Falling unemployment rates and a strengthening economy are good news, but they're not fueling the two-year stock-market bull run, so investors would be wise to ditch equities and buy U.S. Treasurys, says analyst and portfolio manager Gary Shilling.

Stocks have been rising due to the Federal Reserve's $600 billion bond buyback program, but when that program ends, so will the rally, Shilling tells Yahoo Tech Ticker.

"Stocks have had a fantastic revival," Shilling says. "But I think at this point there signs of bubble-like characteristics."

Individual investors are returning to the stock market, and are helping to inflate stock prices.

Furthermore, there are more downside risks to the economy than upside risks. "I really suspect that stocks at some point are going to suffer."

That, Shilling says, means people should return to investing in U.S. Treasurys, often seen as a safe haven when stocks fall.

While the dollar has taken a beating, it will return to its safe-haven status, Shilling says.

Shilling's Treasurys call goes contrarian to many others, including Bill Gross at Pimco, the world's largest bond fund that recently dumped Treasurys.

Pimco's Bill Gross

Gross says Treasurys will suffer when the Fed ceases its bond-buyback program.

"Yields on Treasurys may be too low to sustain demand for U.S. government debt as the Federal Reserve approaches the end of its second round of quantitative easing," Gross writes in a monthly investment outlook, according to the New York Post.

Other star investors have agreed that U.S. debt isn't a good buy.

"U.S. government bonds are not a safe haven," says Jim Rogers, according to Bloomberg. "I cannot conceive of lending money to the U.S. government for 30 years."