Dynamics of Socio-Economic Systems

7/25/2019 Dynamics of Socio-Economic Systems

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B. Rosenow, Bad Honnef, DPG-School on Dynamics of Socio-Economic Systems 2005

Lecture II: Liquidity, Price Impact, and Resiliency

Bernd Rosenow Harvard University

References:

P. Weber and B. Rosenow, Orderbook approach to priceimpact, eprint cond-mat/0311457, Quant. Fin. 05

P. Weber and B. Rosenow, Large Stock price changes:

volume or liquidity?, eprint cond-mat/0401132, Quant. Fin. 05

Dynamics of Socio-Economic Systems: A Physics Perspective,September 20, 2005


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large fluctuations more frequent than expected for a

gaussian distribution

Why is it interesting - stock prices as a random walk?

from. Gopikrishnan et al., Phys. E 60, 5305 (1999)


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T. Lux, Appl. Fin. Econ. 6, 463

(1996)

P. Gopikrishnan et al., Phys. E60, 5305 (1999)

Why is it interesting: power law distribution for stock returns

Cumulative probability distribution

Return


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Why and how stock prices change

Large returns and liquidity fluctuations

Microscopic structure of large returns

Outline


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Liquidity

Concept of market liquidity describes, how easy a

financial instrument can be bought or sold, encompasses

various transactional properties of markets.

Market depth denotes the amount of order flow innovation

which is required to change prices a given amount.

Resiliency describes the speed with which prices recover

from a random uninformative shock, and

Tightness is the cost for turning around a certain amount of

shares within a short period of time.


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Reasons for price changes I

Present value of a company is discounted sum offuture dividends/earnings

Information about economic situation of a company

influences expectations about future earningsvalue

of the company

News/Information influences stock price


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Reasons for Price Changes II

Supply and demand influence price

Measurement of supply and demand by difference Q between

the number of stocks bought and the number of stocks sold

(volume imbalance)

Price impact function describes the relation between return G

and volume imbalance Q

Efficient market: only the information content of Q influences

price; possibly incorrect


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Standard price formation equation

stock price at time t

volume (number of stocks) of transaction i

instantaneous price impact (inverse liquidity)

noise term describing the arrival of new information


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Literature related to price impact

Hasbrouck (1991) concave price impact

Hausmann, Lo, MacKinley (1992) ordered probit model

Kempf und Korn (1999) description of nonlinear effects

Zhang (1999) square root price impactDufour und Engle (200) time and price impact

Plerou, Gopikrishnan, Gabaix, Stanley (2002) square root law

Rosenow (2002) liquidity and volatility

Evans und Lyons (2002) Q determines exchange rates

Hopman (2002) mechanical price pressure

Lillo, Farmer, Mantegna (2003) master curve for price impact

Gabaix, Gopikrishnan, Plerou, Stanley (2003) large G from large Q (*)

Potters und Bouchaud (2003) permanent price impact

Bouchaud, Gefen, Potters, Wyart (2003) correlated Q, uncorrelated G

Lillo und Farmer (2003) criticism of (*)


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Data Sets

Island ECN order book for 2002 , 20% of NASDAQ volume

10 most frequently traded stocks like Cisco, Microsoft, Oracle

(AMAT, BRCD, BRCM, CSCO, INTC, KLAC, MSFT,

ORCL,QLGC, SEBL)

TAQ data base published by the New York stock exchange

44 most frequently traded NASDAQ stocks

all trades and quotes in the year 1997


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Order book

information: all limit orders

complete description of stock market:

limit orders

market orders

bid price = highest buy limit order

ask price = lowest sell limit order

market orders (marketable limit orders) execute limit orders

exclude transactions including hidden limit orders

bid ask

midquote price

limit buy orders limit sell orders

market orders


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generate transaction data from order book

Normalization of returns and volumes

(midquote)return

volume

normalize returns by standard deviation and

volumes by

different stocks are comparable, analysis of ECN and

TAQ data are comparable


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Average price impact

-4

-2

0

2

4

-10 -5 0 5 10

0.1

1

0.1 1 10

0.1

1

0.1 1 10

Volume Q

Return

G

average price impact

as a conditional expectation value

double logarithmic fit yields


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Description of order book

measure prices logarithmically form bid/ask price

describe order book by density function with

reconstruct density function from information aboutplacement, cancellation and execution of limit orders


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Average order book

0

0,05

0,1

0,15

0,2

0,25

0,3

0,35

0,4

0,1 1 10 100 1000

G

V

AMAT

CSCOBRCD

BRCM

INTC

KLAC

MSFT

ORCL

QLGC

SEBL

for details see work by Maslov, Challet and Stinchcomb, Bouchaud

group, Farmer group


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Virtual price impact

-10

-5

0

5

10

-10 -5 0 5 10

-10

-5

0

5

10

-10 -5 0 5 10

0

0.05

0.1

0.15

0.2

0.25

0.1 1 10 100 1000

Volume Q

(b)

Retu

rnG

Orderbook depth

OrderbookvolumeQ

(a)Integration of order book

yields ,

by inverting this relation one

obtains


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dominated by

rare events with low

liquidity

typical price impact better

described by

Averaging and inversion

-10

-5

0

5

10

-15 -10 -5 0 5 10 15

-10

-5

0

5

10

-15 -10 -5 0 5 10 15

-10

-5

0

5

10

-15 -10 -5 0 5 10 15

0.1

1

10

100

0.1 1 10

0.1

1

10

100

0.1 1 10

0.1

1

10

100

0.1 1 10

0.1

1

10

100

0.1 1 10

0.1

1

10

100

0.1 1 10

0.1

1

10

100

0.1 1 10

0.1

1

10

100

0.1 1 10

0.1

1

10

100

0.1 1 10

0.1

1

10

100

0.1 1 10

Volume Q

Ret

urn

G

problem: cannot be calculated by inverting

Hence: invert and average afterwards


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Correlations between return and order flow I

= market market orders in interval

= limit limit orders with

Correlation function


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Correlations between returns and order flow II

market orders

correlated with returns

limit orders

anticorrelated withreturns

limit

market

0

0.1

0.2

0.3

-20 -10 0 10 20 30

-0.3

-0.2

-0.1

0

-20 -10 0 10 20 30

Correlationfun

ctionc

(a)

Time

(b)

Correlationfunctionc


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Correlations between returns and order flow III

anticorrelations between returns and limit orders

describe market resiliency: recovery from uniformativeshocks

value traders become active only at the outside spread

reserve orders are not visible in the order book, order

management systems like Archipelago place new orders

if the old ones are executed

compare Bouchaud et al.: transitory price impact


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Correlation volume

average order flow

integration of yields

order flow due to correlations

saturates for t030 min

integration of yields


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Approximation of stationary returns

Assume ,

total volume

-20

-10

0

10

20

-8 -4 0 4 8

-20

-10

0

10

20

-8 -4 0 4 8

-8

-4

0

4

8

-10 -5 0 5 10

-8

-4

0

4

8

-10 -5 0 5 10

-8

-4

0

4

8

-10 -5 0 5 10

-8

-4

0

4

8

-10 -5 0 5 10

(b)

(a)

Return

G

Return G

VolumeQ

Volume Q

calculate price impact by

inverting

good agreement between

theory and empirical data


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Analysis of extreme events -TAQ data base

44 most frequently traded NASDAQ stocks all trades and quotes in the year 1997

trades:

ticker date time price volume

CSCO 02JAN1997 9:48:04 63 500

CSCO 02JAN1997 9:48:05 63.125 1000CSCO 02JAN1997 9:48:07 63 500

quotes:

stock date time bid ask bid volume ask volume

CSCO 02JAN1997 9:47:40 63.125 63.25 10 10

CSCO 02JAN1997 9:47:53 63 63.125 10 10

CSCO 02JAN1997 9:48:44 62.875 63.125 10 10


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Classification of Transactions

ask price

bid price

midquote price

algorithm of Lee & Ready (1991)

seller induced transaction,

buyer induced transaction,


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Typical data errors

recording errors, e.g. decimal point at wrong position(98.09.80)

artefacts due to combination of different ECNs (Electronic Communications

Networks)

25

30

35

40

45

50

55

60

30000 32000 34000 36000 38000 40000 42000

Time (sec)

Price

($)

0

20

40

60

80

100

120

30000 35000 40000 45000 50000

Time (sec)

Price

($)


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Large returns - filter algorithm for TAQ data

Discard all transactions with

transaction price < 0

bid-ask spread < 0

bid-ask spread > 40% transaction price

transaction price midquote price| > 4 bid-ask spread

T. Chordia, R. Roll, and A. Subrahmanyam, J. Finance 56, 501-530 (2001)


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Large events and average price impact

-15

-10

-5

0

5

10

15

-20 -15 -10 -5 0 5 10 15 20

-15

-10

-5

0

5

10

15

-20 -15 -10 -5 0 5 10 15 20

-15

-10

-5

0

5

10

15

-20 -15 -10 -5 0 5 10 15 20

-15

-10

-5

0

5

10

15

-20 -15 -10 -5 0 5 10 15 20

-15

-10

-5

0

5

10

15

-20 -15 -10 -5 0 5 10 15 20

-15

-10

-5

0

5

10

15

-20 -15 -10 -5 0 5 10 15 20

Volume Q

ReturnG

ReturnG

(a)

(b)

TAQ, 1198 events

Island order book,

210 events

average price impact has weak explanatory power for large returns

returns


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Liquidity measures I: depth and tightness

depth is size of market order

required to change price by 5 G

tightness T is cost of round trip (buying and selling

volume 2 Qover short period of time)

return predicted from average price impact by


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Explanation of extreme returns by depth and tightness

R2= 0.14 R2= 0.11

depth and tightness have explanatory power for large returns


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Liquidity measures II: dynamic liquidity

determin slope (t) of by linear fit in region

0G 5 G

book(,t) density of limit orders in the book in the

beginning of 5 minute interval

flow(,t) density of limit orders added to book within 5

minute interval

calculate by inverting this relation


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Actual price impact for some extreme events

0

1

2

3

4

5

6

0 5 10 15 20

0

1

2

3

4

5

6

0 5 10 15 20

0

1

2

3

4

5

6

0 5 10 15 20

0

1

2

3

4

5

6

0 5 10 15 20

0

1

2

3

4

5

6

0 5 10 15 20

0

1

2

3

4

5

6

0 5 10 15 20

0

1

2

3

4

5

6

0 5 10 15 20

0

1

2

3

4

5

6

0 5 10 15 20

0

1

2

3

4

5

6

0 5 10 15 20

Volume

ReturnG


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Dynamic liquidity and large returns

large returns mostly due to low liquidity (steep price

impact function)

compare Farmer et al. cond-mat/0312703:large returns on tick

basis explained by gaps in the order book

R2= 0.79


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Microscopic structure of large returns

study intervals with fixed number N=100 trades

tick return gi

= ln(si+1

) - ln(si

)

total return

average tick return

N+(N-) trades with nonzero return in (against) the

direction of Gwith nonzero N = N+- N-


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Direction versus average size of tick returns

Direction of tick returns more important than size


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Conclusion

difference between virtual and average price impact due

to resiliencey

large returns mainly due to small liquidity

intervals with large returns: many price changes in the

same direction

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