Here is a description of the Ryan Medicare and Social Security partial privatization plans I found on the League of Women Voters website. It’s not the same as this proposal at all.
http://lwv.org/content/federal-privatization-ryan-plan
If everybody invested even a portion of their SS money in a Vanguard S&P 500 index fund, the money is still going to Wall Street due to the suddenly increased demand for the underlying stocks, the market will skyrocket. Temporarily.