What are the plausible explanations for the contradiction between the bond market and the stock market today (June 2014)?

This has happened many times before.  But it is unusual. Since 1802, this state has existed less than 15% of the time.   The "conflict" must eventually be resolved.   Volatility is now at levels last seen in 2007, just before the worldwide financial crash.  That means people are not fearful right now.   Good arguments could be made on each side.   I am betting we will see a sharp stock market decline within 6 months, followed by another rally.   Good luck!

Long term rates have been low for a while. They rose briefly as people digested the news that the Fed was ending QE3 and the economic data in 2013. However rates declined after that. See So the bigger question is why are rates so low in general right now, in 2014. Long term rates may be lower than people are accustomed to because: Population growth has slowed. We may see 0.5% growth in the working age population or so. Inflation is lower than its historical average The Fed still has 0% interest rates, and all else being equal that lowers long term rates as well. The Fed is distorting the bond market because it has bought a lot of bonds via its QE program. There is s a glut of savings in countries like China because of policies there and in oil producing countries because of oil prices that are high on a historical basis. Those savings-glut countries buy treasuries, and that pushes down yields. The federal budget deficit has shrunk, reducing the supply of treasuries that people can buy. Because of baby boomers' retirement timelines, there are a lot of people that need to own bonds right now, relative to what has been the case historically. Portfolios for institutions like pension funds are still overweight bonds and underweight stocks relative to historical norms post in the wake of the 2008 financial crisis.

The obvious answer is Quantitative Easing. The Fed are engaged in a massive ongoing buy back of their own bonds, which is keeping bond prices artificially high. The cash for those purchases is being directed to the major bondholders, i.e. the banks, with the intention that the money then be loaned to businesses to stimulate the economy. However with many banks still reluctant to lend, much of the money is instead finding its way into the stock market, seeking yield. And it's this that is driving the price of stocks higher. Until this so-called "firehose of money" is turned off, it seems highly likely this relationship will continue.