The stock market dropped precipitously after the announcement that the emphasis of the Troubled Assets Relief Program would be shifted to direct equity infusions into banks and away from buying their “toxic” mortgages. This change was especially confounding, because when he first proposed TARP, Treasury Secretary Henry Paulson suggested that the financial crisis would not end until the mortgage market stabilized. The favorable reaction to the plan to backstop Citigroup’s mortgage portfolio, as well as the government’s announcement that it will buy additional mortgage-backed securities, is powerful evidence that Paulson had it right the first time.

The market wants to understand the dimensions of the losses that banks face from their mortgage holdings. We believe that using a significant portion of TARP’s remaining assets for its original purpose – buying distressed mortgage assets – is the fastest and most reliable way to achieve that.

In 1988, we participated in a fundamental restructuring of the Mellon Bank that holds many lessons for today. At the time, the market had no confidence regarding the size of Mellon’s asset problem. Instead of trying to convince investors that Mellon’s assets were valued accurately, chief executive Frank Cahouet asked that an entity be designed to hold all of Mellon’s nonperforming loans.

The Grant Street National Bank was formed, capitalized with Mellon’s troubled assets and financed as much as possible through debt secured against those loans. Over the next several years, loans were sold expeditiously to private buyers. Substantially all of the proceeds from the financing and the remaining liquid assets after debt repayment went back to Mellon.

Once Mellon no longer had nonperforming loans on its books, the write-downs taken by the bank from asset transfers into Grant Street could quickly be replenished through equity offerings. Mellon did not go through the trauma that other major American banks (including Citi) experienced in the early 1990s. Despite the dilution from the sale of new equity, its stock went up more than tenfold when it merged with the Bank of New York.

This “bad bank” model has been repeated many times since. The concept was used in the savings and loan bailout and in Korea in the 1990s. TARP can similarly foster a virtuous circle by facilitating:

. Investor confidence in the soundness of the banks (after their sale of toxic mortgage assets into TARP), leading to the injection of hundreds of billions of dollars of private equity. To grasp the potential, consider Wells Fargo’s recent sale of $10 billion of equity organized in just four days for the purchase of Wachovia.

. Accelerated activity by private investors already linked up with mortgage servicing organizations to research and bid for TARP assets. Many such pools of capital are being organized to compete aggressively for this business.

. A simple mechanism for individual borrowers to go back to their original banks to get mortgages they can handle. Individuals can use those proceeds to buy out, at a discount, the original mortgage held in TARP. The proceeds of the smaller mortgage may well exceed the value allocated to the mortgage held by the government. Everyone wins: The government makes money and a new, affordable mortgage is issued to the homeowner.

. A visible way for the public and lawmakers to see a resolution that is considered fair to all. The market then would be able to assess the dimensions of the mortgage crisis. The problem may well be less significant than most people assume. But whatever the number, clarity will create confidence.

Critics of TARP’s purchase of toxic mortgage assets say it is impossible to know whether the government is getting a fair price. To address that, the government can accept a price the banks deem fair but insist on a “true up” revision three years later. If the government fails to earn a significant return, it would get equivalent debt of that bank to make up the shortfall. With a “true up” system, banks would be reluctant to seek a windfall on sales to TARP.

Others argue that there are simply too many loans to track and renegotiate through these obscure investment vehicles. But we advocate Marshall Plans for every conceivable urgent public need. Why not devote a similar level of commitment to the creation of a database including a detailed accounting of every troubled mortgage in America? That way, TARP – working with local banks – could focus first on restructuring loans with the highest likelihood of foreclosure.

Finally, it is also said that it will take too long for TARP to do its work and that TARP does not have enough capital to buy all troubled mortgages. But TARP does not have to restructure every loan in America to be effective. Once the mechanism is clear for a fraction of the loans, the likely outcomes for the whole TARP asset base will be visible to all. In the meantime, taxpayers may even get lucky and see home prices stabilize and growing numbers of aggressive bidders for TARP assets start going directly to banks still holding toxic mortgages.

A financial crisis with many dimensions cannot be solved by putting Band-Aids on each tear in the system. The correct approach is to take the biggest wound and stitch it up. Once people see that the contours of the mortgage problem are known and are being dealt with, consumer confidence will return, leading, in turn, to profound improvements in the stock and corporate credit markets.

In the early 1990s, the Japanese government encouraged banks to keep nonperforming loans on their balance sheets and value these loans as if they were not impaired. The loss of transparency (as well as the failure to put these loans into the hands of those who would restructure them) contributed to over a decade of slow growth and an underperforming stock market.

The Obama administration should not make the same mistake. If its economic team uses TARP to enhance price and value discovery of mortgages held in the banking system, we will be a lot closer to the end of the financial crisis.

Peter Ackerman is managing director of Rockport Capital Inc. John Vogelstein is senior adviser at Warburg Pincus LLC, New York.