So how much can investors expect to earn in coming years?

"If you start at 1.5%, history says you're going to get at best 1.5% returns," Jones says.

In other words, the return will equal the yield, since there won't be any gains from rising prices. Price gains are extremely unlikely when yields are already near rock bottom.

In fact, bond risks have now gone up, because interest rates have so much room to rise in coming years. When that happens, investors will prefer the newer, more generous bonds to the stingy ones sold today. The lack of demand will cause prices of today's bonds to fall -- the opposite of what happened during the past three decades. In fact, Jones says, the future could look like the 1940s and early '50s, when bond investments lost 40%, much of it from inflation damage.

The only way to avoid this is to hold a bond to maturity, when the issuer will pay you the bond's face value. But that option means locking into today's low yields for years.

"If you start with rates higher and then they fall, you get a capital gain and you feel like a genius, but if you reinvest at lower yields over a 10-year period, you're going to get back to that starting yield," Jones cautions.

Investors who are concerned about the future of bonds can load up on stocks, which have done well in recent years. But stocks, too, are risky, so people looking for safety might do better with cash. With the averaging one-year certificate of deposit yielding only 0.25%, you won't get rich. But you won't lose money, either, and you'll have quick access to your money when opportunities arise.

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