How long do stock markets usually take to process complex new public information? Here is a question that I've been thinking about for a while:

Theoretically, assuming investors are rational, a stock's price will be equal to its its intrinsic value (present value of discounted expected future cash flows). Therefore, when a share's price is $S_t$ at time $t$, and a new piece of information $I_t$ comes in that signals to investors that the expectation of future cash flows should go up, then at time $t+\epsilon$, the share price $S_{t+\epsilon}$ should immediately jump discontinuously to reflect this new fact.

However, in practice, investors' cognitive capacities are limited. Depending on the complexity of the information, $\epsilon$ could be longer or shorter. 

For example, when news of an acquisition comes out, this will have various complex implications, for the stock price of the acquirer, the target company, and the competitors in both their markets. Compare this with the implications of a simple increase in the interbank rate set by the ECB for example, on the exchange rate between the Euro and the dollar. 

The second information probably has a more simple effect on the exchange rate, than the first type of information has on the various companies that are involved. 

Now my question is: In practice, how long do investors generally take before they've processed complex new information, like the announcement of a lateral acquisition deal? That is, how long till they've reached a new, relatively stable assessment of expected value?

I've seen data where the exchange rate adjusts literally within a matter of seconds to information about the ECB interest rate. But a reaction to such an acquisition should perhaps take days, instead of minutes?
I used to work for a company called Value Line, which is noted for its stock ranking system. Through a number of tests, its statistics department came to the conclusion that it took up to six months for new information (e.g. earnings) to be reflected in stock prices. So they introduced a time decay factor that would reduce the value of information to zero over a six month period in calculating their rankings.