Earlier this month, I debunked the commonly misrepresented concept that pension funds grow investment income out of thin air in such a way the employers and taxpayers only pay 15 or 20 percent of the total cost of the plan — with employee contributions and investment income paying the rest. My column explained that interest rightfully follows principal, and if employers didn't make their contributions, there simply wouldn't be any investment income. So the traditional mantra of investments carrying the vast majority of total costs is a half-truth. If pension funds pay interest on refunds of employee contributions and for retirees' deferred "DROP" accounts, then it is obvious that interest follows principal in practice, and the whole claim is puffery.

But there is a refinement to that analysis that I would like to now add, in the ongoing spirit of fairness to all sides in the pension debates. Last week, I attended a presentation by a respected practitioner in the field, a public pension administrator. He made an interesting point in his discussion of this issue that enlightened my analysis.

As I noted in my original column, employers who don't make actuarial contributions to a pension fund could invest the money themselves and pocket the income. Likewise, employees who contribute to plans could do the same. Thus, pension investment income does not come out of thin air. What my colleague expressed in his presentation was that employees could have invested the money in their own IRA or 457 deferred compensation plan, and that got me to thinking: What would the employers and the employees actually earn on their money if it were not invested in the pension fund? (Hint: it would be less than the fund can earn.)

For the employers, the answer is that their general operating funds must be invested under conservative state investment statutes that prohibit investments in stocks, real estate, private equity, and all the riskier securities that pension funds are allowed by law to purchase. Public employers are allowed to buy government bonds and money-market instruments and not much else. These days, that earns them 1 percent or less — or maybe 2 percent if they were aggressive on the yield curve last year. Those restrictive general investment laws are sensible, because the public employers cannot afford to take risks with principal over short periods of time: they have bills to pay and taxpayers loathe fat reserves so long-maturity investments are discouraged. Even rainy-day funds are seldom invested in maturities beyond five years. Their mantra is safety, liquidity and then yield, in that order.

For the employees who invest in their own deferred compensation accounts, they can invest in retail stock and bond mutual funds, closer to what a pension fund can purchase, but typically at higher fees and with no access to private equity markets, institutional investments and such.

So, there is indeed a certain amount of pension investment income that can rightfully be claimed by the pension funds as unique to their enterprise. It's the risk premium they receive from their highly diversified, professionally managed portfolios — in comparison to Treasury bond yields that would be the very best that the public employers could ever purchase with the same money. And it's the higher returns after fees that pension funds obtain from sophisticated institutional investments with ultra-low fees that employees as retail 457/IRA investors cannot obtain on their own.

Let's look at each of these separately. If a public employer had purchased government bonds over the past 20, 50 or even 85 years, the investment returns on bonds in those periods would have been less than the returns on stocks — except for the past twenty years which have included the Dismal Decade of 2000-2010 and the biggest, longest bond rally in two generations. Historically, the annual returns on bonds including corporate issues were about 5 percent using the 85-year Ibbotson data. Of course one can cherry-pick certain starting points such as 1981-83 when long-term Treasuries yielded 14 percent, so the entry point is critical when performing these studies. But in general, it is fair to say that the additional returns on stocks over bonds over the past 85 years is about 4 or 5 percent. When pension funds invest in those securities, they can derive the classic "risk premium" that is the foundation of modern capital markets theory. Thus, a pension fund with a diversified global stock/bond portfolio should reasonably be expected to earn about 3 or maybe 4 percent more than government bond yields over an extended period of 40 years or more. This is money that the pension fund can earn which the employer could not. Let's call it pension premium income. It's not an infallible formula, but it works over long periods of time, and it has to work ultimately if capitalism is to survive. (However, it's not risk-free, and therein lies an issue we must also address, especially in the aftermath of a decade of investment underperformance.)

Likewise, the investment fees and costs borne by retail investors, plus their lack of sophisticated money management and lack of scale to participate in the big leagues, typically results in a 1 percent relative shortfall in their returns over time. Some studies quantify the difference as even more, because individual investors tend to be more conservative, or more naïve and inexperienced. Again, that 1 percent "institutional advantage" is unique to the pension fund. Let's call this "institutional" pension premium income.

So, with those two sources of pension premium income now identified, it would now be possible for a pension fund to make a far more rational calculation of the amount of investment income the pension funds have produced in the past (and could in the future) vs. the returns their contributors would have earned. If employers made two-thirds of the original contributions and employees paid in the other third, using numbers commonly presented in some of these pie charts we see, then it would be possible to estimate the pension investment income attributable to the employers and employees, and then assign the remainder to the pension fund. Obviously, the math would vary from plan to plan based on its history of contributions and its actual investment experience over the years. But to provide a rough estimate, a little less than half of the investment income derived from employer contributions might be properly claimed as pension plan income and about 15 percent of the historical investment income derived from employees' contributions would meet that standard.

This suggests that overall, about one-third of the total cumulative investment income over several decades could rightfully be earmarked as pension premium income that is unique to its ability to capture the capital markets risk premium and the more efficient returns of institutional investing.

That's not the end of the story, however. Before tallying the results, we also must next account for unfunded liabilities when investments have failed to meet the actuarial expectations. Under today's pension conventions and practices, the employers are entirely liable for this underperformance.

Thus, it is necessary to deduct the outstanding unfunded liabilities owed by the employer for the investment underperformance from any "pension plan income" and attribute this instead to the employer contributions. Otherwise, the computation of employer contributions is incomplete and misleading. Needless to say, the accumulated unfunded liabilities of our nation's public pension funds, which represent more than 40 percent of their total portfolios today, exceed all the pension premium income that can be attributed to the plans in the past 20 years.

I'll leave it to some ambitious graduate student or a research group to perform an historical study across a number of plans to see how the data shake out, and see how far back we need to go in order to actually find any pension premium income in light of current unfunded liabilities.

So I must now confess that I debunked only three-quarters of a half-truth. Some number, perhaps one-third, of pension income can be said to come from thin air, as unique to the special-purpose trust fund used when a pension plan is actuarially funded. But that's before we take into account the unfunded liabilities which come with the package. So let's sharpen our pencils and stop using over-simplifications that grossly distort the primacy of employer contributions, and the risks that taxpayers and the public continue to shoulder.