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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