Privatizing the social security would be damaging in the long term as profit motivation would get in the way of personal need. Too much money would be lost in corporate streamlining excises and consultancy. The people who really needed the money wouldn't see the benefits of privatization and probably would also resent the management.
No, I don't think social security should work that way. I feel that social security should be in better hands that the stock market. I would worry about all of the ups and downs that it would go through on the market. I feel that social security needs to be protected in much stronger ways.
Social care and security is far too important to privatize to individuals and organizations who only care about making fast profits. The risk is too high, if it means putting older peoples future at risk. It is more reasonable to invest more wisely and save sensibly than to gamble on the stock market.
Capital markets promote effective businesses and excessive profits. Social security is definitely not a book primer for any of then. Just look at the name to see why. Social security is a system implied by the state to provide security for the people. There is no place in here for excessive profits or shares record quotes or annual shareholders meetings.