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, covt(CERt,τ,μ(τ)) with
τ → t, is the cross variation between the expected excess return and the cumulated
excess return.
|
________Start value ⅞=1________ |
________Start value Dp=4________ |
GBM | |||||
|
Specification: |
1 |
2 |
3 |
1 |
2 |
3 | |
|
mean annualized volatility of |
0.167 |
0.192 |
0.201 |
0.178 |
0.843 |
0.774 |
0.128 |
|
mean annualized volatility of |
0.166 |
0.168 |
0.181 |
0.177 |
0.624 |
0.583 |
0.128 |
|
mean autocorrelation (lag 1) |
-0.002 |
-0.015 |
-0.011 |
-0.002 |
-0.028 |
-0.023 |
0 |
|
mean autocorrelation (lag 1) of 4-year returns_____________ |
-0.019 |
-0.031 |
-0.055 |
-0.015 |
-0.168 |
-0.179 |
0 |
|
autocorrelation (lag 1) in |
0.064 |
0.900 |
0.890 |
0.006 |
0.966 |
0.964 |
0 |
|
autocorrelation (lag 4) in |
0.094 |
0.891 |
0.895 |
0.040 |
0.963 |
0.959 |
0 |
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.
32