BubblesandCrashes

Click to edit Master title style,Click to edit Master text styles,Second level,Third level,Fourth level,Fifth level,*,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,1,Company X introduced a revolutionary wireless communication technology.,It not only 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 technology stock,About RCA: READ Bernheim et al. (1935)“The Security Market” Findings and Recommendations of a special staff of the 20,th,century fund - p. 475 and following,2,Story of RCA - 1920s,Company:,Radio Corporation of America,(RCA),Technolgoy:,Radio,Year:,1920s,It peaked at $ 397 in Feb. 1929, down to $ 2.62 in May 1932,Dec 25,Dec 50,(was 0,arbs,have to be out of the market,Competition,only,first, 0.,Hence, price would drop already at,t,13,incentive to sell out earlier,well defined density of bursting date,(,t,|,t,i,),for each arb.,Proposition 1: Trigger strategies.,Given c 0, arb,t,i,never sells out only for an instant. He stays out of the market at least until,t,i,+, sells out.,Arb,t,i,+, stays out until,t,i,+ 2, exits and so on.,By trading equilibrium, arb,t,i,stays out until,t,i,+, exits.,also illustrates failure of strategic complementarity,(pre-empt),if traders condition on calendar time,Proposition 1:,16,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*(t,0,)=,min,T,(,t,0,+,),t,0,+ ,h,(,t,|,t,i,)E,t,bubble|, (1-,h,(,t,|,t,i,) (,g - r,),p,t,17,introduction,preliminary analysis,public events,conclusion,price cascades and rebounds,model setup,persistence of bubbles,exogenous crashes,endogenous crashes,lack of common knowledge,18,Persistence of Bubbles,Proposition 1:,Suppose .,existence of a unique trading equilibrium,traders begin attacking after a delay of periods.,bubble does,not,burst due to endogenous selling prior to .,Proposition 2:,19,Sequential awareness,t,trader,t,i,t,i,-,since,t,i,t,0,+,Distribution of,t,0,t,0,t,0,+,since,t,i,t,0,t,i,t,k,Distribution of,t,0,+,(bursting of bubble if nobody attacks),t,trader,t,j,t,j,t,j,-,t,trader,t,k,_,20,Conjecture 1: Immediate attack,Bubble bursts at,t,0,+,when, traders are aware of the bubble,If,t,0,/(1-,e,-,),23,t,hazard rate of the bubble,h,= /(1-exp-(,t,i,+,+,-,t),),t,i,-,t,i,Conj. 2: Delayed attack,by arbitrary,Bubble bursts at,t,0,+, + ,/(1-,e,-,),bubble appreciation,bubble size,/(1-,e,-,),_,_,_,24,Endogenous crashes,Proposition 3:,Suppose .,unique,trading equilibrium.,traders begin attacking after a delay of * periods.,bubble,bursts,due to endogenous selling pressure at a size of,p,t,times,Proposition 3:,arbitrageurs eventually burst bubble but very late(bridge between traditional analysis and Proposition 1),25,Endogenous crashes,t,hazard rate of the bubble,h,= /(1-exp-(,t,i,+,+,-,t),),t,i,-,t,i,-,t,i,lower bound: (,g-r,)/,/(1-,e,-,),Bubble bursts at,t,0,+, + *,t,i,-, +,+*,t,i,+,+*,t,i,+*,optimal,conjecturedattack,bubble appreciation,bubble size,_,26,Endogenous crashes - deriving,*,In equilibrium trader,t,i,=,t,0,+, bursts the bubble.,When she sells his shares her support of,t,0,is ,t,i,-,t,i,hence his hazard rate is,h,= /(,1,-exp-,)(1),The bubble bursts at,t,i,=,t,0,+, + *, hence it bursts at a size of,e,gt,*(*),bubble appreciation/ size =,(,g-r+z,) / *(*) (2),equilibrium,h,(1),bubble appreciation,bubble size,(2),*,27,Comparative statics,Role of information dispersion, ,Prior distribution of,t,0,F(t,0,) = 1 - exp,-,t,0,the smaller , the larger *, the size of bubble, ,t,0,= 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,28,Lack of common knowledge,t,0,t,0,+ ,standard backwards induction cant be applied,t,0,+ ,everybody,knows of the,the bubble,traders,know of,the bubble,everybody knows that,everybody knows of the,bubble,t,0,+ 2,t,0,+ 3,everybody knows that,everybody knows that,everybody knows of,the bubble,(same reasoning applies for,traders),If one interprets,as difference in opinion,lack of common knowledge gets a different meaning too.,29,introduction,preliminary analysis,persistence of,bubbles,conclusion,price cascades and rebounds,synchronizing events,model setup,30,Role of synchronizing events (information),News may have an impact disproportionate 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.,31,Setting with synchronizing events,Focus on 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 became aware of the bubble more than,e,periods ago observe (look out for) this synchronizing event.,32,Synchronizing events - Market rebounds,Proposition 5:,In responsive equilibrium,Sell out,a) always at the time of a public event,t,e,b) after,t,i,+ *,(where * *),except,after a failed attack at,t,p,re-enter,the market for,t, (,t,e,t,e,- ,e,+,*).,Intuition for re-entering the market:,for,t,e,t,e,-,e,-,without public event, they would have learnt this only at,t,e,+,e,-,*.,the existence of bubble at,t,reveals that,t,0,t,-,* -,that is, no additional information is revealed till,t,e,- ,e,+,*,density that bubble bursts for endogenous reasons is zero.,Proposition 5:,33,introduction,preliminary analysis,persistence of,bubbles,public events,conclusion,model setup,price cascades,and,rebounds,34,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 ripe yet,price bounces back and the bubble is strengthened for some time.,35,Price cascades and rebounds (ctd.),Proposition 6: Sell out,a) after a price drop if ,i,p,(H,p,),b) after,t,i,+ *,(where * *),re-enter,the market after a rebound at,t,p,for,t, (,t,p,t,p,- ,p,+,*).,attack is costly, since price might jump 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:,36,Conclusion of Bubbles 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, since,it might serve as a synchronization device.,Rebound,can occur after a failed attack, which temporarily strengthens the bubble.,(technological revolutions etc.),37,Hedge Funds and the Technology Bubble,Markus K. Brunnermeier,Princeton University,Stefan Nagel,London Business School,38,reasons for persistence,data,empirical results,conclusion,39,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,reluctant 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 Security Market” Findings and Recommendations of a special staff of the 20,th,century fund - p. 475 and following,40,data,reasons for persistence,empirical results,conclusion,41,Data,Hedge fund stock holdings,Quarterly 13 F filings to SEC,mandatory for all institutional investors,with holdings in U.S. stocks 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 revolutions etc.),42,data,conclusion,reasons for persistence,empirical results,did hedge funds ride bubble?,did hedge funds timing pay off?,43,Did hedge funds ride the bubble?,44,Fig. 4a: Weight of technology stocks in hedge fund portfolios versus weight in market portfolio,Did Soros etc. ride the bubble?,45,Fig. 4b: Funds flows, three-month moving average,Fund in- and outflows,46,Figure 5. Average share of outstanding equity held by hedge funds around price peaks of individual stocks,Did hedge funds time stocks?,47,Figure 6: Performance of a copycat fund that replicates hedge fund holdings in the NASDAQ high P/S segment,Did hedge funds timing pay off?,48,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,(technological revolutions etc.),49,