Efficient Capital Markets: II 1579 examine the autocorrelation of Wednesday-to- Wednesday returns for size grouped portfolios of stocks that trade on both Wednesdays. Like Lo and MacKinlay (1988), they find that weekly returns are positively autocorre lated, and more so for portfolios of small stocks. The first-order autocorrela tion of weekly returns on the portfolio of the largest decile of NYSE stocks for 1962-1985 is only 09. For the portfolios that include the smallest 40% of NYSE stocks, however, first-order autocorrelations of weekly returns are around. 3, and the autocorrelations of weekly returns are reliably positive out to 4 lags The results of Lo and MacKinlay(1988)and Conrad and Kaul ( 1988)show that, because of the variance reduction obtained from diversification, portfo ios produce stronger indications of time variation in weekly expected returns than individual stocks. Their results also suggest that returns are more predictable for small-stock portfolios. The evidence is, however, clouded by the fact that the predictability of portfolio returns is in part due to nonsyn chronous trading effects that, especially for small stocks, are not completely mitigated by using stocks that trade on successive Wednesdays An eye-opener among recent studies of short-horizon returns is French and Roll (1986). They establish an intriguing fact Stock prices are more variable when the market is open. On an hourly basis, the variance of price changes is 72 times higher during trading hours than during weekend nontrading hours. Likewise, the hourly variance during trading hours is 13 times the overnight nontrading hourly variance during the trading week One of the explanations that French and roll test is a market inefficiency hypothesis popular among academics; specifically, the higher variance of price changes during trading hours is partly transistory, the result of noise trading by uniformed investors( e. g, Black(1986)). Under this hypothesis pricing errors due to noise trading are eventually reversed and this induces negative autocorrelation in daily returns. French and Roll find that the first-order autocorrelations of daily returns on the individual stocks of larger (the top three quintiles of)NYSE firms are positive. Otherwise, the autocor relations of daily returns on individual stocks are indeed negative, to 13 lags Although reliably negative on a statistical basis, however the autocorrela tions are on average close to 0. Few are below -.01 One possibility is that the transitory price variation induced by noise trading only dissipates over longer horizons. To test this hypothesis, French and Roll examine the ratios of variances of N-period returns on individual stocks to the variance of daily returns, for N from 2 days to 6 months. If there is no transitory price variation induced by noise trading(specifically, if price changes are i i.d. ) the N-period variance should grow like N, and the variance ratios(standardized by N)should be close to 1. On the other hand with transitory price variation, the N-period variance should grow less than in proportion to N, and the variance ratios should be less than 1 For horizons(n beyond a week, the variance ratios are more than 2 standard errors below 1, except for the largest quintile of NYSE stocks. But the fractions of daily return variances due to transitory price variation are
1580 The Journal of finance apparently small French and roll estimate that for the average NYSe stock, he upper bound on the transitory portion of the daily variance is 11.7% spurious negative autocorrelation of daily returns due to bid-ask effects(Roll(1984)), the estimate of the transitory portion drops to 4. 1%. The smallest quintile of NYSE stocks produces the largest estimate of the transitory portion of price variation, an upper bound of 26.9%.After correction for bid-ask effects, however, the estimate drops to 4.7%-hardly a number on which to conclude that noise trading results in substantial market inefficiency. French and Roll(1986, p. 23)conclude, "pricing errors. have a trivial effect on the difference between trading and non-trading variances We conclude that this difference is caused by differences in the flow of information during trading and non-trading hours In short, with the crsp daily data back to 1962, recent research is able to show confidently that daily and weekly returns are predictable from past returns. The work thus rejects the old market efficiency-constant expected returns model on a statistical basis. The new results, however tend to confirm the conclusion of the early work that, at least for individual stocks variation in daily and weekly expected returns is a small part of the variance of returns. The more striking, but less powerful, recent evidence on the predictability of returns from past returns comes from long-horizon returns A.2. Long-Horizon Returns The early literature does not interpret the autocorrelation in daily and weekly returns as important evidence against the joint hypothesis of market efficiency and constant expected returns. The argument is that, even when the autocorrelations deviate reliably from 0(as they do in the recent tests) chey are close to 0 and thus economically insignificant The view that autocorrelations of short-horizon returns close to 0 imply economic insignificance is challenged by Shiller(1984)and Summers(1986) They present simple models in which stock prices take large slowly decaying swings away from fundamental values (fads, or irrational bubbles), but short-horizon returns have little autocorrelation. In the Shiller -Summers model, the market is highly inefficient, but in a way that is missed in tests on short-horizon returns value. Suppose daily prices are a first-order autoregression(ARl) with slope less than but close to 1. All variation in the price then results from long mean-reverting swings away from the constant fundamental value. Over short horizons, however, an ARl slope close to 1 means that the price looks like a random walk and returns have little autocorrelation. Thus in tests on short-horizon returns, all price changes seem to be permanent when funda mental value is in fact constant and all deviations of price from fundamental value are temporary In his comment on Summers(1986), Stambaugh(1986)points out that although the Shiller-Summers model can explain autocorrelations of short
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
1582 The Journal of finance the market in subsequent years. They attribute these results to market overreaction to extreme bad or good news about fi rms Chan(1988)and Ball and Kothari (1989)argue that the winner-loser results are due to failure to risk-adjust returns (DeBondt and Thaler(1987) disagree )Zarowin( 1989)finds no evidence for the DeBondt-Thaler hypothe sis that the winner-loser results are due to overreaction to extreme changes in earnings. He argues that the winner-loser effect is related to the size effect of Banz(1981); that is, small stocks, often losers, have higher expected returns than large stocks. Another explanation, consistent with an efficient market, is that there is a risk factor associated with the relative economic performance of firms (a distressed-firm effect) that is compensated in a rational equilibrium-pricing model(Chan and Chen(1991) We may never be able to say which explanation of the return behavior of extreme winners and losers is correct, but the results of DeBondt and Thaler and their critics are nevertheless interesting. ( See also Jagedeesh(1990) Lehmann(1990), and Lo and MacKinlay(1990), who find reversal behavior in the weekly and monthly returns of extreme winners and losers. Lehmann's weekly reversals seem to lack economic significance. When he accounts for spurious reversals due to bouncing between bid and ask prices, trading costs of 0. 2% per turnaround transaction suffice to make the profits from his reversal trading rules close to O. It is also worth noting that the short-term reversal evidence of Jegadeesh, Lehmann, and Lo and MacKinlay may to some extent be due to CRSP data errors, which would tend to show up price reversals. B. Other Forecasting variables The univariate tests on long-horizon returns of Fama and French(1988a) and Poterba and Summers(1988)are a statistical power failure. Still, they provide suggestive material to spur the search for more powerful tests of the hypothesis that slowly decaying irrational bubbles, or rational time-varying expected returns, are important in the long-term variation of prices There is a simple way to see the power problem. An autocorrelation is the slope in a regression of the current return on a past return. Since variation through time in expected returns is only part of the variation in returns tests based on autocorrelations lack power because past realized returns are noisy measures of expected returns. Power in tests for return predictability can be enhanced if one can identify forecasting variables that are less noisy proxies for expected returns that past returns B. 1. The Evidence There is no lack of old evidence that short-horizon returns are predictable from other variables. a puzzle of the 1970s was to explain why monthl stock returns are negatively related to expected inflation(Bodie(1976) Nelson(1976), Jaffe and Mandelker(1976), Fama(1981)and the level of short-term interest rates (Fama and Schwert(1977)). Like the autocorrela tion tests, however, the early work on forecasts of short-horizon returns from
Efficient Capital Markets: II 1583 expected inflation and interest rates suggests that the implied variation in xpected returns is a small part of the variance of returns-less than 3% for monthly returns. The recent tests suggest, however, that for long-horizon returns, predictable variation is a larger part of return variances Thus, following evidence(Rozeff (1984), Shiller(1984) that dividend yields (/P) forecast short-horizon stock returns, Fama and French(1988b)use D/P NYSE stocks for horizons from 1 month to 5 years. As shted portfolios of explains small fractions of monthly and quarterly return variances. frac tions of variance explained grow with the return horizon, however, and are E/Ratios, especially when past earnings(E)are averaged over 10-30 years, have reliable forecast power that also increases with the return horizon Unlike the long-horizon autocorrelations in Fama and French (1988a),the long-horizon forecast power of D /P and E/P is reliable for periods after 1940 Fama and French(1988b) argue that dividend yields track highly autocor related variation in expected stock returns that becomes a larger fraction of return variation for longer return horizons. The increasing fraction of the variance of long-horizon returns explained by D/P is thus due in large part to the slow mean reversion of expected returns. Examining the forecast power of variables like D/P and E /P over a range of return horizons nevertheless res striking perspective on the implications of slow-moving expected turns for the variation of returns B 2. Market Efficiency The predictability of stock returns from dividend yields (or E/P) is not in itself evidence for or against market efficiency. In an efficient market, the forecast power of D/P says that prices are high relative to dividends when discount rates and expected returns are low, and vice versa. On the other hand, in a world of irrational bubbles, low D /P signals irrationally high stock prices that will move predictably back toward fundamental values. To judge whether the forecast power of dividend yields is the result of rational variation in expected returns or irrational bubbles, other information must be used. As always, even with such information, the issue is ambiguou For example, Fama and French (1988b) show that low dividend yields imply low expected returns, but their regressions rarely forecast negative returns for the value. and equally weighted portfolios of NYSE stocks. In their data, return forecasts more than 2 standard errors below 0 are never observed. and more than 50%o of the forecasts are more than 2 standard errors above 0. Thus there is no evidence that low D/P signals bursting bubbles, that is, negative expected stock returns. a bubbles fan can argue, however, that because the unconditional means of stock returns are high, a bursting bubble may well imply low but not negative expected returns. Conversely, if here were evidence of negative expected returns, an efficient-markets type could argue that asset-pricing models do not say that rational expected returns are always positive