Ann: Dividend/Distribution - APX, page-11

It is really interesting, I found it fascinating too, but sadly it doesn't seem to have any practical use. The gain in value from the dividend nearing its ex-date will be spread out over the time since the last dividend ex-date. If there was no other variation in the stock, due to there being no growth expectations or uncertainty, the SP over time would look like this:

In between dividends, the SP growth rate would de the dividend rate. The drop on ex-date would be the dividend value. In this way you would only receive a return for holding the stock over time, irregardless of whether this time included the ex-date or not.

If your hypothesis were true that the stock should on average accumulate value on Monday roughly equal to the dividend value - due to Tuesday being ex-day - then everyone would have been happy to pay an additional 25c on Friday - bidding the SP up until the SP included the value of the dividend (the couple of days interest is less than 1c so we can ignore that). But then since the stock was bid up on Friday instead, the hypothesis would no longer be true as people wouldn't pay another 25c again on Monday. You can then apply this reasoning back, one day at a time, all the way back to the previous dividend and see that the effect will be spread out evenly over the whole period.

Of course in reality, the slight changes in value over time due to the dividend ex-date getting nearer are negligible in size compared to the greater uncertainties of how much a stock will be making (or losing) in the future and how soon that is, so these subtle movements are lost in among the greater noise.
For APX this Tuesday, the dividend going ex is not even a 1% change in the stock's overall value, so even that will most likely be imperceptible in the day's volatility (especially given how high the volatility of APX is right now). But, if Tuesday the SP only goes down by, say, 10c, you can correctly consider the day as being up overall.

You can see the effect of dividend ex-dates on the share price chart in mature (non-growth) stocks with relatively high dividend rates and very dependable and consistent earnings.