The variance of the innovation in price is thus maximized when information about
dividends is revealed in a smooth fashion so that the standard deviation of the new information at time t about a future dividend d,+k is proportional to its weight in the
present value formula in the model (5). Incontrast, suppose all dividends somehow became
known years before they were paid.Then the innovations in dividends would be
so heavily discounted in (5) that they would contribute little to the standard deviation of the innovation in price. Alternatively, suppose nothing were known about dividends
until the year they are paid. Here, although
the innovation would not be heavily discounted
in (5), the impact of the innovation
would be confined to only one term in (5),
and the standard deviation in the innovation
in price would be limited to the standard
deviation in the single dividend.
The variance of the innovation in price is thus maximized when information aboutdividends is revealed in a smooth fashion so that the standard deviation of the new information at time t about a future dividend d,+k is proportional to its weight in thepresent value formula in the model (5). Incontrast, suppose all dividends somehow becameknown years before they were paid.Then the innovations in dividends would beso heavily discounted in (5) that they would contribute little to the standard deviation of the innovation in price. Alternatively, suppose nothing were known about dividendsuntil the year they are paid. Here, althoughthe innovation would not be heavily discountedin (5), the impact of the innovationwould be confined to only one term in (5),and the standard deviation in the innovationin price would be limited to the standarddeviation in the single dividend.
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