If aggregate demand is so low, why are profits so high?

That's not a facetious or sarcastic question, I am puzzled.  Here is one story from yesterday:

Major corporations are expected to report some of their strongest profits in years.

“It has been one of the strongest profits recoveries ever,” said David S. Bianco, chief United States equity strategist for Bank of America Merrill Lynch. “You have got to go back to the Depression to find a profits recovery that outpaces this one.”

What are the options?

1. It's earnings manipulation and real economic profits aren't high at all.  Or they may represent capital consumption.

2. It's an oligopoly model and mark-ups are countercylical (NB: this would eaier to maintain if the recovery in output had been weaker).

3. Aggregate demand is recovering but a) workers are unemployed because, at current margins, their labor simply isn't worth very much, and b) real interest rates are low because of cushions of corporate cash.

4. We're seeing a lot of cost-lowering positive supply shocks, but AD remains stagnant.

Each of these explanations has its problems.  What other hypotheses should I be considering?

Addendum: Arnold Kling comments.