1. CASH BALANCE PENSION PLANS: VALUATION, FUNDING AND OTHER INTERESTING ISSUES Mary Hardy, University of Waterloo IAA Webcast 6 May 2014 IAA Webcast May 2014 1

2. Outline 1. Introductory comments 2. Market valuation method and results 3. Funding 4. Concluding comments and questions IAA Webcast May 2014 2

3. CASH BALANCE PLANS ARE NEWSWORTHY... IAA Webcast May 2014 3

4. 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 1 1 2 3 4

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 IAA Webcast May 2014 5

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 IAA Webcast May 2014 6

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 IAA Webcast May 2014 7

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 IAA Webcast May 2014 8

9. Framework, assumptions, notation IAA Webcast May 2014 9

10. Framework, assumptions, notation IAA Webcast May 2014 10

11. The Valuation Formula IAA Webcast May 2014 11

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 IAA Webcast May 2014 12

13. Fixed crediting rate IAA Webcast May 2014 13

14. Fixed crediting rate IAA Webcast May 2014 14

15. Crediting with the short rate IAA Webcast May 2014 15

16. Crediting with the short rate IAA Webcast May 2014 16

17. Crediting with k-year spot rates IAA Webcast May 2014 17

18. Crediting with k-year spot rates: 4/2013 YC IAA Webcast May 2014 V(0,T) Crediting RateT=5T=10T=20 30-yr1.1681.2351.380 20-yr1.1301.1891.361 10-yr1.0951.1061.230 5-yr+0.25%1.0731.0911.177 1-yr+1.0%1.0621.1201.250 ½-yr+1.5%1.0831.1701.366 short+1.75%1.0911.1911.419 5% fixed1.2291.3401.562 18

19. Impact of the starting YC  Repeat the valuation for yield curves  1998 → 2013 IAA Webcast May 2014 19

20. V, 20 years to retirement IAA Webcast May 2014 20

21. V, 20 years to retirement IAA Webcast May 2014 21

22. V, 20 years to retirement IAA Webcast May 2014 22

23. V, 20 years to retirement IAA Webcast May 2014 23

24. V, 20 years to retirement IAA Webcast May 2014 24

25. V, 20 years to retirement IAA Webcast May 2014 25

26. T=10-years IAA Webcast May 2014 26

27. T=5-years IAA Webcast May 2014 27

28. Comments  What is the most stable choice for r c ?  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? IAA Webcast May 2014 28

29. Questions  Are market values of pension obligations relevant?  Is the volatility surprising?  Can the liability be hedged? IAA Webcast May 2014 29

30. VALUATION AND FUNDING IAA Webcast May 2014 30

31. Actuarial valuations  Principles and notation:  AL t = actuarial liability = target asset requirement  NC t = Normal Contribution = contribution needed to fund the expected increase in AL, t to t+1  i t = valuation interest rate  Under valuation assumptions, ignoring exits IAA Webcast May 2014 31

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. IAA Webcast May 2014 32

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. IAA Webcast May 2014 33

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 IAA Webcast May 2014 34

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  v i (s) denotes the valuation discount factor for s-yrs ahead IAA Webcast May 2014 35

36. CB Valuation 3: Full service, projected credited interest, pro-rata accrual IAA Webcast May 2014 36

37. 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

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) i c (s)= 0.036  Future salary growth assumption 2% p.y. (method 3) IAA Webcast May 2014 38

39. IAA Webcast May 2014 39

40. IAA Webcast May 2014 40

41. IAA Webcast May 2014 41

42. IAA Webcast May 2014 42

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 IAA Webcast May 2014 43

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 IAA Webcast May 2014 44

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. IAA Webcast May 2014 45

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. IAA Webcast May 2014 46