University of Alabama graduates at their 2011 commencement. (Michelle Lepianka Carter — AP Photo/ Tuscaloosa News)

After a proposal to reduce student debt failed in the U.S. Senate on Wednesday, graduates with loans might be looking for financial relief elsewhere. Though there aren't many options, several companies think they've found a way to reduce graduates' monthly payments while earning money for their investors.

One is called Social Finance, or SoFi.  A San Francisco company established in 2011, SoFi is expanding rapidly, recording its first profit this quarter. It now has about 8,000 borrowers on its  books who collectively owe about $650 million, figures that could double as early as this year.

That's a lot of money, but next to the $1.2 trillion in student debt currently outstanding, SoFi's sums are trivial. (Total student debt has tripled over the last decade.) As SoFi and other private-sector lenders seek to add more students to their ledgers, the problems they are encountering show just how hard it is to help graduates pay their debts.

Many graduates are still paying high rates on their loans, even though rates in the market have fallen to extraordinarily low levels since the financial crisis. When interest rates fluctuate, banks usually allow holders of home mortgages and other debts to refinance because lowering rates can be profitable for the bank. That doesn't seem to be the case with student loans, though, because of the high risk that the loans won't be repaid.

Around 11 percent of holders of student debt are at least 90 days delinquent on their repayments (the percentage is lower for holders of credit card debt and home mortgages). While a bank can foreclose on a borrower who defaults on a mortgage, lenders have no collateral when graduates don't pay off their student loans. For these reasons, banks have always shied away from student loans, letting the federal government handle them. The Senate bill would have allowed graduates who borrowed several years ago to pay today's lower interest rates, at a loss to Uncle Sam, according to the Congressional Budget Office.

"There's a huge stigma on the asset class," said Mike Cagney, the chief executive of SoFi, in an interview.

SoFi and competitors such as CommonBond, based in New York and established in 2012, have entered the student-debt market all the same. Their strategy is to take advantage of the fact that once borrowers have earned their degrees and found work, they are less likely to default. The companies use alumni networks to identify borrowers who are likely to pay off their loans -- such as holders of degrees in business -- and offer those graduates more attractive interest rates than the federal government does. Alumni also invest in SoFi, and are paid when graduates repay their loans. Personal relationships with alumni, in turn, help graduates succeed in their careers, making them more reliable borrowers.

Graduates can refinance their student loans with SoFi for rates as low as 2.65 percent. That is about 80 to 100 basis points above what SoFi pays for capital, Cagney said, but far below the rate of 7.9 percent on a typical federal loan for a graduate student. Rates on private loans can run 10 percent or higher.

Part of the reason that SoFi is able to offer such low interest rates is that it requires applicants to have a reliable monthly income and at least two years of professional experience. Half of the firm's new volume comes through referrals from existing customers. The results of this approach are striking. Not only have none of SoFi's borrowers defaulted, none have been delinquent on a loan for more than 90 days, according to the company. Cagney said that a typical borrower pays back a loan in three years, even though the term of the loan might be 10 or 15 years. Some SoFi borrowers can pay off their loans early when they receive a bonus from their employer, for example, which shows how unusual SoFi's borrowers are compared to the population as a whole.

SoFi's underwriters demand nothing less, Cagney said. As a result, his firm can't help those borrowers in the worst financial situation. That group would arguably do the most to stimulate the economy overall if their debts were reduced.

"We can't take all the people that we'd like to take," Cagney said. "We're going after, right now, the best of the batch, the folks who graduate who have relatively high incomes, who we can convince the market are relatively good credits. The challenge for us is there’s a huge bunch of folks in the middle, that we think are good credit, but we're not at a point yet where we can convince the market that they're fundable."

Cagney thinks his firm will gradually be able to offer credit  to a larger group of borrowers. With each passing quarter, the market becomes more accustomed to the new business model for student debt, and funding is easier. SoFi will receive a rating on its student-loan-backed securities from one of the "Big Three" credit agencies this year.

The process, however, is slow, and could be reversed if there is another financial panic. If easing the burden of student debt is a priority for society as a whole, a large-scale, long-term solution will require action from the federal government and probably Congress.