Q. Is it a problem to own stock in Canadian Tire, Walmart or Sears etc.? The stores are open on Shabbos and Yom Tov - not exactly sure how that affects the stock itself.
A. Igrois Moishe (O.H. 4: 54) in a forty year old teshuvo written to Horav Shlomo Miller Shlit"a, permits buying the majority of the stock of a non- Jewish company that works on Shabbos, as all the decision making and managing in every level is done by the non-Jewish directors of the company at their own discretion. Also it will not be publicized who the owner of most of the stock is. Horav Miller added that although halochowise unnecessary, since the buyer is a strictly Hareidi person it is better he should buy less than half of the stock, to what the Igrois Moishe agreed. (See also teshuvo 51 on the same volume)
A similar opinion is to be found in Minchas Yitzchok (3: 1), alsoYalkut Yosef (S'char Shabbos p.129) where he then prohibits buying stock if it is a Jewish directed company albeit employing Gentile workers. (See ibid. note 17 for a source list for other similar teshuvos)
Horav Shlomo Miller Shlit"a also mentioned that the directors should be granted the right to be rewarded with a bonus consisting on a percentage of the yields of the company, to ensure that they are in truth working for their own benefit. That is today a common corporate practice.
Rabbi A. Bartfeld as revised by Horav Shlomo Miller Shlit"a