PensionTsunami.com brings us these remarkably insightful remarks from David Crane that explain why – when already carrying an unfunded liability – a pension system needs to outperform, not merely hit, their investment target in order to reduce their deficit:
Recently newspapers have reported that CalPERS earned 2.4% over the last twelve months and contrasted that return with its 7.5% assumed rate of return. But what those newspapers have not reported is that CalPERS needs to earn much more than 7.5% per annum for its unfunded liability not to grow.
This is because (i) under US public pension fund accounting, liabilities grow at the assumed rate of return and (ii) currently, liabilities exceed assets. That means assets have to grow faster than the assumed rate of return in order to keep up with liabilities.
As a simplified example, let’s say a public pension fund has a 77% funding ratio, which means that it has assets equal to 77% of liabilities. For greater simplicity, let’s say it has assets of $77 and liabilities of $100, and therefore an unfunded liability of $23 (100-77). Because of item (i) above, liabilities grow 7.5% per annum. That means liabilities that today equal $100 will in one year equal $107.50. For the unfunded liability not to be larger than $23 at that time, that means assets have to grow from $77 to $84.50 (107.50-84.50 = 23). That means that the pension fund needs to earn 9.7% ($77 times 1.097 = 84.50). Anything less and the unfunded liability will grow.
This is why it’s so hard for US public pension funds to catch up once they fall behind. See this relevant article from The Economist.