The largest 100 public pension funds have around $1.2 trillion of unfunded liabilities, about $300 billion above the nearly $900 billion they reported themselves, according to a new actuarial study to be released on Monday.

The pension systems reported a median funding level of 75.1 percent. The study by the actuarial firm Milliman, which used different ways to value assets and measure liabilities, finds an aggregate level of funding of 67.8 percent.