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CASH BALANCE PENSION PLANS: VALUATION, FUNDING AND OTHER INTERESTING ISSUES
Mary Hardy, University of Waterloo
IAA Webcast 6 May 2014
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Outline1. Introductory comments2. Market valuation method and results3. Funding4. Concluding comments and questions
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CASH BALANCE PLANS ARE NEWSWORTHY...
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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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Cash Balance PensionsLook like DC
contribution (% of salary) paid into participant’s account
account accumulates to retirement lump sum retirement benefit withdrawal benefit = account value (after vesting)
Regulated like DB Participant accounts are nominal
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Crediting rates Participant’s account accumulates at specified
crediting rate.IRS safe harbor rates:
Yield on 30-year government bonds Yield on 10-year government bonds Yield on 5-year government bonds + 25bp Yield on 1-year government bonds + 100bp Fixed rate, eg 5% p.y. CPI rate
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Cash Balance plans outside the USIn the UK
“Relatively rare” – but gaining traction “Investment risk remains with employer” Treated as money purchase for tax; DB for auto-
enrolmentIn Japan
Credited interest – flat; bond, bond average, combination
Introduced 2002
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Market Valuation: Framework, assumptions, notationParticipant 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 methods
Generates the cost of transferring the pension liability to capital markets
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Framework, 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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Framework, assumptions, notationAssume continuous crediting, given
This is a random variable unless the crediting rate is constant.
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exp ( )T
cT t
t
F F r s ds
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The Valuation FormulaThe market value at t=0 of the benefit is
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0 0 0
0
( ) ( ) ( )
0 0 0 0
( ) ( )
0 0
T T Tc
Tc
r s ds r s ds r s dsQ Q
T
r s r s dsQ
V E F e F E e e
F E e
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The Valuation Formula We let
That is V(t,T) = market value at t of CB benefit at T
per $1 of nominal fund at t No exits No future contributions With continuous compounding
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( , ) exp ( ) ( )T
Q ct
t
V t T E r s r s ds
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Fixed crediting rateSuppose is constant, = , sayThen
The T-year zcb price p(0,T), is known at t=0
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00
(0, ) exp ( ) ( )
exp( ) exp ( )
exp( ) (0, )
TQ c
Tc Q
c
V T E r s r s ds
Tr E r s ds
Tr p T
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Fixed crediting rateFor 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) = 1.4662 That is, with a 10-year horizon to retirement:
every $1 of fund costs $1.44662 6% contribution costs 6% 1.2589 = 7.6%
Model-free valuation result.
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Crediting with the short rateSuppose the crediting rate is the short rate plus a fixed margin That is , then
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00
(0, ) exp ( ) ( )
exp ( ) ( )
TQ c
TQ
mT
V T E r s r s ds
E r s m r s ds
e
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Crediting with the short rateFor example, , with
ThenV(0,5) = e5m = 1.09144
V(0,10) = e10m = 1.19125
V(0,20) = e20m = 1.41908 This will be to the valuation for 3-month T-bill
+175bp crediting rates. For 10-year horizon
6% contribution costs 7.1%Model-free result
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Crediting with k-year spot ratesI we need a market model for We use one-factor Hull-White / ext Vasicek model
Parameters a = 0.02, σ = 0.006 For T=5, 10, 20 years rc(t)= 30-yr spot rate20-yr spot rate
10-yr spot rate
5-yr + 25bp
1-yr + 100bp
0.5-yr+150bp Yield curve from 1/4/13 US treasuries.
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Crediting with k-year spot rates: 4/2013 YC
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V(0,T)Crediting Rate T=5 T=10 T=2030-yr 1.168 1.235 1.38020-yr 1.130 1.189 1.36110-yr 1.095 1.106 1.2305-yr+0.25% 1.073 1.091 1.1771-yr+1.0% 1.062 1.120 1.250½-yr+1.5% 1.083 1.170 1.366short+1.75% 1.091 1.191 1.4195% fixed 1.229 1.340 1.562
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Impact of the starting YCRepeat the valuation for yield curves
1998 →2013
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V , 20 years to retirement
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V , 20 years to retirement
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V , 20 years to retirement
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V , 20 years to retirement
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V , 20 years to retirement
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V , 20 years to retirement
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T=10-yearsIAA Webcast May 2014
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T=5-yearsIAA Webcast May 2014
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CommentsWhat is the most stable choice for rc?
Long rates are more stable than short rates Constant rates are even more stable But long rates and constant rates produce more
volatility than short rates.What about withdrawals?Par yields not spot rates?
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Questions Are market values of pension obligations relevant? Is the volatility surprising?
Can the liability be hedged?
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VALUATION AND FUNDING
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Actuarial valuationsPrinciples and notation:
ALt = actuarial liability = target asset requirement
NCt = Normal Contribution = contribution needed to fund the expected increase in AL, t to t+1
it = valuation interest rate
Under valuation assumptions, ignoring exits
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1( )(1 )t t t tAL NC i AL
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Actuarial valuation for traditional DB Accruals based past service earned benefits are
included in the valuation Accruals methods are PUC and CUC/TUC
Projected 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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Actuarial valuation for Cash Balance Accruals based past service accued contributions
are included in the valuation Accruals methods are PUC and CUC/TUC
Projected 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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CB Valuation 1:Past service, projected credited interest
Past service no allowance for future contributions to participant’s fund
This is the method used above, with market rates and models
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( , )( , )
t t
t t
AL F V t TNC cS V t T
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CB Valuation 2:Past service, current credited interest
Past service no allowance for future contributions to participant’s fund
Current credited interest no allowance for future credited interest
vi(s) denotes the valuation discount factor for s-yrs ahead
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(1 ( )) (1) 1( )t t
t t t tc
ii t
AL F
NC cS F c vS
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CB Valuation 3:Full service, projected credited interest, pro-rata accrual
Let denote the projected final benefit, and let n denote service at the valuation date
Deterministic salary growth and crediting rate assumptions
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( ) ( )t t i
tt
nAL B T v T tn T t
ALNCn
Example• Employee A
• 1 year service• 19 years to retirement• S= 50 000; F= 4 000• c=6%
• Employee B• 10 years service• 10 years to retirement• S=60 000; F=55 000• c=6%
• Employee C • 19 years service• 1 year to retirement• S=75 000; F=100 000• c=6%
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ExampleAssume (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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Method 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 remainder
Even for a fund which is 100% funded
Valuation factors should have floor of 1.0 We should eliminate ‘traditional’ valuation for CB
Move to true accruals aproach
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ConclusionsThe 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 important
Short rates are more stable for crediting Short rates are easier to hedge
Misinformation abounds Within and outside the actuarial community
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Final questionsDoes 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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AcknowledgementsCo-authors David Saunders and Mike Xiaobai ZhuSociety of Actuaries Pension Section Research Committee
Society of Actuaries: Center of Actuarial Excellence GrantGlobal Risk Institute Research Project: Long horizon and Longevity Risks
Natural Science and Engineering Research Council of Canada
Report available from SOA website.
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