CASH BALANCE PENSION PLANS: VALUATION, FUNDING AND OTHER INTERESTING ISSUES Mary Hardy, University of Waterloo IAA Webcast 6 May 2014 IAA Webcast May 2014

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CASH BALANCE PENSION PLANS: VALUATION, FUNDING AND OTHER INTERESTING ISSUES

Mary Hardy,

University of Waterloo

IAA Webcast

6 May 2014

IAA Webcast May 2014

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Outline

1. Introductory comments

2. Market valuation method and results

3. Funding

4. Concluding comments and questions


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CASH BALANCE PLANS ARE NEWSWORTHY...


4IAA 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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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 years

Ignore exits, annuitization.

Value future benefit arising from past contributions

Use 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.


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


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


( , ) 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


0

0

0

0

(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


0

0

0

0

(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

Then

V(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 rate

20-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


V(0,T)

Crediting Rate T=5 T=10 T=20

30-yr 1.168 1.235 1.380

20-yr 1.130 1.189 1.361

10-yr 1.095 1.106 1.230

5-yr+0.25% 1.073 1.091 1.177

1-yr+1.0% 1.062 1.120 1.250

½-yr+1.5% 1.083 1.170 1.366

short+1.75% 1.091 1.191 1.419

5% 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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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 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+1

it = valuation interest rate

Under valuation assumptions, ignoring exits


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


( , )

( , )t t

t t

AL F V t T

NC 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


(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


( ) ( )t t i

tt

nAL B T v T t

n T tAL

NCn

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%

IAA Webcast May 2014 37/40

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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)= 0.036

Future 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

CommitteeSociety of Actuaries: Center of Actuarial Excellence

GrantGlobal Risk Institute Research Project: Long horizon

and Longevity RisksNatural Science and Engineering Research Council of

Canada

Report available from SOA website.


Documents

CASH BALANCE PENSION PLANS: VALUATION, FUNDING AND OTHER INTERESTING ISSUES Mary Hardy, University of Waterloo IAA Webcast 6 May 2014 IAA Webcast May 2014