AMERICA'S government is a willing buyer of bad assets, but are its banks willing sellers? If a lender flogs a loan or security for less than the value at which it is booked on its balance-sheet, it suffers a loss, depleting its capital. It follows that if banks' carrying values are still above those that state-sponsored bidders want to pay, they will not sell voluntarily.

Just how optimistic are banks' books? Two-thirds of the Treasury scheme's purchasing power will be directed towards legacy loans. America's ten biggest banks had plenty of these—$3.6 trillion at the end of 2008, or about a third of their assets. However by global convention loans are not marked to market, but carried at cost and impaired gradually. Some categories of risky loans, for example to private-equity firms, have been written down. But the vast majority of loans have not. In aggregate the carrying value of the top-ten banks' loan books was 3% above the market price in December. That gap may not seem much, but it amounts to over $110 billion; if it were crystallised, it would wipe out a quarter of these banks' tangible common equity, their purest form of capital. The loss is also likely to be concentrated on the dodgiest loans, making them hard to sell.

The remainder of the scheme's firepower will be directed at securities, which at $3.7 trillion comprise another third of the top-ten banks' assets. These are marked to market and have been the main source of the savage write-downs that banks have suffered.

Many fear that banks are still being over-optimistic about their nastiest assets. For the top ten banks, 16% of securities were classified as “Level 3”, equivalent to 1.5 times their equity (see chart). Level 3 means there are no reliable market prices available, leaving the banks free to use models. The assumptions in these may not be particularly pessimistic: at the end of 2008, $12 billion of Citigroup's Level 3 structured-credit exposures were valued according to a fall in house prices of 33% from the peak—a smaller drop than the one in the government's own “stress test”. Those banks with the least capital probably have more generous valuations. And the scheme will buy only securities that originally had an AAA credit rating, which rules out the nastiest stuff.

That still leaves about $3 trillion of securities that are marked to market using more reliable direct or indirect price inputs. But banks may be reluctant to sell their loans and their most toxic securities—exactly what the scheme is meant to target. The obvious remedy is to force banks to write down their assets further as part of the governments' continuing stress tests. But with capital ratios tight and the Treasury's bail-out kitty now almost depleted, that could push several big banks towards insolvency.