which the price moves away from the true value as the investor’s attribution
bias causes him to place more weight, on average, on his private information.
Eventually the public information become precise enough that the investor
revises his valuation of the security downward. This is the correction phase.
A similar hump-shaped pattern holds for an investors’ self-perceived preci-
sion (confidence) as a function of time. This changing confidence is the
source of the overreacting average price trend.
Figure 13.3 presents the unconditionalaverage autocorrelations (at lags
between 1 period and 119 periods), where now are resampled for
each iteration. This figure confirms the intuition derived from figure 13.2
that short-lag price change autocorrelations should be positive and long-lag
autocorrelations should be negative.
Several papers examine “long-horizon” regressions of long period re-
turns on past returns (see, e.g., Fama and French 1988) rather than long-lag
autocorrelations of short-period returns. In our model, it is straightforward
to show that there is a one-to-one mapping between price change autocor-
relations and more standard test statistics such as variance ratios or long-
horizon regression coefficients. In unreported simulations, these coefficients
exhibit behavior similar to that of the autocorrelations. Short-horizon re-
gression coefficients are positive and long-horizon ones are negative, con-
sistent with empirical literature on momentum and reversals.
θ ̃ands ̃ 1INVESTOR PSYCHOLOGY 483
Figure 13.2. Average price path following private information shock. This figure
shows average price path calculated using the simulation in Section 3.B.3, following
a private information shock s 1 =1. The price-path is shown for the dynamic model
with (solid line) and without (dashed line) self-attribution bias.