Halal or not will depend on the portfolio constituting the mutual fund and shares. The legal maxim “everything is permissible (halal) unless stated proven otherwise” applies here.
In simple words: so long as the shares and mutual funds are free from any prohibited elements of the Islamic Law (Shariah), the investment is halal. The word Shariah (Islamic law) is much more comprehensive/inclusive than the predominant definition. Islam encourages trading and investment. However, it is encouraged to look deeper into the end objective and goal of the investment to ensure alignment to our existence and objective in this life.
Investments related to unethical or moral behaviors are forbidden in Islam. Islam prohibits investments in the following areas:
Financial services that feature transactions based on gambling, speculation and/or interest. Examples would include conventional banks, investment companies offering investments in the aforementioned industries, and insurance companies.
Certain food and beverages industries, most scholars agree that investing in tobacco, illegal drugs, alcohol, and other non-halal foods/beverages are prohibited.
Gambling; this means Islamic funds can not invest in online lotteries, casinos, lotto draws and betting transactions.
Some sectors in the Entertainment industry; those shariah prohibitions apply to adult entertainment products including videos, audio recordings, websites, magazines, etc. The same goes to certain types of non-Islamic music and cinema products.