Senate majority leader Mitch McConnell recently suggested that the federal government should not bail out mismanaged state pension plans. I defended those comments in a column, noting among other things that McConnell is right about many state pensions.

Some states have made exorbitant promises to their employees over the years without providing adequate funding. They made up the difference, on paper, by projecting unrealistically high returns on pension investments.

The Federal Reserve, applying a better projection of returns, estimates that pensions are underfunded by $4 trillion.

Reader J.W. pushed back in an email, challenging me to justify the claim that the assumed returns are unrealistic (and, implicitly, to justify the claim that the Fed’s estimates are better).

A “blue ribbon panel” of the Society of Actuaries looked into this issue and related ones a few years ago, and while its precise numbers are dated, its general picture is not. The actuaries’ report noted that private pensions had dropped their estimate for assumed returns from 1993 through 2010 while public ones had not. Since rates on U.S. Treasuries had dropped during this period, the assumed risk of maintaining that return had “increased significantly.” A plan with a 70/30 mix of stocks and bonds, they concluded, ought to be forecasting returns under 4 percent, not above 7.

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But a 70/30 mix is probably too risky for plans that are supposed to deliver legally guaranteed benefits to a population that is increasingly made up of retirees. The Society of Actuaries has rebuked public plans on this point, too:

We are concerned that we see many public sector plans using practices that have not been used by private sector plans or that have been abandoned by private sector plans around the world. We see public sector plans making choices about risk taking that go against basic risk management principles. For example, public sector plans in the U.S. are unique in that they have taken additional risk as the plans have become more mature, compared to private sector plans in the U.S. and private and public sector plans in Canada, UK and the Netherlands, which have taken less risk as plans have matured.

Public pensions are regulated more loosely than corporate ones are, with the former allowed to discount their liabilities based on expected returns and thus required to devote less funding to covering them. The Fed’s estimates, by contrast, take account of the riskiness of a pension plan’s portfolio.

And that’s how you get to a $4 trillion funding shortfall.