PowerPoint PresentationOverviewAllocative vs. Informational EfficiencyEMH ) Martingale PropertyReturn Predictability…Non-Predictability of ReturnsPredictability of ReturnsNon-Predictability of current InformationVersions of EMH/Info-EfficiencyAsymmetric InformationAsym. Info – Higher Order UncertaintyPrice as a SignalEvidence I: Predictabilities Studies…Long-Run ReversalsSlide 15Clash of two ReligionsEvidence II: Event StudiesMarket Efficiency in Event StudiesSlide 19Slide 20Event Study: Stock SplitsEvent Study: Take-over AnnouncementEvent Study: Death of CEOWhat Makes Market Efficient?Grossman-Stiglitz ParadoxFor Whom is it Worthwhile to Collect Information?Evidence III: Outperformance…Outperformance (more recent)Modern Performance EvaluationSurvivorship BiasPersistence of Managers’ SkillsSummary08:5808:58 Lecture 10 Lecture 10 Market EfficiencyMarket EfficiencyFin 501: Asset PricingFin 501: Asset PricingLecture 10: Market EfficiencyLecture 10: Market EfficiencyProf. Markus K. Brunnermeier08:5808:58 Lecture 10 Lecture 10 Market EfficiencyMarket EfficiencyFin 501: Asset PricingFin 501: Asset PricingOverviewOverview•Efficiency concepts•EMH implies Martingale Property•Evidence I: Return Predictability•Mispricing versus Risk-factor•Informational (market) efficiency concepts•Asymmetric Information and Price Signal•Evidence II: Event Study Methodology•Grossman-Stiglitz Paradox•Evidence III: Fund Managers’ Out/underperformance08:5808:58 Lecture 10 Lecture 10 Market EfficiencyMarket EfficiencyFin 501: Asset PricingFin 501: Asset PricingAllocative vs. Informational EfficiencyAllocative vs. Informational Efficiency•Allocative EfficiencyAn allocation is Pareto efficient if there does not exists a possible redistribution which would make at least one person better off without harming another person.In finance: ) optimal risk sharing•Informational (Market) EfficiencyPrice reflects all (xxxxx) informationEfficient Market Hypothesis = “Price is right”-Hypothesis08:5808:58 Lecture 10 Lecture 10 Market EfficiencyMarket EfficiencyFin 501: Asset PricingFin 501: Asset PricingEMH EMH )) Martingale Property Martingale Property•A stock price is always at the “fair” level (fundamental value)• ) discounted stock price/gain process is a Martingale process [using the equivalent martingale measure E*[.] ]A stock price reacts to news without delay.If the price must go up tomorrow – what would happen today?The risk-adjusted likelihood of up- and down-movements of the discounted process are equal.•Any predictable component is due to changes in the risk premium.•Weak-form, semistrong-form and strong-form of EMH differ in underlying filtrations (dynamics of martingale measure)08:5808:58 Lecture 10 Lecture 10 Market EfficiencyMarket EfficiencyFin 501: Asset PricingFin 501: Asset PricingReturn Predictability… Return Predictability… A chartist tries to predict the return of a stock from past returns; using the following diagramWhat will he find?1day ton Returnday ton ReturnDensity1day ton Returnday ton Return08:5808:58 Lecture 10 Lecture 10 Market EfficiencyMarket EfficiencyFin 501: Asset PricingFin 501: Asset PricingNon-Predictability of ReturnsNon-Predictability of Returns•No correlation case: Knowing return on day t gives you no information about the return on day t+1•The expected (excess) return conditional on the date t return Rt is zero:1day ton Returnday tonReturn 1day ton Return0)(1 ttRREKnown:RtConditional DistributionReturn Rt+108:5808:58 Lecture 10 Lecture 10 Market EfficiencyMarket EfficiencyFin 501: Asset PricingFin 501: Asset PricingPredictability of ReturnsPredictability of Returns•Correlation case: Density with correlation between period t return and period t+1 return1day ton Return1day ton ReturnConditional DistributionReturn Rt+1)(1 ttRRER•The expected (excess) return conditional on the date t return Rt is α :08:5808:58 Lecture 10 Lecture 10 Market EfficiencyMarket EfficiencyFin 501: Asset PricingFin 501: Asset PricingNon-Predictability of current Non-Predictability of current InformationInformation•Non-predictability of excess returns – beyond a risk-premium - is the equilibrium condition of a financial market•All available information is already reflected in the price•Prices change only under new information arrival•Let’s be more precise about information It .0)(1 ttIREperiod)futur other any (or 1day t on Return  at time,statistics knownAny tI08:5808:58 Lecture 10 Lecture 10 Market EfficiencyMarket EfficiencyFin 501: Asset PricingFin 501: Asset PricingVersions of EMH/Info-EfficiencyVersions of EMH/Info-Efficiency•Weak-form efficiency:Prices reflect all information contained in past prices•Semi-strong-form efficiency:Prices reflect all publicly available information•Strong-form efficiency:Prices reflect all relevant information, include private (insider) informationall public & private infoall public infopast market infoAccording to each of these theories, which kind of information cannot be used to trade profitably?08:5808:58 Lecture 10 Lecture 10 Market EfficiencyMarket EfficiencyFin 501: Asset PricingFin 501: Asset PricingAsymmetric InformationAsymmetric Information•So far we focused on models where all market participants had the same information at each point in time. (same filtration + distribution)•For strong-form market efficiency different agents must different information at some points in time. 0 1 0 1agents Aagents BWhose filtration is more informative?08:5808:58 Lecture 10 Lecture 10 Market EfficiencyMarket EfficiencyFin 501: Asset PricingFin 501: Asset PricingAsym. Info – Higher Order UncertaintyAsym. Info – Higher Order Uncertainty•All traders know that (e.g. price is too high)•All traders know that all traders know that…•All traders know that … that …•…•…1 mutual knowledge1st order 2nd ordernth order 1 th order=Common knowledge•What’s a bubble?Even though all traders know that price is too high, the price is too high.(since e.g. they don’t know that others know it as well.)08:5808:58 Lecture 10 Lecture 10 Market EfficiencyMarket EfficiencyFin 501: Asset PricingFin 501: Asset PricingPrice as a SignalPrice as a Signal•If information is dispersed among many agents•Price reveals info about many individuals’ signalsInformation aggregation(S1,…,Si,…,SI)  S