Table X

Three-Factor Time Series Regressions Based on Monthly Excess Returns (in Percent) on Portfolios from Two-Way Classification by Prior Return and Analyst Revisions

The regression is estimated over monthly observations from January 1977 to December 1993. The dependent variable is the monthly return in excess of the Treasury bill rate from a strategy of buying a portfolio of stocks ranked highest or lowest (winners and losers respectively) from an independent sort on two classification variables. The classification variables are: the stocks compound return over the past six months, and a moving average of the past six months percentage revisions relative to the beginning-of-month stock price in the mean I/B/E/S estimate of current fiscal-year earnings per share. The portfolio is held for six months, at which time the portfolio is reformed and the strategy repeated. The explanatory variables are the monthly returns from the Fama and French (1993) mimicking portfolios for size and book-to-market factors, and the monthly return in excess of the Treasury bill rate on the value-weighted market portfolio of all the component stocks from the mimicking portfolios. Results are also presented for the difference between the two portfolios, i.e., the zero-cost portfolio of buying past winners and selling past losers. The regression R2 is adjusted for degrees of freedom, and -statistics are shown in parentheses below the coefficient estimates.

stems from the fact that the loser portfolio has persistently low returns, even though it is tilted toward small stocks with high book-to-market ratios (which would tend to raise average returns). The intercept for the arbitrage portfolio is 1.43 percent, with a -statistic of 5.91.

Past winners, if they are riskier than past losers, should have worse (better) performance in bad (good) states of the world, irrespective of the identity of the underlying risk factors. To the extent that bad and good states correspond to low and high excess returns, respectively, on a broad stock market index, we can check if this is the case. In particular, during months where the return on the CRSP value-weighted market index falls below the monthly Treasury bill rate, riskier stocks should earn lower returns. As it turns out, during such down-market months the difference between the returns of the winner and loser portfolios from our two-way sort on prior return and analyst revisions is positive (0.60 percent per month). Conversely, in up-market months (where the return on the value weighted index exceeds the Treasury bill rate) the average difference between the returns of the winner and loser portfolios is 1.79 percent. Strategies exploiting high momentum in stock prices thus seem to do especially well in up-markets. In any event, there is no evidence that the winner portfolio is exposed to larger downside risk.

VI. Conclusions

Unless we understand why a particular investment strategy works, we should be skeptical about its out-of-sample performance. There are several competing hypotheses concerning the profitability of contrarian strategies for short- or long-horizon returns. However, there is a glaring lack of explanations for the continuation in stock prices over intermediate horizons (short of sweeping the issue under the rug by relabeling the phenomenon as part of the normal cross-section of expected returns). This paper fills in some of the gaps in our understanding of two major unresolved puzzles in the empirical finance literature: why two pieces of publicly available information-a stocks prior six-month return and the most recent earnings surprise-help to predict future returns. The drift in future returns is economically meaningful and lasts for at least six months. For example, sorting stocks by prior six-month return yields spreads in returns of 8.8 percent over the subsequent six months. Similarly, ranking stocks by a moving average of past revisions in consensus estimates of earnings produces spreads of 7.7 percent over the next six months. Our results are robust with respect to how we measure earnings surprise: as standardized unexpected earnings, abnormal returns around announcements of earnings, or revisions in analysts forecasts of earnings. In general, the price momentum effect tends to be stronger and longer-lived than the earnings momentum effect.

The bulk of the evidence suggests that the drifts in future returns are not subsequently reversed, so momentum does not appear to be entirely driven by positive feedback trading. The price continuations are particularly notable for stocks with the worst past earnings performance, whose returns are below average for up to three years afterwards. There is stronger evidence of subsequent correction in prices when large, positive prior returns are not validated by good news about earnings. In the first year following portfolio formation, stocks ranked highest by prior return but lowest by abnormal announcement return earn a rate of return (21.3 percent) that is not very different from the average of 20 percent. The fact that returns for the past winners are high only in the first subsequent year, but are not much different from the average in the second or third years, poses a challenge for risk-based explanations of the profitability of momentum strategies. More direct evidence from a three-factor model also suggests that the profitability cannot be explained by size and book-to-market effects.

An alternative explanation is that the market responds gradually to new information. Since earnings provide an ongoing source of information about a firms prospects, we focus on the markets reaction when earnings are released. Indeed, a substantial portion of the momentum effect is concentrated around subsequent earnings announcements. For example, about 41 percent of the superior performance in the first six months of the price momentum strategy occurs around the announcement dates of earnings. More generally, if the market is surprised by good or bad earnings news, then on average the market continues to be surprised in the same direction at least over the next two

subsequent announcements. Clearly, however, the return on a stock also incorporates numerous other sources of news that are not directly related to near-term earnings: stock buybacks, insider trading, and new equity issues, for example. The large drifts in future returns thus paint a picture of a market which underreacts.

Another piece of evidence compatible with the sluggish response of market participants is the prolonged adjustment of analyst forecasts. The inertia in revising forecasts may not be helping the market to assimilate new information in a timely fashion. In particular, analysts are especially slow in revising their estimates in the case of companies with the worst performance. This may possibly be due to their reluctance to alienate management.

When we disentangle the sources of the momentum strategies performance, we find that each of the variables we analyze-prior return, as well as each of the earnings surprise variables considered - has marginal predictive power for the postformation drifts in returns. In cross-sectional regressions of future six-month returns on past returns, the coefficient on prior return is 5.7 percent. Introducing past earnings surprises lowers the coefficient to 2.9 percent, although it is still reliably nonzero. Each momentum strategy thus draws upon the markets underreaction to different pieces of information.

Our evidence that the markets response to news takes time is not an entirely negative verdict on the informational efficiency of the stock market. Note that prior news has already caused a substantial realignment in stock prices over the preceding six months. In Table II, for instance, the past adjustment produces differences in returns of roughly 100 percent between the most favorably and least favorably affected stocks. Put in this perspective, the remaining adjustment that is left on the table for investors, as measured by the spread in future one-year returns of about 15 percent, becomes less striking.

A note of caution is necessary. The spreads we document here for momentum strategies may not be fully capturable. Given the constraints many investors face, it may not be feasible to establish short positions in stocks with low momentum. A momentum strategy is trading-intensive, and stocks with high momentum tend to be smaller issues whose trading costs tend to be relatively high. These implementation issues will reduce the benefits from pursuing momentum strategies. To illustrate the point, suppose an investor wishes to exploit price momentum by buying the top two deciles of stocks ranked by prior return in Table II (so as to have a relatively well-diversified portfolio). This would yield, an average annual return of about 27 percent. If the relevant benchmark is the average return across all the eligible stocks in Table II, roughly 22 percent, this investor earns an extra 5 percent. Chan and Lakonishok (1995) report average trading costs for small firms of about 3 percent (combining a purchase and sale), so the extra returns for a momentum strategy are substantially reduced after accounting for trading costs.

Finally, our evidence of underreaction over intermediate horizons suggests that a stock with low past returns will on average experience low subsequent returns. It might be argued that a contrarian overreaction story would instead predict high subsequent returns for such a stock. Is there any contradiction