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The financial fortunes of large and small private universities are veering in opposite directions, with small colleges under more and more pressure, according to new research released Monday by Moody’s Investors Service.

About a third of small private colleges rated by Moody’s generated operating deficits in the 2016 fiscal year, an increase from 20 percent in 2013. In contrast, just 13 percent of large comprehensive universities posted operating deficits in 2016, down from 20 percent three years before.

The richest universities also held the vast majority of the wealth. The 20 wealthiest universities hold about 70 percent of total wealth in the private college sector. Comprehensive private universities grew their wealth sharply over the last several years. Their spendable cash and investments rose 22.5 percent from the 2012 to 2016 fiscal years.

Universities have been pulling in more money from donors. But again, the wealthiest universities are faring best. Top fund-raising universities -- those with more than $100 million in annual gifts -- account for two-thirds of fund-raising among rated universities. There were 28 universities with more than $100 million in annual gifts. They increased gift revenue by 22 percent between 2012 and 2016. Universities with gift revenue of $10 million to $100 million grew their gift revenue by 19 percent during those years.

In contrast, universities raising less than $10 million per year increased gift revenue by just 4 percent.

The divergence between large and small universities comes at a time of constrained tuition growth. In the 2016 fiscal year, 31 percent of all private universities rated posted declining net tuition revenue. And 57 percent did not grow revenue fast enough to keep up with the inflation rate across higher education, which was 3 percent.

Small private colleges again faced the most pressure, with roughly half unable to grow net tuition revenue. Meanwhile, 83 percent of comprehensive universities were able to grow net tuition revenue.

Some risks do threaten large comprehensive universities more than small ones, however. Comprehensive universities receive more revenue from patient care, grants and contracts. So they are more exposed to potential federal changes to research funding and to health care reform.