Efficient Capital Markets: II 1581 horizon returns that are close to 0, the long swings away from fundamental value proposed in the model imply that long-horizon returns have strong negative autocorrelation. (In the example above, where the price is a station ary ARl, the autocorrelations of long-horizon returns approach.5. ) Intu itively, since the swings away from fundamental value are temporary, over ong horizons they tend to be reversed. Another implication of the negative of returns should grow less than in proportion to the return horicon variance autocorrelation induced by temporary price movements is that the The Shiller-Summers challenge spawned a series of papers on the pre dictability of long-horizon returns from past returns. The evidence at first seemed striking, but the tests turn out to be largely fruitless. Thus, Fama and French(1988a)find that the autocorrelations of returns on diversified portfolios of NYSE stocks for the 1926-1985 period have the pattern pre dicted by the Shiller-Summers model. The autocorrelations are close to 0 at short horizons, but they become strongly negative around -0.25 to-0.4, for 3- to 5-year returns. Even with 60 years of data, however, the tests on long-horizon returns imply small sample sizes and low power. More telling Then Fama and French delete the 1926-1940 period from the tests, the evidence of strong negative autocorrelation in 3-to 5-year returns disappears Similarly, Poterba and Summers(1988)find that, for N from 2 to 8 years the variance of N-year returns on diversified portfolios grows much less than in proportion to N. This is consistent with the hypothesis that there is negative autocorrelation in returns induced by temporary price swings. Even with 115 years (1871-1985) of data, however, the variance tests for long horizon returns provide weak statistical evidence against the hypothesis that returns have no autocorrelation and prices are random walks Finally, Fama and French (1988a)emphasize that temporary swings in stock prices do not necessarily imply the irrational bubbles of the shille Summers model Suppose(1)rational pricing implies an expected return that is highly autocorrelated but mean-reverting, and(2) shocks to expected returns are uncorrelated with shocks to expected dividends. In this situation expected-return shocks have no permanent effect on expected dividends discount rates, or prices. a positive shock to expected returns generates a price decline (a discount rate effect) that is eventually erased by the tem porarily higher expected returns. In short, a ubiquitous problem in time-series tests of market efficiency, with no clear solution, is that irrational bubbles n stock prices are indistinguishable from rational time-varying expected A. 3. The contrarians DeBondt and Thaler(1985, 1987)mount an aggressive empirical attack on market efficiency, directed at unmasking irrational bubbles. They find that the NYSE stocks identified as the most extreme losers over a 3- to 5-year ing years, expecially in January of the following years. Conversely, the stocks identified as extreme winners tend to have weak returns relative to