Market forces I: Price Impact J. Doyne Farmer Santa Fe Institute La Sapienza, 8 marzo Research supported by Barclays Bank.

Market forces I: Price Impact

J. Doyne FarmerSanta Fe InstituteLa Sapienza, 8 marzo

Research supported by Barclays Bank

Market forces

• Supply and demand are in a loose sense like forces in physics.

• What determines supply and demand curves?

• Are they the best approach?– Market dynamics– Observability problems

Standard approach to determining supply and

demand• Assume agents selfishly maximize utility• Make an assumption about optimization algorithm agents use:– Standard: Perfect rationality– “Behavioral”: One rational, others noise

• Make an assumption about markets– Market clearing– Price taking

• Simplifications: (no production, no inter-temporal reasoning, …

• Economy is at a Nash equilibrium• Research since 1980: Modify assumptions

What drives changes in prices?

• Standard view: expectations about future earnings driven by new information– new information alters expected earnings and changes fundamental value

– prices quickly adjust to new fundamental value

– prices are unpredictable because new information is by definition random

Rationality?

Elliot waves

Fibonnaci predicts social trends!

Overfitting

Problems with standard view

• Far too much trading (> 50 x GDP)• Volatility is not random

– size of price changes is correlated in time

• Many price changes not information driven

• Prices deviate from fundamental values• Prices have exploitable patterns

– weak, difficult to find, but not zero

Volatility

Problems with standard view

• Far too much trading (> 50 x GDP)• Volatility is not random

– size of price changes is correlated in time

• Many price changes not information driven

• Prices deviate from fundamental values• Prices have exploitable patterns

– weak, difficult to find, but not zero

Problems with standard view

• Far too much trading (> 50 x GDP)• Volatility is not random

– size of price changes is correlated in time

• Many price changes not information driven

• Prices deviate from fundamental values• Prices have exploitable patterns

– weak, difficult to find, but not zero

Prices do not match fundamental values

Comparison of pseudo S&P index (solid) to fundamental valueestimate based on dividends (dashed)

Problems with standard view

• Far too much trading (> 50 x GDP)• Volatility is not random

– size of price changes is correlated in time

• Many price changes not information driven

• Prices deviate from fundamental values• Prices have exploitable patterns

– weak, difficult to find, but not zero

Prediction Company (cofounded in 1991 with Norman

Packard)

• Does fully automated proprietary trading in international stock markets under profit sharing relationship relationship with United Bank of Switzerland (Warburg Dillon Read)

• “Cerebellar” approach to market forecasting– empirically search for patterns in historical data – keys are feature extraction, central limit theorem– little understanding of origin of patterns– relies on abundant past data, stationary conditions

• 50 employees.

Profits?

• Finding a persistent pattern doesn’t mean you can make an infinite amount of money.– (reason is market impact)– depends on timescale

• How much you can make is sensitively dependent on market impact

Price Impact(also called market

impact)• Response of price to receipt of an order• Related to derivative of aggregate demand function = demand - supply.

• With a few caveats, has the important advantage of being directly measurable.– No information about price level, only price change

€

p = D(q)dp

dq=

dD

dq

Price impact vs. order size for different market

capitalizations

With Fabrizio Lillo and Rosario Mantegna

Data collapse

• Use market capitalization C as liquidity proxy

• Find empirically to minimize variance

γδ yCy

C

xx →→

δγ,

Master price impact curve

Zero intelligence model of price formation

• Assume agents place orders to buy or sell, make cancellations, “at random”– make everything a Poisson process– make distributions and rates uniform– equal for buying and selling.

• What are properties of resulting prices?– Dimensional analysis (price, time, shares)

– Scaling laws for spread and volatility in terms of parameters of order flow

Giulia Iori

Giulia Iori Eric Smith

Laszlo Gillemot Supriya Krishnamurthy

Marcus Daniels

Continuous doubleauction model collaborators

Continuous double auctionContinuous: Market operates asynchronously

Double: Price adjustment in orders both to buy and to sellExecution priority: • Lower priced sell orders or higher priced buy orders have

priority• First order placed has priority when multiple orders have

same price.

price ($)

SPREAD

PRIORITY

PRIORITY

(BEST) BID

(BEST) ASK

VOLUME

SELL

BU

Y

VO

LUM

E

LIMIT ORDERS

price ($)

BID

ASK

VO

LUM

E

Patient trading• Patient traders place non-marketable

limit orders that do not lead to an immediate transaction

• Non-marketable limit orders accumulate

• Limit order book is a storage device

NEW ASK

Limit Order

BUY / SELL

# OF SHARES

LIMIT PRICE

Patient trading• Patient traders place non-

marketable limit orders that do not lead to an immediate transaction

• Non-marketable limit orders accumulate

price ($)

Impatient trading

Market order:• An order to buy or sell up to a given

volume• No limit price is defined• Executed immediately• Often causes unfavorable price impact

Market Order

BUY / SELL

# OF SHARES

BID

ASK

BID

NEW ASK

VO

LUM

E

Impatient trading

Order cancellation

price ($)

Limit order cancellations: • Limit orders can be cancelled by the owner • Market defined expiration

price ($)price ($)

VO

LUM

E

ZI model (Unrealistic but somewhat tractable)

Limit order arrival: Poisson process in time & price;

Market order arrival: Poisson process in time; Cancellation: random in time (like radioactive decay); δ

Separate processes for buying and selling, with same parameters.

Depth profile np,t: Number of shares in limit order book at price p, time t.

BID

SELL LIMIT ORDERS

AS

K

BUY LIMIT ORDERS

SELL MARKETORDERS

BUY MARKET ORDERS

),( tpΩ

p0

),( tpn

Parameters of model

€

=limit order rate (S/PT)μ = market order rate (S/T)δ = order cancellation rate (1/T)σ = typical order size (S)

dp = tick size (P)

Order flow rates

Discreteness parameters

Three fundamental dimensional quantities:shares S, price P, time T

Price impact from ZI modelReal data shows less variation with epsilon

than theory predicts

dots 002.0

dashed 02.0

solid 2.0

======

εεε

Market impact fn- non dim units

Market impact function(non-dimensional units)

€

ˆ N =Nδ

μ

€

Δˆ p =Δpα

μ

Testing prediction of spread

• Equation of state from mean field theory

€

E[s] = μ

αf (

σδ

μ)

From top 10 Russian jokes, Oct. 23, 2003

с сайта "Немецкая волна"http://www.dw-world.de/russian/0,3367,2212_A_985770_1_A,00.htmlУченые-экономисты давно стараются понять закономерности, которымподчиняются биржевые курсы, и используют для этого математическиемодели. На протяжении многих десятилетий такие модели исходили из

представлений о брокерах как об аналитиках с выдающимися умственнымиспособностями, обладающих исчерпывающей информацией о рынке и

действующих исключительно рационально. Однако удовлетворительно описатьреальные изменения биржевых курсов эти модели оказались не в состоянии.

Значительно успешнее справляется с этой задачей новая модель,предложенная Дойном Фармером (J. Doyne Farmer), сотрудником ИнститутаСанта-Фе в штате Нью-Мексико. Она базируется на предположении, что

брокеры Ц полные Ђидиотыї, действующие совершенно случайно и к тому желишенные какой бы то ни было информации. Сравнив данные, рассчитанные наоснове этой модели, с реальными курсами лондонской фондовой биржи запериод с 1998-го по 2000-й годы, ученые выявили очень высокую степень

совпадения

Price impact on longer timescales

• Aggregate signed volumes for N successive transactions.

• Aggregate signed price return for N successive transactions.

• Vary N.• Normalize x and y axis according to mean value of absolute aggregate signed volume.

Price impact on longer time scales

Statistical model

Decomposition of price impact

Price impact has two parts:• Mechanical (direct) impact

– When an order enters the book, it alters the state of the book, which alters future prices even if nothing else changes.

• Indirect impact– Placement of the order may alter placement of future orders -- this measures interaction of agents.

– Change can be due to direct impact or to other factors (e.g. direct observation of order placement)

Is it possible to separate direct and indirect impacts?

Measurement of direct impact

• Any allowed sequence of orders and cancellations yields a unique price series– Cannot cancel an order that doesn’t exist

• Can remove an order and then compute new series of prices– Can also partially remove an order– Can add orders

• Difference in prices measures mechanical (direct) impact