The High-Frequency Trading Arms Race: Frequent

Batch Auctions as a Market Design Response

Eric Budish, Peter Cramton and John Shim

Meeting of the CFTC Technology Advisory Committee

Feb 10th, 2014
The HFT Arms Race: Example

I In 2010, Spread Networks invests $300mm to dig a high-speed ber

optic cable from NYC to Chicago.
The HFT Arms Race: Example

I In 2010, Spread Networks invests $300mm to dig a high-speed ber

optic cable from NYC to Chicago.

I Shaves round-trip data transmission time . . . from 16ms to 13ms
The HFT Arms Race: Example

I In 2010, Spread Networks invests $300mm to dig a high-speed ber

optic cable from NYC to Chicago.

I Shaves round-trip data transmission time . . . from 16ms to 13ms

I Industry observers: 3ms is an eternity. Anybody pinging both

markets has to be on this line, or they're dead
The HFT Arms Race: Example

I In 2010, Spread Networks invests $300mm to dig a high-speed ber

optic cable from NYC to Chicago.

I Shaves round-trip data transmission time . . . from 16ms to 13ms

I Industry observers: 3ms is an eternity. Anybody pinging both

markets has to be on this line, or they're dead

I Joke at the time: next innovation will be to dig a tunnel, avoiding

the planet's pesky curvature
The HFT Arms Race: Example

I In 2010, Spread Networks invests $300mm to dig a high-speed ber

optic cable from NYC to Chicago.

I Shaves round-trip data transmission time . . . from 16ms to 13ms

I Industry observers: 3ms is an eternity. Anybody pinging both

markets has to be on this line, or they're dead

I Joke at the time: next innovation will be to dig a tunnel, avoiding

the planet's pesky curvature

I Joke isn't that funny . . . Spread's cable is already obsolete!
The HFT Arms Race: Example

I In 2010, Spread Networks invests $300mm to dig a high-speed ber

optic cable from NYC to Chicago.

I Shaves round-trip data transmission time . . . from 16ms to 13ms

I Industry observers: 3ms is an eternity. Anybody pinging both

markets has to be on this line, or they're dead

I Joke at the time: next innovation will be to dig a tunnel, avoiding

the planet's pesky curvature

I Joke isn't that funny . . . Spread's cable is already obsolete!

I Not tunnels, but microwaves (rst 10ms, then 9ms, now 8.5ms).
The HFT Arms Race: Example

I In 2010, Spread Networks invests $300mm to dig a high-speed ber

optic cable from NYC to Chicago.

I Shaves round-trip data transmission time . . . from 16ms to 13ms

I Industry observers: 3ms is an eternity. Anybody pinging both

markets has to be on this line, or they're dead

I Joke at the time: next innovation will be to dig a tunnel, avoiding

the planet's pesky curvature

I Joke isn't that funny . . . Spread's cable is already obsolete!

I Not tunnels, but microwaves (rst 10ms, then 9ms, now 8.5ms).

I Analogous races occurring at level of microseconds and

nanoseconds, estimated at $bn's per year (also substantial human

capital)
The HFT Arms Race: Market Design Perspective

I We examine the HFT Arms Race from the perspective of

market design.

I We assume that HFT's are optimizing with respect to market

rules as they're presently given

I But, ask whether these are the right rules

I Avoids much of the is HFT good or evil? that seems to

dominate the discussion of HFT

I Central point: HFT arms race is a symptom of a basic aw in

modern nancial market design: continuous-time trading.

I Proposal: replace continuous-time limit order books with

discrete-time frequent batch auctions

I Frequent batch auctions: uniform-price sealed-bid double

auctions conducted at frequent but discrete time intervals,

e.g., every 1 second or 100ms.
Frequent Batch Auctions

A simple idea: replace (continuous-time) limit-order books with

(discrete-time) frequent batch auctions

1. Continuous limit-order books don't actually work in continuous

time: market correlations break down at high frequency

2. Correlation breakdown > Technical arbitrage opportunities >

Arms Race. Arms Race is a constant of the market design.

3. Model: costs of the arms race

I Harms liquidity (spreads, depth)

I Socially wasteful

4. Frequent Batch Auctions as a market design response

I Benets: eliminates arms race, enhances liquidity, enhances

market stability

I Cost: investors must wait a small amount of time to trade
Frequent Batch Auctions

A simple idea: replace (continuous-time) limit-order books with

(discrete-time) frequent batch auctions

1. Continuous limit-order books don't actually work in

continuous time: market correlations break down at high

frequency

2. Correlation breakdown > Technical arbitrage opportunities >

Arms Race. Arms Race is a constant of the market design.

3. Model: costs of the arms race

I Harms liquidity (spreads, depth)

I Socially wasteful

4. Frequent Batch Auctions as a market design response

I Benets: eliminates arms race, enhances liquidity, enhances

market stability

I Cost: investors must wait a small amount of time to trade
Market Correlations Break Down at High Frequency

ES vs. SPY: 1 Day

09:00:00 10:00:00 11:00:00 12:00:00 13:00:00 14:00:00

1090

1100

1110

1120

1130

1140

1150

1160

1170

Index Points (ES)

Time (CT)

1100

1110

1120

1130

1140

1150

1160

1170

1180

Index Points (SPY)

ES Midpoint

SPY Midpoint
Market Correlations Break Down at High Frequency

ES vs. SPY: 1 hour

13:30:00 13:45:00 14:00:00 14:15:00 14:30:00

1100

1110

1120

1130

1140

Index Points (ES)

Time (CT)

1110

1120

1130

1140

1150

Index Points (SPY)

ES Midpoint

SPY Midpoint
Market Correlations Break Down at High Frequency

ES vs. SPY: 1 minute

13:51:00 13:51:15 13:51:30 13:51:45 13:52:00

1114

1116

1118

1120

Index Points (ES)

Time (CT)

1120

1122

1124

1126

Index Points (SPY)

ES Midpoint

SPY Midpoint
Market Correlations Break Down at High Frequency

ES vs. SPY: 250 milliseconds

13:51:39.500 13:51:39.550 13:51:39.600 13:51:39.650 13:51:39.700 13:51:39.750

1117

1118

1119

1120

Index Points (ES)

Time (CT)

1123

1124

1125

1126

Index Points (SPY)

ES Midpoint

SPY Midpoint
Correlation Breakdown Over Time

0 10 20 30 40 50 60 70 80 90 100

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Return Time Interval (ms)

Correlation

2011

2010

2009

2008

2007

2006

2005

2011

2007

2006

2005

2010

2008

2009
Frequent Batch Auctions

A simple idea: replace (continuous-time) limit-order books with

(discrete-time) frequent batch auctions

1. Continuous limit-order books don't actually work in continuous

time: market correlations break down at high frequency

2. Correlation breakdown > Technical arbitrage opportunities

> Arms Race. Arms Race is a constant of the market

design.

3. Model: costs of the arms race

I Harms liquidity (spreads, depth)

I Socially wasteful

4. Frequent Batch Auctions as a market design response

I Benets: eliminates arms race, enhances liquidity, enhances

market stability

I Cost: investors must wait a small amount of time to trade
Arb Durations over Time: 2005-2011

(a) Median over time (b) Distribution by year
Arb Per-Unit Prots over Time: 2005-2011

01−2005 01−2006 01−2007 01−2008 01−2009 01−2010 01−2011 01−2012

0.025

0.05

0.075

0.1

0.125

0.15

Date

Expected Profits per Arbitrage (index points per unit traded)

(c) Median over time

0.05 0.1 0.15 0.2 0.25

5

10

15

20

Per−Arb Profitability (Index Pts)

Density of Per−Arb Profitability

2005

2006

2007

2008

2009

2010

2011

(d) Distribution by year
Arb Frequency over Time: 2005-2011

01−2005 01−2006 01−2007 01−2008 01−2009 01−2010 01−2011 01−2012

5

10

15

20

25

Date

Number of Arbitrage Opportunities (Thousands)

(e) Median over time

0 5 10 15 20 25

0

5

10

15

20

25

ES Distance Traveled (Index Points, Thousands)

Number of Arbitrage Opportunities (Thousands)

(f) Frequency vs. Volatility
Arms Race is a Constant of the Market Design

I Results suggest that the arms race is a mechanical constant

of the continuous limit order book.

I Rather than a prot opportunity that is competed away over

time

I Competition does increase the speed requirements for

capturing arbs (raises the bar)

I Competition does not reduce the size or frequency of arb

opportunities

I These facts both inform and are explained by our model
Total Size of the Arms Race Prize

I Estimate annual value of ES-SPY arbitrage is $75mm (we

suspect underestimate, details in paper)

I And ES-SPY is just the tip of the iceberg in the race for speed:

1. Hundreds of trades very similar to ES-SPY: highly correlated,

highly liquid

2. Fragmented equity markets: can arbitrage SPY on NYSE

against SPY on NASDAQ! Even simpler than ES-SPY.

3. Correlations that are high but far from one can also be

exploited in a statistical sense. Example: GS-MS

4. Race to top of book (artifact of minimum tick increment)

We don't attempt to put a precise estimate on the total prize at

stake in the arms race, but common sense extrapolation from our

ES-SPY estimates suggest that the sums are substantial
Technical Arbitrage: Other Highly Correlated Pairs

Partial List

E-mini	S&P	500	Futures	(ES)	vs.	SPDR	S&P	500	ETF	(SPY)	

E-mini	S&P	500	Futures	(ES)	vs.	iShares	S&P	500	ETF	(IVV)	

E-mini	S&P	500	Futures	(ES)	vs.	Vanguard	S&P	500	ETF	(VOO)	

E-mini	S&P	500	Futures	(ES)	vs.	ProShares	Ultra	(2x)	S&P	500	ETF	(SSO)	

E-mini	S&P	500	Futures	(ES)	vs.	ProShares UltraPro	(3x)	S&P	500	ETF	(UPRO)	

E-mini	S&P	500	Futures	(ES)	vs.	ProShares	Short	S&P	500	ETF	(SH)	

E-mini	S&P	500	Futures	(ES)	vs.	ProShares	Ultra	(2x)	Short	S&P	500	ETF	(SDS)	

E-mini	S&P	500	Futures	(ES)	vs.	ProShares UltraPro	(3x)	Short	S&P	500	ETF	(SPXU)	

E-mini	S&P	500	Futures	(ES)	vs.	500	ConsJtuent	Stocks	

E-mini	S&P	500	Futures	(ES)	vs.	9	Select	Sector	SPDR	ETFs	

E-mini	S&P	500	Futures	(ES)	vs.	E-mini	Dow	Futures	(YM)	

E-mini	S&P	500	Futures	(ES)	vs.	E-mini	Nasdaq	100	Futures	(NQ)	

E-mini	S&P	500	Futures	(ES)	vs.	E-mini	S&P	MidCap	400	Futures	(EMD)	

E-mini	S&P	500	Futures	(ES)	vs.	Russell	2000	Index	Mini	Futures	(TF)	

E-mini	Dow	Futures	(YM)	vs.	SPDR	Dow	Jones	Industrial	Average	ETF	(DIA)	

E-mini	Dow	Futures	(YM)	vs.	ProShares	Ultra	(2x)	Dow	30	ETF	(DDM)	

E-mini	Dow	Futures	(YM)	vs.	ProShares UltraPro	(3x)	Dow	30	ETF	(UDOW)	

E-mini	Dow	Futures	(YM)	vs.	ProShares	Short	Dow	30	ETF	(DOG)	

E-mini	Dow	Futures	(YM)	vs.	ProShares	Ultra	(2x)	Short	Dow	30	ETF	(DXD)	

E-mini	Dow	Futures	(YM)	vs.	ProShares UltraPro	(3x)	Short	Dow	30	ETF	(SDOW)	

E-mini	Dow	Futures	(YM)	vs.	30	ConsJtuent	Stocks	

E-mini	Nasdaq	100	Futures	(NQ)	vs.	ProShares	QQQ	Trust	ETF	(QQQ)	

E-mini	Nasdaq	100	Futures	(NQ)	vs.	Technology	Select	Sector	SPDR	(XLK)	

E-mini	Nasdaq	100	Futures	(NQ)	vs.	100	ConsJtuent	Stocks	

Russell	2000	Index	Mini	Futures	(TF)	vs.	iShares	Russell	2000	ETF	(IWM)	

Euro	Stoxx	50	Futures	(FESX)	vs.	Xetra	DAX	Futures	(FDAX)	

Euro	Stoxx	50	Futures	(FESX)	vs.	CAC	40	Futures	(FCE)	

Euro	Stoxx	50	Futures	(FESX)	vs.	iShares	MSCI	EAFE	Index	Fund	(EFA)	

Nikkei	225	Futures	(NIY)	vs.	MSCI	Japan	Index	Fund	(EWJ)	

Financial	Sector	SPDR	(XLF)	vs.	ConsJtuents	

Financial	Sector	SPDR	(XLF)	vs.	Direxion	Daily	Financial	Bull	3x	(FAS)	

Energy	Sector	SPDR	(XLE)	vs.	ConsJtuents	

Industrial	Sector	SPDR	(XLI)	vs.	ConsJtuents	

Cons.	Staples	Sector	SPDR	(XLP)	vs.	ConsJtuents	

Materials	Sector	SPDR	(XLB)	vs.	ConsJtuents	

UJliJes	Sector	SPDR	(XLU)	vs.	ConsJtuents	

Technology	Sector	SPDR	(XLK)	vs.	ConsJtuents	

Health	Care	Sector	SPDR	(XLV)	vs.	ConsJtuents	

Cons.	DiscreJonary	Sector	SPDR	(XLY)	vs.	ConsJtuents	

SPDR	Homebuilders	ETF	(XHB)	vs.	ConsJtuents	

SPDR	S&P	500	Retail	ETF	(XRT)	vs.	ConsJtuents	

Euro	FX	Futures	(6E)	vs.	Spot	EURUSD	

Japanese	Yen	Futures	(6J)	vs.	Spot	USDJPY	

BriJsh	Pound	Futures	(6B)	vs.	Spot	GBPUSD	

Australian	Dollar	Futures	(6B)	vs.	Spot	AUDUSD	

Swiss	Franc	Futures	(6S)	vs.	Spot	USDCHF	

Canadian	Dollar	Futures	(6C)	vs.	Spot	USDCAD	

Gold	Futures	(GC)	vs.	miNY	Gold	Futures	(QO)	

Gold	Futures	(GC)	vs.	Spot	Gold	(XAUUSD)	

Gold	Futures	(GC)	vs.	E-micro	Gold	Futures	(MGC)	

Gold	Futures	(GC)	vs.	SPDR	Gold	Trust	(GLD)	

Gold	Futures	(GC)	vs.	iShares	Gold	Trust	(IAU)	

miNY	Gold	Futures	(QO)	vs.	E-micro	Gold	Futures	(MGC)	

miNY	Gold	Futures	(QO)	vs.	Spot	Gold	(XAUUSD)	

miNY	Gold	Futures	(QO)	vs.	SPDR	Gold	Trust	(GLD)	

miNY	Gold	Futures	(QO)	vs.	iShares	Gold	Trust	(IAU)	

E-micro	Gold	Futures	(MGC)	vs.	SPDR	Gold	Trust	(GLD)	

E-micro	Gold	Futures	(MGC)	vs.	iShares	Gold	Trust	(IAU)	

E-micro	Gold	Futures	(MGC)	vs.	Spot	Gold	(XAUUSD)	

Market	Vectors	Gold	Miners	(GDX)	vs.	Direxion	Daily	Gold	Miners	Bull	3x	(NUGT)	

Silver	Futures	(SI)	vs.	miNY	Silver	Futures	(QI)	

Silver	Futures	(SI)	vs.	iShares	Silver	Trust	(SLV)	

Silver	Futures	(SI)	vs.	Spot	Silver	(XAGUSD)	

miNY	Silver	Futures	(QI)	vs.	iShares	Silver	Trust	(SLV)	

miNY	Silver	Futures	(QI)	vs.	Spot	Silver	(XAGUSD)	

PlaJnum	Futures	(PL)	vs.	Spot	PlaJnum	(XPTUSD)	

Palladium	Futures	(PA)	vs.	Spot	Palladium	(XPDUSD)	

Eurodollar	Futures	Front	Month	(ED)		vs.	(12	back	month	contracts)	

10	Yr	Treasury	Note	Futures	(ZN)	vs.	5	Yr	Treasury	Note	Futures	(ZF)	

10	Yr	Treasury	Note	Futures	(ZN)	vs.	30	Yr	Treasury	Bond	Futures	(ZB)	

10	Yr	Treasury	Note	Futures	(ZN)	vs.	7-10	Yr	Treasury	Note	

2	Yr	Treasury	Note	Futures	(ZT)	vs.	1-2	Yr	Treasury	Note	

2	Yr	Treasury	Note	Futures	(ZT)	vs.	iShares	Barclays	1-3	Yr	Treasury	Fund	(SHY)	

5	Yr	Treasury	Note	Futures	(ZF)	vs.	4-5	Yr	Treasury	Note	

30	Yr	Treasury	Bond	Futures	(ZB)	vs.	iShares	Barclays	20	Yr	Treasury	Fund	(TLT)	

30	Yr	Treasury	Bond	Futures	(ZB)	vs.	ProShares UltraShort	20	Yr	Treasury	Fund	(TBT)	

30	Yr	Treasury	Bond	Futures	(ZB)	vs.	ProShares	Short	20	Year	Treasury	Fund	(TBF)	

30	Yr	Treasury	Bond	Futures	(ZB)	vs.	15+	Yr	Treasury	Bond	

Crude	Oil	Futures	Front	Month	(CL)	vs.	(6	back	month	contracts)	

Crude	Oil	Futures	(CL)	vs.	ICE	Brent	Crude	(B)	

Crude	Oil	Futures	(CL)	vs.	United	States	Oil	Fund	(USO)	

Crude	Oil	Futures	(CL)	vs.	ProShares	Ultra	DJ-UBS	Crude	Oil	(UCO)	

Crude	Oil	Futures	(CL)	vs.	iPath	S&P	Crude	Oil	Index	(OIL)	

ICE	Brent	Crude	Front	Month	(B)	vs.	(6	back	month	contracts)	

ICE	Brent	Crude	(B)	vs.	United	States	Oil	Fund	(USO)	

ICE	Brent	Crude	(B)	vs.	ProShares	Ultra	DJ-UBS	Crude	Oil	(UCO)	

ICE	Brent	Crude	(B)	vs.	iPath	S&P	Crude	Oil	Index	(OIL)	

Natural	Gas	(Henry	Hub)	Futures	(NG)	vs.	United	States	Nat	Gas	Fund	(UNG)	
Frequent Batch Auctions

A simple idea: replace (continuous-time) limit-order books with

(discrete-time) frequent batch auctions

1. Continuous limit-order books don't actually work in continuous

time: market correlations break down at high frequency

2. Correlation breakdown > Technical arbitrage opportunities >

Arms Race. Arms Race is a constant of the market design.

3. Model: costs of the arms race

I Harms liquidity (spreads, depth)

I Socially wasteful

4. Frequent Batch Auctions as a market design response

I Benets: eliminates arms race, enhances liquidity, enhances

market stability

I Cost: investors must wait a small amount of time to trade
Model: Key Idea

Key idea: the arms race prots come at the expense of liquidity

providers, which ultimately harms liquidity (bid-ask spreads, market

depth)
Model: Key Idea

Key idea: the arms race prots come at the expense of liquidity

providers, which ultimately harms liquidity (bid-ask spreads, market

depth)

I Why? Consider the race from a liquidity provider's perspective
Model: Key Idea

Key idea: the arms race prots come at the expense of liquidity

providers, which ultimately harms liquidity (bid-ask spreads, market

depth)

I Why? Consider the race from a liquidity provider's perspective

I Suppose there is a publicly observable news event that causes

his quotes to become stale

I E.g., a change in the price of a highly correlated security

(ES/SPY), Fed announcement
Model: Key Idea

Key idea: the arms race prots come at the expense of liquidity

providers, which ultimately harms liquidity (bid-ask spreads, market

depth)

I Why? Consider the race from a liquidity provider's perspective

I Suppose there is a publicly observable news event that causes

his quotes to become stale

I E.g., a change in the price of a highly correlated security

(ES/SPY), Fed announcement

I 1 of him, trying to adjust his stale quotes
Model: Key Idea

Key idea: the arms race prots come at the expense of liquidity

providers, which ultimately harms liquidity (bid-ask spreads, market

depth)

I Why? Consider the race from a liquidity provider's perspective

I Suppose there is a publicly observable news event that causes

his quotes to become stale

I E.g., a change in the price of a highly correlated security

(ES/SPY), Fed announcement

I 1 of him, trying to adjust his stale quotes

I Many others, trying to pick o his stale quotes
Model: Key Idea

Key idea: the arms race prots come at the expense of liquidity

providers, which ultimately harms liquidity (bid-ask spreads, market

depth)

I Why? Consider the race from a liquidity provider's perspective

I Suppose there is a publicly observable news event that causes

his quotes to become stale

I E.g., a change in the price of a highly correlated security

(ES/SPY), Fed announcement

I 1 of him, trying to adjust his stale quotes

I Many others, trying to pick o his stale quotes

I In a continuous limit order book, messages are processed

one-at-a-time in serial ...
Model: Key Idea

Key idea: the arms race prots come at the expense of liquidity

providers, which ultimately harms liquidity (bid-ask spreads, market

depth)

I Why? Consider the race from a liquidity provider's perspective

I Suppose there is a publicly observable news event that causes

his quotes to become stale

I E.g., a change in the price of a highly correlated security

(ES/SPY), Fed announcement

I 1 of him, trying to adjust his stale quotes

I Many others, trying to pick o his stale quotes

I In a continuous limit order book, messages are processed

one-at-a-time in serial ...

I so the 1 usually loses the race against the Many ...
Model: Key Idea

Key idea: the arms race prots come at the expense of liquidity

providers, which ultimately harms liquidity (bid-ask spreads, market

depth)

I Why? Consider the race from a liquidity provider's perspective

I Suppose there is a publicly observable news event that causes

his quotes to become stale

I E.g., a change in the price of a highly correlated security

(ES/SPY), Fed announcement

I 1 of him, trying to adjust his stale quotes

I Many others, trying to pick o his stale quotes

I In a continuous limit order book, messages are processed

one-at-a-time in serial ...

I so the 1 usually loses the race against the Many ...

I Even if they are all equally fast!
Model: Key Idea

Key idea: the arms race prots come at the expense of liquidity

providers, which ultimately harms liquidity (bid-ask spreads, market

depth)

I Why? Consider the race from a liquidity provider's perspective

I Suppose there is a publicly observable news event that causes

his quotes to become stale

I E.g., a change in the price of a highly correlated security

(ES/SPY), Fed announcement

I 1 of him, trying to adjust his stale quotes

I Many others, trying to pick o his stale quotes

I In a continuous limit order book, messages are processed

one-at-a-time in serial ...

I so the 1 usually loses the race against the Many ...

I Even if they are all equally fast!

I Takeaway: in a continuous limit order book, any time there is

public information, there is a race to respond. This race harms

liquidity provision.
Model: Key Idea

I This technical cost of providing liquidity  liquidity-providing

HFTs getting picked o by other HFTs in the race to respond

to symmetrically observable public news  is incremental to

the usual fundamental costs of providing liquidity

I Asymmetric information, inventory costs, search costs

I In a competitive market, picking o costs get passed on to

investors

I Thinner markets, wider bid-ask spreads

I Ultimately, in equilibrium of our model, all of the $ spent in

the arms race come out of the pockets of investors

I Arms-race prize = expenditures on speed = cost to investors
Model: Additional Remarks

The Arms-Race is a Constant

I Comparative static: the negative eects of the arms race do

not depend on either

I the cost of speed (if speed is cheap, there will be more entry)

I the magnitude of speed improvments (seconds, milliseconds,

microseconds, nanoseconds, ...)

I The problem we identify is an equilibrium feature of

continuous limit order books

I not competed away as HFTs get faster and faster

I ties in nicely with empirical results
Model: Additional Remarks

Role of HFTs

I In our model HFTs endogenously perform two functions

I Useful: liquidity provision / price discovery

I Rent-seeking: picking o other HFTs' stale quotes

I HFTs are indierent between these two roles inequilibrium of

our model

I The rent-seeking seems like zero-sum activity among HFTs (all

good fun!)

I we show that it ultimately harms real investors

I Frequent batching preserves the useful function but eliminates

the rent seeking function (or at least reduces)
What's the Market Failure?

Chicago question: isn't the arms race just healthy competition?

what's the market failure?
What's the Market Failure?

Our model yields two responses

1. Model shows that the arms race can be interpreted as a

prisoners' dilemma

I If all HFTs could commit not to invest in speed, they'd all be

better o

I But, each individual HFT has incentive to deviate and invest in

speed

2. Model shows that a violation of the ecient market hypothesis

is built in to the market design

I Violations of the the weak-form EMH are intrinsic to the

continuous limit order book market design

I You can make money from purely technical information (and

HFTs do!)

I Core issue: continuous markets process messages in serial (i.e.,

one-at-a-time)

I Even for public / technical info (e.g., a jump in ES): somebody

is always rst to react
Frequent Batch Auctions

A simple idea: replace (continuous-time) limit-order books with

(discrete-time) frequent batch auctions

1. Continuous limit-order books don't actually work in continuous

time: market correlations break down at high frequency

2. Correlation breakdown > Technical arbitrage opportunities >

Arms Race. Arms Race is a constant of the market design.

3. Model: costs of the arms race

I Harms liquidity (spreads, depth)

I Socially wasteful

4. Frequent Batch Auctions as a market design response

I Benets: eliminates arms race, enhances liquidity,

enhances market stability

I Cost: investors must wait a small amount of time to

trade
Frequent Batch Auctions: Denition

I During the batch interval (eg 1 second), traders submits bids and

asks as price-quantity pairs

I Just like standard limit orders

I At the conclusion of each batch interval, the exchange batches all

of the received orders, and computes market-level supply and

demand curves

I If supply and demand intersect, then all transactions occur at the

same market-clearing price (uniform price)

I Bids and asks of exactly the market-clearing price may get

rationed (pro-rata)

I If there is a range of market-clearing prices, choose the

midpoint (knife-edge case)

I Information policy: orders are not visible during the batch interval.

Aggregate demand and supply are announced at the end.

I Analogous to current practice under the continuous limit-order

book
Frequent Batch Auctions: Illustrated

Price

Quantity

p*

q*

(a) Case 1: No Trade (b) Case 2: Trade
Why and How Batching Eliminates the Arms Race

There are two reasons why batching eliminates the arms race:

1. Batching reduces the value of a tiny speed advantage

I If the batch interval is 1 second, a 1 millisecond speed

advantage is only 1

1000 th as useful

2. Batching transforms competition on speed into competition on

price

I Ex: the Fed announces policy change at 2:00:00.000pm ...

I Continuous market: competition manifests in a race to react.

Someone is always rst.

I Batched market: competition simply drives the price to its

new correct level for 2:00:01.000. Lots of orders reach the

exchange by the end of the batch interval.
Computational Benets of Frequent Batching

I Overall

I Continuous-time markets implicitly assume that computers and

communications technology are innitely fast.

I Discrete time respects the limits of computers and

communications. Computers are fast but not innitely so.

I Algorithmic traders

I Continuous: Always uncertain about current state; temptation

to trade o robustness for speed

I Discrete: Everyone knows state at time t before decision at

time t + 1

I Exchanges

I Continuous: Computational task is mathematically impossible;

latencies and backlog unavoidable

I Discrete: Computation is easy

I Regulator

I Continuous: Audit trail is dicult to parse; who knew what

when? in what order did events occur across markets?

I Discrete: Simple audit trail; state at t, t + 1,...
Costs and Benets of Frequent Batching

I Benets

I Enhanced liquidity

I Narrower spreads

I Increased depth

I Eliminate socially wasteful arms race

I Computational / market stability benets of batching

I Costs

I Investors must wait until the end of the batch interval to

transact

I Unintended consequences
Summary

I We take a market design perspective to the HFT arms race. What

incentivizes HFTs to invest billions in tiny speed advantages? Can

we improve nancial market design?

I Propose a simple idea: replace (continuous-time) limit-order books

with (discrete-time) frequent batch auctions.

1. Show that continuous-time markets are a ction: market

correlations break down at high frequency

2. Correlation breakdown → Technical arbitrage opportunities → Arms

Race. Arms Race is a constant of the market design.

3. Costs of the arms race

I Harms liquidity (spreads, depth)

I Socially wasteful

4. Frequent Batch Auctions as a market design response

I Benets: eliminates arms race, enhances liquidity, enhances

market stability

I Costs: investors must wait a small amount of time to trade,

law of unintended consequences