The Congressional Budget Office said in a report Thursday that propping up Fannie  and Freddie , the government-sponsored mortgage investors, is expected to cost taxpayers $53 billion between 2011 and 2020.

That number is not new. The CBO said last month in issuing its annual summer budget update that declining home losses at Fannie and Freddie and reduced costs in the making home affordable plan had actually reduced the official estimate of the cost of federally supporting the GSEs, from the $64 billion the CBO had projected in January.

What is new is the CBO’s decision to show how much propping up Fannie and Freddie could cost the taxpayer over the next decade, using three different accounting methods.

The cost indicated by the CBO’s preferred method — which takes into account all the risks taxpayers are shouldering in supporting the companies, including uncertainty over future economic conditions — is $97 billion above the tab implied by the rosiest analysis.

The costliest projection is appropriate, the CBO said, because it alone fully “recognizes that there is a cost to taxpayers when the government assumes financial risk.”

The CBO made the estimate in a report issued Thursday in response to a request by U.S. Rep. Barney Frank, the Massachusetts Democrat who runs the House Financial Services committee. Democrats in Washington have been holding hearings over what to do about Fannie and Freddie, the government-supported mortgage investors that have consumed more than $150 billion of taxpayer funds since their federal takeover two years ago.

The Obama administration has promised to present Congress with a plan to fix the housing market and reform the GSEs by January, and Frank has been seen as the congressional leader on the effort. But with Democrats potentially facing huge losses in November, and many Republicans posturing to the effect they would simply shut the companies down, the issue looks increasingly touchy.

Keeping Fannie and Freddie in the government fold looks least costly using a government accounting method introduced with the Federal Credit Reform Act of 1990, which was introduced to make sense of the government’s loan guarantee commitments. The so-called FCRA method supplanted cash accounting, which tended to overstate the costs of loans and understate those of guarantees, even if their economic substance was identical.

The FCRA method calculates costs as the net present value of expected cash flows, discounted by Treasury borrowing costs. Under the FCRA estimate, keeping the government-sponsored enterprises on the federal dole over the next decade could actually result in $44 billion of income to taxpayers. (The cash accounting produces an estimated $8 billion inflow to taxpayers over the next decade.)

But the CBO says using the FCRA method doesn’t present an accurate snapshot of the true costs of subsidizing Fannie and Freddie, because it uses the so-called risk-free government borrowing rate to discount the value of future cash flows.

In essence, it ignores the uncertainty risk taxpayers are taking on by supporting the companies, which have guaranteed timely payments of principal and interest on trillions of dollars of mortgages.

FCRA procedures incorporate the expected cost of defaults on government loans or loan guarantees, but those procedures do not account for the uncertainty about how costly such defaults ultimately will be. Investors require compensation (a “market risk premium”) in order to bear certain types of risk. Such a premium on a risky loan or guarantee compensates investors for the increased likelihood of sustaining a loss when the overall economy is weak and resources are scarce, and it is reflected in higher expected returns, and lower prices, for assets that carry more market risk.

The CBO adds that while Fannie and Freddie have cleaned up their act since the housing boom in the middle of the decade, a weak economy still poses risks that investors would rightly demand compensation for taking on:

Although the new mortgage guarantees projected for the GSEs over the 2011–2020 period appear to be considerably less risky than were the guarantees made during the peak of the housing boom or during the recession, there are still significant risks. The default rates on GSE-guaranteed mortgages issued in 2008 have been consistently worse than the GSEs had expected. Foreclosure rates on houses remain high, and there is continuing uncertainty about whether house prices will fall further than they already have.

Although CBO expects the economy to recover gradually over the next few years, the speed and strength of the recovery are uncertain. High future loss rates on the GSEs’ new guarantees are unlikely, but should they recur, it is likely to be when the overall economy is weak and the cost of those losses is high.

The CBO’s fair value method isn’t perfect, the group says, conceding that it isn’t perfectly comparable with other government accounts. But it says the rewards in this case far outweigh the risks.

Specifically, the fair-value approach provides the Congress with a more comprehensive measure of cost than FCRA or cash-basis accounting because it recognizes that there is a cost to taxpayers when the government assumes financial risk.

That seems like the one statement in the contentious and often ridiculous Fannie-Freddie debate that pretty much everyone will agree on.