1 Bubbles and Crashes q Dilip Abreu Princeton

1 Bubbles and Crashes q Dilip Abreu Princeton University q Markus K. Brunnermeier Princeton University Hedge Funds and the Technology Bubble q Markus K. Brunnermeier q Stefan Nagel Princeton University London Business School

2 Story of a typical technology stock q q q Company X introduced a revolutionary wireless communication technology. It not only provided support for such a technology but also provided the informational content itself. It’s 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.

3 Story of RCA q q q Company: (RCA) Technolgoy: Year: Dec 25 Ø - 1920’s Radio Corporation of America Radio 1920’s Dec 50 It peaked at $ 397 in Feb. 1929, down to $ 2. 62 in May 1932,

4 Internet bubble? NASDAQ Combined Composite Index Chart (Jan. 98 - Dec. 00) 38 day average Loss of ca. 60 % from high of $ 5, 132 q q q - 1990’s NEMAX All Share Index (German Neuer Markt) Chart (Jan. 98 - Dec. 00) in Euro 38 day average Loss 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?

5 Do (rational) professional ride the bubble? q South Sea Bubble (1710 - 1720) Ø Isaac Newton q 04/20/1720 sold shares at £ 7, 000 profiting £ 3, 500 q re-entered the market later - ended up losing £ 20, 000 q “I can calculate the motions of the heavenly bodies, but not the madness of people” q. Internet Bubble (1992 - 2000) ØDruckenmiller of Soros’ Quantum Fund didn’t think that the party would end so quickly. V “We thought it was the eighth inning, and it was the ninth. ” ØJulian Robertson of Tiger Fund refused to invest in internet stocks

6 Pros’ dilemma Ø “The moral of this story is that irrational market can kill you … Ø Julian said ‘This is irrational and I won’t play’ and they carried him out feet first. Ø 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

7 Classical Question Ø Suppose behavioral trading leads to mispricing. q Can mispricings or bubbles persist in the presence of rational arbitrageurs? q What type of information can lead to the bursting of bubbles?

8 Main Literature q Keynes (1936) Ø ) bubble can emerge “It might have been supposed that competition between expert professionals, possessing judgment and knowledge beyond that of the average private investor, would correct the vagaries of the ignorant individual left to himself. ” q Friedman (1953), Fama (1965) Efficient Market Hypothesis ) no bubbles emerge Ø “If there are many sophisticated traders in the market, they may cause these “bubbles” to burst before they really get under way. ” q Limits to Arbitrage Ø Noise trader risk versus Synchronization risk Shleifer & Vishny (1997), DSSW (1990 a & b) q Bubble Literature Ø Symmetric information - Santos & Woodford (1997) Ø Asymmetric information Tirole (1982), Allen et al. (1993), Allen & Gorton (1993)

9 Timing Game - Synchronization q (When) will behavioral traders be overwhelmed by rational arbitrageurs? q Collective selling pressure of arbitrageurs more than suffices to burst the bubble. q Rational arbitrageurs understand that an eventual collapse is inevitable. But when? q Delicate, difficult, dangerous TIMING GAME !

10 Elements of the Timing Game q q Coordination at least > 0 arbs have to be ‘out of the market’ Competition only first < 1 arbs receive pre-crash price. Profitable ride bubble as long as possible. Sequential Awareness A Synchronization Problem arises! Ø Ø Absent of sequential awareness competitive element dominates ) and bubble burst immediately. With sequential awareness incentive to TIME THE MARKET leads to ) “delayed arbitrage” ) persistence of bubble.

11 Wile E. Coyote Effect

12 introduction model setup preliminary analysis persistence of bubbles public events price cascades and rebounds conclusion

13 common action of arbitrageurs sequential awareness (random t 0 with F(t 0) = 1 - exp{-lt 0}). q q pt 1 1/ t 0 0 paradigm shift - internet 90’s - railways - etc. t 0 + random traders starting are aware of point the bubble t 0+ all traders are aware of the bubble bursts for exogenous reasons maximum life-span of the bubble t

14 Payoff structure q Endogenous price path Ø Focus on “when does bubble burst” Ø Only random variable t 0, all other are CK q Cash Payoffs (difference) prior to the crash Ø Sell ‘one share’ at t- instead of at t. pt- e r - pt after the crash where pt = Ø Execution price at the time of bursting pre crash-price for first random orders up to

Payoff structure (ctd. ), Trading q Small transactions costs cert q Risk-neutrality but max/min stock position Ø max long position Ø max short position Ø due to capital constraints, margin requirements etc. q Definition 1: trading equilibrium Definition 1: Ø Perfect Bayesian Nash Equilibrium Ø Belief restriction: trader who attacks at time t believes that all traders who became aware of the bubble prior to her also attack at t. 15

16 introduction model setup Preliminary analysis preemption motive - trigger strategies sell out condition persistence of bubbles public events price cascades and rebounds conclusion

17 Sell out condition for ! 0 periods q sell out at t if appreciation rate h(t|ti)Et[bubble| • ] ¸ (1 - h(t|ti)) (g - r)pt benefit of attacking cost of attacking bursting date T*(t 0)=min{T(t 0 + ), t 0 + } RHS converges to ! [(g-r)] as t ! 1

18 introduction model setup preliminary analysis persistence of bubbles exogenous crashes endogenous crashes lack of common knowledge public events price cascades and rebounds conclusion

19 Sequential awareness Distribution of t 0+ (bursting of bubble if nobody attacks) trader ti ti - since ti · t 0 + ti t since ti ¸ t 0 _ t 0 +

20 Sequential awareness Distribution of t 0+ (bursting of bubble if nobody attacks) Distribution of t 0 trader ti ti - since ti · t 0 + ti t since ti ¸ t 0 trader tj tj tj - t 0 t _ t 0 +

21 Sequential awareness Distribution of t 0+ (bursting of bubble if nobody attacks) Distribution of t 0 trader ti ti - since ti · t 0 + ti t since ti ¸ t 0 trader tj tj tj - t trader tk t 0 tk _ t 0 + t

22 Conjecture: Immediate attack ) Bubble bursts at t 0 + when traders are aware of the bubble ti - ti t

23 Conjecture: Immediate attack ) Bubble bursts at t 0 + when traders are aware of the bubble ti - If t 0< ti - , the bubble would have burst already. ti t

24 Conjecture 1: Immediate attack ) Bubble bursts at t 0 + when traders are aware of the bubble Distribution of t 0 /(1 -e- ) ti - If t 0< ti - , the bubble would have burst already. ti t

25 Conjecture 1: Immediate attack ) Bubble bursts at t 0 + when traders are aware of the bubble Distribution of t 0 + /(1 -e- ) ti - If t 0< ti - , the bubble would have burst already. ti ti + t

26 Conj. 1 (ctd. ): Immediate attack ) Bubble bursts at t 0 + Distribution of t 0 /(1 -e- ) ti - ti ti + t

27 Conj. 1 (ctd. ): Immediate attack ) Bubble bursts at t 0 + Distribution of t 0 /(1 -e- ) ti - ti ti + Bubble bursts for sure! t

28 Conj. 1 (ctd. ): Immediate attack ) Bubble bursts at t 0 + Distribution of t 0 /(1 -e- ) ti - ti ti + Bubble bursts for sure! t

29 Conj. 1 (ctd. ): Immediate attack ) Bubble bursts at t 0 + Distribution of t 0 /(1 -e- ) ti - ti ti + Bubble bursts for sure! t

30 Conj. 1 (ctd. ): Immediate attack ) Bubble bursts at t 0 + hazard rate of the bubble h = /(1 -exp{- (ti + - t)}) Distribution of t 0 /(1 -e- ) ti - ti ti + Bubble bursts for sure! t

31 Conj. 1 (ctd. ): Immediate attack Recall the sell out condition: ) Bubble bursts at t 0 + hazard rate of the bubble h = /(1 -exp{- (ti + - t)}) Distribution of t 0 /(1 -e- ) ti - ti ti + Bubble bursts for sure! t

32 Conj. 1 (ctd. ): Immediate attack Recall the sell out condition: ) Bubble bursts at t 0 + hazard rate of the bubble h = /(1 -exp{- (ti + - t)}) bubble appreciation / bubble size _ lower bound: (g-r)/ > /(1 -e- ) Distribution of t 0 /(1 -e- ) ti - ti ti + t optimal time ) “delayed attack is optimal” to attack ti+ i

_ _ 33 Endogenous crashes for large enough (i. e. ) q Proposition 3: Suppose . Ø ‘unique’ trading equilibrium. Ø traders begin attacking after a delay of tau* periods. Ø bubble bursts due to endogenous selling pressure at a size of pt times

34 Endogenous crashes ) Bubble bursts at t 0 + + * hazard rate of the bubble h = /(1 -exp{- (ti + + ’ - t)}) bubble appreciation bubble size _ lower bound: (g-r)/ > /(1 -e- ) ti - ti ti - + + * conjectured attack ti + * ti + + * optimal t

_ 35 _ Exogenous crash for low (i. e. ) q Proposition 1: 2: Suppose . Ø existence of a unique trading equilibrium Ø traders begin attacking after a delay of periods. Ø bubble does not burst due to endogenous selling prior to.

36 Delayed attack by ' _ ) Bubble bursts at min{t 0 + + ’, t 0 + } bubble appreciation bubble size hazard rate for t 0 + + ’ h = /(1 -exp{- (ti + + ’ - t)}) _ lower bound: (g-r)/ < /(1 -e- ) ti - ti ti + ’ ti + + ’ t

37 Delayed attack by ' _ ) Bubble bursts at min{t 0 + + ’, t 0 + } bubble appreciation bubble size hazard rate for t 0_+ h = /(1 -exp{- (ti + - t)}) _ lower bound: (g-r)/ > /(1 -e- ) ti - ti attack ti + ’ ti + _ ) bubble bursts for exogenous reasons at t 0 + t

38 Lack of common knowledge ) standard backwards induction can’t be applied endogenous burst t 0+ + * t 0 + everybody knows of the bubble traders know of the bubble t 0 + 2 everybody knows that everybody knows of the bubble t 0 + 3 … everybody knows that everybody knows of the bubble (same reasoning applies for traders) …

39 introduction model setup preliminary analysis persistence of bubbles synchronizing events price cascades and rebounds conclusion

40 Role of synchronizing events (information) q News may have an impact disproportionate to any intrinsic informational (fundamental) content. Ø News can serve as a synchronization device. q Fads & fashion in information Ø Which news should traders coordinate on? q When “synchronized attack” fails, the bubble is temporarily strengthened.

41 Setting with synchronizing events Ø Focus on news with no informational content (sunspots) Ø Synchronizing events occur with Poisson arrival rate . q Note that the pre-emption argument does not apply since event occurs with zero probability. Ø Arbitrageurs who are aware of the bubble become increasingly worried about it over time. q Only traders who became aware of the bubble more than e periods ago observe (look out for) this synchronizing event.

42 Synchronizing events - Market rebounds q Proposition 5: In ‘responsive equilibrium’ Sell out a) always at the time of a public event te, b) after ti + ** (where **< *) , except after a failed attack at tp , re-enter the market for t 2 (te , te - e + **). q Intuition for re-entering the market: Ø for te < t 0 + + e attack fails, agents learn t 0 > te - Ø without public event, they would have learnt this only at te + e - **. q the existence of bubble at t reveals that t 0 > t - ** - q that is, no additional information is revealed till te - e + ** q density that bubble bursts for endogenous reasons is zero.

43 introduction model setup preliminary analysis persistence of bubbles public events price cascades and rebounds conclusion

44 Price cascades and rebounds q Price drop as a synchronizing event. Ø through psychological resistance line Ø by more than, say 5 % q Exogenous price drop Ø after a price drop q if bubble is ripe ) bubble bursts and price drops further. q if bubble is not ripe yet ) price bounces back and the bubble is strengthened for some time.

45 Price cascades and rebounds (ctd. ) q 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 2 (tp , tp - p + ***). Ø attack is costly, since price might jump back ) only arbitrageurs who became aware of the bubble more than p periods ago attack bubble. Ø after a rebound, an endogenous crash can be temporarily ruled out and hence, arbitrageurs re-enter the market. Ø Even sell out after another price drop is less likely.

Conclusion of Bubbles and Crashes q Bubbles Ø Dispersion of opinion among arbitrageurs causes a synchronization problem which makes coordinated price corrections difficult. Ø Arbitrageurs time the market and ride the bubble. Ø ) Bubbles persist q Crashes Ø can be triggered by unanticipated news without any fundamental content, since Ø it might serve as a synchronization device. q Rebound Ø can occur after a failed attack, which temporarily strengthens the bubble. 46

47 Extensions q International finance Ø International finance – carry trades Ø Dynamic currency attack models (Gara Alfonso 2007) q Any form of mispricing (AB 2002) Ø Ø Ø x 2 [-x, +x] positive or negative g=r holding costs cx (if x 0) Price correction would occur at t 0 + 1 q Hence, assumed (¢) declines after t 0 + ’

48 (1+ ) ert p, v ert + p 0 = 1 (1 - ) ert - 1/ t 0 + 0 t 0 random 0 arbs are starting aware of the point mispricing t 0+ all arbitrageurs are aware of the mispricing _ t 0+ t price correction for exogenous reasons

49 Hedge Funds and the Technology Bubble q Markus K. Brunnermeier Princeton University q Stefan Nagel London Business School http: //www. princeton. edu/~markus

50 reasons for persistence data empirical results conclusion

Why Did Rational Speculation Fail to Prevent the Bubble ? 1. Unawareness of Bubble ) Rational speculators perform as badly as others when market collapses. 2. Limits to Arbitrage Ø Ø Fundamental risk Noise trader risk Synchronization risk Short-sale constraint ) Rational speculators may be reluctant to go short overpriced stocks. 3. Predictable Investor Sentiment Ø AB (2003), DSSW (JF 1990) ) Rational speculators may want to go long overpriced stock and try to go short prior to collapse. 51

52 reasons for persistence data empirical results conclusion

Data q Hedge fund stock holdings Ø Quarterly 13 F filings to SEC Ø mandatory for all institutional investors q with holdings in U. S. stocks of more than $ 100 million q domestic and foreign q at manager level Ø Caveats: No short positions q 53 managers with CDA/Spectrum data Ø excludes 18 managers b/c mutual business dominates Ø incl. Soros, Tiger, Tudor, D. E. Shaw etc. q Hedge fund performance data Ø HFR hedge fund style indexes 53

54 reasons for persistence data empirical results did hedge funds ride bubble? did hedge funds’ timing pay off? conclusion

55 Did hedge funds ride the bubble?

56 Did Soros etc. ride the bubble? Fig. 4 a: Weight of technology stocks in hedge fund portfolios versus weight in market portfolio

57 Fund in- and outflows Fig. 4 b: Funds flows, three-month moving average

58 Did hedge funds time stocks? Figure 5. Average share of outstanding equity held by hedge funds around price peaks of individual stocks

59 Did hedge funds’ timing pay off? Figure 6: Performance of a copycat fund that replicates hedge fund holdings in the NASDAQ high P/S segment

Conclusion q Hedge funds were riding the bubble Ø Short sales constraints and “arbitrage” risk are not sufficient to explain this behavior. q Timing bets of hedge funds were well placed. Outperformance! Ø Rules out unawareness of bubble. Ø Suggests predictable investor sentiment. Riding the bubble for a while may have been a rational strategy. ) Supports ‘bubble-timing’ models 60

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