Social Security funds aren't allowed to be invested in the stock market, and are held in the form of US Treasuries [0]. There was talk of changing that under Bush 44, but his reform plans never gained any serious traction.
It depends on your definition of "best bang for your buck".
Social Security doesn't exist to maximize returns, it exists to protect the elderly from extreme poverty once they are no longer able to work. Because of that, the funds are invested in a very risk averse manner.
I'd certainly be open to the idea of a US sovereign wealth fund in some sense, but I don't think privatization or anything else where individuals are making decisions about their own Social Security account is a good idea, since we'll have to create another Social Security-like program to support the people who invested poorly and are unable to support themselves.