Mary Hardy University of Waterloo IAA Webcast 6 May 2014 IAA Webcast May 2014 1 Outline Introductory comments Market valuation method and results Funding Concluding comments and questions ID: 776016
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Cash Balance Pension plans: Valuation, Funding and other interesting issues
Mary Hardy, University of WaterlooIAA Webcast 6 May 2014
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Slide2Outline
Introductory commentsMarket valuation method and resultsFundingConcluding comments and questions
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Slide3Cash Balance Plans are newsworthy...
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Slide4IAA Webcast May 2014
A way out of Pa. pension mess
This year, Simpson proposed a “cash balance” pension compromise, in which new employees would be offered an investment plan with a guaranteed 2 percent earning rate.
Sources:
Kravitz
2012 National Cash Balance Research Report; Lancaster Newspapers, April 11 2014; MarcoNews.com April5, 2014
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Slide5Cash Balance Pensions
Look like DCcontribution (% of salary) paid into participant’s accountaccount accumulates to retirementlump sum retirement benefitwithdrawal benefit = account value (after vesting)Regulated like DBParticipant accounts are nominal
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Slide6Crediting rates
Participant’s account accumulates at specified crediting rate.IRS safe harbor rates:Yield on 30-year government bondsYield on 10-year government bondsYield on 5-year government bonds + 25bpYield on 1-year government bonds + 100bpFixed rate, eg 5% p.y.CPI rate
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Slide7Cash Balance plans outside the US
In the UK“Relatively rare” – but gaining traction“Investment risk remains with employer”Treated as money purchase for tax; DB for auto-enrolmentIn JapanCredited interest – flat; bond, bond average, combinationIntroduced 2002
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Slide8Market Valuation: Framework, assumptions, notation
Participant with n years service at valuation date.At valuation t=0.Retires at T with n+T yearsIgnore exits, annuitization.Value future benefit arising from past contributionsUse market valuation methodsGenerates the cost of transferring the pension liability to capital markets
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Slide9Framework, assumptions, notation
denotes the participant’s fund at , denote the crediting rates at denotes the -year spot rate at denotes the short rate at denotes the price at of a $1, -year zero coupon bond.
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Slide10Framework, assumptions, notation
Assume continuous crediting, given This is a random variable unless the crediting rate is constant.
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Slide11The Valuation Formula
The market value at t=0 of the benefit is
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Slide12The Valuation Formula
We letThat isV(t,T) = market value at t of CB benefit at Tper $1 of nominal fund at tNo exitsNo future contributionsWith continuous compounding
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Slide13Fixed crediting rate
Suppose is constant, = , sayThenThe T-year zcb price p(0,T), is known at t=0
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Slide14Fixed crediting rate
For example, Using US yield curve at 1/May/2014 V(0,5) = (1.05)5 (0.92007) = 1.1743 V(0,10) = 1.2589 V(0,20) = 1.4662That is, with a 10-year horizon to retirement: every $1 of fund costs $1.446626% contribution costs 6% 1.2589 = 7.6%Model-free valuation result.
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Slide15Crediting with the short rate
Suppose the crediting rate is the short rate plus a fixed margin That is , then
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Slide16Crediting with the short rate
For example, , with Then V(0,5) = e5m = 1.09144 V(0,10) = e10m = 1.19125 V(0,20) = e20m = 1.41908This will be to the valuation for 3-month T-bill +175bp crediting rates.For 10-year horizon6% contribution costs 7.1%Model-free result
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Slide17Crediting with k-year spot rates
I we need a market model for We use one-factor Hull-White / ext Vasicek modelParameters a = 0.02, σ = 0.006For T=5, 10, 20 years rc(t)= 30-yr spot rate 20-yr spot rate 10-yr spot rate 5-yr + 25bp 1-yr + 100bp 0.5-yr+150bpYield curve from 1/4/13 US treasuries.
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Slide18Crediting with k-year spot rates: 4/2013 YC
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V(0,T)Crediting RateT=5T=10T=2030-yr1.1681.2351.38020-yr1.1301.1891.36110-yr1.0951.1061.2305-yr+0.25%1.0731.0911.1771-yr+1.0%1.0621.1201.250½-yr+1.5%1.0831.1701.366short+1.75%1.0911.1911.4195% fixed1.2291.3401.562
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Slide19Impact of the starting YC
Repeat the valuation for yield curves 1998 →2013
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Slide20V
, 20 years to retirement
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Slide21V
, 20 years to retirement
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Slide22V
, 20 years to retirement
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Slide23V
, 20 years to retirement
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Slide24V
, 20 years to retirement
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Slide25V
, 20 years to retirement
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Slide26T=10-years
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Slide27T=5-years
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Slide28Comments
What is the most stable choice for rc?Long rates are more stable than short rates Constant rates are even more stableBut long rates and constant rates produce more volatility than short rates.What about withdrawals?Par yields not spot rates?
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Slide29Questions
Are market values of pension obligations relevant?Is the volatility surprising?Can the liability be hedged?
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Slide30Valuation and funding
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Slide31Actuarial valuations
Principles and notation:ALt = actuarial liability = target asset requirement NCt = Normal Contribution = contribution needed to fund the expected increase in AL, t to t+1it = valuation interest rateUnder valuation assumptions, ignoring exits
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Slide32Actuarial valuation for traditional DB
Accruals based past service earned benefits are included in the valuationAccruals methods are PUC and CUC/TUCProjected accrued benefits from past service indexed to retirement by salary scale.Current accrued benefits from past service valued assuming no further salary increases.
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Slide33Actuarial valuation for Cash Balance
Accruals based past service accued contributions are included in the valuationAccruals methods are PUC and CUC/TUCProjected accrued benefits from past service indexed to retirement by credited interest.Current accrued benefits from past service valued assuming no further interest credits.
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Slide34CB Valuation 1:Past service, projected credited interest
Past service no allowance for future contributions to participant’s fundThis is the method used above, with market rates and models
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Slide35CB Valuation 2:Past service, current credited interest
Past service no allowance for future contributions to participant’s fundCurrent credited interest no allowance for future credited interest vi(s) denotes the valuation discount factor for s-yrs ahead
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Slide36CB Valuation 3:Full service, projected credited interest, pro-rata accrual
Let denote the projected final benefit, and let n denote service at the valuation dateDeterministic salary growth and crediting rate assumptions
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Slide37Example
Employee A1 year service19 years to retirementS= 50 000; F= 4 000c=6%Employee B10 years service10 years to retirementS=60 000; F=55 000c=6%
Employee C 19 years service1 year to retirementS=75 000; F=100 000c=6%
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Slide38Example
Assume (i) risk free rate (ii) Corporate Bond ratesCrediting rate = 0.036 (30-year rate)Future crediting rate assumption (for method 3) ic(s)= 0.036Future salary growth assumption 2% p.y. (method 3)
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Slide43Method 3: The ‘traditional’ valuation approach
Non-accrual based CB valuation + high discount rate AL may be considerably less than fund values Every exiting participant diminishes the security of the remainderEven for a fund which is 100% funded Valuation factors should have floor of 1.0We should eliminate ‘traditional’ valuation for CBMove to true accruals aproach
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Slide44Conclusions
The CB benefit isn’t as simple as we thoughtThis benefit isn’t as cheap as we thought/thinkDB valuation methods do not adapt to CBDesign is importantShort rates are more stable for creditingShort rates are easier to hedgeMisinformation aboundsWithin and outside the actuarial community
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Slide45Final questions
Does the Cash Balance Pension really meet the objectives of sponsors or participants?Costs are volatile.Hedging is complex.Commonly used funding methods obfuscate costs.Benefit security may be significantly compromised, even for “100% Funded” plan.
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Slide46Acknowledgements
Co-authors David Saunders and Mike Xiaobai ZhuSociety of Actuaries Pension Section Research CommitteeSociety of Actuaries: Center of Actuarial Excellence GrantGlobal Risk Institute Research Project: Long horizon and Longevity RisksNatural Science and Engineering Research Council of CanadaReport available from SOA website.
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