Return Predictability and Stock Market Crashes in a Simple Rational Expectations Model

Figure 6: Serial covariance of the asset return as a function of the
monthly dividend.

The figure shows the instantaneous serial covariance of the monthly asset return
as a function of the monthly dividend for declining aggregate RRA as shown in
Specification 1 (gray line), Specification 2 (black line) and Specification 3 (dotted
line) (Figure 1-3). In the benchmark case of constant aggregate RRA there is no
serial correlation. The instantaneous serial covariance, cov_t(CER_t,_τ,μ(τ)) with
τ → t, is the cross variation between the expected excess return and the cumulated
excess return.

Table 2: Characteristics of excess returns and excess return volatil-
ity.

The table shows the mean annualized volatility of monthly and 4-year-returns, the
lag 1-serial correlation of these returns as well as lag 1- and lag 4-serial correla-
tions in return volatility. For comparison we also show the theoretical values for a
geometric Brownian motion (constant aggregate RRA). Results are shown for two
different start values (D0 =1 and D0 = 4) of the dividend process. Specifications
1 to 3 correspond to the aggregate RRA shown in figures 1 to 3.

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