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The financial health of defined benefit pension plans for state and local government workers is a matter of policy concern and analytical contention. Pensions have come under increased scrutiny as funding levels have dropped and required contributions have risen. According to standard actuarial accounting, the average public pension was 76 percent funded in 2009, down from 95 percent in 2001.1 Likewise, annual required contributions (ARCs) — the costs of benefits accruing in a given year plus the amortization (generally over a 30-year period) of unfunded liabilities from prior years — were over $74 billion in 2009, up from around $29 billion in 2001, with further increases likely in future years.2 Overall, public pensions reported underfunding of $660 billion as of mid-2009, the most recent date for which complete information is available.3
Around the nation elected officials have undertaken pension reforms to correct those funding shortfalls, which were caused by market declines, funding holidays, and benefit increases passed during the prosperous days of the late 1990s. Numerous states have enacted pension reforms, although those mostly have been incremental reforms such as increasing contributions or retirement ages and most significant benefit or structural changes have been aimed only at newly hired employees. A few states, such as Utah, have made more far-reaching reforms to limit pension liabilities. Michigan and Alaska have shifted newly hired employees into defined contribution (DC), 401(k)-style pension plans. In other places, attempted reforms have been rebuffed by powerful public employee unions.
Unfortunately, these reforms won’t come close to restoring plans to true full funding, because current accounting conventions systematically understate pensions’ benefit liabilities and thereby overstate their financial health. Current pension accounting standards also encourage pensions to take excessive investment risk. Correct accounting reveals that the costs of putting the plans back on a stable financial basis is likely be prohibitive, which may prompt a shift to defined contribution pensions, mirroring the shift experienced in the private sector and in other countries.
Market Valuation of Pension Liabilities
The critical question is how to value benefit liabilities that will be paid years or decades in the future to make them comparable to the assets held by plans today. The current value of a plan’s liabilities depends crucially on the interest rate at which the liabilities are discounted. Under standard actuarial accounting, a public pension plan discounts its liabilities using the return expected to be generated by the portfolio of assets it holds. The average expected return on assets used in those valuations is close to 8 percent, with a range from 6 percent to 8.5 percent. The discounted value of plan liabilities is then compared with the value of assets to calculate the plan’s funding ratio (assets divided by liabilities) and its unfunded liability (assets minus liabilities). Similar values are used to calculate the plan’s annual required contribution (ARC).
“Current public pension accounting rules cause the plans to promise too much, contribute too little, and take too much investment risk.” — Andrew Biggs
The effects of changes in the discount rate can be dramatic. Under standard actuarial accounting, the same plan, with the same dollar value of assets and same dollar value of future benefit payments, can reduce its measured liabilities by nearly one-third by shifting from a portfolio with an expected return of 6 percent to one with an expected return of 8.5 percent. As explained below, that reduction in measured liabilities is illusory. After all, the value of the pension’s investment portfolio has not changed — it merely has been shifted from lower-risk to higher-risk investments. Likewise, the plan’s future liabilities have not changed. Yet a plan that was 70 percent funded under a low-risk portfolio “becomes” 100 percent funded once its assets are invested in a higher-risk portfolio.
Financial economists say that the discount rate applied to a benefit liability should have nothing to do with how the plan’s assets are invested. Rather, the discount rate for a given liability should be defined by the riskiness of the liability. The appropriate discount rate is not a matter of choice. If public pension benefits are guaranteed — as they are intended to be, and as legal rulings and state constitutions have determined them to be — they should be discounted using the interest rates that the markets pay on guaranteed investments, such as U.S. Treasury securities.4 On that point there is essentially no disagreement among economists. As Federal Reserve Board economist David Wilcox wrote:
These happen to be really simple cash flows to value. They’re free of credit risk. There’s only one conceptually right answer to how you discount those cash flows. You use discount rates that are free of credit risk. This is one of those things where it just really is that simple.5
Moreover, this is how financial markets value liabilities. If a pension fund sought to transfer its liabilities to a private insurance company — something that is common in the United Kingdom, though not in the United States — the insurer would base its price on the size and risk of the liabilities, without reference to the risk or expected return of the asset backing those liabilities.
Joshua Rauh of Northwestern University estimated that, when correctly discounted using the Treasury yield curve, total unfunded liabilities for public-sector pensions as of October 2011 are roughly $4.4 trillion, sharply higher than the 2009 figure of $660 billion computed under standard actuarial valuation.6 This amount exceeds total outstanding state and local government debt and is equal to nearly 30 percent of annual gross domestic product.7 These figures are so large that it is difficult to put them into context.
Context can be provided, however, through a smaller scale example. A March 2011 analysis prepared for the Florida Retirement System (FRS) by the actuarial firm Milliman calculates the costs of nine pension plans under the FRS using a range of discount rates,8 illustrating how market valuation would alter the measured value of pension liabilities and the costs of funding them. The FRS assumes an expected rate of return of 7.75 percent on plan assets and discounts plan liabilities accordingly. Under that baseline, the cost of funding benefits accruing in a given year — the so-called normal cost — equaled 11.96 percent of employee payroll, while the cost of amortizing unfunded liabilities from prior years equaled 3.35 percent of payroll, for a total ARC of 15.31 percent. But the correctly measured normal cost, using a 4 percent discount rate, the approximate yields available until recently on U.S. Treasury securities, is 31.33 percent of payroll. Likewise, the use of the correct discount rate raises the amortization costs to 13.95 percent, for a total ARC of 45.28 percent of employee payroll. Similar, and often larger, cost adjustments would apply to public pension plans around the country.
The use of the correct market valuation also reveals the true value of public employees’ pension benefits and of their total compensation. Normal costs discounted at a riskless return approximate the current value of pension benefits to public employees; netting out the employee contributions reveals the effective employer contribution. For most public employees, the correctly computed employer contribution far exceeds even the most generous private-sector employer contributions to defined contribution pension plans. For example, Florida public employees recently were required to contribute 3 percent of pay toward their pensions (previously they had made no contributions at all). If the true normal cost of pensions is roughly 31 percent of salaries, as indicated by the Milliman study, the net effective employer contribution is 28 percent of pay. Part of that contribution is made upfront, with the remainder in the form of a guarantee that full benefits will be paid even if the upfront contribution plus accrued investment earnings proves insufficient. This 28 percent employer contribution vastly exceeds the contributions made by private employers; according to the Bureau of Labor Statistics, the median private-sector employer pension contribution was 3 percent of pay, and 90 percent of employers contributed less than 6 percent.9
Simply put, public-sector pensions are significantly more generous than private-sector plans, more than sufficient to make up for the small salary penalty suffered by state and local government employees compared with private-sector workers with similar education and experience. It is highly unlikely that public-sector defined benefit pensions would continue in their current form if these cost levels were reported in a transparent manner and required to be funded.
Given the potential importance of these results, it is worthwhile to explore objections to the market valuation approach. To economists, discounting pension liabilities at the interest rate appropriate to the riskiness of the liabilities seems obvious, so much so that they sometimes fail to adequately explain their rationale to non-economists and defend against seemingly reasonable objections. The following sections discuss and rebut common counterarguments to the market valuation approach.
Does Market Valuation Make Unrealistic Assumptions About Asset Holdings?
Perhaps the most common objection is that the use of a risk-adjusted discount rate is appropriate only if pensions were to invest in riskless assets, which they do not and will not do. According to that objection, market valuation is simply unrealistic. For example, writing in Governing Magazine, Gerard Miller said, “Pension funds are not going to invest their entire portfolio in 3 percent Treasury bonds right now — or ever — so the risk-free model is not even descriptive of reality and has little normative value.”10
This objection misses the point of market valuation, which is that the value of a liability is distinct from the manner in which it is funded. Market valuation need not, and does not, make any assumption about how the pension assets are invested, precisely because the investment of the assets does not affect the value of the liability.
A relatively simple example demonstrates that market valuation does not ignore the reality of pension investments. In fact, market valuation precisely measures the cost of the investments required to actually pay the plan’s liabilities. The problem is that those required investments go beyond the assets held by the plan. As discussed below, options must also be held.
Consider a pension that owes a guaranteed lump sum payment of $1 million in 15 years time. Under standard actuarial accounting rules, if the plan invests $301,194 today — the current value of $1 million discounted at an 8 percent interest rate11 — it can call itself fully funded. But according to market valuation, this riskless payment should be discounted at a riskless interest rate. If the riskless return is 4 percent, the true value of the liability is $548,812. To truly be fully funded, the pension plan must contribute almost twice as much upfront as is required under the actuarial approach. It is understandable that most pension stakeholders prefer the actuarial approach.
But which approach is right? If the pension’s assets have an expected return of 8 percent, investing $301,194 will deliver an expected payoff of $1 million in 15 years, which may seem sufficient to fund the plan’s $1 million liability. Unfortunately, that is not the case.
The problem is that investment in assets with an expected return of 8 percent involves significant market risk, implying that the portfolio’s value after 15 years will almost surely not equal $1 million — it will end up being higher or lower than the desired amount. Assuming a 13 percent standard deviation of annual returns, the initial investment has a 42 percent probability of exceeding the $1 million goal and a 58 percent probability of falling short.12 A plan that has less than a 50 percent chance of being able to meet its obligations is not fully funded, given that the benefits must be paid 100 percent of the time. That mismatch exposes the fallacy of current accounting rules.
In reality, neither overshooting nor undershooting is what the plan is looking for. If it overshoots, some initial money was wasted upfront. If the investments come up short, by contrast, the plan won’t be able to pay what it owes and must turn to the taxpayer for a bailout. However, there are financial products — called options — that provide a solution. A call option allows the pension plan to sell off any surplus if the plan’s investment turns out to be worth more than $1 million. The proceeds of that sale can be used to offset the cost of the initial investment. Likewise, a put option can be used to top up the difference between the assets’ actual value and $1 million if the investment comes up short. So the plan will always be able to pay exactly the promised $1 million, with no wasted money, if it invests $301,194 in safe assets and sells a call option to dispose of any surplus and purchases a put option to cover any shortfall.
That means that the true cost of fully funding the $1 million future liability — meaning, funding it so that it is guaranteed to be paid without recourse to a taxpayer bailout and without any wasted surplus — is the $301,194 initial investment minus the $11,436 proceeds from selling the call option, plus the $259,053 cost of purchasing the put option. The net cost is $548,812, precisely the same as if the liability had been discounted and funded using the 4 percent riskless rate of return.13
This result is known as “put-call parity” and reflects the fact that market-based valuation methods produce the same end result even if they calculate that result using different methods.14 The same $548,812 value would emerge under any assumption about the investment choices made by the pension plan, provided that the cost of purchasing the put option and the proceeds of selling the call option were properly included.
When economists say that the true value of the liability is $548,812, they are not assuming that the plan invests in safe assets that yield a 4 percent return. As we have seen, the same $548,812 value arose from a computation that fully recognized the plan’s actual investment in risky assets that yield an 8 percent expected return, but that also accounted for the purchase of a put option to insure against shortfalls and the sale of a call option to dispose of surpluses. Of course, the plan won’t actually purchase the put or sell the call, but that simply means that the plan is not fully funded and the cost of the implicit put option is being imposed on taxpayers. If the plan invests $301,194 in the risky assets and stops there, the taxpayers are left with the obligation to make up the potential shortfalls, offset by the right to claim the potential surpluses.15 Because that obligation has a cost of $259,053 while the offsetting right has a value of $11,436, a plan that simply invests $301,194 in the risky assets has left taxpayers on the hook for $247,619. The $548,812 value is the true cost of the liability, the amount invested by the plan plus the underfunding imposed on the taxpayers.
This example shows that market valuation does not ignore the investments that public pensions actually make. Rather, market valuation fully accounts both for their expected returns and for their risk, and reveals the hidden liability imposed on future taxpayers who may have to bail out an underperforming pension fund. Market valuation also accounts for the possibility that future taxpayers may be able to claim a surplus from an overperforming fund, for instance, by reducing government contributions.
“It is highly unlikely that public-sector defined benefit pensions would continue in their current form if these cost levels were reported in a transparent manner and required to be funded.”
Why does it cost $259,053 to buy the put option that protects against shortfalls when only $11,053 can be obtained from selling the call option that gives up the investment surpluses? The reason is that the value of a dollar paid or received depends on what else is going on in the world at the time. A pension fund is likely to generate surplus dollars in strong economic times, when incomes are high and jobs are plentiful, meaning that people will not pay as much for that dollar as if it were paid when times were bad and money was hard to come by. As Washington state’s actuaries noted regarding their plan’s financing, “Weak economic environments were correlated with weak investment returns. Lower investment returns created the need for increased contributions at a time when employers and members could least afford them.”16 In other words, when it rains, it pours: The taxpayer guarantee to pay full pension benefits is likely to be needed in times of high unemployment, low tax revenue, and other pressures on state and local budgets. That is, taxpayers will be asked to pay at the time that they are least able to do so.17
The market value of the liability illustrates the lowest cost at which a guaranteed benefit can be guaranteed to be paid, without recourse to additional taxpayer funds. Current pension accounting rules rely on a potential taxpayer bailout to lower measured funding costs, but never reveal the importance of this potential recourse to taxpayers, nor discuss its costs. The cost of the put option in the illustration above represents the value of the contingent liabilities that have been placed on future taxpayers based on funding decisions made today. This cost is not a worst-case scenario; rather, it represents the price that future taxpayers would willingly pay to rid themselves of the risk of being called on to make good on promises that were made by, and should have been paid for, by today’s taxpayers.
Do Long Time Horizons Reduce Risk?
It is often argued that government, because of its supposedly longer time horizons, does not have to worry about year-to-year fluctuations in asset returns. That argument is based on the idea of “time diversification,” which holds that the risk of investments like stocks declines over longer holding periods. If the government is perpetual, it can focus on the long term and ignore shorter-term risk. For instance, the actuarial firm Segal states:
.. . the longer time horizon of DB plan allows the DB plan to diversify along the time axis as well. A retired DC member must choose less and less risky assets as he or she ages in order to be certain the DC member can draw a steady income. This means he or she must accept a lower return as the member ages. Alternatively, an ongoing DB plan can spread the investment risk over a population of both young and old members.1
Most financial economists believe that Segal’s statements about diversifying over time are simply wrong. Indeed, the results of a simple Internet search on time diversification will often pair it with the words “fallacy,” “myth,” and other such hints that caution should be used in applying the theory to multi-billion-dollar investments. Even the investment firm Vanguard — well known as an advocate of buy-and-hold investing — states that “there is little evidence to support the notion that time moderates the perceived volatility inherent in risky assets.”19
Why is that the case? Actuaries rely on the fact that the standard deviation of annual returns — a common measure of investment risk — declines over longer holding periods.20 If stock returns have a standard deviation of 20 percent over one year, the standard deviation of the annual rate of return declines to 8.9 percent for a five-year investment. The standard deviation falls to 6.3 percent for a 10-year investment and 4.5 percent for a 20-year investment. It therefore appears that an entity with longer time horizons can reap the high returns from equity investment with only a fraction of the risk.
But here’s the error: The effects of compounding trump the effects of lower risk. For example, an investor who holds stocks for one year and receives a return one standard deviation below the mean ends up with around 19 percent less wealth after one year than someone who received the average return. But over five years, an investor who received an annual return one standard deviation below the mean ends up with 35 percent less wealth. Over 10 years, the shortfall is 45 percent. As the holding period becomes longer, the standard deviation of annual returns declines, but the standard deviation of the total return — that is, the actual end values relative to the initial investment — grows larger. Unfortunately, it is the total return that matters. This explains why guarantees against low market returns, such as put options, actually grow more, not less, expensive as the time horizon is lengthened.21
Is Government Different?
Some analysts also argue that the standards applied to private-sector firms and private financial markets do not have to apply to government, which is fundamentally different from other financial actors. Although that view appears reasonable at first glance, it falls apart under scrutiny.
A comparison to private corporations is helpful. One of the insights of financial economics, in particular the Modigliani-Miller theorem of corporate finance, is that a corporation should be analyzed from the standpoint of the individuals who participate in it, principally stockholders and bondholders. Similarly, government should be analyzed from the standpoint of the citizens who participate in it. As the Congressional Budget Office has pointed out, “The government does not have a capacity to bear risk on its own.”22 Rather, government transfers risk between different stakeholders, including taxpayers, public employees, investors in government debt, and beneficiaries of government programs.
To realize the truth of that statement, we merely have to look around us: All over the country, taxpayers are contributing more to pensions, other programs are starved of revenue, and bondholders are beginning to worry about the safety of their investments. It is those individuals, not “the government,” who pay the cost of the market declines that have hit pension investments. The implication of that, as the CBO has argued in contexts ranging from student loan guarantees, to bank deposit insurance, to guarantees against market risk for Social Security personal accounts, is that governments generally should value risk the same way that their stakeholders do, using market prices. This explains why, in a recent analysis widely taken as a confirmation of the market valuation approach, the CBO noted that:
By accounting for the different risks associated with investment returns and benefit payments, the fair-value approach provides a more complete and transparent measure of the costs of pension obligations. . . . The fair-value approach also gives a more complete picture of the costs of changes in policy, to the extent that such changes would affect pension benefits (and possibly wages) for current employees.23
Economic theory does reveal some instances in which government can ignore risk, namely when those risks are both small and uncorrelated to the government’s other assets and liabilities.24 Of course, the market valuation of that risk would also be zero. For example, something like building a public university might qualify. The investment of billions of dollars in equities and other risky assets is an entirely different story. Despite the prevailing story that government can ignore risk, the academic research undermines this claim.
Robert Merton, the 1997 winner of the Nobel Prize in economics, wrote:
the conventional actuarial practice of using the expected return on the assets of the pension fund to determine the discount rate for valuing pension liabilities systematically understates their value by large amounts. . . . Furthermore, because larger expected return on assets generally implies that the assets have greater risk, the pension fund that invests in riskier assets will have a lower actuarial valuation of its pension liabilities and thus a lower required contribution rate. This process not only distorts the economic valuation of pension liabilities, it creates incentives for more risk taking in the pension fund.25
The long and short of it is that if you want to fully fund a guaranteed future payment, the price of doing so is the riskless rate of return. Can a future liability be funded at lower cost by making it non-guaranteed? Of course. Likewise, a guaranteed liability could be financed at lower cost by holding risky assets and imposing on taxpayers the obligation to step in to top up the fund if it falls short of their goals. As explained above, the cost savings to the plan would then be exactly offset by an increase in the taxpayers’ costs. But neither of those are what public-sector pensions purport to do. They claim to fully fund future benefits that are without risk to the beneficiary. The cost of doing that is almost inescapably given by the riskless interest rate.
Put simply, current public pension accounting rules cause the plans to promise too much, contribute too little, and take too much investment risk. To understand the real cost of state and local pensions, we must turn to market valuation.
Andrew G. Biggs is a resident scholar at AEI.
1 Author’s calculations from Public Plans Database.
3 Pew Center on the States, “The Widening Gap: The Great Recession’s Impact on State Pension and Retiree Health Care Costs,” Apr. 25, 2011.
4 Brown and Wilcox discuss legal protections for accrued pension benefits in Jeffrey R. Brown and David W. Wilcox, “Discounting State and Local Pension Liabilities,” American Economic Review, vol. 99, May 2009.
5 David Wilcox, testimony before the Public Interest Committee Forum sponsored by the American Academy of Actuaries, Sept. 4, 2008.
6 Joshua Rauh, “Shortfall for State and Local Pension Systems Today: Over $4 Trillion,” Everything Finance blog, Oct. 6, 2011, available at http://kelloggfinance.wordpress.com/2011/10/06/shortfall-for-state-a nd-local-pension-systems-today-over-4-trillion/. For more details of the method, see Robert Novy-Marx and Joshua D. Rauh, “The Liabilities and Risks of State-Sponsored Pension Plans,” Journal of Economic Perspectives 23(4), Fall 2009.
7 As of 2009, total outstanding state and local debt equaled $2.9 trillion. Bureau of the Census. “State and Local Government Finances Summary: 2009,” issued Oct. 2011.
8 Robert S. DuZebe, “Study Reflecting Impact to the FRS of Changing the Investment Return Assumption to One of the Following: 7.5%, 7.0%, 6.0%, 5.0%, 4.0% and 3.0%,” Milliman, Mar. 11, 2011.
9 Bureau of Labor Statistics. National Compensation Survey. Savings and thrift plans: Maximum potential employer contribution, (1) private industry workers, 2010, available at http://www.bls.gov/ncs/ebs/detailedprovisions/2010/ownership/private/table28a.txt.
10 See http://www.governing.com/columns/public-money/col-pension-puffery.html.
11 Throughout the example, I calculate current values using continuous discounting. The current value equals the size of the future payment divided by the exponential of (r*n), in which r is the annual discount rate and n is the number of years until the future payment will be made.
12 The reason for this is that stock returns are skewed, causing the mean return to exceed the median return.
13 The listed numbers contain a $1 discrepancy, reflecting rounding error.
14 H.R. Stoll, 1969. “The Relationship Between Put and Call Option Prices.” The Journal of Finance 24 (December): 801-824.
15 In some pension plans, surpluses are partially credited toward benefit increases, while in other cases informal political pressure arises during good economic times to increase benefits. See Richard J. Aronson, James A. Deardon, and Vincent G. Munley, “Public Employee Defined Benefit Pension Systems: The Impact of Explicit Surplus Sharing Contracts and Stakeholder Influence on Investment Strategies,” Public Choice 140 (1-2), July 2009.
16 Office of the State Actuary. “Washington State 2009 Actuarial Valuation Report.” Oct. 2010; and Office of the State Actuary. “2010 Risk Assessment: Moving Beyond Expectations.” Aug. 31, 2010.
17 This approach is used to value public pension liabilities nationwide in Andrew G. Biggs, “An Options Pricing Method for Calculating the Market Price of Public Sector Pension Liabilities.” Public Budgeting and Finance, Fall 2011.
18 The Segal Co., “Public Employees’ Retirement System of the State of Nevada. Analysis and Comparison of Defined Benefit and Defined Contribution Retirement Plans,” Dec. 14, 2010.
19 Vanguard Investment Counseling & Research, “Time Diversification and Horizon-Based Asset Allocations,” 2008.
20 The standard deviation of annual returns for each holding period is equal to the single-year standard deviation divided by the square root of the holding period.
21 Zvi Bodie, “On the Risk of Stocks in the Long Run,” Financial Analysts Journal, May-June 1995.
22 Congressional Budget Office, “Estimating the Value of Subsidies for Federal Loans and Loan Guarantees,” Aug. 2004.
23 Congressional Budget Office. “The Underfunding of State and Local Pension Plans.” May 2011.
24 Kenneth J. Arrow and R.C. Lind, “Uncertainty and the Evaluation of Public Investment Decisions,” American Economic Review, Vol. 60, 1970.
25 Robert C. Merton, Introduction to Pension Finance, by M. Barton Waring, Wiley Finance, 2012.
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