(This is a question, not an answer, by the way. I have no idea.)
http://www.bloomberg.com/markets/rates-bonds/government-bond...
(.27% for 3 month treasuries, just .79% for 2 year)
Longer-term bonds are significantly higher risk than a savings account.
I don't deny that there are better investment vehicles than a savings account. I'm just asking whether there is something of similarly low risk with a better interest rate. Stocks are definitely not lower-risk.
See the chart below [0] - If you invested all your money in 1965, there is only a 8 year window at the end of the 90s where you would have averaged a 3% return per year. Much of the rest of the time you're looking at negative returns.
[0]: https://static01.nyt.com/packages/images/newsgraphics/2011/0...
A comment further up the thread asked for "very low risk"; the reply to that changed it to "near-zero risk".
Better to consider the type of risk you care about, and how much money you want associated with each type of risk. Checking accounts and index funds both make sense as part of an overall strategy. I don't know that savings accounts do, though, except perhaps as a purely organizational tool.
These conditions that led to a higher interest rate are probably also leading to a higher inflation rate. So my $1000 is locked up for 20 years in an instrument where it's decreasing in real value.
But you wanted to know "What gives higher returns but near-zero risk?" and assuming by "risk" you meant "default risk" there you go....a high interest low denomination savings instrument backed by the federal government.