Rise of the Machines: Algorithmic Trading in the Foreign...

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Rise of the Machines:

Algorithmic Trading in the

Foreign Exchange Market Alain Chaboud, Benjamin Chiquoine, Erik

Hjalmarsson, and Clara Vega

And MQL event study Preliminary results

April 2013

Rise of the Machines’ Main Question

What role do algorithmic traders (AT) play

in the price discovery process? Do ATs

make prices more or less informative?

Triangular arbitrage opportunities

Autocorrelation of high frequency returns

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Question (continued)

What is the mechanism? Does the impact

depend on whether AT provides liquidity or

demands liquidity? AT measured in five different ways

• AT participation (VAT)

• AT liquidity provision (VCm)

• AT liquidity demand (VCt)

• AT “signed” liquidity demand (OFCt)

• Correlation of AT trading actions (ln(R))

3

Question (continued)

Main problem in answering question:

endogeneity (reverse-causality)

Granger causality and Heteroskedasticity identification

approach (Rigobon (2003), Rigobon and Sack (2003,

2004))

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Theory

Excellent review of the literature: Biais and Woolley

(2011) and Foucault (2012)

Disagreement on the effect AT may have on price

discovery (Foucault (2012))

Positive effect: Oehmke (2009) and Kondor (2009),

competition among convergence traders makes prices more

informationally efficient

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Theory (continued)

Positive effect: Biais, Foucault, and Moinas (2011) and

Martinez and Rosu (2011)

Computers are fast and better informed than other traders

Computers use market orders to exploit their informational

advantage

Computers make prices more informationally efficient, but

increase adverse selection costs for slow traders

Positive effect: Hoffman (2013) fast computer liquidity

providers are better informed.

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Theory (continued)

Negative effect: Jarrow and Protter (2011): computers

reacting to a common signal, create price momentum and

push prices further away from fundamentals

Negative effect: “crowding effect”: Kozhan and Wah

Tham (2012) and Stein (2009) computers entering the

same trade at the same time push prices further away from

fundamentals

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Theory (continued)

Negative effect: If computers are “noise” traders: Delong

et al. (1990), Froot, Scharfstein, and Stein (1992)

Positive feedback traders who predictably extrapolate past price

trends

Short-term speculators (chartist) herd and put too much emphasis

on some (short-term) information and not enough on fundamentals

AT could cause “excessive” volatility

Foucault (2012) effect may depend on strategy computers

specialize on.

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Our Data

EBS (essentially the global site of price discovery in

interdealer FX market for several large currencies) records

when a trade is placed manually (keyboard) or by a

computer interface

Minute-by-minute data from 2003 to 2007

Three currency pairs (EUR-USD, USD-JPY, EUR-JPY)

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Our Data (continued)

Volume and direction of trade breakdown each minute by

AT (Computer) and non-AT (Human).

We know how much computers “take” from human “makers.”

Four possible types of transactions: HH, HC, CH, CC

(maker-taker).

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Algorithmic Trading Growth in EBS

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0

10

20

30

40

50

60

70

80

90

Jan-03 Jan-04 Jan-05 Jan-06 Jan-07

Pa

rtic

ipa

tio

n (

Per

cen

t)

USD/EUR JPY/USD JPY/EUR

Our Data (continued) Five different measures of AT activity

AT participation:

Vol(CH+HC+CC)/Vol(CH+HC+CC+HH)

AT liquidity supply:

Vol(CH+CC)/Vol(CH+HC+CC+HH)

AT liquidity demand:

Vol(HC+CC)/Vol(CH+HC+CC+HH)

AT signed liquidity demand:

|OF(HC+CC)|/(|OF(HC+CC)|+|OF(CH+HH)|)

Correlation of AT trading actions: R-measure

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arcache

Barrer

What if algorithmic traders (ATs) all did the

same trade at the same time?

Correlated strategies can make prices more informationally

efficient (“convergence” trades)

Correlated strategies can cause excess volatility

e.g., Yen-Dollar market on August 16, 2007

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Do algorithmic trades tend to be correlated?

We do not know strategies, we do not have orders, only

completed trades.

Instead: Do computers trade with each other as much as

expected, as much as random matching would predict? If

computer strategies are correlated, we should observe less

trading among computers than expected.

More precisely: Do computers “take” from humans and

computers in the same proportion as humans take from

humans and computers?

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Prob(HC)/Prob(CC) = computer taker ratio = RC

Prob(HH)/ Prob(CH) = human taker ratio = RH

In a world with more human makers than computer makers

(our world), we expect Prob(HC)/Prob(CC) > 1, i.e.,

computers take more from humans than from other

computers. And we expect Prob(HH)/ Prob(CH) > 1, i.e.,

humans take more from humans than from computers.

However we expect RC/RH=1, i.e., humans take more

from humans in a similar proportion that computers take

more from humans.

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Assuming Prob(HH)= (1 - αm)(1 – αt), RC/RH>1 implies

that either:

Prob(HC) > (1 - αm) αt

or

Prob(CH) > αm(1 – αt)

or

Prob(CC) < αm αt

If we find that RC/RH>1, then we conclude that computers

take more from humans, than humans themselves, in other

words, computer trading is more correlated than expected,

as computers trade less with other computers than expected

or computers trade more with humans than expected.

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We estimate:

R= RC/RH= 𝑉𝑜𝑙(𝐻𝐶)

𝑉𝑜𝑙(𝐶𝐶)

𝑉𝑜𝑙(𝐻𝐻)𝑉𝑜𝑙(𝐶𝐻)

At 1-minute, 5-minute and daily frequency

Report ln(R)

If we find that ln(R)>0, then we conclude that computer

trading is more correlated than expected

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ln(R ) ln(R ) ln(R )

1-min 5-min Daily

EUR/USD

Mean 0.222*** 0.367*** 0.531***

(std. err.) (0.0031) (0.0036) (0.0118)

Fraction of obs.>0 0.599 0.723 0.99

No. of non-missing observations 143421 52101 880

Total no. of obs. 512160 102432 1067

JPY/USD

Mean 0.310*** 0.392*** 0.5849***

(std. err.) (0.0037) (0.0043) (0.0131)

Fraction of obs.>0 0.611 0.703 0.99


Total no. of obs. 512160 102432 1067

JPY/EUR

Mean 0.698*** 0.687*** 0.813***

(std. err.) (0.0049) (0.0051) (0.0173)

Fraction of obs.>0 0.696 0.758 0.98


Total no. of obs. 512160 102432 1067

Do algorithmic trades tend to be correlated?

Answer: Yes. It seems that computers do not trade with

each other as much as random matching would predict.

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Relationship between algorithmic trading

activity and triangular arbitrage

opportunities

Graphical evidence

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Percent of seconds with triangular arbitrage profit

greater than 1 basis point, in 3-11 time interval

What is the effect of algorithmic trading on

triangular arbitrage opportunities?

Endogeneity (reverse causality) problem:

Triangular arbitrage must clearly also cause

AT Granger Causality at high frequency (minute-by-

minute)

and

Heteroskedasticity identification

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Structural VAR Estimation

𝑌𝑡 = (𝐴𝑟𝑏𝑡 , 𝐴𝑇𝑡)

Φ 𝐿 Lag-polynomial, 20-lags

𝑋𝑡−1:𝑡−20 Controls for past volatility and liquidity (volume)

𝐺𝑡 deterministic intra-daily patterns and time trend

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𝐴𝑌𝑡 = Φ 𝐿 𝑌𝑡 + Λ𝑋𝑡−1:𝑡−20 +Ψ𝐺𝑡 + 𝜀𝑡

Test of AT causing triangular arbitrage opp.

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Test of AT Causing Triangular Arbitrage VAT VCt VCm OFCt ln(R )

Sum of coeffs. on AT lags -0.0027*** -0.0061*** 0.0049*** -0.0117*** -0.1202***

Chi-squared (Sum=0) 7.7079*** 25.2501*** 14.435*** 142.46*** 15.39***

p-value 0.0055 0 0.0001 0 0.0001

Chi-squared (All coeffs. on AT lags=0) 91.4066*** 149.588*** 46.51*** 317.38*** 40.99***

p-value 0 0 0.0007 0 0.0037

Contemporaneous coeff. X σ(AT) -0.1932*** -0.813*** -0.0406*** -0.4813*** -1.5193**

No. of obs. 512016 512016 512016 511688 176713

Test of triangular arbitrage opportunities

causing AT

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Test of Triangular Arbitrage causing AT VAT VCt VCm OFCt ln(R )

Sum of coeffs. on AT lags 0.0140*** 0.0219*** -0.0022 0.0345*** 0.0005

Chi-squared (Sum=0) 19.5814*** 56.9040*** 0.82 75.95*** 1.69

p-value 0 0 0.36 0 0.1925

Chi-squared (All coeffs. on AT lags=0) 83.0479*** 118.9288*** 31.00* 459.30*** 84.92***

p-value 0 0 0.055 0 0

Contemporaneous coeff. X σ(AT) 2.0405*** 1.6185*** 0.1832*** 4.3776*** 0.5308***

No. of obs. 512016 512016 512016 511688 176713

Triangular Arbitrage Causality Tests

AT reduces triangular arbitrage opportunities

Predominantly AT acts on posted quotes by other traders

that enable the profit opportunity

Increase the speed of price discovery, but increase adverse

selection costs of slow traders

Some evidence that algorithmic traders make prices more

efficient by posting quotes that reflect new information

quickly

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Does algorithmic trading increase or

decrease “excess” volatility: autocorrelation

of high frequency returns?

Graphical evidence

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5-second return autocorrelation

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Test of AT participation causing HF return

autocorrelation

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VAT

Test of AT Causing HF return Autocorrelation USD/EUR JPY/USD JPY/EUR

Sum of coeffs. on AT lags -0.039*** -0.025*** -0.01539***

Chi-squared (Sum=0) 33.75*** 25.26*** 14.96***

p-value 0 0 0.0001

Chi-squared (All coeffs. on AT lags=0) 43.05*** 45.54*** 15.1881***

p-value 0 0 0.0043

Contemporaneous coeff. X σ(AT) -0.3438*** -0.244*** -0.5011***

No. of obs. 102432 102427 102113

Test of AT liquidity demand causing HF return

autocorrelation

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VCt


Sum of coeffs. on AT lags -0.043*** -0.021*** -0.01069**

Chi-squared (Sum=0) 23.01*** 11.88*** 6.12*

p-value 0 0.0006 0.0134

Chi-squared (All coeffs. on AT lags=0) 24.79*** 20.87*** 6.65

p-value 0.0001 0.0003 0.155

Contemporaneous coeff. X σ(AT) -0.1568*** -0.050*** -0.0369

No. of obs. 102432 102427 102113

Test of AT liquidity supply causing HF return

autocorrelation

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VCm


Sum of coeffs. on AT lags -0.046*** -0.0362*** -0.02146***

Chi-squared (Sum=0) 29.72*** 28.84*** 17.88***

p-value 0 0 0

Chi-squared (All coeffs. on AT lags=0) 44.16*** 38.86*** 18.90***

p-value 0 0 0.0008

Contemporaneous coeff. X σ(AT) -0.3844*** -0.311*** -0.295***

No. of obs. 102432 102427 102113

Test of AT correlated actions causing HF

return autocorrelation

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OFCt


Sum of coeffs. on AT lags -0.00481 -0.0015 0.00013

Chi-squared (Sum=0) 2.3 0.2637 0.0021

p-value 0.12 0.607 0.963

Chi-squared (All coeffs. on AT lags=0) 2.82 1.85 1.38

p-value 0.58 0.76 0.84

Contemporaneous coeff. X σ(AT) 0.098 -0.144 -0.032

No. of obs. 102250 1019992 100815

Test of HF return autocorrelation causing AT

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VAT


Sum of coeffs. on AT lags -0.0068* -0.010* -0.0208***

Chi-squared (Sum=0) 3.0155* 3.49** 7.8843***

p-value 0.0825 0.0616 0.005

Chi-squared (All coeffs. on AT lags=0) 12.87** 4.026 12.21**

p-value 0.0119 0.4 0.0158

Contemporaneous coeff. X σ(Autocorrelation) 0.036* 0.011 0.608***

No. of obs. 102432 102427 102113

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Conclusion We find evidence of algorithmic trading improving price efficiency:

Reduces triangular arbitrage opportunities: mainly by acting on the posted quotes of other traders that enable the profit opportunity

Reduces HF return autocorrelation: mainly by providing liquidity

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Event Study:

Minimum Quote Life on EBS

Work in progress

EBS Imposed a MQL of 250 milliseconds on

June 15, 2009

Is it a binding constraint? Why did EBS impose it?

Theory

What happened to AT volume?

What happened to bid-ask spreads? Depth? Auto-correlation

of 5-second returns? Triangular-arbitrage opportunities?

Can we find a counterfactual to compare it to?

Are the results applicable to equity markets?

BIG CAVEAT, this is a market where EBS has certain monopoly

power: investors “do not have much of a choice” of trading venues.

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It is a binding constraint

I II III IV I II III IV I II III IV I II III IV I II III IV I II III IV

2007 2008 2009 2010 2011 2012

Date

Percent of QI< 250ms out of all QI

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EBS wants to promote “genuine interest in trading”

I II III IV I II III IV I II III IV I II III IV I II III IV I II III IV

2007 2008 2009 2010 2011 2012

Date

Fill Ratio

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Theory regarding the effects of MQL

Imposing a MQL will make it more costly for computers to post a quote:

Increase bid-ask spreads

Decrease depth (because there is less willingness to post quotes)

Increase high-frequency return autocorrelation

Imposing a MQL may lower adverse selection costs for some humans (slow traders)

Ambiguous effect on triangular arbitrage opportunities

Increased bid-ask spreads makes triangular arbitrage opportunities less likely to happen

Decreased trading activity by computers increases triangular arbitrage opportunities (as we showed previously)

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Caveats

Caveat 1: If trading venue has a “monopoly” then the effect on the willingness to post quotes may be very small

Caveat 2: Quotes interrupted within 250ms were not intended to lead to transactions anyway, so getting rid off these quotes may have a minimal effect on: “transactable” bid-ask spreads, “transactable” depth.

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What is the counterfactual?

Reuters (the other large FX interbank dealer trading venue) imposed MQL in 2005

EBS currencies where MQL is not a binding constraint, e.g., EUR-JPY currency pair

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MQL may affect EUR/JPY the least

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Diff -in-diff

methodology:

trend needs to

be similar

prior to

“event”

I II III IV I II III IV

2006 2007

Date

Volume CH

EUR/USD

USD/JPY

EUR/JPY

I II III IV I II III IV

2006 2007

Date

Volume HC

EUR/USD

USD/JPY

EUR/JPY

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Diff -in-diff

methodology:

during event 8 22 5 19 3 17 31 14 28 12 26 9 23 6 20

M3 M4 M5 M6 M7 M8 M9

Date

Volume CH

EUR/USD

USD/JPY

EUR/JPY

8 22 5 19 3 17 31 14 28 12 26 9 23 6 20

M3 M4 M5 M6 M7 M8 M9

Volu

me

Date

Volume HC

EUR/USD

USD/JPY

EUR/JPY

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Diff -in-diff results CC HC CH Total

EUR/USD

diff -14.6% -16.0% -16.0% -16.7%

p-value 0.280 0.177 0.232 0.142

diff in diff -21.8% -32.5% -35.5% -32.2%

p-value 0.150 0.055 0.083 0.051

UDS/JPY

diff -20.4% -17.4% -18.0% -14.5%

p-value 0.173 0.228 0.248 0.295

diff in diff -28% -34% -38% -30%

p-value 0.059 0.028 0.035 0.043

EUR/JPY

diff 7.1% 16.4% 19.5% 15.5%

p-value 0.382 0.232 0.248 0.252

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Diff -in-diff results

Bid-Ask Spread Depth Autocorrelation Triangular Arbitrage

EUR/USD

diff 3% -4% 8% 24%

p-value 0.13 0.33 0.09 0.15

diff in diff 5% -5% 0%

p-value 0.17 0.24 0.48

UDS/JPY

diff -2% -9% -3%

p-value 0.26 0.11 0.26

diff in diff 0% -10% -11%

p-value 0.46 0.11 0.09

EUR/JPY

diff -1% 1% 8%

p-value 0.35 0.35 0.13

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Bid-Ask Spread

.010

.015

.020

.025

.030

.035

.040

.0001350

.0001400

.0001450

.0001500

.0001550

.0001600

8 22 5 19 3 17 31 14 28 12 26 9 23 6 20

M3 M4 M5 M6 M7 M8 M9

Sp

rea

d

Date

Bid Ask Spread

EUR/USD

USD/JPY

EUR/JPY

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Depth

2

3

4

5

6

7

8 22 5 19 3 17 31 14 28 12 26 9 23 6 20

M3 M4 M5 M6 M7 M8 M9

Depth

0

Date

Depth0

EUR/USD

USD/JPY

EUR/JPY

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Auto-correlation

.09

.10

.11

.12

.13

.14

.15

8 22 5 19 3 17 31 14 28 12 26 9 23 6 20

M3 M4 M5 M6 M7 M8 M9

Auto

corr

ela

tion

Date

Autocorrelation

EUR/USD

USD/JPY

EUR/JPY

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Triangular Arbitrage Opportunities

.1

.2

.3

.4

.5

.6

.7

8 22 5 19 3 17 31 14 28 12 26 9 23 6 20

M3 M4 M5 M6 M7 M8 M9

Pro

port

ion

Date

Triangular Arbitrage Opportunities

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Need to find a better counterfactual

Preliminary evidence indicates

Trading volume decreased around the imposition of MQL

There was no statistically significant change on other variables: bid-ask spreads, depth, HF return autocorrelation, triangular arb opportunities

Caveat: the conclusions cannot be generalized to a fragmented equity market. Unless, perhaps MQL is imposed simultaneously on all trading venues.

Need more research in this area. Analyze other events, other markets.

Conclusion

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MQL Effect on Quote Posting Behavior

2006 2007 2008 2009 2010 2011 2012

Date

Quotes Submitted

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MQL Effect on Volume-Transactions

2006 2007 2008 2009 2010 2011 2012

Date

Transactions

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Backup Slides

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Theory (continued) Foucault, Kadan, and Kandel (2009) model AT as

lowering monitoring costs

Pareto optimal (lower trading costs, increase trading

rate)

Ambiguous effect on bid-ask spread (liquidity)

• When monitoring costs for market-makers

liquidity informational efficiency

• When monitoring costs for market-takers liquidity

informational efficiency

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We have four events: H-make, C-make, H-take, C-take.

The probability of each event at time k is

Prob(C-take) = αt , Prob(H-take) = 1 – αt

Prob(C-make) = αm, Prob(H-make) = 1 - αm

Assuming each event is independent, the probabilities of

each trading event are:

Prob(HH) = (1 - αm)(1 – αt)

Prob(HC) = (1 - αm) αt

Prob(CH) = αm(1 – αt)

Prob(CC) = αm αt

We can write the following identities:

Prob(CH)×Prob(HC) ≡ Prob(CC)×Prob(HH)

Prob(HC)/Prob(CC) ≡ Prob(HH)/ Prob(CH) 62


𝑦 = 𝛽1𝑥 + 𝜀 𝑥 = 𝛽2𝑦 + 𝜂

4 parameters: 𝛽1, 𝛽2, 𝜎𝜀 , 𝜎𝜂

3 moments: Var y , Var x , 𝐶𝑜𝑣(𝑥, 𝑦)

System is not identified

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Two regimes, keep coefficients constant across regimes

𝑦1 = 𝛽1𝑥1 + 𝜀1 𝑦2 = 𝛽1𝑥2 + 𝜀2 𝑥1 = 𝛽2𝑦1 + 𝜂1 𝑥2 = 𝛽2𝑦2 + 𝜂2

6 parameters: 𝛽1, 𝛽2, 𝜎𝜀1, 𝜎𝜂1, 𝜎𝜀2, 𝜎𝜂2

6 moments:

Var 𝑦1 , Var 𝑦2 , Var 𝑥1 , Var 𝑥2 , 𝐶𝑜𝑣 𝑥1, 𝑦1 , 𝐶𝑜𝑣(𝑥2, 𝑦2)

System is exactly identified

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