1. Pension Risk Management in the Enterprise Risk Management Framework Yijia Lin University of Nebraska - Lincoln Richard MacMinn Illinois State University Ruilin Tian North Dakota State University Jifeng Yu University of Nebraska – Lincoln Presented at International Conference on Financial and Insurance Risk Management Beijing, China July 4, 2015

2. Enterprise risk management (ERM)  Assess all enterprise risks and coordinate various risk management strategies in a holistic fashion

3. Enterprise risk management (ERM)  Assess all enterprise risks and coordinate various risk management strategies in a holistic fashion  Superior to the silo-based risk management  Facilitate risk control (Lam, 2001)  Mitigate information asymmetry (Liebenberg and Hoyt, 2003)  Generate synergies between different risk management activities (Lin et al., 2012; Gamba and Triantis, 2014)  Optimize the trade-off between risk and return (Nocco and Stulz, 2006)

4. Motivations  The current ERM practice and literature disregard off-balance-sheet items.  Defined benefit (DB) pensions are the most significant off-balance-sheet item: $2.34 trillion in 2012  DB pensions introduce significant risks  Market downturns  Low interest rates  New pension accounting standards  Improved life expectancy of retirees

5. Motivations (Cont’)  From the 2008 Coca-Cola annual report  DB plans of General Motors (GM) were underfunded by $8.7 billion in 2012  Reduce GM’s share value (Bunkley, 2012) “… As a result of the decline in the fair value of our pension plans assets and a decrease in the discount rate used to calculate pension benefit obligations, we have made and will consider making additional contributions to our U.S. and international pension plans in 2009.”

6. Motivations (Cont’)  The implications of pension risk on firm overall risk have been largely unexplored.

7. Motivations (Cont’)  The implications of pension risk on firm overall risk have been largely unexplored.  How significant is it to incorporate pension risk in an ERM program?  No ERM model currently exists to integrate the pension scheme into a firm's decision making process (Kemp and Patel, 2011)  Ai et al. (2012) present an ERM framework but they do not consider pensions.

8. Contributions  We propose an ERM optimization model by consolidating pension risk with various business risks for a firm sponsoring defined benefit (DB) plans.  If we manage pension risk and different business-related risks in a holistic way, it will notably increase firm value by 17%.

9. Contributions  We propose an ERM optimization model by consolidating pension risk with various business risks for a firm sponsoring defined benefit (DB) plans.  If we manage pension risk and different business-related risks in a holistic way, it will notably increase firm value by 17%.  We study how much pension risk a plan should transfer given that pension risk and other business risks are managed holistically.  Ground-up strategy (e.g. pension buy-ins and buy-outs, ₤5.5 billion in 2013)  Excess-risk strategy (e.g. longevity swaps, ₤8.9 billion in 2013)

10. Contributions (Cont’)  The existing literature suggests that the excess- risk hedging strategy is more attractive.  The ground-up strategy is more capital intensive and expensive (Lin and Cox, 2008; Lin et al., 2013).  We show the excess-risk strategy is less effective in improving overall firm performance in the ERM framework.

11. Two Divisions of a DB Pension Firm Operation Division Involves real project investments Faces project risk, operational risk, insurable hazard risk, and etc. DB Pension Division Deals with pension assets and liabilities Faces investment risk, interest rate risk and longevity risk.

12. Risks from the Operation Division  Project risk: The risk of potential losses due to unsatisfactory performance of a firm’s real project operations.

13. Risks from the Operation Division  Project risk: The risk of potential losses due to unsatisfactory performance of a firm’s real project operations.  Hazard risk: The risk related to safety, fire, theft and natural disasters.  Suppose the annual hazard loss per dollar invested, h, is a lognormal random variable:

14. Risks from the Operation Division  Project risk: The risk of potential losses due to unsatisfactory performance of a firm’s real project operations.  Hazard risk: The risk related to safety, fire, theft and natural disasters.  Suppose the annual hazard loss per dollar invested, h, is a lognormal random variable:  Operational risk: The risk of unexpected changes in elements related to operations arising, directly or indirectly, from people, systems and processes.  The loss caused by the operational risk from project j in period t, op jt, equals a proportion,, of project j’s total return where is the net return of project j in period t.

15. Risks from the DB Pension Division  Pension risk: Pension investment risk, interest rate risk and longevity risk

16. Risks from the DB Pension Division  Pension risk: Pension investment risk, interest rate risk and longevity risk  Assumptions  A pension cohort joins the plan at the age of x 0 at time 0 and retires at the age of x at time T.  Annual survival benefit B after retirement  The pension fund is invested in n assets.  The annual pension cost (PC) is paid by the operation division.  The pension cost is the sum of a constant normal contribution (NC) and a supplementary contribution (SC).

17. Overall Risk  Considers different risks at a holistic level.  The risk that the total value of all projects net of costs of operational risk, pension contributions and retained hazard losses is not sufficient to cover the entire financial obligations.

18. Model Setup A firm has a total capital of M 0 allocated to m investment projects and a DB plan at time 0. A proportion w jp of M 0 is invested in project j (j = 1, 2,…,m). After financing m projects at time 0, the remaining amount PA 0 goes to the pension plan and is invested in n assets with the weights of w 1,w 2,…, w n.

19. Basic Optimization Problem  Our ERM optimization model is to solve for the optimal project investment proportions w p =[w 1p,w 2p,…,w mp ], the hazard insurance ratio u, the pension asset weights w=[w 1,w 2,…,w n ] and the pension normal contribution NC, so as to maximize the expected value of the adjusted operation fund at time  : subject to the following constraints:

20. Constraints  Constraint 1: Project risk  Constraint 2: Operational risk

21. Constraints (Cont’)  Constraint 3: Hazard risk  Constraint 4: Pension risk I  Constraint 5: Pension risk II

22. Constraints (Cont’)  Constraint 6: Overall risk

23. Constraints (Cont’)  Constraint 6: Overall risk  Constraint 7: Budget constraint  Constraint 8: Strategic constraint  Constraint 9: Range constraints

24. Numerical Example We focus our study on a cohort with all members who join the plan at age x 0 =50 in time 0 and retire at age x=65 after T=15 years. Total raised capital M 0 =200

25. Numerical Example (Cont’)

28. What if Pension Risk is not Integrated?  Assume the firm manages its pension risk separately.  Suppose at time 0, the firm allocates an amount of 40 to the pension fund, the same amount as the optimal PA 0 in the ERM case.

29. What if Pension Risk is not Integrated?

30.  Given the available fund 160 at time 0 for the real project investment, we maximize, the expected value of the operation fund for the firm at time  :

31. What if Pension Risk is not Integrated?  In this scenario when the real projects and the pension plan are managed separately, the expected firm value is notably reduced to = 9012.34 from the previous optimum with ERM of = 10857.02, a 17% drop!!

32. What if Pension Risk is not Integrated?  In this scenario when the real projects and the pension plan are managed separately, the expected firm value is notably reduced to = 9012.34 from the previous optimum with ERM of = 10857.02, a 17% drop!!

33. Ground-up De-Risking Strategy  The pension ground-up de-risking strategy, including buy-ins and buy-outs, transfers a proportion of the entire pension liabilities to a third party.

34. Ground-up De-Risking Strategy  The pension ground-up de-risking strategy, including buy-ins and buy-outs, transfers a proportion of the entire pension liabilities to a third party.  The pension firm needs to pay a hedge price equal to

35. Ground-up: Numerical Example  As long as the firm transfers some of its pension risk with a positive hedge ratio, the firm can achieve a higher firm value than the value (10857.02) when the firm does not hedge.

36. Ground-up: Numerical Example  As long as the firm transfers some of its pension risk with a positive hedge ratio, the firm can achieve a higher firm value than the value (10857.02) when the firm does not hedge.

37. Excess-Risk De-Risking Strategy  The pension excess-risk de-risking strategy, such as longevity insurance, only cedes a proportion of the high-end longevity risk embedded in a pension plan to a risk taker. ……

38. Excess-Risk De-Risking Strategy  The pension excess-risk de-risking strategy, such as longevity insurance, only cedes a proportion of the high-end longevity risk embedded in a pension plan to a risk taker.  The pension firm needs to pay a hedge price equal to ……

39. Excess-Risk: Numerical Example  The hedge ratio and the pension asset allocation are not sensitive to the hedge cost.

40. Excess-Risk: Numerical Example  The hedge ratio and the pension asset allocation are not sensitive to the hedge cost.

41. Excess-Risk: Numerical Example  The hedge ratio and the pension asset allocation are not sensitive to the hedge cost.

42. Excess-Risk: Numerical Example  The hedge ratio and the pension asset allocation are not sensitive to the hedge cost.  The excess-risk strategy is less effective in improving the overall firm performance than the ground-up strategy.

43. Sensitivity Analyses

44. Conclusion  We study how to make an optimal strategic decision considering pension effects in an ERM framework.  The performance of a DB firm will be greatly improved if it integrates pension risk with other risks in an ERM program.  The excess-risk pension de-risking strategy underperforms the ground-up strategy in terms of value creation under the ERM framework.