Cash Balance Pension plans: Valuation, Funding and other interesting issues

1. Cash Balance Pension plans: Valuation, Funding and other interesting issues Mary Hardy, University of Waterloo IAA Webcast 6 May 2014

2. Outline • Introductory comments • Market valuation method and results • Funding • Concluding comments and questions

3. Cash Balance Plans are newsworthy...

4. 1 2 A way out of Pa. pension mess 3 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

5. Cash Balance Pensions • Look 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

6. 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

7. Cash 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-enrolment • In Japan • Credited interest – flat; bond, bond average, combination • Introduced 2002

8. Market Valuation: Framework, assumptions, notation • Participant 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

9. 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.

10. Framework, assumptions, notation • Assume continuous crediting, given • This is a random variable unless the crediting rate is constant.

11. The Valuation Formula • The market value at t=0 of the benefit is

12. 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

13. Fixed crediting rate • Suppose is constant, = , say • Then • The T-year zcb price p(0,T), is known at t=0

14. Fixed 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) = 1.4662 • 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.

15. Crediting with the short rate • Suppose the crediting rate is the short rate plus a fixed margin • That is , then

16. Crediting with the short rate • For example, , with • Then V(0,5) = e5m= 1.09144 V(0,10) = e10m= 1.19125 V(0,20) = e20m= 1.41908 • 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

17. Crediting with k-year spot rates • I we need a market model for • We use one-factor Hull-White / extVasicek 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.

18. Crediting with k-year spot rates: 4/2013 YC

19. Impact of the starting YC • Repeat the valuation for yield curves • 1998 →2013

20. V , 20 years to retirement

21. V , 20 years to retirement

22. V , 20 years to retirement

23. V , 20 years to retirement

24. V , 20 years to retirement

25. V , 20 years to retirement

26. T=10-years

27. T=5-years

28. Comments • What 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?

29. Questions • Are market values of pension obligations relevant? • Is the volatility surprising? • Can the liability be hedged?

30. Valuation and funding

31. 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

32. 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.

33. 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.

34. 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

35. 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

36. 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

37. Example • Employee A • 1 year service • 19 years to retirement • S= 50000; F= 4000 • 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%

38. Example • Assume (i) risk free rate (ii) Corporate Bond rates • Crediting 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)

43. 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

44. Conclusions • The CB benefit isn’t as simple as we thought • This benefit isn’t as cheap as we thought/think • DB valuation methods do not adapt to CB • Design is important • Short rates are more stable for crediting • Short rates are easier to hedge • Misinformation abounds • Within and outside the actuarial community

45. Final 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.

46. Acknowledgements • Co-authors David Saunders and Mike Xiaobai Zhu • Society of Actuaries Pension Section Research Committee • Society of Actuaries: Center of Actuarial Excellence Grant • Global Risk Institute Research Project: Long horizon and Longevity Risks • Natural Science and Engineering Research Council of Canada • Report available from SOA website.