PERA – Why 8% Isn’t 8%

State Treasurer Walker Stapleton has been on the hustings, touting the need for PERA reform.  His oped in the Denver Post a little while ago pointed out that the fund’s actuaries assume an 8% return on investments.  If we don’t do something about the underfunding, Stapleton noted, we’ll be forced to take on more risk to try to reach the fund’s investment goals.

Now, PERA’s been criticized for assuming an 8% return, but that’s not really the problem.  Eight percent is, in fact, the average annual return on US stocks since about 1870, according to data collected by Robert Shiller, he of the half-eponymous Case-Shiller Housing Index.  The problem is, the standard deviation – the range within which about 5/8 of the returns actually fall – is 18%:

Annual Returns

Which means that a lot of the time – almost one-third – you’re getting negative returns.  For Backbone Business, I worked up a little scenario where you’re starting with $100,000, paying out certain portion each year, getting 8% return a year on your balance, and you come out even.  But what should be apparent is that there are lots of scenarios that get you 8% average return, but force you to pay out more than you’re getting in the early years, and you never make up the difference.  Here are some very basic scenarios:

And the graphs of the balances:

Now, here’s part of the reason that people get fooled by the 20-year returns number.  In fact, for 20 years, the average return, as you would expect, is about 8%.  But the standard deviation is much, much smaller, about 3%, which makes sense statistically if you’re averaging lots of the same random variable:

20-Year Returns

The average is the same, but you also get a skew to the left: you’re more likely to make more than 8%, but the downside range is larger.)  Moreover, you can’t really use the 20-year average for planning purposes, since you’re paying out benefits every year. The problems with this for planning purposes by now should be obvious.

What does this mean for actual chances of ruin?  Nothing good, I’m afraid.  Shiller has 139 years of annual returns (prices + reinvested dividends), so he has 120 groups of 20-year returns.  I set up my baseline scenario – which remember, is perfectly balanced, 100% funded for its obligations, and ran it against every group of 20 years:

Better Feed the Pig

Roughly 5/8 of the time, you end up with a negative balance.  Shiller’s annual returns are positive almost 70% of the time, the 20-year returns are more than the necessary 8% about 55% of the time.  But it’s still not enough to let you recover from bad years early on.  In fact, the correlation between each of the first few years’ returns and the final balance is about 0.40, very high, and it declines steadily as balances decline (i.e., the path has already been set), and mean reversion kicks in:

Get off to a good start.  Seriously.

Also remember, even those 20-year returns can be lousy.  The best 20 years on record?  1942-1961 (beating out 1980-1999 by 4 one-thousandths of a percent).  The worst?  1962-1981, years of then-unheard-of regulatory intervention, budgetary profligacy, and later on, inflation and repeated recession.

Obviously, this is an exceedingly simple model I’m using.  You can probably hedge a little of the downside risk and pick up a few basis points doing that.  But on the whole, risk is related to reward.  Still, I think it argues for using a statistical model of solvency rather than assuming a linear rate of return.  We do this sort of thing, very imperfectly, for pricing options using the Black-Scholes method, and there we’re actually dinging a company’s balance sheet.  Here’s we’re just trying to figure out if there’s enough in the bank to make ends meet.

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