As PERA prepares to release its 2011 Comprehensive Annual Financial Report, keep an eye on 2011’s returns. \u00a0Treasurer Walker Stapleton understatedly calls 2001’s anemic 1.8% return, a “serious warning sign<\/a>.” \u00a0I’d call it a big, red, flashing LED billboard.<\/p>\n

“What’s the big deal? \u00a0It’s only one year,” I hear you cry.<\/p>\n

Well, it turns out that if you’re projecting returns over a long period, the early returns have a disproportionate effect on whether or not you’ll make your targets. \u00a0And while PERA projects an overly-optimistic 8% annual return, even meeting that as an average cumulative return is no guarantee of solvency to the end.<\/p>\n

Returns aren’t smooth, they vary over time, and while the exact distribution is a matter of dispute, that fact isn’t. \u00a0While the actuarial outlays are relatively smooth, returns can bounce around all over the place, and poor early returns can mean that you’re eating into your principal, and won’t be able to make it up on the back end, even if the returns rise to meet your project cumulative average.<\/p>\n

Take three sets of return profiles, one constant, one with slightly higher-than-expected returns the first two years, and one where the fund loses 5% a year for the first two years, but settles in at a higher rate.<\/p>\n

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All of them converge to the save Cumulative average at the end of the 20-year run:<\/p>\n

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But because they have to take money out each year, the end of year balances tell a starkly different story for the three funds:<\/p>\n

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One fund slowly declines from $1 million balance to $800K. \u00a0The one with higher early returns also declines, but ends up above its starting balance. \u00a0And the one with poor early returns never recovers.<\/p>\n

In fact, 20 data points is a very small sample, and even a distribution of returns that averages 8% could easily produce, over 20 samples, returns far higher or, more likely, far lower. The graph below shows the average returns and final balances\u00a0from a 10,000-run Monte Carlo simulation:<\/p>\n

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Below about 10%, there’s a virtual guarantee that some of the funds will go bankrupt. \u00a0Let me emphasize that this is a very simplified model, for display purposes only. \u00a0Do not try this at home. \u00a0(Actually, go ahead and try this at home. \u00a0You’ll probably be as depressed and I was.)<\/p>\n

What this shows, though, is that even using a lower rate of return doesn’t necessarily guarantee the fund’s soundness, and certainly doesn’t model the fund’s future. \u00a0The only way to do that is through a Monte Carlo simulation, using the historical returns of the assets in which the fund is invested.<\/p>\n

While more complex to do, and very hard to model on a spreadsheet, there is precedent for incorporating Monte Carlo modeling into financial planning<\/a>, pension solvency analysis<\/a>, and even into accounting. \u00a0The Black-Scholes method, for instance, is used to calculate the value of stock options granted to employees and expensed on corporate financial statements. \u00a0And allowances for bad debt are routinely audited for fidelity to previous customer defaults. There’s no reason that we couldn’t require pensions to do the same.<\/p>\n

At the very least, it would perhaps keep today’s 1.8% return announcements from being such a surprise, and from taking such a toll on PERA’s solvency estimates.
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