It is permissible to invest in, hold and derive benefit from realization of equity shares of a Company. However, Equity is only a format of investment. Equity comes along with ownership.
So, we need to look at other aspects too. The first is whether the business of the company whose shares are being considered, is permissible according to Shariah. Secondly, one needs to understand the manner in which the business is being operated, from two aspects:
a. Whether it is involved in any interest-based transactions and to what extent, and
b. Whether its operations involve transactions which show gharar (excessive uncertainty or ambiguity) or other unethical practices.
Allah knows Best....