit. Interestingly,the change in inter-trade duration coincides with an increase in the frequency of largertrades; again, possibly suggestive of at least two automatic trading systems, with differentfrequencies and typical sizes, at work. A marked decrease in inter-trade durations is incommon with the US and the UK. Unlike the US, the typical order size distribution hasstayed the same over the years.

2.4 Australia revisited: Higher Frequency Periodicities?

In the light of the apparently strong periodic signal in Japan, and the suspicious hump inthe frequency distribution in Australia, we reanalyzed Australian trade data with a viewto seeing if a search at higher frequency would reveal some periodicity. The results arepresented in figure 5. A striking evolution of periodicity to towards 100ms is observed in theperiod till 2003; by 2005, intertrade duration has become shorter than 100ms typically, andthe 100ms peak attenuates - and, as it does so, the size peak corresponding to 1000 sharesalso decreases in prominence. It is worth noting that a second peak at 200ms is also visible.

2.5 Local market microstructure: Hong Kong

In Hong Kong (figure 6), like Japan, we see marked periodicities in inter-trade durations.One period (approximately 3 seconds) dominates all others initially. As time progresses theinter-trade duration tends downwards, though this is not uniformly the case. For instance, wesee a shift in this period to 2 seconds, then to 1, then to something marginally greater than 1.Also as time progresses, the strength of the periodic signals in small time periods decreases;possibly evidence of more market participants. The trade size distribution becomes skewedto the left; as time passes, smaller trades are more likely.

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Figure 4: Market Microstructure Redux: Japan. Use the arrow button to play animationforward, < and > buttons to switch animation slide-by-slide, the back arrow button to playanimation backwards. Data sourced from Reuters.

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Figure 5: Market Microstructure Redux: Australia, higher frequencies. Use the arrow buttonto play animation forward, < and > buttons to switch animation slide-by-slide, the backarrow button to play animation backwards. Data sourced from Reuters.

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Figure 6: Market Microstructure Redux: Hong Kong. Use the arrow button to play anima-tion forward, < and > buttons to switch animation slide-by-slide, the back arrow button toplay animation backwards. Data sourced from Reuters.

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2.6 Local market microstructure: Singapore

In 1996, even with liquid stocks, there appeared to be little or no structure in the typicalperiod between trades, in Singapore (figure 7). A strong structure with a period of around1 second seems to be induced around October 2002. The period over which this changeis induced coincides with both an increase in the typical number of trades and an increasein the prominence of the first peak on the trade size distribution. Taken together, thesearguments seem to indicate that at least one automatic trading system may have startedaround this period. This “algorithmic footprint” is still very observable even in October2008.

2.7 Local market microstructure: Korea

In Korea (figure 8), we start with multimodal trading frequency distribution; the typicalperiod between trades is around 1 second. Then, around 2006, this disappears, as tradingfrequency increases. In 2007 a second periodicity imposes itself on our inter-trade durationprobabilities; you are much more likely to have a trade 5 seconds after the last trade, thanhave one that is 2, 3 or 4 seconds after the last trade. In Korea, specifically, the number oftrades per minute shows quite a different pattern over the past years: specifically, we haveseen a drop in trading since March of this year.

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Figure 7: Market Microstructure Redux: Singapore. Use the arrow button to play animationforward, < and > buttons to switch animation slide-by-slide, the back arrow button to playanimation backwards. Data sourced from Reuters.

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Figure 8: Market Microstructure Redux: Korea. Use the arrow button to play animationforward, < and > buttons to switch animation slide-by-slide, the back arrow button to playanimation backwards. Data sourced from Reuters.

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3 A comparative view of market microstructure

Having covered in detail a number of different regional market microstructures, for liquidstocks, what common threads can we draw, if any, on considering the changes that havetaken place in the last years? We review results on size and speed, first.

3.1 Size and Speed

There are at least two good reasons to believe in the existence of a downward pressure ontrade size. Firstly, algorithmic trading systems frequently slice an order into smaller chunks.Smart order routers behave similarly when they split an order into smaller child orders, intheir search for best execution venue.

There is at least one market in which this downward pressure has had a marked effect.Whilst the typical trade size in US markets has remained nearly static (and small) sincedecimalization in April 2001, the relative frequency of smaller sized trades has increased; seefigure 1.

In other markets, the evolution of the size of a trade has not taken as consistent a pathdownwards. There have been recent years ( eg. 2005-2006, in the UK, figure 2) where thetypical trade size actually increased. Increasingly, in europe, over the last three years, thetrend has been downwards. In most Asian markets, in contrast, this trend has yet to manifestitself strongly.

With trading speed, the trend is certainly up, to differing degrees in different regions andmarkets. In the US, we estimate that trading speed has increased by two orders of magnitudein the period since decimalization, with around 100 trades per second in 2008. For Europe,the UK, then France appear to be the fastest markets, followed by Germany; even now,however, the speed is typically 5-10 times slower than the US. Despite this, the speed oftrading, especially in London, has increased significantly in the past two years. With theexception of Australia, which trades more like the US or Europe, most Asian markets stillhave less than 10 trades per second. Given this, the necessity of nanosecond latencies inconnecting to exchanges, as advertized by certain vendors, appears questionable in Asia.

What happens to speed as markets become more volatile? Typically, we see the increasein activity pointed to by Flatley [6]. Figure 9 shows spikes in trading in Aug ’07, Nov ’07and Jan ’08 clearly in all three regions. The effect these periods have, on the typical impacta trade has, will be the subject of a forthcoming paper.

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Jan−07 Apr−07 Jul−07 Oct−07 Jan−08 Apr−08 Jul−08 Oct−080

0.5

1

1.5

2

2.5

Rel

ativ

e ac

tivity

inde

x

Time

Relative activity across different regions

UKJapanHong KongUS

Figure 9: Relative Trading activity in different markets

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3.2 Inter-Trade Seasonality: Periodicity ex Machina ?

One of the striking features of a number of the market microstructures considered is, ofcourse, the multimodality of the inter-trade duration distribution. We have presented theresults for the Asian markets, but the phenomenon generalizes, albeit at higher frequencies;speedier European, and even US markets have exhibited this periodicity historically; seefigure 5. It should be noted throughout, that the data used throughout this study is sourcedfrom Reuters datascope. The timeframes are indicated on the top of the animations.

There are at least two explanations for this effect, and it is hard at this stage to becategorical about the cause. The first explanation posits the existence of automatic tradingsystems (ATS), which either schedule trades, or scan the market, in a periodic manner.Either scheduling, or scanning, could give rise to the increased probability of observing atrade at a particular period; the latter, though it does not guarantee a trade, would naturallyincrease the probability of a trade at a point in time.

Over time, the recalibration of these ATS’s could result in the distinct change in periodsexhibited for most of Asia, over the years. Another possible explanation for this change inperiod could be an ATS being switched on (possibly in Singapore, 2002, figure 7), or off.The dual periods observed in most of the asian markets could easily be explained by morethan one autotrader. As one ATS dominates another, in terms of activity, different patternsin periodicity and trade size would naturally emerge.

An alternative explanation for the multimodality would be timestamp rounding, eitherby the exchange, or by Reuters. The marked evolution in duration seems to argue againstthis. It would in addition be hard to explain the existence of the (at least) dual periodicitiesobserved in a number of markets. However, the nature of market data is such that wecertainly cannot rule this explanation out. A more interesting argument against timestamprounding is in the changes in the size distribution that appear to coincide with changes inperiod; we see some evidence of this in the results above, for a number of markets.

What is clearer, is that the variety of fragmentation and velocity found in different mar-kets suggests they are subject to very different pressures. Generalizing about microstructure,from more liquid markets to the less liquid markets, is therefore fraught with difficulty. Theability to identify and use market–specific microstructure features is, in addition, importantto the construction of the trading algorithms, which increasingly work standard order sizesacross the regions. [1], [7].

Despite some commonalities, a lack of regional uniformity, particularly in inter-tradedurations, is clearly apparent — and the differences are not just a matter of scale .

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Market microstructure is evidently dynamic , and each of the last five years have broughtsignificant change to almost every market considered. These changes are not merely of aca-demic interest; they are, or should be, of particular import to algorithm designers, who haveto be in the business of guessing when they should cross the spread, and when they shouldwait. Non monotonic inter-trade duration distributions exist, and some high frequency sys-tem designers appear more complacent about these, and the potential observability of theirATS’s, than others. Whether this complacency evolves, remains to be observed.

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References

[1] D. Shakin Anatolyev S., A.Gerko and O. Kryukovskaya. Dynamics and predicatabilityin russian financial markets, 2003. Working Paper.

[2] Torben G. Andersen and Tim Bollerslev. Heterogeneous information arrivals and re-turn volatility dynamics: Uncovering the long-run in high frequency returns. Journal ofFinance, 52 (3):975–1005, 1997.

[3] Ole E. Barndorff-Nielsen and Neil Shephard. Variation, jumps, market frictions and highfrequency data in financial econometrics, 2005. manuscript University of Oxford.

[4] L. Harris. Trading and Exchanges: Market Microstructure for Practitioners. OxfordUniversity Press, USA, 2002.

[5] Quantitative Products One. Adv models performance testing, 2008. Deutsche Bankinternal document.

[6] Flatley R. Algorithmic trading in turbulent markets. The Journal of Trading, Fall2008:7–13, 2008.

[7] Anatolyev S. and D. Shakin. Trade intensity in the russian stock market: dynamics,distribution and determinants. Applied Financial Economics, 17(2):87–104, 2007.

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