公共养老金计划资金政策：随机回报下摊销方法的有效性

Public pension plan funding policy:Effectiveness of amortization methodsunderstochastic returns Daniel WadeArthur Rains-McNallyJessica Gardner One of the most important decisions made for public sector pension plansis adopting a funding policy that balances the needs of all stakeholders. Ingeneral, larger benefits require larger contributions. For a given benefitlevel, the purpose of a fundingpolicy is to balance the level and volatility ofcontributions with the fundedratioof the plan. In this article, we continue to explore, compare, and contrast various methods of amortizing liabilities and their impacton the contribution rates allocated to employers. Plan sponsors use a variety of methods to determine the amortization amount. This article examines the followingmethods, withamortization periodsvarying from 10 years to 30 years. Layered method, where an additional layer of amortizationis calculated each year based on the experience orassumption changes made that year. In this article, the first layer is the current unfunded liability, also known asthe net pension liability, or the difference between the actuarial value of assets andthe total pension liability.Rolling method, where the amortization is reset annually based upon the entire net pension liability. Theamortization period remains constant,resulting in a consistent percentage of the net pension liability paid each year.Aggregate cost method, which considers the entire actuarial present value of benefits. The difference betweenthe actuarial present value of benefits and the actuarial value of assets is divided by the actuarial present valueof future salaries for membersas of the valuation date to calculate the contribution rate. This contribution rate isthen applied to current salaries. In the first article of this series,Public pension plan funding policy: Effectiveness of amortization methods,wedeveloped a framework to help plan sponsors understand the funding policy implications of their choice ofamortization method if all actuarial assumptions are perfectly met.In the second article,Public pension plan fundingpolicy: Effectiveness of amortization methods under projected investment scenarios,we studied how the variousamortization methods reacted to different pathsofasset returns.This article expands that discussion to focus on howthe various amortization methods handlea larger set ofdeviations from expectationsandreact to volatility ininvestment markets. Stochasticmodeling Stochasticmodelinginvolves using a random number generator to perform a statistical analysis where 1,000 or moreruns are created to test the likelihood of future events. This is also sometimes referred to as Monte Carlo analysis. In this article,wefocus onthevolatility inherent in investment markets.We developed1,000 “random walk” scenariosfor theplan’sactual asset returns via stochastic projectionsusing a random number generator.Throughout theremainder of thisarticle,wereviewhow each of the amortization methods react to these scenarios. Stochastic projections over the 40-year period were generated using a normal distribution, a 7.00% geometricaverage annual return, and a standard deviation of 12.00%. The equivalent average arithmetic return is 7.72%. Plan modeled For purposes of this article, we modeled a “typical” public plan. We use a 7.0% expected return on assets, which is acommon assumption among public pension plans, anentry age normal actuarial cost method,and a fresh start forthe amortization of the unfunded liabilities. We then explored multiple amortization methodologies. We set assetsequal to 79% of liabilities, which is the aggregated funding level in theMilliman Public Pension Funding Index (PPFI)as of January 1, 2021. Additional key methods, assumptions,and plan provisions are listed in our appendix. In our projections, other than the actual investment returns, we assume that all assumptions are met and thatthereare noother actuarial experiencegains or losses. “Cones ofuncertainty” forcontributionratesandfundedratios To give an idea of the potential range of future contribution rates and fundedratios, we ran a stochastic projection asdescribed above and summarized the results to develop a “cone of uncertainty”for each amortization method studied.This type of projection allows the assessment of the likelihood of certain events in the 1,000 scenarios modeled. Thisstochastic projection usestheseresults to generate a distribution of future contribution rates and fundedratios. Under this type of analysis,wereview the probability of an event occurring rather than the specific results of anyone scenario. Figures1to6summarizethe results over time.The median(or the 50thpercentile)at any given timeis shown bytheredline. Half of the resultsare above the medianeach year, and half of the results are below the median. Thelightgreenand light blueshaded areareflectsthe25thand75thpercentiles;50% of the results arein thelightgreenandlight blueshaded area, whil