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Recorded-price bias in holding-period returns occurs when one or both of
the prices used in calculating holding-period returns are measured with
error. For example, let P∣t be the true equilibrium price of firm i's stock
at time t, let p,t be the recorded price of firm i's stock at time t, and
let 6it be the measurement error in p∣t (that is, plt = Pit + Sit>∙ The
observed holding-period return for firm i at time t, r∣t, equals the true holding
period return R∣t plus the measurement error λit.
( 1 ) λ∣t = fit ~ R I t = (P I t + 6 ( t ) / ( P l t _ , + ɛit-l) ~ P i t/P I t- I .
Observed portfol io returns should be less sensitive to recorded-price errors
because the magnitude and sign of Ait varies across the firms in the port-
folio. As seen in equation (2), the measurement error in portfolio returns,
A,,, is the weighted sum of the measurement errors of the securities in
the portfolio.
(2)
rpt = ∑wlr,t = ∑w∣(R∣t + A∣t) = Rpt + ∑wiAit = Rpt + ʌpt'
One hopes that by grouping firms into portfolios, the pricing errors will can-
cel out. However, during periods of flow-supply and flow-demand pressures,
the pricing errors may become nonrandom in the time series of the individual
firms and in the cross section of the firms in the portfolio. In this case,
grouping will remove relatively little of the recorded-price error from
observed portfolio returns.
Recorded-price errors in individual firm stock returns and portfolio
returns cause the market model to be misspecified. As seen in equation <3)>
the error term in the market model, ept, now consists of the standard error
term, εpt (which measures unexpected returns), the measurement error in
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