Why this divergence? The biggest reason is the credit crunch. Says the WSJ:
In short, Supply and Demand: an absence of $1.9 trillion in lending supply has driven up the price of borrowing, despite the federal funds rate.
Banks have lost roughly $480 billion in the past year, but have raised only about $345 billion in new capital, estimates James Bianco, president of Bianco Research. Assuming they weren't overcapitalized before, that leaves them about $135 billion undercapitalized.
With leverage, that capital translates into roughly $1.9 trillion in lending capacity now off the market, he estimates.