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during the TOY period, the market model slope coefficient, 8, would exhibit an
upward shift during the TOY period.,0
On the other hand, the empirical observation that the market model slope
coefficient exhibits TOY-related seasonality may not be the result of an
increase in systematic risk. One consequence of nonrandom recorded-price
errors is that the estimated regression coefficients from the market model
will be biased and inconsistent. In fact, we argue earlier in this paper that
nonrandom recorded-price errors may result in high-biased estimates of 8.
Therefore, TOY-related shifts in the estimates of a and/or β support the
LPSH. If TOY-related seasonality is present in the regression coefficients of
the market model, then there are two hypotheses to test. First, we must test
the LPSH versus the hypothesis that the TOY is a size-related effect. Second,
we should test the LPSH against the hypothesis that the anomalous TOY returns
are the result of an increase in systematic risk during the TOY period.
To test the LPSH against the two alternative hypotheses, the following
modified market model regression is estimated for the MV, PR, SIZE, PRICE, and
MVPR portfolios using version 3.0.2 of SHAZAM [32]:
( 5 ) r∣t ~ Rft = ct, i D1 + α21 D2 + <x 31 + β i ∣ Si + β21 S2 + β ɜ∣(ɛm t ~ Rft) + B∣ t ∙
Equation (5) is equation (3) modified to include intercept- and slope-dummy
variables for the pre- and post-yearend periods to test for changes in the
observed risk-return relationship during the TOY period. O, (D2) is the
intercept-dummy variable for the pre-yearend (post-yearend) period, and S1
(S2) is the slope-dummy variable for the pre-yearend (post-yearend) period.
Di (D2) equals one during the pre-yearend (post-yearend) period and is
zero otherwise. Si (S2) equals O1 (D2) times the return on the market
portfol io, rmt.
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