Stocks are far less risky in the long run than they are in the short run because the ups and downs balance out over a long period of time. It is virtually impossible to find any 40-year period in which the stock market has not paid a higher rate of return on your money than you get from Social Security.
There are some mutual funds that simply buy a mixture of the stocks that make up the Dow Jones average (or Standard & Poor's), so that their clients will have the kind of return on their investments that the stock market as a whole has. They don't make a killing but they don't get killed either.
How did Social Security get into its present mess in the first place? Because politicians made it the "risky scheme" that they now claim privatization would be.
The same political expediency which caused Social Security to be called "insurance," in order to get public support, guaranteed that it would be nothing of the sort. Unlike an insurance company, Social Security has never had enough money to pay for all the pensions it promised.
Instead, Social Security has been run like a pyramid scheme, where the first people to pay in get money back from the second wave of people who pay in, and the second wave get money back from the third wave, etc. This is so risky that pyramid schemes are illegal -- except when the government does it.
They have gotten away with this thus far because the first generation covered by Social Security was an unusually small generation that was followed by the unusually large "baby boomer" generation. But when the baby boomers retire, the pyramid scheme will no longer bring in enough money to pay for their pensions.
Nothing is more risky than depending on politicians.