Economic capital, the 0.5th percentile result of a stochastic projection, is the primary risk measure employed. The research examines not only the difference in economic capital requirements between typical plans in the three countries, but also its sensitivity to changes in asset allocation, contributions, and starting funded status

Bonnar, Stephen

Pittea, Aniketh

Tapadar, Pradip

Kent Academic Repository

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Users should always cite the published version of record.EnquiriesFor any further enquiries regarding the licence status of this document, please contact: researchsupport@kent.ac.ukIf you believe this document infringes copyright then please contact the KAR admin team with the take-down information provided at http://kar.kent.ac.uk/contact.htmlCitation for published versionBonnar, Stephen and Pittea, Aniketh and Tapadar, Pradip  (2019) Measuring pension plan riskfrom an economic capital perspective.    In: Joint CIA, IFoA, SOA Webcast, 15 May 2019.DOILink to record in KARhttps://kar.kent.ac.uk/74548/Document VersionPresentationMeasuring Pension Plan Risk from an Economic Capital PerspectiveSteve Bonnar, Aniketh Pittea and Pradip TapadarUniversity of Waterloo and University of KentMay 15, 20191 / 44AcknowledgementsFunding for this project has come from a variety of sources:Canadian Institute of ActuariesInstitute and Faculty of ActuariesInternational Congress of ActuariesSocial Sciences and Humanities Research Council (SSHRC)Society of Actuaries2 / 44Overall ProjectContentsOverall ProjectIntroduction to Pension ModelAssumptions and MethodologyUK’s Universities Superannuation Scheme (USS)Stylized US Pension PlanCanadian Pension PlanSummary3 / 44Overall ProjectMotivation for Overall ProjectBaby boomers entering retirementconcerns of diminished returns, compromised pensionsHigher old-age dependency ratio may lead toless saving (dissaving) and investmentshift in asset allocation toward low risk / low return assetsreduced labour force growthWith implications for asset returns and retirement outcomes4 / 44Overall ProjectModel Framework / Results – Economic Demographic ModelOverlapping Generations Model (OLG) with:aggregate uncertaintytwo asset classes (risky and risk-free)multi-pillar pension systems (saving, pay-go, earnings based)endogenous labour supplyGenerates standard age-specific labour, consumption, asset holdings and portfolioallocation qualitatively consistent with dataOlder population results in moderately lower asset returnsIncreasing survival probability for age 65+ (20% increase at oldest ages) reduces returns byapproximately 4%Higher pension replacement ratio results in lower asset accumulations5 / 44Introduction to Pension ModelContentsOverall ProjectIntroduction to Pension ModelAssumptions and MethodologyUK’s Universities Superannuation Scheme (USS)Stylized US Pension PlanCanadian Pension PlanSummary6 / 44Introduction to Pension ModelMotivationTypical pension plan valuation compares assets to liabilitiesThis comparison looks at expected values (perhaps including some margin)One approach to pension plan risk assessment is Economic Capital [see Porteous, et al.(2012)]Used for banking and insurance sectors under Basel 2, 3 and Solvency 2Sufficient to cover 99.5th percentile outcome7 / 44Introduction to Pension ModelMethodologySelect a representative pension planUniversities Superannuation Scheme (UK) 2014 Actuarial ValuationStylized US pension planCanadaian pension planSelect an economic modelGraphical Model [see Oberoi, et al. (2019)]Select a mortality modelM7 from Cairns, et al. (2007)Quantify pension risk [see Porteous, et al. (2012)]8 / 44Assumptions and Methodology Economic ModelContentsOverall ProjectIntroduction to Pension ModelAssumptions and MethodologyUK’s Universities Superannuation Scheme (USS)Stylized US Pension PlanCanadian Pension PlanSummary9 / 44Assumptions and Methodology Economic ModelGraphical Model - BackgroundGraphical models are probabilistic models for which a graph expresses the conditionaldependence structure between random variables.We use graphical models to simulate economic variables over long time horizons.The approach we use is:transparentflexibleeasy to implement10 / 44Assumptions and Methodology Economic ModelMethodology - forecastingBA CAssume 3 economic variables A,B and C.The individual economic random variables, Zits, are modelled as:Zit = µi + Yit , where Yit = βiYi(t−1) + εit and εit ∼ N(0, σ2i ).Correlation of the error terms is represented by a graphical model.The error terms:are assumed to be independently distributed across time t;which are directly connected to each other are dependent;which are indirectly connected are still dependent, but more weakly so.11 / 44Assumptions and Methodology Economic ModelMethodology - selecting a correlation structureWe use simultaneous p-values to select a graphical structure.Hojsgaard et al. (2012). provide guidance on the use of packages written in R to estimategraphical models.We use the following UK and US economic time series data:Price InflationSalary InflationDividend YieldDividend GrowthConsols Yield12 / 44Assumptions and Methodology Economic ModelEconomic Model – Graphical Model for UKModel UK: Graphical model with 6 edges.DividendYieldDividendGrowthPriceInflationBondYieldSalaryInflation13 / 44Assumptions and Methodology Economic ModelCorresponding P-ValuesP−valueEdge1−21−31−41−52−32−42−53−43−54−50.00.10.20.30.40.50.60.70.80.91.01  PriceInflation2  SalaryInflation3  DividendYield4  DividendGrowth5  ConsolsYield14 / 44Assumptions and Methodology Economic ModelEconomic Model – Graphical Model for USModel US: Graphical model with 6 edges.DividendYieldDividendGrowthPriceInflationBondYieldSalaryInflation15 / 44Assumptions and Methodology Economic ModelMarginal distribution – Price InflationUK Price InflationYear1924 1964 2004 2044 2084 2124−0.100.000.050.100.150.200.2510%30%50%70%90%US Price InflationYear1914 1956 1998 2040 2082 2124−0.100.000.050.100.150.200.2510%30%50%70%90%16 / 44Assumptions and Methodology Economic ModelMarginal distribution – Dividend YieldUK Dividend YieldYear1924 1964 2004 2044 2084 21240.000.020.040.060.080.1010%30%50%70%90%US Dividend YieldYear1914 1956 1998 2040 2082 21240.000.020.040.060.080.1010%30%50%70%90%17 / 44Assumptions and Methodology Economic ModelMarginal distribution – Long Bond YieldUK Long Bond Yield (Consols Yield)Year1924 1964 2004 2044 2084 21240.000.050.100.1510%30%50%70%90%US Long Bond YieldYear1914 1956 1998 2040 2082 21240.000.050.100.1510%30%50%70%90%18 / 44Assumptions and Methodology Economic ModelJoint distribution (1)−0.1 0.0 0.1 0.2 0.3−0.3−0.2−0.10.00.10.20.3UKPrice inflationSalary inflation19751980−0.1 0.0 0.1 0.2 0.3−0.3−0.2−0.10.00.10.20.3USPrice inflationSalary inflation192119221931193219331942Figure: Plots of simulated price and salary inflation for UK and US. 19 / 44Assumptions and Methodology Economic ModelJoint distribution (2)−0.6 −0.4 −0.2 0.0 0.2 0.4 0.6−0.6−0.4−0.20.00.20.40.6UKShare total returnBond total return193919732015−0.6 −0.4 −0.2 0.0 0.2 0.4 0.6−0.6−0.4−0.20.00.20.40.6USShare total returnBond total return1933 1937193919832010Figure: Plots of simulated share and bond returns for UK and US. 20 / 44Assumptions and Methodology Mortality ModelMortality Model – M7 from Cairns, et al. (2007)logit q(t, x) = κ(1)t + κ(2)t (x − x¯) + κ(3)t ((x − x¯)2 − σˆ2x) + γ(4)t−xModel assumes a functional relationship between ages (and hence smoothness).One of the better fit models to England and Wales data (Cairns et al. (2007)).21 / 44Assumptions and Methodology Mortality ModelMortality Model – M7 from Cairns, et al. (2007)2010 2015 2020 2025 2030 20350.0060.0080.0100.0120.014Male q(65) and 90% CIYear(t)USUK2010 2015 2020 2025 2030 20350.0150.0200.0250.0300.0350.040Male q(75) and 90% CIYear(t)USUK22 / 44Assumptions and Methodology Economic CapitalEconomic Capital ApproachUse asset yield at time t, discount future benefits/expenses to obtain best estimate assetrequirementSurplus/deficit at time t (profit vector) given byPt = Lt−1It−1,t − Xt − LtPresent value of future profits given by:V0 =T∑t=1PtD(0,t)23 / 44Assumptions and Methodology Economic CapitalEconomic Capital ApproachPresent value of future profits, V0, can also be expressed as follows:V0 = A0 −T∑t=0XtD(0,t)Repeat previous steps 10,000 times to obtain a distribution of V0. The required economiccapital is the 0.5th percentile of the V0 distribution24 / 44UK’s Universities Superannuation Scheme (USS)ContentsOverall ProjectIntroduction to Pension ModelAssumptions and MethodologyUK’s Universities Superannuation Scheme (USS)Stylized US Pension PlanCanadian Pension PlanSummary25 / 44UK’s Universities Superannuation Scheme (USS)USS Pension Scheme – Benefits1/80th final salary benefit for service to April 1, 20161/75th career revalued benefit for service from April 1, 2016Lump sum at retirement = 3 × annual pensionPension increases based on min [CPI, 5%]Contribution rate: 24% of salary (8% employee + 16% employer)26 / 44UK’s Universities Superannuation Scheme (USS)USS Pension Scheme – DataActive Members Number 167,545Average pensionable salary £42,729Average age 43.8Average past service 12.5Deferred Members Number 110,430Average deferred pension £2,373Average age 45.1Pensioners Number 70,380(including dependents) Average pension £17,079Average Age 71.127 / 44UK’s Universities Superannuation Scheme (USS)USS Pension Scheme – AssetsAssets Benchmark AllocationUK equities 16%Overseas equities 31Alternative assets 19Property 7Total real 73%Fixed interest 27Cash 0Total fixed 27%Note: Modelled as 70% Equities and 30% Bonds28 / 44UK’s Universities Superannuation Scheme (USS)USS Economic Capital – Sensitivity to Asset Allocation Strategy−300 −200 −100 0 1000.0000.0100.02070% equitiesPVFP (as a % of A0)DensityPercentiles50th10th0.5th−300 −200 −100 0 1000.0000.0100.02030% equitiesPVFP (as a % of A0)DensityPercentiles50th10th0.5th29 / 44UK’s Universities Superannuation Scheme (USS)USS Economic Capital – Sensitivity to Contribution Rates−300 −200 −100 0 1000.0000.0100.020Contribution rate − 20%PVFP (as a % of A0)DensityPercentiles50th10th0.5th−300 −200 −100 0 1000.0000.0100.020Contribution rate − 25%PVFP (as a % of A0)DensityPercentiles50th10th0.5th30 / 44Stylized US Pension PlanContentsOverall ProjectIntroduction to Pension ModelAssumptions and MethodologyUK’s Universities Superannuation Scheme (USS)Stylized US Pension PlanCanadian Pension PlanSummary31 / 44Stylized US Pension PlanSylized US Pension Plan – BenefitsBenefits based on USS pension scheme, except for the following1.5% final average salary for all pension serviceNo lump sum payment on retirementNo pension increasesContribution rate: 10.8% of salary32 / 44Stylized US Pension PlanUS Stylized Plan Economic Capital – Sensitivity to Asset Allocation Strategy−400 −200 0 1000.0000.0100.02075% equitiesPVFP (as a % of A0)DensityPercentiles50th10th0.5th−400 −200 0 1000.0000.0100.02025% equitiesPVFP (as a % of A0)DensityPercentiles50th10th0.5th33 / 44Stylized US Pension PlanUS Stylized Plan Economic Capital – Sensitivity to Contribution Rate−400 −200 0 1000.0000.0100.020Contribution rate − 13.3%PVFP (as a % of A0)DensityPercentiles50th10th0.5th−400 −200 0 1000.0000.0100.020Contribution rate −  8.3%PVFP (as a % of A0)DensityPercentiles50th10th0.5th34 / 44Canadian Pension PlanContentsOverall ProjectIntroduction to Pension ModelAssumptions and MethodologyUK’s Universities Superannuation Scheme (USS)Stylized US Pension PlanCanadian Pension PlanSummary35 / 44Canadian Pension PlanOTPP – BenefitsPension payment: 1.7% of 5-year average salary benefitPension increases based on CPINo lump sum paymentContribution rate: 20.8% of salary up to YMPE and 24% for earnings exceeding YMPE.36 / 44Canadian Pension PlanOTPP – DataActive Number 144,325Average pensionable salary $90,468Average age 44.4Average past service 14.6Deferred Members Number 71,205Average deferred pension $1,965Average age 45.1Pensioners Number 129,785Average lifetime pension $41,154Average age 71.137 / 44Canadian Pension PlanOTPP – Economic ModelModel Canada: Graphical model with 6 edges.DividendGrowthDividendYieldBondYieldPriceInflationSalaryInflation38 / 44Canadian Pension PlanOTPP Economic Capital−400 −300 −200 −100 0 100 2000.0000.0050.0100.0150.02055% EquityPVFP (as a % of A0)DensityPercentiles50th10th0.5th39 / 44Canadian Pension PlanOTPP Economic Capital – Sensitivity to Asset Allocation Strategy−400 −200 0 1000.0000.0100.02075% EquityPVFP (as a % of A0)DensityPercentiles50th10th0.5th−400 −200 0 1000.0000.0100.02025% EquityPVFP (as a % of A0)DensityPercentiles50th10th0.5th40 / 44Canadian Pension PlanOTPP Economic Capital – Sensitivity to Contribution Rate−400 −200 0 1000.0000.0100.020Contribution rate − 18.3%PVFP (as a % of A0)DensityPercentiles50th10th0.5th−400 −200 0 1000.0000.0100.020Contribution rate − 23.3%PVFP (as a % of A0)DensityPercentiles50th10th0.5th41 / 44SummaryContentsOverall ProjectIntroduction to Pension ModelAssumptions and MethodologyUK’s Universities Superannuation Scheme (USS)Stylized US Pension PlanCanadian Pension PlanSummary42 / 44SummarySummaryThere is a very large range of potential resultsThe stylized US plan is more volatile than the USSEconomic capital twice as large as a percentage of starting assetsEconomic capital also larger in absolute termsThe beneficial effect on economic capital of increasing the allocation to long bonds isgreater in the stylized US planLarger proportion of nominal (rather than inflation protected) benefitsContinuing to analyze Canadian plan resultsInitial results look similar to USSWill consider implications of reduced inflation protection and differing levels of plan maturity43 / 44SummaryReferencesCairns, A.J.G., Blake, D., Dowd, K., Coughlan, G.D., Epstein, D., Ong, A., and Balevich,I. A quantitative comparison of stochastic mortality models using data from England andWales and the United States. North American Actuarial Journal 13, no. 1: 1-35, 2009.Hojsgaard, S., Edwards, D. and Lauritzen, S. Graphical models with R. Springer Science &Business Media 2012.Oberoi, J., Pittea, A. and Tapadar, P. A graphical model approach to simulating economicvariables over long horizons. To appear in Annals of Actuarial Science, 2019.Porteous, B.T., Tapadar, P. and Yang, W. Economic capital for defined benefit pensionschemes: An application to the UK Universities Superannuation Scheme. Journal ofPension Economics & Finance, 11, no. 4: 471-499, 2012.44 / 44

Measuring pension plan risk from an economic capital perspective

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Measuring pension plan risk from an economic capital perspective

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