One of the biggest problems with the way that pension plans report their solvency numbers is the assumption of constant returns over the life of the plan. By assuming constant returns, plans end up hiding the single biggest factor in why they’re likely to go bust: risk. This post will try, with a hugely (and unrealistically) simplified example, to illustrate the problem this poses when trying to figure out whether a plan has enough money to cover its liabilities.

For this first cut, the aspect I want to capture is that with mandatory annual outflows, a pension fund puts itself at risk of falling behind, and never being able to catch up.

Let’s take this example: a $1,000,000 liability, timed to last 30 years, with $250,000 annual payouts, and payments into the fund that are calculated based on the expected return on assets. Here’s what the fund balance will look like if we assume a constant 8% return on assets:

Payments into the fund each year are calculated to be a little over $161,000 a year in order to make this happen. Also note that all this is being conducted in real dollars; we’re ignoring inflation, which is going to drive some people up the wall, but 1) we can always make a calculation in real dollars, 2) there’s really no good way of predicting inflation over a 30-year span, and 3) this is a thought exercise.

Where can I get an 8% a year return for 30 years? Well, I could put it in bonds that return 8%, but those may not always exist. Right now, we have a low-interest rate environment, and even corporate bonds that are highly-rated don’t necessarily return 8%. Surely investment-grade municipal bonds don’t get me 8% at 30 years. And remember, I need to find a place to put each year’s inflow, so by the end of the 30 years, I’m unlikely to find a 1-year corporate or municipal bond that pays me 8%, absent a pretty severe inflationary environment.

One investment that is liquid, that also provides reliable 30-year returns over 8%, is the S&P 500 index of large-cap US stocks. The S&P has been around since 1926. So starting in 1955, we have 30-year return profiles for it. Here’s the distribution of annualized 30-year returns for the S&P 500, from 1955 – 2011:

The thing has *never* returned less than 8.5% over that time, and averages 11.76% (although the median is lower). This is a period of time that covers a World War, a Depression, inflation, the Korean and Vietnam Wars, the 2000 Tech Bubble Burst, and the 2008 Real Estate Bubble Burst. That’s a pretty good track record.

Here’s the rub. Here are the *annual *S&P 500 returns over that time:

Not so good. You have a pretty good chance of losing money; in 11 years out of 85 you’d be down 10% or more, and in 6 of those years, down 20% or more. In three of those years, you’d lose 35% or more of your total investment. You can see the problem: the risk of running one really bad year, or a couple of moderately bad years, early on, where you might have to spend your seed corn, is high enough to be worrisome, even if the total 30-year return is comfortably higher than your planning.

In order to see our imaginary fund’s chances of making to 30 years solvent, we need to put in not a constant 8% return, but a random variable that looks like the S&P 500 annual return. Surprisingly, there’s considerable debate over whether or not such a variable is even possible to construct. The returns are clearly not normally distributed, and adding more moments (skewness, how fat the tails are, etc.), doesn’t produce unique random variables. When you look at the returns, it also looks as though the year-to-year returns may not really be independent, either; that is, a losing year seems to follow another losing year.

Given all this debate, I just figured that, with 57 separate 30-year runs available to us, the easiest thing to do would be to use those 30-year runs themselves. I.e, 1956 – 1985, 1957 – 1986, etc. Here’s a pretty typical return profile:

One really bad year, a couple of downers soon after, but positive almost all the time, and a number of eye-popping returns of over 40% to make up for it. Should work out, ok, right?

Not so much:

The actual balance in the account falls below the projection in Year 9, and never really is able to gain altitude again. By Year 20, the fund is bust, and has to either get bailed out or stop making payments.

What’s interesting is that it’s not the Year 6 Catastrophe that does the fund in. Given the good years that preceded it, the balance after Year 6 is right at the projected levels. A fund manager could easily persuade himself that everything’s going to be ok. What really causes the problem is the two bad-but-not-disastrous Years 9 and 10 consecutively. The S&P comes back in consecutive years with 20%, 25%, 20%, 35%, and it’s still not enough to put any real air between the balance and the ground. So by Year 15, when the S&P loses less than 10% – less than it had lost in any of the previous losing sessions – it’s effectively all over.

How often does this happen? Well, here are the failure rates for various return assumptions, starting with the average of 11.76% that the S&P actually returns, and going to 7%, for the ultra-conservative fund manager:

The manager who doesn’t leaving himself any breathing room cashes out over 60% of the time, which might be a little surprising. It’s not until we assume a 10% return (corresponding to annual pay-ins of $143,000), that we get to a 50-50- chance of seeing 30 years. Our 8% manager still fails over a quarter of the time, and it’s not until we get past a 7% assumed return (pay-ins of $169,000) – where we’re effectively giving up *40%* *of the actual S&P historical return *in our planning, that we almost get to an 80% chance of solvency in Year 30.

Now, to be clear, you don’t end up in such bad shape most of the time that you don’t go bust. You’re often well in the black. For the fund manager who’s planning on 7%, he ends up over $10,000,000 in the black over a third of the time. So often, when you win, you win really big.

But in pensions as in baseball, you can’t spend those winnings from other timelines. The Cardinals beat the Reds 15-2 today, but tomorrow, it’s 0-0 when the pitcher takes the mound. My concern as a pensioner is being able to plan on a certain amount of money coming my way after I retire. If the plan goes bust when I’m 75, it’s too late for me to make other plans. And if the plan ends up with an extra $9,000,000 on-hand when I’m 80, there’s not much benefit in that, either. The cost of losing is very, very high; the unlikely rewards from extra winnings don’t make up for that, which is why I put my money into a “safe” pension plan in the first place.

Understand, as stated at the outset, this is a hugely simplified example, on about 100 different levels. Real pension plans don’t consist of a single individual. They generally don’t make payouts at the same time they’re collecting contributions. The lifetime of the plan for an individual is longer than 30 years. Their portfolio is more diversified than putting everything in US stocks. Inflation actually matters to pensions, possibly for benefits, certainly for wage calculations.

But the basic point – that the actuarial assumptions of flat returns, assumptions that fail to take into account *risk* as well as *reward* – are serious planning flaws that can ultimately lead to a plan’s demise.

My hope is, over time, to make these models more complex, remove some of the simplifications, give something approaching actual likelihoods of Colorado’s PERA going bust, and ultimately, create an online model where you, the reader, can enter your own assumptions and see what happens to PERA’s long-term prospects. That’s a big project, and it’s going to take a long time to complete. But there’s nothing in the finish product that isn’t here in the basic principles: returns move around all over the place, and the cost of providing ownership in a liability rather than an asset can be ruinous.