Deborah Lucas Northwestern University and NBER

1. Discussion of“On Asset-Liability Matching and Federal Deposit and Pension Insurance”by Zvi Bodie Deborah Lucas Northwestern University and NBER

2. Overview • Decomposing PBGC’s Risk Exposure • What Does a Matched Portfolio Look Like?

3. PBGC’s Risk Exposure • Results drawn from: “The Risk Exposure of the Pension Benefit Guarantee Corporation” • CBO study by Kiska, Lucas and Phaup • available at www.cbo.gov

4. PBGC’s Risk Exposure • Two conditions must be met simultaneously for PBGC to assume pension plans: • 1. Firm bankruptcy • 2. Under-funded pension plan • The probability of a joint occurrence is much lower than the probability that a pension plan is under-funded. • Fair premium for below-investment grade firms would have to be 18.5 times higher to match the current cost for investment-grade firms. • The fair price of PBGC premiums includes a significant charge for market risk, as both bankruptcy and under-funding are correlated with market downturns.

5. PBGC’s Risk Exposure • PBGC insurance is a compound put option. • It can be valued using options pricing methods. • Monte Carlo model takes into account the evolution over time of: • Firm assets (stochastic) • Firm liabilities (deterministic) • Pension assets (70% stocks and 30% bonds) • Pension liabilities (deterministic) • and interactions with program rules

6. CBO Estimates of PBGC’s Deficit

7. Cost Components

8. Summary of Findings • As Bodie suggests, more closely matching pension assets and liabilities significantly lowers PBGC’s projected costs. • But even with a matched portfolio, the model predicts that the PBGC will bear considerable costs. • Reason is that termination liabilities are systematically greater than current liabilities (i.e.,required funding levels). • We assume 20 percent mark-up of liabilities over assets at termination, following Pennachi and Lewis, and historical experience • e.g., U.S. Air > 90% funded in year prior to termination, <45% funded at termination

9. Summary of Findings • Costs not arising directly from asset-liability mismatch can be attributed to regulatory forbearance, and to accounting conventions. • Forcing firms to fund to level of termination liabilities would result in systematic over-funding.

10. The S&L analogy revisited • Similarities: • Mismatch in market sensitivity of assets and liabilities creates potentially huge costs for the insurer. • Regulatory forbearance exacerbates problem. • Differences: • Much less severe moral hazard due to compound option. Sound companies have very little chance of putting their plan to the PBGC. • Little evidence that distressed companies gamble more with pension plan assets. • Significantly lower projected costs.

11. What perpetuates the mismatch? • Why don’t healthy companies use more bonds in funding their pensions, reducing volatility? • Why are policymakers reluctant to lower PBGC costs via restrictions on asset-liability mismatch? • Tentative answers: • Firms follow established norms. • The investment strategy that minimizes risk has not been fully articulated.

12. Is the best hedge a bond portfolio? • Bodie’s example: • Pension liability of $1000 in 10 years • Put away present value = $1000/(1+r)10 in risk-free bonds • This is a perfect hedge

13. The optimal hedge portfolio with wage indexation • Typical DB pension promises a fraction of terminal wages, a random variable. • e.g., annual pension = .4 x wage10 • Now the best hedge is the portfolio maximally correlated with wage10 • If wages and stock returns are correlated, the optimal portfolio will contain stocks was well as bonds. • How much stock? It depends…

14. Finding the best hedge portfolio • When wages and stocks are correlated, the value of the pension liability can be modeled as a derivative. • The value of the pension liability, and the hedge portfolio, can be found using options pricing methods. • The optimal portfolio is dynamic, changing over time with the demographics of the labor force. • Bonds still play a big role: • Firms with predominantly retired workers should invest predominantly in bonds. • Firms with young workers should invest more in stocks. • When workers separate from the firm, their benefit becomes like a bond.

15. An example • The following joint process for stocks, human capital and wages generates: • 1. an almost a zero correlation between wage growth and stock returns at a one-year horizon • 2. a correlation of .11 between wage growth and stock returns over 3 years, and .36 over five years • The aggregate value of stock evolves according to: • The aggregate value of human capital evolves according to: • Wages evolve according to:

16. An example parameters

17. An example -- results Bottom line: Optimal share in stocks increases with employment horizon.

18. Final thoughts • Asset-liability mismatch is a major source of risk, but restricting investments to bonds may not be the right answer. • Any policy that seriously addresses the PBGC funding gap will likely accelerate the switch from DB to DC pensions. • Hence, the costs of PBGC insurance must be considered in the broader context of the goals of an employer-based retirement savings system.