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Forecasting the Si Effect 161
stocks. For holding periods of 1 year, abnormal returns were positive,
but only weakly significant.
schultz (1983) extended the analysis to Amex stocks. Using
this broader universe, he found that smaller stocks exhibited significant
risk-adjusted returns after transaction costs, even over short
holding periods. Schultz also noted that transaction costs cannot
plain the periodic sign reversal found by Brown, Kleidon, and
Marsh (1983) or the abnormal January behavior of smaller firms.
M u d and Mendelson (1986a and 1986b) hypothesized that
investors demand compensation for illiquidity, and the that size effect
proxies for an illiquidity premium. They employed bid/ask the
spread as a measure of market thinness. This spread is inversely
correlated with attributes that reflect liquidity, such as trading volume,
number of shareholders, number of dealers making a market,
and degree of price continuity. They found that returns, both gross
and net of trading costs, were an increasing function of the bid/ask
spread; the effect of firm size was negligible after controlling li- for
quidity.
Chiang and Venkatesh (1988) maintained that the higher
spread for small firms is not due to illiquidity, but results rather
from the higher proportion of “insiders” trading these stocks. The
presence of such informed traders leads dealers to raise the spread,
which in turn causes ordinary investors
require a higher expected
return on small stocks.
Slze and Risk Measurement
Roll (1981~) proposed that a bias in beta estimates leads to an overstatement
of the small-firm effect. Because small stocks trade less
frequently than large stocks, their risk as estimated from daily returns
understates their actual risk. Roll estimated the impact of
nonsynchronous trading on beta by using Dimson‘s (1979) aggregated
coefficients method. (Dimson betas are formed by regressing
security returns on lagged, contemporaneous, and leading market
returns, then summing the three slope coefficients.) The use of
Dimson betas moderated the observed small-firm effect, but
Reinganum (1982) found it insufficient to explain the full magnitude
of the effect.