The stock market seems to already be back on its feet since the recession, but recent college graduates are still having as hard a time finding work as they ever have.

According to the Huffington Post, a new study from the Center for College Affordability and Productivity found the job market is especially tough on Americans aged 18 to 29. The study found the unemployment rate for that age range to still be double what it was at the start of the recession. The study also found that nearly 50 percent of recent college graduates are working jobs that do not require degrees.

Meanwhile, CNN Money reported the Dow Jones industrial average hit all-time highs 52 times in 2013. MarketWatch reported both Nasdaq and S&P have made record closings in the past week.

While students at elite schools have much less trouble finding work after graduation, Yale president Peter Salovey told the HP more students need job preparation. Practices like interview and resume preparations are now normal for Ivy League students, when they were not always. Lack of jobs, decent wages or even job security can quickly lead to unpaid college loans, deferments and forbearances, which of course can drive the interest rates up.

"That used to be more in the background, it's a little more in the foreground now because of the job market and because of the anxiety that it's created," Salovey said.

Previous studies say, while many college grads are working where their degree is not necessary, the job search becomes even more difficult without a degree. Salovey said with rising public university costs and the pile of national student debt, private schools like Yale are actually becoming more cost effective.

Many elite private schools have massive endowment funds set aside for worthy students who qualify academically and financially. Salovey said when a family can get a better break at a school like Yale then at a state school, a problem exists.

"It troubles me deeply that for a middle class student, let alone a working class student, if they're admitted to a place like Yale University, their families will pay less for that college education than typically if they went to the state university in their own state as state tuition payers," Salovey said. "That is a challenging model."