A Theory of Blind Trading

Transcription

1 Cyril Monnet 1 and Erwan Quintin 2 1 University of Bern and Study Center Gerzensee 2 Wisconsin School of Business June 21, 2014

2 Motivation Opacity is ubiquitous in financial markets, often by design This suggests that opacity plays an essential role What fundamental frictions does opacity help mitigate? We propose a simple answer: 1. Expert investors are needed to address moral hazard issues 2. But it is costly to produce experts, so it is optimal to economize on their number 3. Juxtaposing expert and non-expert investors, in turn, creates adverse selection problems 4. Opacity mitigates that problem Put another way, transparent markets would feature a suboptimal fraction of unsophisticated investors

3 The market for Mortgage Pass-Through Securities Most agency MBS are issued in TBA markets (see Vickery, 2013) Investors buy pools before they exist with the GSE having only committed to a few pool-wide characteristics The market also features a specified market where existing pools with favorable characteristics are sold In other words, primary MBS markets feature an opaque end and a more transparent end The more transparent market features investors that can process finer pool information This creates a cheapest-to-deliver problem

4 Literature Hirshleifer (1971, ) Dang, Holmstrom and Gorton (2012), Andolfatto, Berentsen and Waller (2012), Monnet and Quintin (2014) Rock (1986), Pagano and Volpin (2012) Di Maggio and Pagano (2014) Grossman and Stiglitz (1980), Kyle (1985)

5 The model t = 0, 1, one good Mass one of investors with one unit of good at t = 0 They can store any fraction of that endowment at a zero net return Large mass of prospectors with no endowment characterized by a prospection cost k 0 H Provided they incur an additional diligence/effort cost k, the project yields payoff r > 0 at date 1 with probability λ F We assume df > k but ( H ) df k df < 1

6 Informed investors Investors can become experts at a utility cost γ They can see and interpret project types (λ) Uninformed investors can t learn from expert bids Formally, we assume that prospectors meet non-experts first, then they meet expert investors

7 First-best Consider a planner who wants to maximize total welfare by choosing: 1. How many prospectors to activate ( a threshold k 0 ) 2. A fraction µ of investors to inform 3. Consumption profiles: c u 0, c i 0 and c p 0 4. Storage amounts: s u, s i Assume the planner can observe whether prospectors bore the effort cost k but does observe prospector types

8 First-best max (1 µ)c u + µ(c i γ) + subject to: k0 0 k0 0 (c p k 0 k)dh(k) c p dh(k 0 ) + (1 µ)s u + µs i 1 (1) c i γ, c u 1 (2) (1 µ)(c u s u ) + µ(c i s i ) = H( k 0 ) df (3)

9 No need for experts at the first-best Proposition The first best allocation satisfies µ = 0, s u = 1 H(k 0 )(k 0 + k), c u = 1, and c p = k + k 0 where df = k 0 + k.

10 Moral hazard Assume that effort is private information Now the planner needs a positive mass of informed agents Informed agents can make λ dependent transfers, q i (λ), while other agents only make blind transfers q u to active prospectors IC requires c p (λ)df k k 0 c p (0) k 0 Feasibility requires H( k 0 )q u (1 µ)(1 s u ) and H( k 0 ) q i (λ)df µ(1 s i ).

11 Constrained-optimal solution with moral hazard Proposition With unobservable effort, the optimal allocation satisfies µ = kh( k 0 ), s i = 0, where k 0 solves df = k 0 + k + γk.

12 Markets Two Walrasian markets All investors can participate in the first one, only informed investors participate in the second one Projects sell for p u on uninformed market, p i (λ) on informed market Let V (λ) = max [p u, p i (λ)] Active prospectors exert effort provided V (λ)df(λ) k p u Prospectors become active provided { max V (λ)df (λ) k, p u } k 0

13 Uninformed investors Uninformed investors form expectations about the set Λ u of projects sold in the first market In equilibrium, Λ u = {λ : p u p i (λ)} Then uninformed investors solve V u = max s u [0,1] su + θ u df(λ) Λ u F(Λ u ) subject to 1 s u = θ u p u.

14 Informed investors Informed agents solve the following problem V i = max s i + θ i (λ)dλ s i,θ i (λ) Λ i subject to 1 s i = θ i (λ)p i (λ)dλ. Λ i

15 Informed investors Informed agents solve the following problem V i = max s i + θ i (λ)dλ s i,θ i (λ) Λ i subject to In any equilibrium, on Λ i, 1 s i = θ i (λ)p i (λ)dλ. Λ i p i (λ) R i.

16 Informed investors Informed agents solve the following problem V i = max s i + θ i (λ)dλ s i,θ i (λ) Λ i subject to In any equilibrium, on Λ i, 1 s i = θ i (λ)p i (λ)dλ. Λ i p i (λ) R i. Since investors can choose whether to become informed, µ (0, 1) if and only if V i γ = V u

17 Market equilibirium A market equilibrium is a set of beliefs and strategies for all agents such all agents behave optimally and beliefs are borne out.

18 Market equilibirium A market equilibrium is a set of beliefs and strategies for all agents such all agents behave optimally and beliefs are borne out. Remark 1. A market equilibrium where all investors are informed always exists 2. A market equilibrium with both types of investors may exist 3. No market equilibrium with only uninformed agents exists

19 Markets vs. second-best Lemma In any equilibrium where a positive mass of projects is activated, prices are given by p u E(λ λ Λ u )r and R i = p i (λ) = 1 + γ for all λ Λ i. Furthermore, p u = E(λ λ Λ u )r whenever s u < 1.

20 Markets vs. second-best Lemma In any equilibrium where a positive mass of projects is activated, prices are given by p u E(λ λ Λ u )r and R i = p i (λ) = 1 + γ for all λ Λ i. Furthermore, p u = E(λ λ Λ u )r whenever s u < 1. Proposition At a market equilibrium, fewer projects are activated and the ratio of informed to uninformed is higher than at the second best.

21 Project quality threshold In an equilibrium with both types of investors, a threshold exists with E(λ λ )r = r 1 + γ

22 Intuition λm 0 E(λ λ )rdf γ df = k M 0 + k.

23 Intuition But 0 λm 0 E(λ λ )rdf + E(λ λ )rdf+ 1 + γ df = k M 0 + k. 1 + γ df = df γ 1 + γ df

24 Intuition But 0 λm 0 E(λ λ )rdf + E(λ λ )rdf+ and 1 + γ df = k M 0 + k. 1 + γ df = df ( ) 1 + γ E(λ λ )r df k. γ 1 + γ df

25 Intuition But 0 λm 0 E(λ λ )rdf + E(λ λ )rdf+ and 1 + γ df = k M 0 + k. 1 + γ df = df ( ) 1 + γ E(λ λ )r df k. γ 1 + γ df so γ df > kγ. 1 + γ

26 Intuition But 0 λm 0 E(λ λ )rdf + E(λ λ )rdf+ and 1 + γ df = k M 0 + k. 1 + γ df = df ( ) 1 + γ E(λ λ )r df k. γ 1 + γ df hence so γ df > kγ. 1 + γ df > k M 0 + k(1 + γ).

27 Intuition But 0 λm 0 E(λ λ )rdf + E(λ λ )rdf+ and 1 + γ df = k M 0 + k. 1 + γ df = df ( ) 1 + γ E(λ λ )r df k. γ 1 + γ df hence so whereas γ df > kγ. 1 + γ df > k M 0 + k(1 + γ). df = k SB 0 + k(1 + γ).

28 Optimal opacity Assume that he planner can set up a technology that sends a public message m once λ is realized The planner can choose any message function in the following set: {m : [0, 1] B([0, 1]) : λ m(λ) for almost all λ [0,1]}

29 Optimal opacity Assume that he planner can set up a technology that sends a public message m once λ is realized The planner can choose any message function in the following set: {m : [0, 1] B([0, 1]) : λ m(λ) for almost all λ [0,1]} Proposition The optimal message function is binary and partitions the set of types in two subsets Λ u = [0, λ B ] and Λ i = [λ B, 1] where ( ) 1 + γ E(λ λ λb )r df = k. λ B Projects in Λ u are sold to uninformed investors while projects in Λ i. are sold to informed investors.

30 Key consequences With opacity: 1. An equilibrium with both types of investors always exists 2. Welfare can only improve and generally does

31 Implementation Implementation by delegation: ex-post agency conflicts Implementation via forward markets

32 Testable implications vs. IPO markets 1. IPOs tend to be underpriced 2. IPOs that feature more representation from institutional investors tend to be more underpriced and institutional investors earn higher returns on IPOs than do retail investors 3. Underpricing rises with valuation uncertainty.

33 Testable implications vs. IPO markets 1. IPOs tend to be underpriced 2. IPOs that feature more representation from institutional investors tend to be more underpriced and institutional investors earn higher returns on IPOs than do retail investors 3. Underpricing rises with valuation uncertainty. Our model s distinguishing prediction: More information should cause the fraction of experts to go up, hence average underpricing to rise

34 Summary Financial markets naturally feature a juxtaposition of expert and non-expert investors... which makes opacity essential Imposing transparency, in our model, is a bad idea