However, the pension deficit decreased by $28 billion to finish out 2015 at a level of $291 billion; that's compared with the $319 billion deficit that existed at the end of 2014.

"An increase in corporate bond rates in advance of the Fed's recent interest rate decision, combined with a flat global stock market, contributed to keeping pension plans in roughly the same financial shape as the previous year," Alan Glickstein, a senior retirement consultant at Towers Watson, said in a statement.

Read: Non-financial corporate pension underfunding to shrink

Glickstein continued, "While pension obligations declined last year, so did assets. There was a lot of movement in the funded status throughout the year, but at the end of the year, essentially nothing changed overall. In contrast, the preceding two years were more volatile, one up and one down plans."

The analysis estimated that, during 2015, companies contributed $32 billion to their pension in 2015—enough to cover new benefits earned by employees during the year, but not enough to cut the overall funded status deficit.

Employer contributions have been falling steadily for the last several years, in part because of legislated funding relief.

Pension plan assets dropped by an estimated 6 percent in 2015, taking them to an estimated $1.33 trillion at the close of the year compared with $1.41 trillion at the end of the previous year.

The change reflects increases of roughly 2 percent due to investment returns and employer contributions, which were offset by a decline of 8 percent from benefit payments and settlement transactions.