SIZE-RELATED ANOMALIES AND
STOCK RETURN SEASONALITY
Further Empirical Evidence by Donald B. KEIM
Received June 1981, final version received June 1982
Stacey Basallo
Rina Bryan
Lais Ogata
Jenna Yered
INTRODUCTION
 As discussed by last week’s presentation on Banz and Reinganum’s study,
there is a significant negative relation between abnormal returns and
market value
 This study looks at the month to month stability of the size anomaly
 Daily abnormal return distributions in January have large means relative
to the remaining months in the year
 The relationship between abnormal returns and size is always negative
and much more defined in January
SIZE EFFECT HYPOTHESES
 Hypotheses that were implied by others to explain the size effect do
not seem to explain the January Effect
 Brown, Kleidon, Marsh argued that the size effect may be explained by
an omitted risk factor in the pricing model; would not explain just the
January returns
 Stoll and Whaley – transaction costs
DATA AND PORTFOLIO SELECTION
 CRSP Daily Stock Returns
 Returns from 1963-1979 (17 years)
 NYSE and AMEX Listings – firms listed and had returns the entire
calendar year
 Sample size ranges from 1,500 – 2,400 firms throughout the study
 Beta estimates that adjust for non-synchronous trading
DATA AND PORTFOLIO SELECTION CONT.
 Negative relationship between firm size (market value = # of shares
outstanding at YE * YE Price per share of common shares) and abnormal risk
adjusted returns (security daily return less equal weighted daily return of the
control portfolio)
 Divide into 10 portfolios; 1 being small firms, 10 being large
 Re-rank and assess annually
 Annually firms enter and leave the sample due to bankruptcies, de-
listings, mergers, etc.
SENSITIVITY OF SIZE ANOMALY TO
TRADING INFREQUENCY
 Roll suggests that the size effect could be due to improperly measured
risk
 Dimson points out a downward bias for small firms (infrequently
traded) and an upward bias for large firms (frequently traded)
 Reinganum acknowledges this, however it is not large enough to explain
returns
 Even when the betas are adjusted for trading frequency, they still show
a pronounced negative relationship between small and large portfolios
 Table 2 shows the average differences between daily CRSP excess
returns of small and large portfolios by month
SIZE RELATED ANOMALIES AND STOCK
RETURN SEASONALITY
 50% of the size anomaly occurs in January
 February, March, July also show higher returns but much lower than
January
 October displays the opposite; size discount
 All other months are concentrated around 0% abnormal return
 This seasonality is even more pronounced in the small firms portfolio
compared to the large firms portfolio
SIZE RELATED ANOMALIES AND STOCK
RETURN SEASONALITY
 Reignanum suggested that the size anomaly was obtained continuously
month to month year to year
 However this report contradicts the month to month stability of the
size effect and shows January return premiums occurred every year
 Average annual size premium of 30.3% declines to 15.4% when the
January data is removed
FIGURE 2: STOCK RETURN SEASONALITY AND SIZE
EFFECT
A CLOSER LOOK AT THE JANUARY EFFECT
 Large portion of the size effect occurs during the first 5 trading days
and more specifically the first day
 The first day’s difference is positive in every year
 10.5% of the annual size effect for an average year happens on the first
day
 26.3% occurs in the first week
 If we took the average of the size anomaly, only .4% would be expected
each day; however the first week of January averages 8%
THE JANUARY ANOMALY
 Even during periods (1969-1973) where large firms had higher returns
than small firms, the size premium was still significantly positive in
January
 After accounting for the always positive January effect, the year to year
instability of the size anomaly remains
 Even when the size effect does not hold, January still outperforms other
months
HYPOTHESES REGARDING THE JANUARY
EFFECT
 Tax Loss Selling Hypotheses – small firms are biased towards inclusion
of large price declines in share price and are more likely to experience
tax loss selling
 However, if this hypothesis held, the significance of the January Effect
should vary with changes to personal income tax rates
 One way to test this would be to look at countries with tax codes
similar to the United States but with differing tax year ends and see if
January still outperforms
ALL HYPOTHESES WERE NOT TESTED AND WERE DEFERRED FOR
FURTHER RESEARCH
HYPOTHESES REGARDING THE JANUARY
EFFECT
 Information Hypotheses – January marks a period of increased
uncertainty and anticipation due to the impending release of important
information related to company’s prior year performance
 Approximately 60% of the firms listed on NYSE and AMEX have a fiscal
year end date of December 31st
 To test this hypothesis, you could align all firms’ excess returns in event
time (fiscal year end) rather than in calendar time to see if returns
increase following the fiscal year end
ALL HYPOTHESES WERE NOT TESTED AND WERE DEFERRED FOR
FURTHER RESEARCH
CONCLUSION
 Abnormal returns are negatively related to size
 Daily abnormal returns in January have large means relative to the rest
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of the year
Relationship between size and returns is always negative in January even
in years where large firms outperformed small firms
No other month had abnormal behavior in this study
50% of the size effect from 1963-1979 is due to January abnormal
returns
Almost 27% of the premium is due to large abnormal returns in the first
week of the trading year
Almost 11% is due to the first trading day of the year