Asset Pricing under Asym Information Limits to Arbitrage Historical Bubbles Symmetric Information Pricing Equation Ruling out Asset Pricing under Asymmetric Information Bubbles Limits to Arbitrage Asymmetric Information Expected Strong Bubble Necessary Conditions Limits to Arbitrage Noise Trader Risk Synchronization Risk Markus K Brunnermeier Princeton University August 17 2007 Asset Pricing under Asym Information Overview Limits to Arbitrage Historical Bubbles Symmetric Information Pricing Equation Ruling out Asymmetric Information Expected Strong Bubble Necessary Conditions Limits to Arbitrage Noise Trader Risk Synchronization Risk All agents are rational Bubbles under symmetric information Bubbles under asymmetric information Interaction between rational arbitrageurs and behavioral traders Limits to Arbitrage Fundamental risk Noise trader risk Endogenous short horizons of arbs Synchronization risk Asset Pricing under Asym Information Historical Bubbles Limits to Arbitrage Historical Bubbles Symmetric Information Pricing Equation Ruling out Asymmetric Information Expected Strong Bubble Necessary Conditions Limits to Arbitrage Noise Trader Risk Synchronization Risk 1634 1637 Dutch Tulip Mania Netherlands 1719 1720 Mississippi Bubble France 1720 South Sea Bubble England 1990 Japan Bubble 1999 Internet Technology Bubble Asset Pricing under Asym Information Limits to Arbitrage A Technology Company Historical Bubbles Symmetric Information Pricing Equation Ruling out Asymmetric Information Expected Strong Bubble Necessary Conditions Limits to Arbitrage Noise Trader Risk Synchronization Risk 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 Asset Pricing under Asym Information Limits to Arbitrage Historical Bubbles Symmetric Information The Story of RCA in 1920 s Company Technology Years Radio Corporate of America RCA Radio 1920s Pricing Equation Ruling out Asymmetric Information Expected Strong Bubble Necessary Conditions Limits to Arbitrage Noise Trader Risk Synchronization Risk Figure RCA s Stock Price from Dec 25 to Dec 50 RCA peaked at 397 in Feb 1929 down to 2 62 in May 1932 Asset Pricing under Asym Information Limits to Arbitrage NASDAQ and Neuer Markt Historical Bubbles Symmetric Information Pricing Equation Ruling out Asymmetric Information Expected Strong Bubble Necessary Conditions Limits to Arbitrage Noise Trader Risk Synchronization Risk Figure NASDAQ and Neuer Markt during Technology Bubble Asset Pricing under Asym Information Limits to Arbitrage Bubbles under Symmetric Information Historical Bubbles Symmetric Information Pricing Equation Ruling out Asymmetric Information Expected Strong Bubble Necessary Conditions Limits to Arbitrage Noise Trader Risk Synchronization Risk Keynes distinction between speculation and long run investment Speculation Buy overvalued in the hope to sell it to someone else at an even higher price Investing Buy and hold strategy Fundamental value Was ist das highest WTP if one forces agents to buy hold the asset no uncertainty uncertainty w risk neutral agent uncertainty w risk averse agents discounted value of dividends expected discounted value take expectations w r t EMM Asset Pricing under Asym Information Limits to Arbitrage Bubbles under Symmetric Information Historical Bubbles Symmetric Information Pricing Equation Ruling out Asymmetric Information Expected Strong Bubble Necessary Conditions Limits to Arbitrage Noise Trader Risk Synchronization Risk Problem of Keynes buy and hold definition of fundamental value Retrade does also occur to dynamically complete the market not only for speculation With retrade a different allocation can be achieved and hence the EMM is different Allow for retrade and take EMM which leads to highest fundamental value Asset Pricing under Asym Information Limits to Arbitrage Historical Bubbles Symmetric Information Pricing Equation Ruling out Asymmetric Information Expected Strong Bubble Necessary Conditions Limits to Arbitrage Noise Trader Risk Synchronization Risk Bubbles under Symmetric Information with stochastic discount factor mt or pricing kernel mt the price of an asset is given by mt pt Et mt 1 pt 1 dt 1 where mt 1 is related to MRS divided by prob of state Alternatively one can also write pricing equation in terms of the equivalent martingale measure 1 Q pt Et pt 1 dt 1 1 rtf Securities with Finite Maturity Reiterate pricing equation Backwards induction rules out bubbles Asset Pricing under Asym Information Limits to Arbitrage Historical Bubbles Symmetric Information Pricing Equation Ruling out Asymmetric Information Expected Strong Bubble Necessary Conditions Limits to Arbitrage Noise Trader Risk Synchronization Risk Bubbles under Symmetric Information Securities with Infinite Maturity Backwards induction argument fails since there is no well defined final period Lack of market clearing at t Split the price in a fundamental component ptf and a bubble component bt By pricing equation we get the following expectational difference equation 1 bt EtQ b t 1 1 rtf Example 1 deterministic bubble has to grow at the risk free rate Example 2 Blanchard Watson 1982 risk neutral investors bubble bursts in each period with prob 1 persists with prob f t bubble has to grow by a factor 1 r if it doesn t burst Asset Pricing under Asym Information Limits to Arbitrage Historical Bubbles Symmetric Information Pricing Equation Ruling out Asymmetric Information Expected Strong Bubble Necessary Conditions Limits to Arbitrage Noise Trader Risk Synchronization Risk Bubbles under Symmetric Information How can we rule out bubbles Negative bubbles Blanchard Watson 1982 Diba Grossman 1988 For bt 0 difference equation implies that pt will become negative Free disposal rules out negative prices Positive bubbles on assets with positive net supply if g r Brock Scheinkman Tirole 85 Santos Woodford 97 Argument bubbles would outgrow the economy if r g At any point in time t the aggregate wealth of the economy contains bubble component b NPVt of aggregate wealth Wt does not converge to zero as If aggregate consumptiont is bounded or grows at a rate g r NPVt Ct 0 as Household wealth exceeds PV of C for all t sufficiently far in the future This