As the taxi pulled away from Grand Central Station on a late November afternoon in 2002, Bill Ackman was bracing for a fight.

The 36-year-old co-founder of a hedge fund firm called Gotham Partners LP in New York had been summoned to a meeting with Jay Brown, the chief executive officer of MBIA. MBIA’s general counsel wouldn’t say what Brown wanted to discuss, but Ackman had a suspicion.

Gotham had placed a bet against the company that could make the fund $2 billion if MBIA filed for bankruptcy. The hedge fund planned to issue a critical research report questioning the bond insurer’s AAA rating. Ackman had described the situation in an October 2002 letter to his investors.....