How Low Can They Go?
Some day bond yields will go up. When? No one knows. How far? Your guess is as good as anyone's. Lots of expert prediuctions have been made over the past few years and most of them have been dead wrong. Predicting the future is both impossible and pointless. Particularly when it comes to bond yields and prices.
Bonds should not be "played" for gain. A smart investor understands that the biggest bang for their risky buck comes from equities, not bonds. Since they represent the businesses that make up the global economy, stocks, in general have always, eventually risen in value. However, stocks are highly volatile investments. In that volatility lies the potential rewards.
Bonds do not (generally) become more valuable. They offer a small interest payment in return for the temporary use of your money. There is no inherent growth potential. Bonds have only risen in price when interest rates are falling. The longer the bond maturity, and the lower the quality, the greater the risk. Since bonds cannot reward you with growth, there is too much risk for too little reward in longer maturity or lower quality fixed income investments.
You should only use bonds in your portfolio to mitigate the volatility from your potentially very rewarding equity holdings. The only bonds with a decent enough risk/return profile are short/intermediate government bonds. They can't default (for all reasonable intents and purposes) and, since they mature in just a few years at face value don't experience as much interest rate volatility.
A recent New York Times article by James B. Stewart explains this quite clearly. It's w worthwhile read.