1、1,Bubbles and Crashes,Dilip Abreu Princeton University,Markus K. Brunnermeier Princeton University,Hedge Funds and the Technology Bubble,Markus K. Brunnermeier Princeton University,Stefan Nagel London Business School,2,Company X introduced a revolutionary wireless communication technology. It not on
2、ly provided support for such a technology but also provided the informational content itself. Its IPO price was $1.50 per share. Six years later it was traded at $ 85.50 and in the seventh year it hit $ 114.00. The P/E ratio got as high as 73. The company never paid dividends.,Story of a typical tec
3、hnology stock,About RCA: READ Bernheim et al. (1935)“The Security Market” Findings and Recommendations of a special staff of the 20th century fund - p. 475 and following,3,Story of RCA - 1920s,Company: Radio Corporation of America (RCA) Technolgoy: Radio Year: 1920sIt peaked at $ 397 in Feb. 1929, d
4、own to $ 2.62 in May 1932,Dec 25,Dec 50,(was $ 14 till June 1945),4,Internet bubble? - 1990s,NASDAQ Combined Composite Index,NEMAX All Share Index (German Neuer Markt),38 day average,Chart (Jan. 98 - Dec. 00),38 day average,Chart (Jan. 98 - Dec. 00) in Euro,Loss of ca. 60 % from high of $ 5,132,Loss
5、 of ca. 85 % from high of Euro 8,583,Why do bubbles persist? Do professional traders ride the bubble or attack the bubble (go short)? What happened in March 2000?,Was it a bubble?,If it was a bubble, the question arises ,Moving right along to the 1990s,5,Do (rational) professional ride the bubble?,S
6、outh Sea Bubble (1710 - 1720) Isaac Newton 04/20/1720 sold shares at 7,000 profiting 3,500 re-entered the market later - ended up losing 20,000 “I can calculate the motions of the heavenly bodies, but not the madness of people”,Internet Bubble (1992 - 2000) Druckenmiller of Soros Quantum Fund didnt
7、think that the party would end so quickly. “We thought it was the eighth inning, and it was the ninth.” Julian Robertson of Tiger Fund refused to invest in internet stocks,6,“The moral of this story is that irrational market can kill you Julian said This is irrational and I wont play and they carrie
8、d him out feet first. Druckenmiller said This is irrational and I will play and they carried him out feet first.” Quote of a financial analyst, New York Times April, 29 2000,Pros dilemma,7,Classical Question,Suppose behavioral trading leads to mispricing.Can mispricings or bubbles persist in the pre
9、sence of rational arbitrageurs?What type of information can lead to the bursting of bubbles?,8,Main Literature,Keynes (1936) bubble can emerge “It might have been supposed that competition between expert professionals, possessing judgment and knowledge beyond that of the average private investor, wo
10、uld correct the vagaries of the ignorant individual left to himself.” Friedman (1953), Fama (1965) Efficient Market Hypothesis no bubbles emerge “If there are many sophisticated traders in the market, they may cause these “bubbles” to burst before they really get under way.”,Limits to Arbitrage Nois
11、e trader risk versus Synchronization risk Shleifer & Vishny (1997), DSSW (1990 a & b) Bubble Literature Symmetric information - Santos & Woodford (1997) Asymmetric information Tirole (1982), Allen et al. (1993), Allen & Gorton (1993),9,Timing Game - Synchronization,(When) will behavioral traders be
12、overwhelmed by rational arbitrageurs? Collective selling pressure of arbitrageurs more than suffices to burst the bubble. Rational arbitrageurs understand that an eventual collapse is inevitable. But when? Delicate, difficult, dangerous TIMING GAME !,10,Elements of the Timing Game,Coordination at le
13、ast 0 arbs have to be out of the market Competition only first 1 arbs receive pre-crash price. Profitable ride ride bubble (stay in the market) as long as possible. Sequential Awareness A Synchronization Problem arises! Absent of sequential awareness competitive element dominates and bubble burst im
14、mediately. With sequential awareness incentive to TIME THE MARKET leads to “delayed arbitrage” and persistence of bubble.,11,model setup,introduction,preliminary analysis,persistence of bubbles,public events,conclusion,price cascades and rebounds,12,Model setup,t,t0,t0+ ,t0 + ,random starting point,
15、t0+ ,maximum life-span of the bubble , traders are aware of the bubble,all traders are aware of the bubble,bubble bursts for exogenous reasons,0 paradigm shift - internet 90s - railways - etc.,common action of arbitrageurs sequential awareness (random t0 with F(t0) = 1 - exp-t0).,1,1/,pt,13,Payoff s
16、tructure,Cash Payoffs (difference) Sell one share at t- instead of at t. pt- e r - ptwhere pt =Execution price at the time of bursting.,prior to the crash after the crash,for first random orders up to all other orders,14,Payoff structure (ctd.), Trading,Small transactions costs cert Risk-neutrality
17、but max/min stock position max long position max short position due to capital constraints, margin requirements etc. Definition 1: trading equilibrium Perfect Bayesian Nash Equilibrium Belief restriction: trader who attacks at time t believes that all traders who became aware of the bubble prior to
18、her also attack at t.,Definition 1:,15,introduction,persistence of bubbles,public events,conclusion,price cascades and rebounds,model setup,Preliminary analysis,preemption motive - trigger strategies,sell out condition,16,Trigger Strategies,Bursting date T*(t0)=minT(t0 + ), t0 + Role of Preemption M
19、otive Rules out coordinated sell out on Friday July 13th. Bubble never bursts with strictly positive prob. at some t13. Suppose it would, then selling pressure would exceed with prob0. Hence, price would drop already at t13 incentive to sell out earlier well defined density of bursting date (t|ti) f
20、or each arb. Proposition 1: Trigger strategies. Given c 0, arb ti never sells out only for an instant. He stays out of the market at least until ti + sells out. Arb ti + stays out until ti + 2 exits and so on. By trading equilibrium, arb ti stays out until ti + exits.,also illustrates failure of str
21、ategic complementarity,(pre-empt),if traders condition on calendar time,Proposition 1:,17,Sell out condition for periods,sell out at t if,appreciation rate,benefit of attacking,cost of attacking,RHS converges to (g-r) as t ,bursting date T*(t0)=minT(t0 + ), t0 + ,h(t|ti)Etbubble| (1-h(t|ti) (g - r)p
22、t ,18,introduction,preliminary analysis,public events,conclusion,price cascades and rebounds,model setup,persistence of bubbles,exogenous crashes,endogenous crashes,lack of common knowledge,19,Persistence of Bubbles,Proposition 1: Suppose . existence of a unique trading equilibrium traders begin att
23、acking after a delay of periods. bubble does not burst due to endogenous selling prior to .,Proposition 2:,20,Sequential awareness,t,trader ti,ti - ,since ti t0 + ,Distribution of t0,t0,t0+,since ti t0,ti,tk,_,21,Conjecture 1: Immediate attack, Bubble bursts at t0 + when traders are aware of the bub
24、ble,/(1-e-),t,ti - ,ti - ,ti + ,ti,22,Conj. 1 (ctd.): Immediate attack,t, Bubble bursts at t0 + ,Distribution of t0 + ,Bubble bursts for sure!,hazard rate of the bubbleh = /(1-exp-(ti + - t),/(1-e-),ti - ,ti - ,ti + ,ti,Distribution of t0,23,Conj. 1 (ctd.): Immediate attack,t, Bubble bursts at t0 +
25、,Bubble bursts for sure!,hazard rate of the bubble h = /(1-exp-(ti + - t),/(1-e-),ti - ,ti - ,ti + ,ti,Distribution of t0,Recall the sell out condition:,_,24,t,hazard rate of the bubble h = /(1-exp-(ti + + - t),ti - ,ti,Conj. 2: Delayed attack by arbitrary , Bubble bursts at t0 + + t0 + ,ti - + +,ti
26、 + +,ti +,optimal to delay attack even more,conjectured attack, attack is never successful bubble bursts for exogenous reasons at t0 + ,lower bound: (g-r)/ /(1-e-),bubble appreciation bubble size,/(1-e-),_,_,_,25,Endogenous crashes,Proposition 3: Suppose . unique trading equilibrium. traders begin a
27、ttacking after a delay of * periods. bubble bursts due to endogenous selling pressure at a size of pt times,Proposition 3:,arbitrageurs eventually burst bubble but very late (bridge between traditional analysis and Proposition 1),26,Endogenous crashes,t,hazard rate of the bubble h = /(1-exp-(ti + +
28、- t),ti - ,ti - ,ti,lower bound: (g-r)/ /(1-e-), Bubble bursts at t0 + + *,ti - + +*,ti + +*,ti +*,optimal,conjectured attack,bubble appreciation bubble size,_,27,Endogenous crashes - deriving *,In equilibrium trader ti = t0 + bursts the bubble. When she sells his shares her support of t0 is ti - ,
29、ti, hence his hazard rate is h = /(1-exp-) (1) The bubble bursts at ti = t0 + + *, hence it bursts at a size of egt *(*) bubble appreciation/ size = (g-r+z) / *(*) (2),equilibrium h,(1),bubble appreciation bubble size,(2),*,28,Comparative statics,Role of information dispersion , Prior distribution o
30、f t0 F(t0) = 1 - exp-t0 the smaller , the larger *, the size of bubble t0 = 0, no info dispersion no bubble 0 distributions uniform size is (g-r) Dispersion of opinion as bubbles size for exogenous crash Role of momentum traders same as for , More synchronization required,29,Lack of common knowledge
31、,t0,t0 + , standard backwards induction cant be applied,t0 + ,everybody knows of thethe bubble, traders know ofthe bubble,everybody knows that everybody knows of the bubble,t0 + 2,t0 + 3,everybody knows that everybody knows that everybody knows of the bubble,(same reasoning applies for traders),If o
32、ne interprets as difference in opinion,lack of common knowledge gets a different meaning too.,30,introduction,preliminary analysis,persistence of bubbles,conclusion,price cascades and rebounds,synchronizing events,model setup,31,Role of synchronizing events (information),News may have an impact disp
33、roportionate to any intrinsic informational (fundamental) content. News can serve as a synchronization device. Fads & fashion in information Which news should traders coordinate on? When “synchronized attack” fails, the bubble is temporarily strengthened.,32,Setting with synchronizing events,Focus o
34、n news with no informational content (sunspots) Synchronizing events occur with Poisson arrival rate . Note that the pre-emption argument does not apply since event occurs with zero probability. Arbitrageurs who are aware of the bubble become increasingly worried about it over time. Only traders who
35、 became aware of the bubble more than e periods ago observe (look out for) this synchronizing event.,33,Synchronizing events - Market rebounds,Proposition 5: In responsive equilibrium Sell out a) always at the time of a public event te,b) after ti + * (where * te - e - without public event, they wou
36、ld have learnt this only at te + e - *. the existence of bubble at t reveals that t0 t - * - that is, no additional information is revealed till te - e + * density that bubble bursts for endogenous reasons is zero.,Proposition 5:,34,introduction,preliminary analysis,persistence of bubbles,public eve
37、nts,conclusion,model setup,price cascades and rebounds,35,Price cascades and rebounds,Price drop as a synchronizing event. through psychological resistance line by more than, say 5 % Exogenous price drop after a price drop if bubble is ripe bubble bursts and price drops further. if bubble is not rip
38、e yet price bounces back and the bubble is strengthened for some time.,36,Price cascades and rebounds (ctd.),Proposition 6: Sell out a) after a price drop if i p(Hp)b) after ti + * (where * *) ,re-enter the market after a rebound at tp for t (tp , tp - p + *). attack is costly, since price might jum
39、p back only arbitrageurs who became aware of the bubble more than p periods ago attack the bubble. after a rebound, an endogenous crash can be temporarily ruled out and hence, arbitrageurs re-enter the market. Even sell out after another price drop is less likely.,Proposition 6:,37,Conclusion of Bub
40、bles and Crashes,Bubbles Dispersion of opinion among arbitrageurs causes a synchronization problem which makes coordinated price corrections difficult. Arbitrageurs time the market and ride the bubble. Bubbles persist Crashes can be triggered by unanticipated news without any fundamental content, si
41、nce it might serve as a synchronization device. Rebound can occur after a failed attack, which temporarily strengthens the bubble.,(technological revolutions etc.),38,Hedge Funds and the Technology Bubble,Markus K. Brunnermeier Princeton University,Stefan Nagel London Business School,http:/www.princ
42、eton.edu/markus,39,reasons for persistence,data,empirical results,conclusion,40,Unawareness of Bubble Rational speculators perform as badly as others when market collapses. Limits to Arbitrage Fundamental risk Noise trader risk Synchronization risk Short-sale constraint Rational speculators may be r
43、eluctant to go short overpriced stocks. Predictable Investor Sentiment AB (2003), DSSW (JF 1990) Rational speculators may want to go long overpriced stock and try to go short prior to collapse.,Why Did Rational Speculation Fail to Prevent the Bubble ?,About RCA: READ Bernheim et al. (1935)“The Secur
44、ity Market” Findings and Recommendations of a special staff of the 20th century fund - p. 475 and following,41,data,reasons for persistence,empirical results,conclusion,42,Data,Hedge fund stock holdings Quarterly 13 F filings to SEC mandatory for all institutional investors with holdings in U.S. sto
45、cks of more than $ 100 million domestic and foreign at manager level Caveats: No short positions 53 managers with CDA/Spectrum data excludes 18 managers b/c mutual business dominates incl. Soros, Tiger, Tudor, D.E. Shaw etc. Hedge fund performance data HFR hedge fund style indexes,(technological rev
46、olutions etc.),43,data,conclusion,reasons for persistence,empirical results,did hedge funds ride bubble?,did hedge funds timing pay off?,44,Did hedge funds ride the bubble?,45,Fig. 4a: Weight of technology stocks in hedge fund portfolios versus weight in market portfolio,Did Soros etc. ride the bubb
47、le?,46,Fig. 4b: Funds flows, three-month moving average,Fund in- and outflows,47,Figure 5. Average share of outstanding equity held by hedge funds around price peaks of individual stocks,Did hedge funds time stocks?,48,Figure 6: Performance of a copycat fund that replicates hedge fund holdings in th
48、e NASDAQ high P/S segment,Did hedge funds timing pay off?,49,Conclusion,Hedge funds were riding the bubble Short sales constraints and “arbitrage” risk are not sufficient to explain this behavior. Timing bets of hedge funds were well placed. Outperformance! Rules out unawareness of bubble. Suggests predictable investor sentiment. Riding the bubble for a while may have been a rational strategy. Supports bubble-timing models,
