1. The effect of market structure on the plausibility of REE Markets, the more the better ?

2. Introduction. Friedman’s argument. – –Speculation is stabilizing. – –Speculators   sell when the price is high   Buy when it is low   They stabilize the market. – –Friedman’s argument has been incredibly influential and is still. The challenge. – –With RE, new markets may create sunspot equilibria.   Bowman-Faust – –New markets threaten « eductive » stabillity.   Guesnerie-Rochet – –New markets destabilize « evolutive » learning.   Brock, Hommes, Wagener.

3. Bowman-Faust (1997) The model. The model. –3 periods, 2 agents, log. Utility.. –one firm…equity is exchanged.. –0 decision on firm’s investment, reaped at 2. –At 1, one of the agent, randomy picked, desires immediate consumption, (zero value), the other one postponement… The equilibrium with one asset The equilibrium with one asset –Is not P.O : not zero consumption in the bad event.. –No sunspot. An option : An option : –Completes the market : PO with the option.. –Creates sunspots

4. Guesnerie-Rochet. The model : The model : –A manna of crop at each period w(t), t=1,2 –Part on the market, the other goes to inventories. –Inventory Cost : Cx 2 /2, –P(t)=k{d(t) - w(t) (+/–) S(t)}, S(t), quantity on the market. Profitability of inventories. Profitability of inventories. –Mean-variance utility : E(  ) – (1/2)b(Var  ) –ΔP(t)=k{Δ d(t) -2X- Δw(t)}, (k=1/B), Var(w(2)) = v 2 –x() = k(X_ -2X(e))/{bk 2 v 2 +C} –Inventory mass N –X= kN(X_ -2X(e))/{bk 2 v 2 +C} Equilibrium inventories : Equilibrium inventories : –X* = X_/{2+C/kN + bkv 2 /N} –Plausible…..

5. The « eductive » process :the inventory variant An « eductive » story : An « eductive » story : –Expectations X(e), –Realizations : –-2kNX(e))/{bk 2 v 2 +C} Results : Results : –N<{bk 2 v 2 +C}/2k – Bad  More traders  Less risk averse  Less uncertainty  Less costly.. -2kN/{bk 2 v 2 +C} X

6. Inventories with futures markets M mass of « speculators » : intervene on the market of futures, price P(f), one unit of wheat to morrow. M mass of « speculators » : intervene on the market of futures, price P(f), one unit of wheat to morrow. Hedging behaviour from primary traders : Hedging behaviour from primary traders : –N[p(f)-p(1)]/C = (N+M)[p(2)-p(1)]/bk 2 v 2. –Previously X = X*/{2+C/kN + bkv 2 /N} Now : X = X*/{2+C/kN + bkv 2 /(N+M)} Now : X = X*/{2+C/kN + bkv 2 /(N+M)} –Intuition : uncertainty cost born by N+M agents. –The variance of prices is decreased Eductive stability : Eductive stability : –C/kN + bkv 2 /(N+M) >2 –Intuition.N(M), N decreasing function of M. M>0 is bad.

7. An « evolutive » learning model.. From Brock-Hommes-Wagener : « more hedging instruments may destabilize markets ». The model (sketch). – –Stock p(0,t)  q(t+1,s)=p(0,t+1) + y(s), s=1,…S, prob.  – –N Arrow securities, i pays the vector d(i), i.e pays 1 in state i=1,..N<S, price p(i,t); – –Mean variance utility. The demand : – –Z(t)=IV(N)[-R(p(0,t)+E{q(t+1)}, -Rp(t)+E{d}] t – –V(N) prop. cov (q(t+1)/d) – –Steady state.   p(0,*)= (y*-a  Q)/(R-1),  variance of the stock, a coef risk aversion, Q total amount of the stock.   p(s,*)=(1/R)(  -abQ), cov. Vect. q,d

8. An « evolutive » learning model.. The learning process : – –Heterogenous expectations away from the RE benchmark. – –Deviations f(h,t) depends on the type of the traders. – –Remarks.   Along the path, Arrow securities are correctly priced in the REE   If beliefs are homogenous, no trade on Arrow securities – –The fraction of agents following a given strategy depends on its fitness : average profit of the previous period corrected by riskiness – –The speed of adjustment measured by c>0, – –c small, the fundamental equilibrium is stable – –When c becomes large, the fundamental equilibrium is destabilzed Results. – –With one more Arrow security, the fundamental equil. Is destabilized earlier for a smaller c ! – –The mechanism : Optimists (resp. pessimists) buy (resp. sell) the stock and hedge with Arrow securities…

9. An « evolutive » learning model.. Results. – –With one more Arrow security, the fundamental equil. Is destabilized earlier for a smaller b ! – –The mechanism. – –With more insurance possibility more hedging and risk taking, and profit if you are on the right side of the opinion, and these strategies through reinforcement mechanisms will attract more followers, – –And vice versa… – –More movement of opinion and of prices…. Other results. – –« Rational » agents may or may not stabilize the market… – –Dubious…

10. Excess confidence. A cognitive bias A cognitive bias –Well established ? Modelling : Investors. Modelling : Investors. –Random variable v, mean 0, 2 signals t(1)=v+e(1), t(2)=v+e(2), –e(1),e(2) mean zero, precision (e(i))= ρ –2 categories of investors A and B –A, (resp.B) over estimates precision t(1),cρ,(resp.t(2),cρ), c>1 Modelling : the firrm. Modelling : the firrm. –Long term value w = u+v+e’, u mean u >0 – signal s, on u, centered on u, precision ρ(s). –u,v,e’, s, normal precision denoted ρ(.) –Without cognitive bias : E(w/s,t)= –u + [ρ(s)/(ρ(u)+ ρ(s))][s - u] +  i [ρ/(ρ(v)+2ρ)][t(i)] –+  i [1/(ρ*+2)][t(i)], with ρ*= ρ(v)/(ρ).

11. Excess confidence Modelling : the firm Modelling : the firm –Long term value w =u+v+e’, u mean u >0 –signal s, on, mean u, precision ρ(s). –U,v,e’,e(i),s, normal precision ρ(.) Cognitive bias : Cognitive bias : –With bias : E(w/s,t)= –u + [ρ(s)/(ρ(u)+ ρ(s))][s- u] + –For A : [cρ/(ρ(v)+ρ(1+c)][t(1)] + [ρ/(ρ(v)+ρ(1+c)][t(2)] –The difference between the a posteriori belief of A and B rewrites : –[(c-1)/(ρ*+1+c)][t(1)-t(2)] –Exchange of shares after observation of t (with or without s)  Si t 2 > t 1 B too optimistic /w : B buys shares to A at his valuation  Si t 1 > t 2 then A too optimistic, but cannot buy to B. Value of the firm ex ante : Value of the firm ex ante : –V(0) = u+ [(c-1)/(ρ*+1+c)][  [ρ*(c+1)/2c  ](écart type (v)) –Hint : increasing the standard deviation of v a value for initial owners.