Errors in recorded security prices and the turn-of-the year effect

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the portfolio return, Λ_pt, and the measurement error in the return of the
market portfolio, A,_ll   scaled by the regression slope coefficient, β _p.3

Γ_pt - Rft = a, + βp(r_mt - Rft> + ʌpt - βpΛmt + ɛpt

Under the classical conditions, E<Λ_mt> = E(A_pt) = O and Cov(R_pt,Λ_mt) =
Cov(R_pt,Λ_pt) = Cov(R_mtjA_rnt) = Cov(R_mtjA_pt) = Cov(A_ptjA_mt) = O, nonzero A_pt
causes the estimate of a, to be a high-biased estimate of the true a,
but it does not affect the estimate of β. Unfortunately, because βΛ_mt is
correlated with r,, the measurement error in the market portfolio causes
the estimate of β_p to be low-biased. However, if one or more of the clas-
sical conditions fail to hold, the direction of the bias in the estimates of
a and β is generally ambiguous (see Maddala [20] c chapter 13).

During periods not characterized by flow-supply or flow-demand pressures,
the classical conditions should hold. Indeed, we argue that in the absence of
flow-supply and flow-demand pressures, recorded-price errors are random enough
across securities that Λ_mt is insignificant. Therefore, the remaining
source of bias in the estimated coefficients of equation (3) is A_pt
<λ∣_t for individual stock returns), which only affects estimates of a.

During periods of flow-supply or flow-demand pressures, both A and
Ap_t will be sources of bias in regressions on the market model. In addi-
tion, the flow-supply or flow-demand pressures will cause A_mt and A_pt
to be positively correlated and the estimate of β to be a high-biased estimate
of the true β.⁴ β estimates are high-biased because the positive
correlation between A_mt and A,, causes the observed returns r_pt and
r to be more highly correlated than the true returns R_pt and R_mt∙⁵

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