McGraw-Hill

Forecasting the Si Effect 183
ENDNOTES
1. Rozeff (1984), Keim and Stambaugh (1986), and Fama and French
(1988a and 19886).
2. For some empirical results, see Amihud and Mendelson (1988) and
Gilmer and Swanson (1988).
3. See also Arbel (1985) and Carvell and Strebel (1987).
4. See Table I in Jacobs and Levy (19886) for references to earlier
studies. The 25 measures used were low P/E, small size, yield, zero
yield, neglect, low price, book/price, sales/price, cash/price, sigma,
beta, CO-skewness, controversy, three measures of trends in analysts’
eamings estimates, three measures of earnings surprise, earnings
torpedo, relative strength, two measures of return reversal, and two
measures of potential tax-loss-selling. Also, 38 industry measures
were utilized to purify returns further.
5. For a synthesis of the calendar literature, see Jacobs and Levy
(198%).
6. See Gibbons and Hess (1981), Keim and Stambaugh (1984), Harris
(1986), and Keim (1987). However, Miller (1988) argues that
intraweek patterns in returns size to are unrelated to the long-run
size effect.
7. The payoffs shown are for an exposure of 1 cross-sectional standard
deviation to the smallsize attribute. For details, see Jacobs and Levy
(19886). The results from that article have been extended through the
end of 1987.
8. The current observation in an autoregressive (AR) process of order p
is generated by a weighted average of p lagged observations.
Similarly, the current observation in a moving-average (MA) process
of order 9 is generated by a weighted average of 9 lagged errors.
Methods for idenhfymg and fitting time-series models are provided
in Box and Jenkins (1976).
9. The autocorrelation function is used to determine the order of the
stochastic process. It provides a measure of the correlation between
sequential data points. The nth-order autocorrelation is defined as
the covariance between each observation and of that n periods
earlier, divided by the variance of the process.
10. While these studies find short-term autocorrelation patterns, Grant
(1984) documents long-term cycles in the daily returns of small-firm
portfolios, and Fama and French (19886) find strong negative serial
correlation for long-horizon returns of duration 3 to 5 years,
especially for smaller
firms.