Impact of Financial Regulation and Innovation on Bubbles and Crashes due to Limited Arbitrage: Awareness Heterogeneity

Transcription

1 1 September 15, 2013, 14:50~15:50 JEA Meeting, U. Kanagawa, Room 7-13 Impact of Financial Regulation and Innovation on Bubbles and Crashes due to Limited Arbitrage: Awareness Heterogeneity Hitoshi Matsushima University of Tokyo, Faculty of Economics February 6, 2013

2 2 Bubbles may be harmful under weak regulation and high enthusiasm Unproductive company can raise huge funds by issuing shares cf. After-crash financial crises: Brunnermeier and Oehmke (2012) Bubbles may be beneficial as collaterals, otherwise. Regulator cannot identify whether it is productive or not. How can we deter harmful bubbles without identification?

3 3 Naked credit default swap (naked CDS) can be an effective policy method, if we assume: Naked CDS is designed as secured contract with reserve requirement. Naked CDS is a time bomb otherwise. (Warren Buffett) Naked CDS payments are utilized for debt obligation.

4 4 Covered CDS What are CDSs? Naked CDS Insurance against own default risk Hedge against third party default risk Underlying assets required No underlying assets required

5 5 Main Statements of This Paper Without naked CDS, weak regulation on leverage fosters bubble, With naked CDS, weak regulation on leverage deters bubble. With weak regulation on leverage and/or with high enthusiasm, availability of naked CDSs deter (harmful) bubble, With strong regulation on leverage and/or with low enthusiasm, availability of naked CDSs foster (beneficial) bubble.

6 6 How can we describe bubbles and crashes? Key Concept: Awareness Heterogeneity between arbitrageurs and positive feedback traders (PFTs) Arbitrageurs are: (mostly) rational aware of bubbles and crashes have limited funds ex. Goldman Sachs PFTs are: slave to euphoria unaware of bubbles and crashes have a plenty of free money ex. AIG Related (but Different) Literatures: Limited Arbitrage: Shleifer and Vishny (92) Heterogeneous Beliefs: Harrison and Kreps (78) Informational Asymmetry: Allen and Gorton (93)

7 7 Debt Contracting: Financial Interactions between Arbitrageurs and PFTs For purchasing shares, arbitrageurs borrow money from PFTs under regulation on leverage. No premium, because of their awareness heterogeneity in bubbles. Naked CDS Trading: Arbitrageurs purchase naked CDS from PFTs. No premium, because of their awareness heterogeneity in crashes. Arbitrageurs expect naked CDS payment riskless.

8 8 PFTs Sell new shares Company Lending Sell naked CDS Sell new shares Arbitrageurs Naked CDS is beneficial for arbitrageurs, but PFTs spend free money on shares and loan. Reserve for naked CDS = PFTs Free Money PFTs Share Value PFTs Loan Greater PFTs share value and PFT s loan crowd out reserve for naked CDS. Arbitrageurs relative future benefit decreases. Arbitrageurs are willing to time earlier.

9 9 How can we formulate arbitrageurs incentive? Timing Game with Behavioral Types: Matsushima (JET 2013, Theory of Reputation) Symmetric arbitrageurs compete with each other to win the earliest. n players (Arbitrageurs) i 1,..., n. Each player selects time a i in bounded time interval [0,1]. Earliest to time wins: Winner payoff i () v t is greater than loser payoff vi () t. Winner payoff is increasing in time, v() t 0.. Player is behavioral, i.e., never times, with tiny probability 0 Player is rational with probability 1 0. Strategy qi :[0,1] [0,1] Player times at or before time t with probability qi () t. (No-bubble is a unique NE if 0) i

10 10 Bubble-Crash Strategy Profile q Arbitrageur never times before critical time. Rational arbitrageur randomly times according to hazard rate () t q i ( ) 0. 1 t 1exp[ ( ) d ] q1 () t n for all t, Critical time 0 : exp[ ( ) d] n n v 1() t Hazard rate () t n 1 v ( t) v ( t) 1 1 after. No-Bubble Strategy Profile Rational arbitrageur times at initial time 0 with certainty. q * (0) 1 i * q

11 11 Characterization Theorems Theorem 1: Bubble-Crash q is NE if and only if 1 1 I1 exp[ ( ) d ]. It is a unique NE if and only if I1. n 0 * Theorem 2: No-Bubble strategy profile q is NE if and only if v1(0) v1(0) ( n 1)! 1 l 1 1 I2 [ ( ) ]. v (1) v (0) l!( n1 l)! l l n1 Indices I 1 and I 2 imply (inverse of) relative future benefit for arbitrageur. [Greater I 1, greater I 2, smaller, smaller () t ] [Bubble is less likely to persist]

12 12 Stock Market Formulation Company s total share, S() t, increases in time. Arbitrageur s shareholdings, Si () t S1 () t. Bubble crashes once arbitrageurs shareholdings become less than 100 Company issue shares as much as possible, S () t S() t. PFTs have sufficient free money, B() t. i n %. Arbitrageurs borrow money from PFTs through short-term non-recourse debt contracts with leverage ratio L 0. P() t PFTs perceive share price as unchanged over time, but PFTs unconsciously reinforce price perception, P() t 0. ex. Abreu and Brunnermeier (2003)

13 13 Exogenous Bubble Price Path, Endogenous Crash Time Share Price 0 Crash Time 1

14 14 Arbitrageur s debt obligation L 1 PtS () i () t L Arbitrageur s Personal Capital: PtS () i () t Wi () t L PtS () i() t P() tsi() t W i () t L... (A) Arbitrageur earns capital gain Si (){ t P( t ) P()} t from t to t : W() t S () t P() t... (B) i i From (A) and (B), we can derive: Total Share: Arbitrageur s Share: Arbitrageur s Personal Capital: Pt () L1 St () S(0)( ) P(0) Pt () L1 Si () t S(0)( ) P(0) PtS () i () t Pt () Wi () t P(0) S(0)( ) L L P(0) L

15 15 Incorporation of Stock Market into Timing Game Specification of winner and loser payoffs depends on whether CDSs are available. 1) Basic Model: No CDS available 2) Covered CDS Model 3) Naked CDS Model

16 16 1) Basic Model: No CDS Available Sell Shares Short-Term Lending PFTs Company Sell Shares Arbitrageurs Winner payoff: vi() t Wi() t Loser Payoff vi () t 0 Non-Recourse

17 17 Hazard rate Index Index Critical time n P() t P() t * (, t L) L is increasing in L and. n 1 Pt () Pt () L * P(0) P n1 I1 ( L) ( ) is decreasing in L and (1). P(1) P(0) * 1 P I2 ( L) is decreasing in L and (1). P(1) L P(0) ( ) 1 P(0) * P() t is increasing in L and. Pt () [Greater leverage ratio, greater enthusiasm] [Bubble is more likely to persist]

18 18 2) Covered CDS Model Only losers receives CDS payment Zi () t, but have debt obligation ( L 1) Wi ( t). Sell Shares Short-Term Lending PFTs Sell Covered CDS Cancel + Re-contract Sell Shares Company Arbitrageurs Winner payoff: vi() t Wi() t Loser Payoff v () t Z () t ( L1) W() t W() t v () t : Full Insurance i i i i i No-Crash Bubble is unique NE, because of full insurance.

19 19 3) Naked CDS Model Both winner and losers receive CDS payment Zi () t. Sell Shares Short-Term Lending PFTs Sell Naked CDS Company Sell Shares Payment reserve for naked CDS = PFTs Personal Capital PFTs Share Value PFTs Loan Winner Payoff: Loser Payoff: Arbitrageurs L 1 nz1( t) B() t (1 n ) P( t) St ( ) n P( t) S() t L Pt ( ) L vi() t Wi () t Zi() t Bt () ( ) P(0) S(0)( ) n n L P(0) 1 1 ( L 2) P( t) vi() t Zi() t ( L1) Wi( t) Bt () { } P(0) S(0)( ) n n L P( 0) L

20 20 Instantaneous gain is greater in naked CDS model than in basic model, because both winner and losers receive CDS payments and both have debt obligations in naked CDS model, while loser is exempted from debt obligation in basic model. Naked CDS is more beneficial than shareholdings Expansion of PFTs share value and loan is necessary for bubble persistence. High leverage and great enthusiasm need large expansions. Large expansions crowd out reserve for naked CDS.

21 21 Theorem 3: Under high leverage ratio and high enthusiasm, naked CDS deters bubble: If Z 1() t ( L 1) W 1() t for all t [0,1], then ** * ** * ** * ** * ( L) ( L), (, t L) (, t L), I ( L) I ( L), I ( L) I ( L) Under low leverage ratio and low enthusiasm, naked CDS fosters bubble:, then Z () t ( L 1) W () t for all t [0,1] If 1 1 ** * ** *, ( L) ( L) (, t L) (, t L), I ( L) I ( L), ** * 1 1 I ( L) I ( L). ** * 2 2 Theorem 4: Suppose L 2n. Then, high leverage ratio deters bubble: ** ( L) 0 L, ** (, tl) 0 L, L I ** ( L) 0 1, and L I ** ( L) 0 2.

22 22 Conclusion Naked CDS is an effective policy method for deterring harmful bubbles, if it is well secured and utilized for debt obligation High leverage ratio deters bubbles: It crowds out reserve for naked CDS, lowering arbitrageurs future benefit. Regulator should keep weak regulation on leverage irrespective of whether company is productive or not. Under high leverage ratio and high enthusiasm, naked CDS deters harmful bubbles: Even losers are not exempted from debt obligation. Under low leverage ratio and low enthusiasm, naked CDS fosters beneficial bubbles: Naked CDS increases arbitrageurs absolute future benefit.