STATE pensions in American are in trouble.Just how underfunded they are depends on how you calculate their assets and liabilities. Some estimates suggest the unfunded liability is several times larger than all outstanding municipal debt.

Many states assume that their investments will generate about an 8% annual return. States justify this assumption based on the fact that most of their assets, about 70%, are invested in equity. But whether or not stocks will return 8% is uncertain. If you invested in a well diversified equity fund over the last ten years you'd have been lucky to average 2% annually. And so some critics argue that 8% is almost certainly too high. I am not convinced 8% is necessarily so terrible, however. When estimating the equity-risk premium states should use decades of data because state pension funds have a long investment horizon. And if you estimate the equity premium using several decades of data, you can justify an 8% annual return. Perhaps the equity market has entered a new era with permanently lower returns, but that's unknowable at this point. Based on long history alone, an 8% annual return is not totally crazy.

What does bother me about the 8% assumption, however, is that states don't adequately account for risk. Average equity returns may well be 8%, but that comes with about a 20% standard deviation. Riskier portfolios do typically pay higher returns, but with the obvious downside of higher risk. What's outrageous is that states use their expected return as the discount rate when they calculate their liabilities. The discount rate you apply to a series of liabilities is supposed to reflect the likelihood that the payment will be made. It forces you to account for the fact that you still may still have to make payments when markets are down and capital is dear. It's written into many state constitutions that pension benefits are guaranteed, so benefits are as close to risk free as they come (though there may be scope for states to cut benefits in real terms by adjusting how much they're indexed to inflation). States must make payments no matter what happens in financial markets, even if markets crash and asset values plummet.

The expected return as a discount rate is often rationalised because, the thinking goes, states can always get more revenue from the taxpayer. But this is precisely what troubles me; states are free to invest how they like and all the risk is borne by the taxpayer. It gives states every incentive to use a high return assumption because it increases projected assets and lowers liabilities. They can always justify higher expected returns by investing in riskier, higher yielding assets. Assume a high enough return and your short-fall disappears altogether.

When I researched this briefing on the state pension crisis, no one I spoke to thought that accounting rules actually induced states to take on more risk. That was a few years ago. I wonder if, after states saw their funding ratios decimated in the financial crisis, that's still true. Lately states seem to have been investing in riskier assets; moving more into private equity.

At the same time, pension plans everywhere are also desperate for yield. Pension plans are reportedly underfinanced by anywhere from $700 billion to as much as $4 trillion, depending on the calculations. Poor returns over the last few years have not helped. Over the last five years, the average state and local pension fund has returned 4.7 percent, according to Callan Associates. Pension plans hope to make up these lost years and reach performance targets that in some cases are still set at a hopeful 7 to 8 percent a year. Private equity has traditionally been a high-performing asset class, and shifting more assets into this and other alternative investments like hedge funds is seen as a possible solution. Wilshire & Associates recently found that the average pension fund had increased its allocation to private equity to 8.8 percent in 2010 from 3 percent in 2000.

States investing in private equity is not necessarily a scandal. If these are superior assets to which pensioners don't have direct access, it may be a positive development. But what worries me is the risk and fees involved. The accounting rules give pension funds every incentive to chase whatever asset has the highest expected return and to stick the beleaguered taxpayer with the downside.