Zero hedge has a piece this morning that calls out the unrealistic assumptions about future returns being made by public pension funds. Unfortunately the piece then presents an example that fails to take into account the most serious problem facing them.

Let’s take a simple example. Imagine a city with a single employee who’s been promised a lump sum pension of $1,000,000, which is due to be paid in 2025. And let’s say the city set aside $300,000 to fund that pension. If the pension fund earns an annual return of 8%, it’ll have $755,451 in 2025, leaving a funding gap of $244,549 – roughly 24%. This is close to the Pew estimate of a 26% funding gap for the cities in its study.

And if the fund doesn’t deliver triple today’s long-term Treasury yields? If its managers outperform Treasuries by only a moderate amount after fees and earn, say, 4%?

With a 4% annual return, the city would have $480,310 in 2025 – a shortfall of 52% against its $1,000,000 obligation.

In other words, a small dose of realism more than doubles the funding gap, which climbs from 24% to 52%.

The most serious problem is the drawdown problem. The lump sum distribution in the example is unrealistic – it makes the math easy, but is not the way that pensions work. Most pensions provide a stream of payments – typically monthly – which are meant to replace the salary the employee received when working. When figuring the amount of money needed to fund a person’s pension, the first thing to do is to make an actuarial estimate of the person’s life expectancy. Then the estimated return comes into play and we calculate how much cash is needed at retirement to pay the committed pension amount for the rest of the person’s life. Since compounding and annuity calculations are involved, we have to dust off the HP-12C. Now if we are buying Treasuries, which are considered risk-free, with a maturity that matches the expected life, we can stop now and hit the links. But if we have used a higher return than the Treasuries, which means taking investment risk, then we have to do more. We have to take into account the fact that the price and yield of our investment will change over time, even though the average return ends up where we guessed it would. Here’s my example.

Imagine a city with a single employee who’s been promised a typical monthly pension of $10,000, starting now, and an actuarial life expectancy of 30 years. If the pension fund earns the annual return of 8% – every year -that most are assuming, it will need to set aside $1.35 million. If we do the simple calculation above, using the 3% after expenses that we get from 30-year Treasuries, the city needs to set aside $2.35 million to fund that pension, nearly twice as much.

But it is not that simple. Let’s assume the city goes all in the stock market for the 8% and in fact makes it. But it is not level, and the next ten years are like the last ten, and the stock market is flat. Then for the remaining 20 years it is hot and averages 12.2% a year so that 30 years from now, looking back to the present we see an average 8% return. The problem is that for those 10 years the city had to pay out $120,000 a year. If the city only set aside the $1.35 million at the end of 10 years there is only $150,000 left in the kitty, enough to fund only a $1,700 per month pension. Oops. So clearly we need to go back to the drawing board and re-figure our stake. In this example, we need to have $883,000 left at the end of 10 years, so our initial stake needs to be $883K+$1.2M, roughly $2.1 million. Given current valuations, a flat market for the next 10 years is highly optimistic and so if you put in any negative returns it gets worse – much worse.

Let’s assume what John Hussman says is the central case – a 40% loss over the next 5 years. Then we continue to assume the market recovers to make our original 8% average, coincidentally it needs to make that same 12.2% per year. We need to have $930,000 invested at the end of year 5, so we need to have started with $1.55M (930K/.6) plus $824K to make the 5 annual payments – $2.37M.

In these realistic – even optimistic – scenarios, the simple minded calculation leaves the pension 36-43% underfunded even though the city would report it as 100% funded based on a constant 8% return.

The short summary is that shooting for returns higher than Treasuries leaves a huge exposure to volatility of returns that no-one is talking about.