BubblesandCrashes

1、1Bubbles and CrashesDilip AbreuPrinceton UniversityMarkus K. BrunnermeierPrinceton UniversityHedge Funds and the Technology Bubble.Markus K. BrunnermeierPrinceton University.Stefan NagelLondon Business School2Company X introduced a revolutionary wireless communication technology.It not only provided

2、 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 stockA

3、bout RCA: READ Bernheim et al. (1935)“The Security Market” Findings and Recommendations of a special staff of the 20th century fund - p. 475 and following3Story of RCA - 1920sCompany: Radio Corporation of America (RCA) Technolgoy: RadioYear:1920sIt peaked at $ 397 in Feb. 1929, down to $ 2.62 in May

4、 1932, 050100150200250300350400450time$Dec 25Dec 50(was Druckenmiller of Soros Quantum Fund didnt think that the party would end so quickly.V“We thought it was the eighth inning, and it was the ninth.” Julian Robertson of Tiger Fund refused to invest in internet stocks6“The moral of this story is th

5、at irrational market can kill you Julian said This is irrational and I wont play and they carried 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 2000Pros dilemma7Classical QuestionC

6、an mispricings or bubbles persist in the presence of rational arbitrageurs?What type of information can lead to the bursting of bubbles?8Main LiteratureKeynes (1936) “It might have been supposed that competition between expert professionals, possessing judgment and knowledge beyond that of the avera

7、ge private investor, would correct the vagaries of the ignorant individual left to himself.”Friedman (1953), Fama (1965) Efficient Market Hypothesis “If there are many sophisticated traders in the market, they may cause these “bubbles” to burst before they really get under way.”.Limits to ArbitrageN

8、oise trader risk versus Synchronization riskShleifer & Vishny (1997), DSSW (1990 a & b).Bubble LiteratureSymmetric information - Santos & Woodford (1997)Asymmetric information Tirole (1982), Allen et al. (1993), Allen & Gorton (1993) 9Timing Game - Synchronization(When) will behavior

9、al traders be 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 !10Elements of the Timing GameKCoordinat

10、ionat least 0 arbs have to be out of the marketLCompetition only first 0.Hence, price would drop already at t13 incentive to sell out earlierwell defined density of bursting date (t|ti) for each arb.Proposition 1: Trigger strategies.Given c 0, arb ti never sells out only for an instant. He stays out

11、 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 strategic complementarity(pre-empt)if traders condition on calendar timeProposition 1:17Sell out condition for periodssel

12、l out at t ifappreciation ratebenefit of attackingcost of attackingRHS converges to (g-r) as t bursting date T*(t0)=minT(t0 + ), t0 + h(t|ti)Etbubble| (1-h(t|ti) (g - r)pt 18introductionpreliminary analysispublic eventsconclusionprice cascades and reboundsmodel setuppersistence of bubblesexogenous c

13、rashesendogenous crasheslack of common knowledge19Persistence of BubblesProposition 1: Suppose .existence of a unique trading equilibriumtraders begin attacking after a delay of periods.bubble does not burst due to endogenous selling prior to . Proposition 2:20Sequential awarenessttrader titi - sinc

14、e ti t0 + Distribution of t0t0t0+since ti t0titkDistribution of t0+(bursting of bubble if nobody attacks)ttrader tjtjtj - ttrader tk_21 Conjecture 1: Immediate attack Bubble bursts at t0 + when traders are aware of the bubbleIf t0 /(1-e-) 24thazard rate of the bubbleh = /(1-exp-(ti + + - t)ti - tiCo

15、nj. 2: Delayed attack by arbitrary Bubble bursts at t0 + + /(1-e-)bubble appreciation bubble size/(1-e-)_25Endogenous crashesProposition 3: Suppose .unique trading equilibrium.traders begin attacking after a delay of * periods.bubble bursts due to endogenous selling pressure at a size of pt timesPro

16、position 3:arbitrageurs eventually burst bubble but very late(bridge between traditional analysis and Proposition 1)26Endogenous crashesthazard rate of the bubbleh = /(1-exp-(ti + + - t)ti - ti - tilower bound: (g-r)/ /(1-e-) Bubble bursts at t0 + + *ti - + +*ti + +*ti +*optimalconjecturedattackbubb

17、le appreciation bubble size_27Endogenous crashes - deriving * In equilibrium trader ti = t0 + bursts the bubble.When she sells his shares her support of t0 is ti - , 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 appreciat

18、ion/ size = (g-r+z) / *(*) (2)equilibrium h(1)bubble appreciation bubble size(2)*28Comparative staticsRole of information dispersion , Prior distribution of t0 F(t0) = 1 - exp-t0the smaller , the larger *, the size of bubble t0 = 0, no info dispersion no bubble 0 distributions uniform size is (g-r)

19、Dispersion of opinion as bubbles size for exogenous crash Role of momentum traders same as for More synchronization required29Lack of common knowledget0t0 + t0 + everybody knows of the the bubble traders know of the bubbleeverybody knows thateverybody knows of thebubblet0 + 2t0 + 3everybody knows th

20、ateverybody knows thateverybody 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.30introductionpreliminary analysispersistence of bubblesconclusionprice cascades and reboundssynchronizing eventsmo

21、del setup31 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 informationWhich news should traders coordinate on?When “synchronized attack” fails, th

22、e bubble is temporarily strengthened. 32 Setting with synchronizing eventsFocus 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 awar

23、e 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.33Synchronizing events - Market reboundsProposition 5: In responsive equilibriumSell out a) always at the time of a publi

24、c event te, b) after ti + * (where * *) , except after a failed attack at tp , re-enter the market for t (te , te - e + *).Intuition for re-entering the market:for te te - e - without public event, they would have learnt this only at te + e - *. the existence of bubble at t reveals that t0 t - * - t

25、hat is, no additional information is revealed till te - e + * density that bubble bursts for endogenous reasons is zero.Proposition 5:34introductionpreliminary analysispersistence of bubblespublic eventsconclusionmodel setupprice cascades and rebounds35Price cascades and reboundsPrice drop as a sync

26、hronizing event.through psychological resistance lineby more than, say 5 %Exogenous price drop after a price dropif 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.36Price cascades and rebounds (ctd.)Propo

27、sition 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 jump back only arbitrageurs who became aware of the bubble more than p periods ago attack the bubble. after a reboun

28、d, 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 6:37Conclusion of Bubbles and CrashesBubblesDispersion of opinion among arbitrageurs causes a synchronization problem which makes coordina

29、ted price corrections difficult.Arbitrageurs time the market and ride the bubble. Bubbles persistCrashescan be triggered by unanticipated news without any fundamental content, sinceit might serve as a synchronization device.Reboundcan occur after a failed attack, which temporarily strengthens the bu

30、bble.(technological revolutions etc.)38Hedge Funds and the Technology BubbleMarkus K. BrunnermeierPrinceton UniversityStefan NagelLondon Business School39reasons for persistencedataempirical resultsconclusion40. Unawareness of Bubble Rational speculators perform as badly as others when market collap

31、ses. 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

32、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 20th century fund - p. 475 and following41datareasons for persistenceempirical resultsconclusion4

33、2DataHedge fund stock holdingsQuarterly 13 F filings to SECmandatory for all institutional investorswith holdings in U.S. stocks of more than $ 100 milliondomestic and foreignat manager levelCaveats: No short positions53 managers with CDA/Spectrum dataexcludes 18 managers b/c mutual business dominat

34、esincl. Soros, Tiger, Tudor, D.E. Shaw etc.Hedge fund performance dataHFR hedge fund style indexes(technological revolutions etc.)43dataconclusionreasons for persistenceempirical resultsdid hedge funds ride bubble?did hedge funds timing pay off?44Did hedge funds ride the bubble?Fig. 2: Weight of NAS

35、DAQ technology stocks (high P/S) in aggregate hedge fund portfolio versus weightin market portfolio. 0.000.000.250.300.35Mar-98 Jun-98 Sep-98 Dec-98 Mar-99 Jun-99 Sep-99 Dec-99 Mar-00 Jun-00 Sep-00 Dec-00Hegde Fund PortfolioMarket PortfolioProportion invested in NASDAQ high P/S stocksNAS

36、DAQ Peak45Fig. 4a: Weight of technology stocks in hedge fund portfolios versus weight in market portfolio0.000.200.400.600.80Mar-98 Jun-98 Sep-98 Dec-98 Mar-99 Jun-99 Sep-99 Dec-99 Mar-00 Jun-00 Sep-00 Dec-00Proportion invested in NASDAQ high P/S stocksZweig-DiMennaSorosHusicMarket PortfolioOmegaTigerDid Soros etc. ride the bubble?46Fig. 4b: Funds flows, t