A member of the Troubled Asset Relief Program Congressional Oversight Panel is wondering how the government will extricate itself from its current entanglement with American International Group Inc.

“The panel has yet to produce a report on AIG or Treasury’s exit strategy with respect to its TARP-funded investments,” Jeb Hensarling, a panel member, writes in a comment on the report.

The panel has not held a public hearing with AIG or most other TARP participants, either Hensarling writes.

Hensarling’s comments accompany a panel report on guarantees and contingent payments in TARP and related programs.

Officials at the U.S. Treasury Department came up with TARP in late 2008, as large financial services companies seemed to be preparing to collapse like a row of dominos.

TARP let the Treasury Department stop “runs on the banks,” and other financial services companies, by offering direct financial assistance, and also by offering direct and indirect financial guarantees.

The “guarantees bear no upfront price tag,” panel officials write in the main part of their report. “The low upfront cost of guarantees also allowed Treasury, in coordination with other federal agencies, to leverage a limited pool of TARP resources to guarantee a much larger pool of assets.”

The guarantees played a significant role in calming the financial markets in 2008, panel officials write.

But, “at its high point, the federal government was guaranteeing or insuring $4.5 trillion in face value of financial assets under the three guarantee programs discussed in this report,” officials write.

In additional to exposing taxpayers to default risk, the guarantees created “moral hazard,” by limiting investors’ losses, the officials write.

Treasury officials seem to be running the guarantee programs well, and they have taken an “aggressive and commercial” approach to safeguarding taxpayer assets in connection with the guarantees, but the guarantee programs should be subject to “extraordinary transparency,” officials write.

In the report, the panel officials focus mainly on the money market fund guarantees; aid to Citigroup Inc., New York; and guarantees provided to Bank of America Corp., Charlotte, N.C., that Bank of America did not actually use.

Excluding the money market fund program, the programs reviewed now provide a total of about $320 billion in guarantees, have suffered only $2 million in losses, and have generated about $17 billion in fee revenue.

At one point in the report, panel officials use the arrangement the Federal Reserve Bank of New York made with AIG as an example of how a rescue should work.

Treasury officials gave Citigroup and Bank of America guarantee protection without punishing their shareholders, panel officials note.

It would “be useful to understand why these institutions received asset guarantees instead of the approach used with AIG,” panel officials write. “AIG received cash and its shareholders were wiped out.”