Section6 Random Walks(1).ppt

Stock market prices do not follow random walks:evidence from a simple specification test,Andrew W.LoA.Craig MacKinlayThe review of financial studies 1988,Abstract,Menu,1.The Specification Test2.The random walk hypothesis for weekly returns3.Spurious autocorrelation induced by nontrading4.The mean-reverting alternative to the random walk5.Conclusion,Introduction,Fama(1970):most studies were unable to reject the EMH of common stocks Forecastability of common stock returns:Random walk theory.But some papers find predictable stock returns componentsFama and French(1987):negatively serially correlated returns,This article provide evidence that stock prices do not follow random walks by using a simple specification test based on variance estimators.Results:RW not consistent with weekly returns.But positive serial correlation for weekly and monthly returns,Data:1962-1985 weekly,CRSP return index AR(1)=0.3This result may not imply inefficiencyEconomic model of price generating:other models,This test:the variance of the increments of a random walk is linear in the sampling interval,1.The specification test,Deviate from normalityDevelop a test statistic which is robust to many forms of heteroscedasticity and nonnormality,1.1 Homoscedastic increments,Main estimators,Some intuition of these variance ratios,1.2 Heteroscedastic increments,Volatilities do change over timeNeed to develop a specification test of the random walk model that is robust to changing variances,2.The random walk hypothesis for weekly returns,1962-1985 CRSP weekly data(Wednesday)Test both equal and value-weighted CRSP indexes,q=2 to 16The ratios should be 1+AR(1),The rejection of RW is weaker for the value-weighted index.But the general pattern persistThe variance ratios exceed 1 and the z(q)decline as q increases,Four week data,Cannot reject the RW model even for the equal-weighted index.Using monthly data will have similar results previously,2.2 results for size-based portfolios,Smallest quintile has a AR of 0.42But using a base observation interval of four weeks.Even for the smallest,z(2)is only 3.09,2.3 results for individual securities,Negative serial correlation for individual securities,but insignificant.Idiosyncratic noise,uncovered by combining them,3.Spurious autocorrelation induced by nontrading,A return-generating process,Rejection of RW cannot be attributed solely to infrequent trading,4.The mean-reverting alternative to the random walk,If mean-reverting,the variance ratios should be less than 1 and the z(q)is larger when q is larger.But the empirical results contradict.So do not fit a stationary mean-reverting alternative any better,5.Conclusion,Reject the RW for weekly stock market returns by volatility test.These cannot be explained by infrequent trading or time-varying volatilities.But the rejection does not mean inefficiency implications for economic models.But which stochastic best fits the data is unknown.Long and short term,What we can learn from these papers,Econometric:cross section and time series;proxy;parametric and nonparametricFinance theory:EMH;CAPM;APT,asset pricing;behavior financeEconomic theory:the transfer from economic basic model to financial models,