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Adjusting for Size and Book-to-Market Factors

Our earlier results in Tables II to V raise the possibility that the predictive power of prior returns or prior earnings surprises may be confounded with the effects of book-to-market or firm size. In this section we investigate whether the behavior of returns on our different momentum portfolios can be explained by factors related to size and book-to-market. This is done in the context of the Fama-French (1993) three-factor model, given by time series regressions of the form

rpt -rft= ap+ bp{rmt - rft) + spSMBt + hpHMLt + ept. (4)

Here rpt is the return on portfolio p in month t\ rft and rmt are the Treasury bill rate and the return on the value-weighted market index, respectively; SMB, is the return on the mimicking portfolio for size; and HML, is the return on the mimicking portfolio for book-to-market.11 If the momentum strategies performance is just a manifestation of size and book-to-market effects, then the intercept of the equation, ap1 should not be significantly different from zero.

Fama and French (1996) use equation (4) to analyze the performance of portfolios sorted by prior return. Here we examine the evidence when earnings momentum is brought into the picture as well.12 In particular, we focus on the double-sort portfolios based on prior return and revisions in consensus esti mates. Table X reports summary statistics of the time series regressions for the highest- and lowest-ranked portfolios (portfolios (3,3) and (1,1) respectively in Panel РЎ of Table VI). We track the monthly returns from a strategy of buying each portfolio and holding it for six months, when a new portfolio is formed and the process repeated. Table X also reports results for the arbitrage portfolio formed by buying the highest-ranked portfolio, or the winners, and selling the lowest-ranked portfolio, or the losers.

The portfolios of winners and losers have very similar market risk exposures (bp). In other respects, the results in Table X generally confirm our earlier findings. Both portfolios load significantly on size. The portfolio of winners concentrates more heavily on glamour stocks, so it loads negatively on the book-to-market factor, while the portfolio of losers is more oriented towards value stocks, and so loads positively on the book-to-market factor. The main conclusion from Table X is that adjusting for size and book-to-market does not change the observed pattern in returns. The intercept for the loser portfolio ( ”0.953 percent per month) is especially eye-catching. This poor performance 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.