Discussion of The endogenous dynamics ofmarkets: price impact, feedback loops and

inabilities by J-P. BouchaudOxford University, Oct. 2, 2012

J. Doyne Farmer

Institute for New Economic Thinking and MathematicsDepartment, Oxford University

External Professor, Santa Fe Institute

J. Doyne Farmer

Discussion of The endogenous dynamics of markets: price impact, feedback loops and inabilities by J-P. Bouchaud

Market impact

I = E

[ε(pf − p0)

p0

].

The expected shift in price from the price p0 observed before thefirst trade to the price pf of the last trade. ε = +1 for buying,ε = −1 for selling.

In contrast to early theories1, impact I (Q) is a concavefunction of Q. This is because liquidity does not remainconstant during the execution of a large order.

1Kyle (1985) and Huberman and Stanzl (2004).J. Doyne Farmer

Discussion of The endogenous dynamics of markets: price impact, feedback loops and inabilities by J-P. Bouchaud

Conjectured universal functional form

Both empirical data and theory2 indicate that under normalconditions, for large orders market impact is of the form

I (Q) = Y σ

√Q

V

where σ is the daily volatility, V is daily share transactionvolume, and Y a numerical constant of order unity.

This holds at intermediate points 0 < q(t) < Q.

2Empirical studies: Torre (1997), Engle et al. (2008), Moro et al. (2009);Theory: Farmer et al. (2011), Toth et al. (2011)

J. Doyne Farmer

Discussion of The endogenous dynamics of markets: price impact, feedback loops and inabilities by J-P. Bouchaud

What happens if theory of Toth et al. is violated?

Diffusion is nonlinear and arbitrage is possible.

Figure: Price variance vs. time, (Daniels et al., 2003)

Square root impact rises from no arbitrage assumption + diffusion.J. Doyne Farmer

Discussion of The endogenous dynamics of markets: price impact, feedback loops and inabilities by J-P. Bouchaud

Is knowing the functional form of impact important?

Quote from a referee (for Reviews of Financial Studies):

”In the introduction the authors mention that studying the shapeof the price impact function for metaorders is important since‘market impact reflects the shape of excess demand’. I simply donot understand this point. What does it mean?”

J. Doyne Farmer

Discussion of The endogenous dynamics of markets: price impact, feedback loops and inabilities by J-P. Bouchaud

Uses of market impact

Poor man’s substitute for excess demand

Arises naturally from perturbing excess demandFunctional form and scale but floating reference pointUniversal functional form!Both friction and motive forceMarket dynamics: Transactions cause price movements, pricemovements cause transactions, . . .

Execution tactics. Essential for optimizing.

Allometry. Limits fund size.

Market ecology. Understanding how strategies interact, whichwill grow and which will die out3.

Accounting. Limits to leverage and position size.

3Farmer (2002), ”Market force ecology and evolution”J. Doyne Farmer

Discussion of The endogenous dynamics of markets: price impact, feedback loops and inabilities by J-P. Bouchaud

Market ecology

Friedman Paradox: Market efficiency requires arbitrageurs butarbitrageurs require inefficient markets. Implies markets areefficient at first order but inefficient at second order.

Inefficiencies are driven by demand for liquidity anddiversification. Supports a rich ecology of predators.

Hypothesis: Market crises are driven by disruptions of ecology.

Market impact makes it possible to compute market food web.

Pairwise interactions: predator-prey, competition, symbiosis.

Can build up ecology by studying ability to invade.

Generalized Lotka-Volterra dynamics for capital of strategies.

Empirical study requires data with counterparty identifiers.We have no grounded understanding of market ecology!

J. Doyne Farmer

Discussion of The endogenous dynamics of markets: price impact, feedback loops and inabilities by J-P. Bouchaud

Impact-based valuation

(with Fabio Caccioli and J-P. Bouchaud)

Assume a sequence of N sales of size v to liquidate Q = Nv . Ifmarket-to-market price is p0, the impact-adjusted valuation is

V(Q) =N

∑t=1

vp0(1− I (vt)).

Integrating in continuous limit with I (Q) = Y σ√Q/V implies

V(Q) ≈ p0Q(

1− 23Y σ√Q/V

).

Average liquidation price

p̃ = V/Q.Impact-adjusted accounting: Use p̃ rather than p to value assets.

J. Doyne Farmer

Discussion of The endogenous dynamics of markets: price impact, feedback loops and inabilities by J-P. Bouchaud

0 Q/2 Q Q/2 00

5

10

15

20

25

30

q

leve

rage

mark−to−marketimpact−adjustedno impact

0 Q/2 q_c Q Q/2 00

5

10

15

20

25

30

q

leverage

impact−adjustedno−impactmark−to−market

Figure: Leverage as one enters and then exits a position. The position q(t)varies from 0 to Q in the left half of each panel and from Q to 0 in the righthalf of each panel. Three different measures are used for leverage. The dashedblack line shows what the leverage would be if there were no impact and theprice didn’t change; the solid blue line shows the leverage including impactunder mark-to-market accounting, and the dotted-dashed red line shows theleverage using impact-adjusted valuation.

J. Doyne Farmer

Discussion of The endogenous dynamics of markets: price impact, feedback loops and inabilities by J-P. Bouchaud

What causes financial instabilities?

Most network models so far treat cascading failures due tocounterparty risk.

Cascading counterparty failure is not believed to be a commoncause of financial crises.

NY Fed: Crisis of 2007 - 2009 was transmitted throughcommon asset portfolios.

Can understand contagion via models that combine marketimpact with network effects.

J. Doyne Farmer

Discussion of The endogenous dynamics of markets: price impact, feedback loops and inabilities by J-P. Bouchaud

Portfolio contagion4

Main channel of contagion in 2007-9 crisis was common assets

Assume N funds holding an average of µb assets each out ofM possible assets, equally weighted portfolio, leverage λ.

Assume µb = pM (Erdos-Renyi).

How does contagion depend on µb,M,N, λ, market impact?

Impact/network approach allows us to estimate the effect of amacroprudential stress test analytically.

Let M → ∞, N → ∞ with N/M finite.Treat as branching process.

4(Caccioli, Shrestha, Moore and Farmer, 2012)J. Doyne Farmer

Discussion of The endogenous dynamics of markets: price impact, feedback loops and inabilities by J-P. Bouchaud

Analytic model vs. simulation

Diversification leads to systemic risk!

0 2 4 6 8 10 120

2

4

µb

ξ 1

0 2 4 6 8 10 120

0.5

1

prob

abili

ty o

f con

tagi

on

Figure: Largest eigenvalue of contagion matrix and contagion probabilityas a function of diversification parameter µb. Dashed line = 1.

J. Doyne Farmer

Discussion of The endogenous dynamics of markets: price impact, feedback loops and inabilities by J-P. Bouchaud

Contagion vs. crowding, diversification and leverage

µb

N/M

2 4 6 8 10 12 14

1

2

3

4

5

6

7

8

9

10

µbλ

0 1 2 3 4 5 6 7 8 9 108

10

12

14

16

18

20

22

24

26

28

30

Figure: Contagion window is shown in red.

J. Doyne Farmer

Discussion of The endogenous dynamics of markets: price impact, feedback loops and inabilities by J-P. Bouchaud

Clustered volatility and heavy tails are (mainly)endogenously generated

Clustered volatility and heavy tails with agent-based models.Trend followers and value investors (SFI stock market model)Leveraged value investors (Thurner, Farmer, Geankoplos)

Randomly generated games, players use reinforcement learning(which Camerer and Ho claim is a good behavioral model)

1.5×105 2.0×105t

-0.05

0

0.05

Figure: Total payoff vs. time (Galla and Farmer, 2011)J. Doyne Farmer

Discussion of The endogenous dynamics of markets: price impact, feedback loops and inabilities by J-P. Bouchaud

Figure: Transition to turbulence in learning dynamics

J. Doyne Farmer

Discussion of The endogenous dynamics of markets: price impact, feedback loops and inabilities by J-P. Bouchaud

How efficient are markets at processing information?

Richard Roll (2000): ”The origin of heavy tails in price returnsis not an interesting problem. We know where they comefrom – they are driven by fluctuations in information arrival,which cause clustered volatility, which causes heavy tails”.

Opinion post-crisis?

Correct statement: At least on short time scales heavy tailsare mainly driven by fluctuations in liquidity5which are largelyendogenously generated.

5”There’s more to volatility than volume”, Gillemot, Farmer, Lillo, 2007)J. Doyne Farmer

Discussion of The endogenous dynamics of markets: price impact, feedback loops and inabilities by J-P. Bouchaud

Main points

Market impact is a useful substitute for excess demand.

Accounting should take market impact into account.

Market impact is the vector of financial contagion; Systemicrisk control should make use of emerging quantitative models.

Can make simple models for asset portfolio contagion that canpotentially be calibrated against real data.

Clustered volatility and extreme risks are largely endogenousand (at least) on short time scales are driven by liquidityfluctuations, i.e. fluctuations in market impact.

Expectations have endogenous dynamics!

In economics structure is often more important than strategy.

J. Doyne Farmer

Discussion of The endogenous dynamics of markets: price impact, feedback loops and inabilities by J-P. Bouchaud