Investors in U.S. bonds should expect little in the way of New Year cheer — their annual statements are expected to show 2013 was the weakest year for bond returns in more than a decade, according to the Financial Times.

In fact, the Barclays U.S. Aggregate bond index produced its first negative year of total returns since 1999, the Times estimated, with a total return of -2.1 percent for 2013.

"Investors tend to reassess their portfolios after they receive their statements for the past year in early January," said Jack Ablin, chief investment officer at Harris Private Bank. "We could see some reaction in January and investors seek alternatives to bonds."

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The most likely place investors may flee to, aside from cash, may be equities. The S&P 500 rose about 32 percent in 2013, including dividends.

The Federal Reserve has begun to withdraw its massive monetary stimulus, including tapering its Treasury and mortgage-debt asset purchases. The result recently pushed 10-year yields over 3 percent, and could prompt more bond fund outflows.

"If you look at retail investors, they have a tendency to chase performance and we may see that in the new year," predicted Jay Mueller, portfolio manager at Wells Capital, referring to the potential for mom-and-pop investors to jump into stocks.

However, the Times noted professional investors and, in particular, pension funds and insurers with long term liabilities, may not be ready to throw in the towel on bonds.

"We are seeing interest from pension plans that want to take advantage of higher Treasury yields and offset their liabilities," Mueller said. "We could see retail and institutional investors move in opposite directions."

Richard Gilhooly, U.S. director of interest rate strategy at TD Securities, said in a research note, "10-year Treasury yields at 3 percent leaves us on the cusp of a renewed push to new highs in yield, the next level being the 3.2 percent high from July 1, 2011, ahead of a more serious break to the 3.60/70 percent high area from Feb-April 2011," MarketWatch reported.

But Wlliam Riegel and Lisa Black of TIAA-CREF sounded a more moderate tone, according to MarketWatch.

"Investors have already 'priced in' both the Fed's taper announcement and the economy's improved economic growth. This has helped temper the recent rise in interest rates," they said in a separate analysis.

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