With Detroit’s bankruptcy in the news, the Grumpy Economist looks at the unfunded promises of public sector pensions — or pension bombs:
Maybe it would clear things up if pensions had to report a “shortfall probability” or “value at risk” calculation like banks do. OK, you are assuming an 8% discount rate because you’re investing in stocks. What’s the chance that your investments will not be enough? Coincidentally, when I saw Josh’s piece I was putting together a problem set for my fall class that illustrates the issue well.
Here is the distribution of how much money you will have in 1, 5, 10, and 50 years if you invest in stocks at 6% mean return, 20% standard deviation of return. I added the mean in black, the median (50% of the time you earn more, 50% less) and the results of a 2% risk free investment in green. (The geometric mean return is 4% in this example.)
The mean return looks pretty good. After 50 years, you get $20 for every dollar invested, or contrariwise an accountant discounting a promise to pay $20 of pensions in 50 years reports that the present value of the debt is only $1. But you can see that stock returns (these are just plots of lognormal distributions) are very skewed. The mean return reflects a small chance of a very large payoff.
In these graphs the chance of a shortfall is 54, 59, 62, and 76% respectively. As horizon increases, you are almost guaranteed not to make the projected (mean) return! The median returns — with 50% probability of shortfall, in red — are a good deal lower. And the modal “most likely” return is below the risk-free rate in each case.