as the share price invariably drops accross the ex-div date, does that
make it possible to profit by short selling a stock across the ex-div
date?

Hi flypaperman,

No, sorry, that won't work.  The price drops because the owner of a
share before the ex-dividend date gets a dividend and the owner of a
share after the ex-dividend date doesn't, and the stock is worth more
with the expectation of the dividend than without it.  When you have a
short position, you have to pay dividends instead of receiving them. 
So if you sell a stock short before the ex-dividend date, you have to
pay the dividend, which decreases your proceeds from the sale by the
amount you would gain by covering your position when the price goes
down after the ex-dividend date (disregarding other fluctuations in
the price).

For example, say a stock sells for $20 a share and has declared a $1
per share dividend.  On the ex-dividend date, the price falls to $19. 
So if you sell it short at $20 and cover your position at $19, you
make $1 per share.  But it doesn't do you any good, because you have
to pay out the $1 as a dividend.


Additional Link

The Investment FAQ page on shorting stocks explains why short sellers
have to pay dividends.
http://invest-faq.com/articles/trade-short.html


I hope this is a satisfactory answer to your question, if not the
answer for which you had hoped.  If it is not clear enough, please ask
for a clarification.

Regards,

--efn