This month marks five years since Lehman Brothers filed for bankruptcy. Many Americans can recall the shock and anxiety they felt over the next few weeks as banks of all sizes went insolvent, the stock market plunged nearly 800 points in a single day, and national housing prices sank 30%.

Yet five years later, major components of the crisis have been left completely unaddressed: Fannie Mae, Freddie Mac and our system of housing finance.

Despite being at the center of the storm and requiring a $200 billion taxpayer bailout, these two mortgage behemoths have not been reformed. The model of private gains and public losses should be eliminated once and for all.

With one proposal working its way through the House, another gaining traction in the Senate, and President Obama moving the issue to the forefront last month, we are on a trajectory to dramatically modernize the way our country's housing finance system works. This is good news. But the stakes are high, and we must get this right.

Reform should begin with a fundamental understanding of Fannie and Freddie as government-sponsored enterprises with collective balance sheets of close to $5 trillion. At their best, the GSEs provide valuable technology, systems and legal infrastructure to connect banks in towns all across our country to global investors from London to Frankfurt to Hong Kong. At their worst, they are corporations that have historically leveraged their special relationship with the taxpayer to run thinly capitalized institutions that enriched shareholders when the economy was humming but relied on the taxpayers when the economy tanked.

Our public policy challenge is: how do we deal with twin entities that currently play an integral role in our economy but are rooted in a fundamentally flawed arrangement as semi-private, semi-public firms? Fannie and Freddie have crowded out competitors and prevented innovation in the secondary mortgage market.

Compounding this challenge, we know we must ensure a system of housing finance that isn't prone to frequent disruption and can consistently provide sufficient credit to meet the needs of American homeowners and our multitrillion-dollar mortgage market. And we cannot accidentally tip the competitive balance in favor of the largest financial institutions – the ones that can access the global capital markets without an intermediary – while leaving community lending institutions in the dust. To these ends, we have spent the past year assessing what is worth preserving in the current system and what needs to be scrapped.

Our bipartisan bill, the Housing Finance Reform and Taxpayer Protection Act, would keep the technology and infrastructure of Fannie and Freddie, but redeploy it into an updated system where duopolies can no longer exist. In addition, capital levels for private-sector participants that take on credit risk would be substantially higher than they were in the past. We would require at least 10% capital – more than twice the amount Fannie and Freddie lost during the last crisis before there can be any taxpayer exposure.

Further, our bill would ensure that companies issuing mortgage-backed securities are legally separated from the entities that take on the risk of credit loss, so that if one firm makes bad bets and gets into trouble it can be allowed to fail without disrupting the rest of the system. And our proposed Federal Mortgage Insurance Corp. would explicitly charge for the taxpayers' backstop risk – much like the FDIC's operation – by assessing an up-front fee on loans that go into a government-insured mortgage-backed security. Finally, we maintain and improve existing efforts to help creditworthy Americans access homeownership, including the popular 30-year fixed mortgage. But we would completely wall off the government's risk management and taxpayer protection roles from social purpose initiatives and make them more accountable, transparent and subject to strict oversight.

It is past time to address this unfinished business remaining from the financial crisis. The bill we are advocating along with eight other members of the Senate Banking Committee – a strong coalition that continues to grow – can usher in a 21st-century model of housing finance that will create a dramatically better model for responsible, sustainable homeownership in this country.

Bob Corker, R-Tenn., and Mark Warner, D-Va., are U.S. senators, members of the Banking, Housing and Urban Affairs Committee, and lead sponsors of Housing Finance Reform and Taxpayer Protection Act, S. 1217.