The Federal Reserve is sitting on billions of dollars in paper profits from its controversial effort to unwind credit insurance contracts that AIG provided to banks such as Goldman Sachs, people familiar with the matter said.

The Fed rescue has generated criticism because the banks received 100 cents on the dollar for credit insurance they bought from AIG on collateralised debt obligations – financial instruments that promise the buyer cash flows from pools of bonds or loans. This had led to claims that AIG's rescue was a “backdoor bail-out” of big banks.

However, the central bank is in a position to reap profits from this part of the rescue, which involved the purchase of the underlying CDOs by a New York Fed-financed vehicle, called Maiden Lane III, so that the insurance contracts written on them could be terminated.

At the time of their purchase, the CDOs had a face value of $62.1bn and an estimated market value of $29.6bn. Now, the estimated market value of the CDOs is at least $45bn, according to several people with direct knowledge of the portfolio.

“With the rally in the credit markets and tightening spreads, the Fed has made a killing – on paper,” said one person familiar with the portfolio.

The people familiar with the portfolio said that it would be difficult to sell all the CDOs because they are generally illiquid. A rapid sale of CDOs could also depress their prices.

At the time of the Fed intervention, the value of the CDOs insured by AIG was falling dramatically and AIG was facing a credit downgrade.

AIG declined to comment.