STUMP » Articles » Causes of Public Plan Insolvency: On Public Pension Valuation » 15 November 2018, 08:39

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Causes of Public Plan Insolvency: On Public Pension Valuation   


15 November 2018, 08:39

As noted in my prior post, I am walking through aspects of the paper co-written with W. Gordon Hamlin, Jr. As I am not a lawyer, I’m not going to talk much about the legal aspects, though that is the key new idea in the paper itself.

Section 3 of the paper details the reasons that public pension DB plans have been running into financial trouble, and 3.1 is where we look at how public pension funds are valued for both solvency and funding purposes. I’m covering all the subsections of 3.1 for this paper.

The primary driver here is the rate at which future liability cash flows are valued. There have been some minor changes to this, but in general, the expected rate of return on assets (unadjusted for embedded asset risk) is what is used.

Let’s go through the argument.

3.1 Use of the Expected Rate of Return as the Discount Rate

The full text of this section:

Almost alone among the world’s public pension plans, the United States plans have slavishly stuck to the expected rate of return as the discount rate for calculating the present value of future liabilities, resulting in enormous controversy. Some authors have concluded that a partial explanation for this phenomenon is a conflict between the interests of current employees and retirees, with board members and elected officials opting to use higher discount rates and pursuing riskier investments, all to maintain lower annual contribution rates.(Andonov, Bauer and Cremers, Pension Fund Asset Allocation and Liability Discount Rates 2017) We will address chasing yield via investments in Section 3.4.

Here is the paper we reference: Pension Fund Asset Allocation and Liability Discount Rates: Camouflage and Reckless Risk Taking by U.S. Public Plans?

Date Written: May 1, 2012


We use an international pension fund database to compare the asset allocation and liability discount rates of public and non-public funds in the U.S., Canada and Europe. We document that U.S. public funds exploit the opaque incentives provided by their distinct regulatory environment and behave very differently from U.S. corporate funds and both public and non-public pension funds in Canada and Europe. In the past two decades, U.S. public funds uniquely increased their allocation to riskier investment strategies in order to maintain high discount rates and present lower liabilities, especially if their proportion of retired members increased more. In line with economic theory, all other groups of pension funds reduced their allocation to risky assets as they mature, and lowered discount rates as riskless interest rates declined. The arguably camouflaging and risky behavior of U.S. public pension plans seems driven by the conflict of interest between current and future stakeholders, and could result in significant costs to future workers and taxpayers.

The higher the discount rate, the smaller future cash flows look today (and thus, future promises look cheaper). We will see the myriad effects the use of a high discount rate has in the below.

Related posts:

Public Pensions Primer: How Discount Rates Work

Public Pensions Primer: The Choice of Discount Rate and Return Volatility

3.1.1 The Effect of High Discount Rates on Normal Cost

Normal cost is the amount that needs to be contributed (under a variety of assumptions) to pay for the pension benefits accrued in the specific accounting period. This has nothing to do with amortizing the unfunded liability.

Let us consider the effect of the choice of assumed rates of return (used as the liability discount rate) on the normal cost for a standard defined benefit plan. Don Boyd and Yimeng Yin of the Rockefeller Institute of Government did a projection of the normal cost as a level percentage of payroll under a certain set of simplifying assumptions to see the effect of the choice of the discount rate assumption for an entry-age normal cost method. (Boyd and Yin 2018) Assuming a benefit of 2% times a 3-year final average salary times years of service, a COLA (cost of living adjustment) of 1% per year, with employee contributions of 4% of pay for a worker hired at age 25, retiring at age 60, and dying at age 80, we get the result seen in Figure 1. The age of death makes for an annuity-certain, instead of the actuarial approach with a standard mortality table, but it isolates the effect of the assumed rate of return to simplify analysis.

Figure 1

Source: (Boyd and Yin 2018)

This relationship is closely described by a logarithmic function, with a slope that flattens the higher the discount rate. We see the stark differences of an over-40% contribution of payroll, assuming a return of 2% per year, against a 5% contribution of payroll if one has 8% per year returns. Also, one can see the effect of going up the slope – changing from 8% to 7.5% in discount rate makes for an increase of 136 basis points contribution rate; changing from 2.5% to 2% increases the contribution rate by 553 basis points. The pension plan sponsors who are allowed to set this key assumption, and who want to minimize cost, are not ignorant of this relationship, at least qualitatively.

We received the data from the researchers Boyd and Yin, who are researchers at the Rockefeller Institute. You can see a variety of their papers here, on public pensions.

I have a later post after I go through my items of argument, where someone argues using lower valuation rates will make public pensions far more expensive.

Well, it definitely boosts the normal costs, but ultimately, the benefits cost what they cost. The accounting/valuation method is just a way to approximate the evolution of that cost. Once everybody’s dead, we’ll know, retrospectively, what it really cost.

But you can see why there is so much argument over even dropping the valuation rate only 25 basis points (aka 0.25 percentage points) — it has a nonlinear effect on the calculated costs.

Forcing them to drop valuation rates from 8% down to 4%… that would make a huge difference in the numbers being officially reported.

3.1.2 Using Risk-Free Rates for Valuation

I’m not going to quote this full section in the way I did for the prior one, due to our lengthy block quote from somebody else.

Modern finance theory requires that present values be calculated based upon risk-adjusted discount rates. Because public pensions are protected to a certain extent by the federal and state constitutions from legislative impairment, and because most local governments are not likely to file for bankruptcy protection or debt adjustment, these pensions are presumed to be virtually risk-free. One can argue about whether it would be more appropriate to use a tax-adjusted municipal bond rate or U.S. Treasuries to reflect this risk-free aspect of public pensions, and there are many thorough and readable discussions of this issue. (Waring 2012) (A. H. Munnell, State and Local Pensions: What Now? 2012) (Novy-Marx and Rauh 2011) In recent years, many actuaries have begun to accept the notion that economic liabilities of pension plans should be calculated using a risk-free discount rate.

However, when a Joint Task Force of the Society of Actuaries and the American Academy of Actuaries produced a draft report calling for public pensions plans to use a risk-free discount rate to calculate their liabilities, the Task Force was disbanded, and a huge controversy ensued. (Burr 2016) (Bartholomew, et al. 2016) Because the appropriate discount rate for economic accounting purposes is bond-like, and because there are valid arguments for pension plans to invest in public equities, confusion is rampant.


The difference in annual contributions required between an 8% expected rate of return and a risk-free rate of return is stark. If the employer normal cost is five times higher at a 3.5% discount rate than at a 7.5% discount rate, governments have a powerful incentive to keep annual costs lower by using the higher discount rate, and they have done exactly that.

For what it’s worth, the people making the valuation rate decisions are generally politicians, though in some place the rates are set by people with a bit more financial knowledge than what one usually finds with politicians.

But politicians can generally do basic arithmetic, even if it’s just to count the votes: they know that the promises being made would look ginormous if they had to value at a much lower rate. Again, think of all the agita over dropping 8% to 7.5% for many plans.

3.1.3 Investment Return Assumptions of U.S. Plans versus Investment Performance

So, we’re valuing at the expected rate of return for assets… but how are those assets actually stacking up? Is 8% really what’s “expected”?

Let’s check that assumption.

Again, I’m not going to quote this part, mainly because I was to show the graphs and then explain what they show.

These box-and-whisker plots are using information from the Public Pensions Database. What we see here is a migration of 8% being the median for assumed return on assets, down to 7.5% as the median. The boxes go from the 25th to the 75th percentiles, and you’ll see this is often in a narrow range – only 25 bps sometimes. Those are the assumptions being used.

What have the longer-term returns actually been?

(These are time-weighted, not dollar-weighted, returns)

Now, what you’re looking at here are the box-and-whisker plots for 10-year average returns (note: I use a geometric average, as one should.). Given the Public Plans Database starts with fy 2001 info, my graph starts with 2010. Obviously, this history includes the crappy markets of 2008 (and also the crappy markets of 2001).

We had median 10-year average returns peak around 2014, at about 7%. There is a lot of spread in results here, too, far more than one sees with the assumptions.

Unsurprisingly, the dismal returns of 2008 and 2009 affect the 10-year returns, but even after multiple years of a bull market, the rates are generally well below the discount rate being used. The slowness for the valuation assumption to align with reality means that unfunded liabilities due to investment underperformance accrue.

And there’s nothing particularly magic about the number 8%. Why do they use 8%? Well, once upon a time, it made sense. Perhaps it no longer makes sense as an assumed expected return on pension portfolios.

3.1.4 Other Valuation Assumptions and Funding Approaches to Reduce Current Contributions

Let me quote the beginning of this section:

As seen in Section 3.1.1, the setting of the investment return/discount rate assumption has a very large effect. However, there are several other valuation assumptions and decisions in valuing defined benefit pensions, such as:
* Mortality rates (and trends)
* Salary growth rates
* Payroll growth rates
* Disability rates
* Beneficiary rates (for spousal or other benefits)
* Retirement rates at various ages
* Any early retirement adjustments
* COLAs (whether automatic or discretionary)

As mentioned earlier, the discount rate assumption tends to swamp the effects of the other choices, especially the higher that discount rate is. As many plans have lowered their discount rates, other assumption choices have come to the fore.

In many cases, the effects combine to reduce the amount needed to be paid now, while expecting future contributions to grow. A particular combination of assuming a steadily growing payroll and setting contribution rates as a level percentage of payroll has led to interesting effects for plans where full payments of normal cost and amortized unfunded liability costs are always made as calculated. When both payroll does not grow as expected, and investment results fall short (even if not by much), we see eroding funding ratios for plans that would seem well-run otherwise.

In Figure 4, we see the median funded ratio for U.S. public pension plans in the Public Plans Database that have always paid 100% of the ARC (annually required contribution) or ADEC (actuarially determined employer contribution) for the record of the Public Plans Database. As with the prior graph, data do not exist for all plans for all fiscal years, but the median is not affected by this as much as, say, a mean. There were 72 plans in the database out of the 170 that were 100% ARC payers. While there were a few periods of improvement, the plans have slid from full-funded in 2001, down to 75% funded in 2016.

This is figure 4:

Again, from the Public Pensions Database data.

Many aspects drive these results, but the main concept is that actual experience has been diverging from the assumptions made in valuing pensions. The pension cash flows ultimate cost cannot be known until after they are made; valuations are intended to make a fair estimate of where we expect these costs to land, and these drive funding policies. The more the valuations diverge from the emerging experience, costs rise to make up for those shortfalls.

Something is awry with methods of valuing the pensions for fundedness, if we have a secular trend.

The use of a too-high assumption to value the future cash flows is the largest driver, but there have been aspects, especially with regards to amortizing over what is assumed to be a growing payroll, that also lead to eroding funded ratios.


Here is the point: actuaries come up with a current-day valuation for public pension plans. The inputs being used to do this valuation (whether selected by an actuary (some of them) or a different party (usually discount rate is given by plan sponsor)) tend to be chosen to make these promises look a lot smaller than they have ultimately turned out to cost.

While we can’t know the “true” cost until all the benefits have been paid to a particular group of people, we have indicators, such as eroding funded ratios, that indicate there is something wrong with current valuation (and funding) approaches.

In subsequent sections, we will see the effects of this low-balling the promise value.

That’s all for today!

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